Error Analysis of Bistatic SAR Imaging and Stereoscopy Bistatic SAR

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

1

Error Analysis of Bistatic SAR Imaging and Stereoscopy Bistatic SAR Yunfeng Shao, Robert Wang, Senior Member, IEEE, Yun Kai Deng, Member, IEEE, Yue Liu, Runpu Chen, Gang Liu, Timo Balz, Member, IEEE, and Otmar Loffeld, Senior Member, IEEE

Abstract— The flexible geometry configuration of the bistatic synthetic aperture radar (SAR) has many advantages. However, it causes serious measurement error in the bistatic SAR system, which degrades the quality of the SAR images and the precision of the digital elevation model (DEM) obtained using stereoscopy bistatic SAR. In this paper, the influence of the scene height estimation error, trigger delay, transmitter position measurement error, receiver position measurement error, and transmission line length measurement error are analyzed. These analyses are very useful in bistatic SAR system design. The scene height estimation error, trigger delay, transmitter position measurement error, and synchronization receiver position measurement error affect both the quality of the images and the precision of the DEM obtained by stereoscopy bistatic SAR slightly. The echo receiver position measurement error and transmission line length measurement error affect the quality of the imaging only slightly, but seriously affect the precision of the DEM obtained by stereoscopy bistatic SAR. Luckily, their measurement precision can be quite satisfactory. Simulations and real bistatic experimental results verify the proposed theoretical analysis. Index Terms— Bistatic synthetic aperture radar (SAR) imaging, stereoscopy bistatic SAR, system error analysis.

I. I NTRODUCTION

T

HE bistatic synthetic aperture radar (SAR) system and its configurations have been attracting scientists’ interests in the last few years. Because of the advantages of bistatic SAR, such as better flexibility, many bistatic SAR experiments have been carried out [1]–[7], such as bistatic imaging and stereoscopy bistatic SAR. Stereoscopy bistatic SAR is a technique of obtaining the DEM by SAR image pair. Compared to InSAR, which uses the phase of the SAR data to obtain the DEM, the stereoscopy bistatic SAR uses only the imaging geometry information and the slant range of SAR images to obtain the DEM. However, compared to monostatic SAR, bistatic imaging and stereoscopy bistatic SAR processing are

Manuscript received June 28, 2012; revised November 15, 2012; accepted January 24, 2013. This work was supported by the “Hundred Talents Program” of The Chinese Academy of Sciences. Y. Shao, R. Wang, Y. K. Deng, Y. Liu, R. Chen, and G. Liu are with the Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; liugangiecas@ gmail.com). T. Balz is with the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China (e-mail: [email protected]). O. Loffeld is with the Center for Sensor Systems, University of Siegen, Siegen 57076, Germany (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2013.2245902

more challenging. Because the receiver is separated from the transmitter, it requires time synchronization, phase synchronization, and precise geometry measurement in the bistatic SAR system, which affects the quality of SAR image and the precision of the DEM obtained using stereoscopy bistatic SAR. The error in synchronization has been analyzed by many researchers. In the literature [8], the frequency error between the transmit carrier frequency and receiver’s oscillator frequency has been analyzed. The frequency error was divided into a fixed frequency error and a stochastic frequency error and it was concluded that the fixed frequency error makes a shift of the main lobe of azimuth compress signal and the stochastic frequency error leads to an increase in the side lobes of the azimuth compress signal. The model and effects of the phase synchronization errors between transmitters and receivers were analyzed in [9]–[11]. The chirp ratio error and a nonlinear phase error were considered in [9]. These errors brought about a shift in the main lobe and an increase in side lobes during compression. In [10], the phase error was divided into a fixed phase error, a linear phase error, and a random phase error. The fixed and linear phase errors, which give rise to an apparent Doppler centroid [11], introduce a range migration error, and the random phase error affects the integrated side-lobe ratio. In [11], more analysis on the random phase error was carried out, reaching the conclusion that the high-frequency parts result in spurious side lobes, whereas the low-frequency parts reduce the azimuth resolution and shift the targets along the range direction. In [12], an error model of antenna directing synchronization was established and the effects of the antenna directing synchronization error were analyzed. In [13], an error transfer model was established from the error of the time and frequency synchronization to the error of the interferometric phase. The time and the frequency errors were also divided into a fixed part and a random part. It was concluded that the fixed interferometric phase error and the linear time synchronization error bring about a linear phase error to the interferometric phase, and the fixed time synchronization error gives rise to a constant phase error to the interferometric phase. However, the measurement error of the bistatic SAR, including scene height estimation error, trigger delay, transmitter position measurement error, receiver position measurement error, and transmission line length measurement error, were not dealt with. These error analyses are also important in bistatic imaging and stereoscopy bistatic SAR processing. In this paper, we analyze the influence of measurement error on bistatic SAR imaging and on the precision of

0196-2892/$31.00 © 2013 IEEE

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 1.

Geometry of the configuration of the bistatic SAR.

DEM obtained by the stereoscopy bistatic SAR technique. In Section II, the bistatic SAR backpropogation (BP) algorithm and stereoscopy bistatic SAR algorithm are presented. In Section III, influence of the measurement error is analyzed. In Section IV, simulations and experiments are carried out to verify the presented error analysis. Conclusions are reported in Section V.

(a)

II. P ROCESSING OF B ISTATIC SAR I MAGING AND S TEREOSCOPY B ISTATIC SAR A. Configuration of Stereoscopy Bistatic SAR The presented bistatic SAR system fixed the transmitter subsystem on the satellite and the receiver subsystem on the ground, as shown in Fig. 1. The ground receiver subsystem contains two categories of receivers [14]. One is the synchronization receiver, which directly receives the chirp signal from the transmitter on the satellite, shown as receiver A in Fig. 1. The other is echo receiver, which receives the echo from the ground, shown as receiver Bn in Fig. 1. The synchronization receiver has two applications. First, the synchronization receiver triggers the echo receivers to sample the echo. Second, the signal sampled by the synchronization receiver is used as the match filter to compress the echo data sampled by the echo receiver during the range compression process. The geometry of the bistatic SAR configuration is shown in Fig. 1. The position of satellite S is S(x s , ys , z s ). The position of the synchronization receiver A is A(x A , y A , z A ) and the position of the echo receiver Bn is Bn (x Bn , y Bn , z Bn ). The position of the target on the ground is T (x T , yT , z T ). Fig. 2 shows the block diagram of our bistatic SAR receiver subsystem. The direct signal is received by the synchronization receiver, and the echo is received by the echo receiver. Both the received signal in the synchronization receiver and echo receiver are mixed using the same oscillator. An A/D converter uses the same local clock. Fig. 2(a) is a block diagram of one synchronization receiver and one echo receiver. Fig. 2(b) is a block diagram of one synchronization receiver and two echo receivers. The stereoscopy bistatic SAR has two configurations, namely a double-pass single-receiver configuration, and a single-pass double-receiver configuration [5], [6]. In the first configuration, the satellite passes over the scene twice and the ground receiver subsystem has only one echo receiver.

(b) Fig. 2. Block diagram of the bistatic SAR receiver. (a) One synchronization receiver and one echo receiver. (b) One synchronization receiver and two echo receivers.

This configuration is shown in Fig. 3(a) and the block diagram is shown in Fig. 2(a). Comparing with the stereoscopy monostatic SAR, the position of the ground receiver can be arranged to get perfect geometrical parameters, but the time decorrelation is also very serious. Another drawback of this configuration is that the measurement error of the satellite orbit seriously affects the precision of DEM, and high-precision measurement of the satellite orbit is difficult to carry out. In the second configuration, the satellite passes over the scene only once and the ground receiver subsystem has two echo receivers. That configuration is shown in Fig. 3(b) and its block diagram is shown in Fig. 2(b). Besides its geometrical parameter flexibly, this configuration can overcome the time decorrelation problem. Another advantage of this configuration is that the measurement error of the satellite orbit only slightly affects the precision of the DEM. Though the measurement error of the receiver position seriously affects the precision of the DEM, high-precision measurement of the receiver position is easy to carry out. B. Process of Receiving Synchronization Signal and Echo The working mode of the proposed system is shown in Fig. 4. The receiver subsystem has two states: the monitor state and the record state. In the monitor state, the synchronization receiver and the echo receiver only sample their received

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

3

0 -10 -20

Amplitude (dB)

-30 -40 -50 -60 -70

(a)

-80 -90

0

2000

4000

6000

8000 10000 12000 14000 16000 Range Position

18000

(a) 0

-20

(b) Fig. 3. Stereoscopy bistatic configuration. (a) Double-pass single-receiver configuration. (b) Single-pass double-receivers configuration.

Amplitude (dB)

-40

-60

-80

-100

monitor state synchronization receiver detected the chirp signal

after a fixed record time record state

Fig. 4.

-120

0

0.5

1 1.5 Range Position

(b)

2

2.5 4

x 10

Fig. 5. Signal to noise of the L-band SAR result. (a) Compressed result of synchronization signal using L-band SAR. (b) Compressed result of synchronization signal using X-band SAR (TerraSAR-X).

Block diagram of states translation.

signal, but do not record the data. In the record state, the synchronization receiver and the echo receiver sample and record their received signals. In the beginning, the state of the receiver is in monitor state. When the synchronization receiver detects the chirp signal, the state of the receiver changes into the record state. The receiver holds the record state for a fixed time, which is shorter than pulse repetition interval; then it changes to the monitor state. C. Bistatic SAR Imaging Processing The bistatic SAR imaging algorithms can be classified into two categories: frequency-domain algorithms and time-domain algorithms [16]–[26]. Although the computational complexity of time-domain algorithms is higher than that of the frequencydomain algorithms, its precision, especially the phase precision, is higher, which is very important in the bistatic InSAR processing. With the development of graphics processing units,

the time-domain bistatic SAR imaging algorithms can be applied in massively parallel processors, which relieves the drawback of high computational complexity [26]. All the bistatic BP algorithms analysis uses the same chirp signal as the matched filter in each range line to carry out the range compression process. The proposed analysis uses the signal received by a synchronization receiver to compress the echo in the range direction, which brings in some advantages. First, the proposed method can reduce the precision requirements of the measurement. Second, the proposed method can reduce additional time and phase synchronization operations. Third, the proposed method can reduce the effect of trigger delay. However, this method using the synchronization signal to compress the echo in the range compression requires a high signal-to-noise ratio (SNR) at the output of the synchronization antenna. Generally, the SNR is high enough in our experiment, as shown in Fig. 5. Fig. 5(a) is the compressed result of synchronization signal using L-band SAR and Fig. 5(b) is the compressed result of synchronization signal using X-band

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

The echo signal of the target T (x T , yT , z T ) sampled and recorded by the echo receiver B is

shift along y (m)

-27.2622 -27.2623 -27.2624

S B (τ, η; x T , yT , z T ) = σ (x T , yT , z T )Wr (τ − R B (η; x T , yT , z T )/c)

-27.2625 -27.2626

×WaT (x s (η) − x T )Wbi (x T , yT , z T ) × exp{− j 2π f 0 R B (η; x T , yT , z T )/c}

-27.2627 -27.2628 -10

-5

0

5

10

azimuth(km) (a)

-18.0594 -18.0596 -18.0598 -18.06 -10

-5

0

5

10

azimuth(km) (b) Fig. 6. Effect of the 30-m scene height estimation error. (a) Change of y for a near target. (b) Change of y for a far target.

SAR (TerraSAR-X). If the SNR is not high enough, the synchronization signal can be reconstructed by an estimation method. The processing of the bistatic data with the BP algorithm needs two steps. In the first step, range compression is carried out, and in the second step the process of azimuth compression is done.

where σ (x T , yT , z T ) is the backscatter coefficient of the target, T ,Wr (τ ) is the envelope of the transmitted radar pulse, WaT (η) is the antenna beam pattern in the azimuth direction of the transmitter, Wbi (x T , yT , z T ) is the antenna beam pattern of the ground echo receiver for the target T . RT (η; x T , yT , z T ) is the range between the satellite S and target T at azimuth time η, R R (x T , yT , z T ), is the range between the ground echo receiver Bn and target T . Here we assume that all the antenna beam patterns are rectangle functions. Equations (1) and (3) in the frequency domain are derived by Fourier transform based on the principle of stationary phase (POSP) [27] Sˆ A ( f, η) = W f ( f )Wa (x s (η) − x A ) × exp{− j 2π( f 0 + f )R D (η)/c} × exp{ j π f 2 /K r } Sˆ B ( f, η; x T , yT , z T )

In the range compression, the signal sampled and recorded by the synchronization receiver A is used as reference signal to compress the echo signal. The signal sampled and recorded by the synchronization receiver A is [27] S A (τ, η) = Wr (τ − R D (η)/c)WaT (x s (η) − x A )Wa R (x s (η) − x A ) × exp{− j 2π f 0 R D (η)/c} exp{ j π K r (τ − R D (η)/c)2 } (1) where Wr (τ ) is the envelope of transmitted radar pulse, WaT (η) is the transmitter’s antenna beam pattern in the azimuth direction, Wa R (η) is the synchronization receiver’s antenna beam pattern in azimuth direction, R D (η) is the range between the satellite S, and the synchronization receiver A at azimuth time η 

(x s (η) − x A )2 + (ys (η) − y A )2 + (z s (η) − z A )2 . (2)

(5)

Sˆ B ( f, η; x T , yT , z T )

= σ (x T , yT , z T )W f ( f )Wa (x s (η) − x T ) ×Wbi (x T , yT , z T ) exp{− j 2π( f 0 + f )

D. Step 1: Range Compression

R D (η) =

(3)

= RT (η; x T , yT , z T ) + R R (x T , yT , z T )  = (x s1 (η) − x T )2 + (ys1(η) − yT )2 + (z s1 (η) − z T )2  + (x B1 − x T )2 + (y B1 − yT )2 + (z B1 − z T )2 (4)

-18.0592

shift along y (m)

× exp{ j π K r (τ − R B (η; x T , yT , z T )/c)2 } R B (η; x T , yT , z T )

×R B (η; x T , yT , z T )/c} exp{ j π f 2 /K r }. (6) Matched filtering can be implemented in the frequency domain using conjugate multiplication [27] Sˆ = Sˆ B ( f, η; x T , yT , z T ) · Sˆ ∗A ( f, η) = σ (x T , yT , z T )W f ( f )Wa (x s1(η) − x A ) ×Wbi (x T , yT , z T )Wa (x s (η) − x T ) exp{− j 2π( f 0 + f ) (7) ×[R B (η; x T , yT , z T ) − R D (η)]/c}. Applying inverse Fourier transform to Sˆ based on POSP yields [27] S(τ, η) = σ (x T , yT , z T ) pr (τ − [R B (η; x T , yT , z T ) − R D (η)]/c) Wa (x s1 (η) − x A )Wbi (x T , yT , z T )Wa (x s (η) − x T ) × exp{− j 2π f 0 [R B (η; x T , yT , z T ) − R D (η)]/c} = σ  (η; x T , yT , z T ) × exp{− j 2π f 0 R(η; x T , yT , z T )/c} (8)

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

where

5

F. Processing of Stereoscopy Bistatic SAR

R(η; x T , yT , z T ) = R B (η; x T , yT , z T ) − R D (η)  = (x s (η) − x T )2 + (ys (η) − yT )2 + (z s (η) − z T )2  − (x s (η) − x A )2 + (ys (η) − y A )2 + (z s (η) − z A )2  + (x B − x T )2 + (y B − yT )2 + (z B − z T )2 (9) σ  (η; x A , x T , yT , z T ) = σ (x T , yT , z T ) pr (τ − R(η; x T , yT , z T )/c) ×WaT (x s (η) − x A )Wa R (x s (η) − x A ) ×Wbi (x T , yT , z T )WaT (x s (η) − x T ).

(10)

E. Step 2: Azimuth Compression Note that the range-compressed data are oversampled along the range direction by zero-padding the spectrum, using a property of Fourier transformation [27]. Then we set the image grid on the ground plane (x n , ym ) and estimate the average height of the scene z ave . Assume that the interval of the image grid along the azimuth and range direction are ρa and ρr . Then  x n = nρa , n = 1, 2, . . . , N (11) ym = mρr , m = 1, 2, . . . , M. The azimuth focusing formulation is d(n, m) =

N−1 

dr (i, index(ηi ; x n , ym )) · ϕc (ηi ; x n , ym ) (12)

Stereoscopy bistatic SAR obtains the DEM using only the geometry information. Compared to InSAR, which uses the phase information to obtain DEM for distributed scatters, stereoscopy bistatic SAR has some advantages. The equivalent phase of the distributed scatters changes with the variation of the look angle, which affects the precision of the DEM obtained by InSAR. However, stereoscopy bistatic SAR does not use the phase to obtain the DEM, so the change of the equivalent phase does not affect the precision of the DEM obtained by stereoscopy bistatic SAR. If the image matching precision can be satisfied for the distributed scatters, the precision of the DEM will not be affected. First, images should be matched to each other. Therefore, we assume d1 (n, m) in image 1 is matched with d2 (n, m) in image 2. Based on the geometry of the double-pass single-receiver configuration, we have the set (18), shown at the bottom of the page, and based on the geometry of the single-pass doublereceiver configuration, we have the set (19), shown at the bottom of the page. Then we solve the set (18) or (19) to get the height information of the scene. We assume that yT , z T is the solution of (18) or (19), and the height of (x n , yT ) is z T . Comparing with the double-pass single-receiver configuration, the single-pass double-receiver configuration has three advantages. First, time decorrelation can be overcome. Second, the baseline of this configuration is more flexible than that of the doublepass single-receiver configuration. Third, the precision of the baseline measurement of this configuration is more precise than that of the double-pass single-receiver configuration.

i=0

where d(n, m) is an element of the image, dr [i, index(ηi ; x n , ym )] is an element of the range-compressed data, φc (ηi ; x n , ym ) is the compensation phase, and ηi is the azimuth time of the i th range line index(η; x n , ym ) = round(R(η; x T , yT , z ave )Fs β/c) φc (ηi ; x n , ym ) = exp{ j 2π f 0 R(η; x T , yT , z ave )/c}

(13) (14)

where round(X) is a function of rounding the elements of X to the nearest integers, Fs is the range sampling rate, and β is the range oversampling ratio.

III. E RROR A NALYSIS A. Estimation Error of the Scene Average Height Because the imaging grid is built on the ground plane, the scene height must be estimated first. The scene height is variable and its precise value cannot be obtained, so the estimated scene average height is used in image processing. Assume that the satellite travels along the x-axis, the velocity is v, and the scene height estimation error is z in the z-direction. Note that z and z  present the real value and the

⎧ 2 + (z (η ) − z)2 ; + (x − x )2 + (y − y)2 + (z − z)2 R (η ; x , y , z ) = (y (η ) − y) ⎪ 1 n n m1 ave s1 n s1 n B T B B ⎪ ⎪ ⎪ ⎪ ⎨ − (x s1 (ηn ) − x A )2 + (ys1(ηn ) − y A )2 + (z s1 (ηn ) − z A )2 ⎪ ⎪ R2 (ηn ; x n , ym2 , z ave ) = (ys2 (ηn ) − y)2 + (z s2 (ηn ) − z)2 + (x B − x T )2 + (y B − y)2 + (z B − z)2 ⎪ ⎪ ⎪ ⎩ − (x s2 (ηn ) − x A )2 + (ys2 (ηn ) − y A )2 + (z s2 (ηn ) − z A )2 ⎧ 2 2 2 2 2 ⎪ ⎪ R1 (ηn ; x n , ym1 , z ave ) = (ys (ηn ) − y) + (z s (ηn ) − z) + (x B1 − x T ) + (y B1 − y) + (z B1 − z) ⎪ ⎪ ⎪ ⎨ − (x s (ηn ) − x A )2 + (ys (ηn ) − y A )2 + (z s (ηn ) − z A )2 ⎪ ⎪ R2 (ηn ; x n , ym2 , z ave ) = (ys (ηn ) − y)2 + (z s (ηn ) − z)2 + (x B2 − x T )2 + (y B2 − y)2 + (z B2 − z)2 ⎪ ⎪ ⎪ ⎩ − (x s (ηn ) − x A )2 + (ys (ηn ) − y A )2 + (z s (ηn ) − z A )2

(18)

(19)

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 6

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

TABLE I S IMULATED B ISTATIC SAR PARAMETERS

value with the scene height estimation error, respectively z  = z + z.

(15)

Simulation Parameter Effective radar velocity

Assume that the imaging position shift caused by the scene height estimation error is y R(η; x T , yT + y, z T ) = (x s +ηv −x T )2 +(ys −(yT + y))2 +(z s −z T )2  − (x s +ηv −x A )2 +(ys − y A )2 +(z s −z A )2  + (x B −x T )2 +(y B −(yT + y))2 +(z B −z T )2 R(η; x T , yT , z T + z) =

(x +ηv −x T )2 +(ys − yT )2 +(z s −(z T + z))2  s − (x s +ηv −x A )2 +(ys − y A )2 +(z s −z A )2  + (x B −x T )2 +(y B − yT )2 +(z B −(z T + z))2 .

(16)

(17)

(20)

R(η; x T , yT + y, z T )

 ys − y T y B − yT = R(η; x T , yT , z T ) −

y (21) + RT RR R(η; x T , yT , z T + z) 

zs − zT z B − zT = R(η; x T , yT , z T ) −

z (22) + RT RR where RT represents RT (η; x T , yT , z T ) and R R represents R R (x T , yT , z T ). Solving (20) for y yields

(23)

Expanding (23) using the first-order Taylor series with η, we obtain

y = yconst + y(η) cos θT + cos θ R | z| | yconst | = sin θT + sin θ R sin (θ R − θT ) (x s − x T ) vη | y (η)| ≈ RT0 RT 0 (sin θT + sin θ R )2 

Ls 2 | z| | z| ≤ RT 0

position

Parameter Value

Km/s

7.2

km

(0, 400, 693)

km m m

(0, 0, 533) (0, −900, 120) (0, −9000, 120)

where L s is the synthetic aperture length and RT 0 represents RT (0; x T , yT , z T ) ys − y T RT (0; x T , yT , z T ) zs − zT cos θT = RT (0; x T , yT , z T ) y B − yT sin θ R = R R (0; x T , yT , z T ) z B − zT . cos θ R = R R (0; x T , yT , z T )

sin θT =

Since y = RT (η; x T , yT , z T ), y = R R (x T , yT , z T ) and

z = RT (η; x T , yT , z T ), z = R R (x T , yT , z T ), (16) and (17) can be simplified by expanding them using the first-order Taylor series

z B − zT zs − zT + RT (η; x T , yT , z T ) R R (x T , yT , z T )

z.

y = ys − y T y B − yT + RT (η; x T , yT , z T ) R R (x T , yT , z T )

center

Receiver position (X, Y, Z ) Near target position (X, Y, Z ) Far target position (X, Y, Z )

Due to using the same data for processing, we have R(η; x T , yT , z T + z) = R(η; x T , yT + y, z T ).

Transmitter (X, Y, Z )

Unit

(24) (25)

(27) (28) (29) (30)

Equation (24) shows that the effect of y contains a constant part and a variable part. The amplitude of the constant part is similar to z and it changes with the look angle of the transmitter and the receiver. The larger the look angle, the smaller the amplitude. The look angle of the transmitter and the receiver both increase with the distance between the target and the receiver. That is to say, the scene height estimation error will change the imaging position, and a target near to the receiver changes more than a far target. The amplitude of the variable part is much smaller than z, because the synthetic aperture length is several kilometers or tens of kilometers and the range is hundreds of kilometers, so (L s /RT 0 )2 is very small. That is to say, the scene height estimation error affects the property of the images slightly. Fig. 6(a) shows the change of y with a 30-m scene height estimation error. The simulation parameters are listed in Table I. Fig. 6(a) shows the change of y for a near target and Fig. 6(b) shows the change of y for a far target. The simulation result shows that a 30-m scene height estimation error bring about a 27.26-m shift along the y-direction for a near target and an 18-m shift along the y-direction for a far target. And the variation of the shift for both the near and far targets is less than 1 mm, which is much smaller than the wavelength of the L-band and the X-band. Equations (18) and (19) show that the DEM obtained by stereoscopy bistatic SAR is not related to y and z. So the scene height estimation error does not affect the result of the DEM. Table I shows the parameters used for analyzing the effect of scene average height estimation error. B. Trigger Delay of the Synchronization Receiver

(26)

Because of the noise and the attenuation as the chirp signal passes through the aerosphere, the amplitude of the

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

chirp signal changes when it arrives at the synchronization receiver. Thus the first several chirp signals cannot trigger the synchronization receiver. Because the echo receivers need the synchronization receiver to trigger to sample and record the echo, trigger delay exists in both the synchronization receiver and the echo receivers. The trigger delay time of the synchronization receiver is the same as that of the echo receivers. The synchronization signal and the echo signal with trigger delay is S A (τ, η) =

τ = S B (τ, η) =

τ =

Wr (τ − R D /c) × exp {− j 2π f 0 R D /c} 

× exp j π K r (τ − R D /c)2   Tr R D Tr R D + T − , − +T (31) c 2 c 2 Wr (τ − R B /c) × exp {− j 2π f 0 R B /c} 

× exp j π K r (τ − R B /c)2   Tr R D Tr R D + T (32) − , − +T c 2 c 2

where T denotes trigger delay, Tr is the transmitted pulse time duration, and T is the sample time duration. In order to obtain more precise expressions, the correlation computation is used in time domain. The range-compressed result using the synchronization signal is  +∞  S (τ ) = S B (t)S ∗A (t − τ ) dt (33)

=

−∞ Wr (t −  +∞ −∞

R B /c) × exp {− j 2π f 0 R B /c}  j π K r (t − R B /c)2 Wr (t − τ − R D /c) dt

× exp{ j 2π f 0 R D /c} exp{− j π K r (t − τ − R D /c)2 } τ = (R B − R D ) /c

(34)

S(τ ) reaches the maximum value, which is S ([R B − R D ] /c) = exp {− j 2π f 0 [R B − R D ] /c} = exp {− j 2π f 0 [R B − R D ] /c}



+∞

Wr

−∞  +Tr /2

(t − R B /c) dt

−Tr /2+ T

1dt

= (Tr − T ) · exp {− j 2π f 0 [R B − R D ] /c} .

(35)

The synchronization signal and the echo signal without trigger delay are expressed as S A (τ ) = Wr (τ − R D /c)

5 4 3 2 1 0 0

1

2

3

4

5

Lost ratio (%) Fig. 7.

Effect of the trigger delay.

The synchronization signal is used to compress the echo signal  +∞ S B (t)S ∗A (t − τ )dt S (τ ) = −∞

×Wr (t − R B /c) exp {− j 2π f 0 R B /c}  +∞

 exp j π K r (t − R B /c)2 Wr (t −τ − R D /c)dt = −∞

× exp{ j 2π f 0 R D /c} exp{−j π K r (t −τ − R D /c)2 } (38) when τ = (R B − R D )/c

(39)

S(τ ) reaches the maximum value, which is S ([R B − R D ] /c) = exp {− j 2π f 0 [R B − R D ] /c} = exp {− j 2π f 0 [R B − R D ] /c}



+∞

Wr (t − R B /c) dt

−∞  +Tr /2 −Tr /2

1dt

= Tr · exp {− j 2π f 0 [R B − R D ] /c} .

(40)

The error at the maximum value position of S(τ ) is

when



7

Amplitude effect (%)

SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR



× exp {− j 2π f 0 R D /c} exp j π K r (τ − R D /c)2   Tr R D Tr RD − , + +T (36) τ = c 2 c 2 S B (τ ) = Wr (τ − R B /c)

 × exp {− j 2π f 0 R B /c} exp j π K r (τ − R B /c)2   Tr R D Tr RD − , + +T . (37) τ = c 2 c 2

e S = S ([R B − R D ] /c) − S  ([R B − R D ] /c) = T · exp {− j 2π f 0 [R B − R D ] /c} .

(41)

From (34) and (39), we can find that the trigger delay does not affect the maximum value position and it also does not affect the phase of the compressed signal at the maximum value position. It only affects the amplitude of the maximum value a little, and the ratio of the error to the signal is T /Tr . Based on (18) and (19), because the maximum value position is not changed, the trigger delay does not affect the value of the stereoscopy bistatic SAR. Fig. 7 shows the effect of the trigger delay. C. Orbital Measurement Error The measurement precision of the satellite position is limited, meaning there are measurement errors of the satellite position. The measurement this position error can be classified as two types: the orbital measurement systematic error, and the orbital measurement random error. The orbital measurement systematic error does not vary as the platform position changes, which is generally larger than the random orbital measurement error.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 8

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

1) Orbital Measurement Systematic Error: Assume that the satellite travels along the x-axis at a velocity v, and the orbital measurement systematic error is σcy in the y-direction. ys (η) and ys (η) present the real value of the satellite position and the measurement value of the satellite position with orbital measurement systematic error, respectively ys (η) = ys (η) + σcy .

(42)

Assume that the imaging position shift caused by the orbital measurement systematic error is y y   R η; x T , yT + y y , z T  2   = (x s +ηv −x T )2 + ys − yT + y y +(z s −z T )2  − (x s +ηv −x A )2 +(ys − y A )2 +(z s −z A )2    2 + (x B −x T )2 + y B − yT + y y +(z B −z T )2 (43) R  (η; x T , yT , z T )    2 = (x s +ηv −x T )2 + ys +σcy − yT +(z s −z T )2    2 − (x s +ηv −x A )2 + ys +σcy − y A +(z s −z A )2  + (x B −x T )2 +(y B − yT )2 +(z B −z T )2 . (44) Due to using the same data for processing, we have   R η; x T , yT + y y , z T = R  (η; x T , yT , z T ) .

(45)

Since σcy = ys (η) and y y = yT , (44) can be reformulated using the Taylor series   R η; x T , yT + y y , z T



= R (η; x T , yT , z T ) − R  (η; x T , yT , z T ) = R (η; x T , yT , z T ) +



y B − yT ys − y T + RT RR ys − y A ys − y T − RT RD



y y (46)  σcy .

(47)

Solving (45) for y yields ys − y T ys − y A − RT (η; x T , yT , z T ) R D (η; x T , yT , z T ) σcy .

y y = − ys − y T y B − yT + RT (η; x T , yT , z T ) R R (x T , yT , z T )

(50)

y y = y yconst + y y (η) sin θ R R R R R σcy (51) y y = const sin θ + sin θ R σcy ≤ R T R T0 T0 sin2 θ R R R (x s − x T ) vη y y (η) ≈ σcy (sin θ + sin θ )2 RT 0 RT 0 RT 0 T R

2 RR Ls σcy . ≤ (52) RT 0 RT 0 Similar to the analysis of orbital measurement systematic error in the y-direction, the effect along the z-direction is presented as

yz = yzconst + yz (η) yzconst ≤ R R |σcz | RT 0

 RR Ls 2 | yz (η)| ≤ |σcz | . RT 0 RT 0

(53) (54) (55)

The orbital measurement systematic error along the x-direction causes an imaging shift both along the x- and y-direction, which is different from the monostatic SAR. The orbital measurement systematic error along the x-direction causes the imaging shift only along the x-direction for monostatic SAR. Similar to the analysis of the orbital measurement systematic error in the y-direction, the orbital measurement systematic error is presented as x A − xT (RT − R D ) (x s + ηv − x T ) σcx σcx + RT (η; x T , yT , z T ) (RT )2

 x s + ηv − x T x B − xT =− +

x RT (η; x T , yT , z T ) R R (x T , yT , z T )

 y B − yT ys − y T + −

yx . (56) RT (η; x T , yT , z T ) R R (x T , yT , z T ) Equation (56) shows that x has a fast variation term of variation η, and σcx has both a fast variation term and a slow variation term of variation η, so RR RT − R D σcx ≈ σcx (57) RT RT x A − xT RT (η; x T , yT , z T )  σcx . (58)

yx = −

ys − y T y B − yT + RT (η; x T , yT , z T ) R R (x T , yT , z T )

x =

Then we assume

(48) The distance between satellite and the synchronization receiver is much more than that between the target on the ground and the synchronization receiver. Typically, the distance between the satellite and the synchronization receiver is about 800 km, and the distance between the target on the ground and the synchronization receiver is about 10 km. So in order to simplify the analysis, we assume RT (η; x T , yT , z T ) ≈ R D (η; x T , yT , z T ) .

Expanding (48) in first-order Taylor series gives

(49)

yx = yxconst + yx (η) yx ≤ R R |σcx | const RT 0



 Ls 2 RR | yx (η)| ≤ |σcx | . RT 0 RT 0

(59) (60) (61)

So the orbital measurement systematic error along the range direction presented as

y = yx + y y + yz = yconst + y (η) (62) RR | yconst | ≤ σc (63) RT 0

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

-0.284

-0.54

-0.286

-0.545

-0.288

-0.55

-0.29

-0.555

-0.292

-0.56

-0.294

-0.565

-0.296

-0.57

0.02

-0.298

-0.575

0.015

-0.3

0.0709

The error of Y (m)

shift along y (m)

0.0709

0.0709

0.0709

0.0709 -5

0

5

shift along y (mm)

azimuth(km) (a)

0

0.01

200

300

400

500

-0.58 600

The error of the orbit(m) Fig. 9.

0

Error in DEM caused by the orbital measurement error.

-0.005 0

5

azimuth(km) (b) 0.03

range error (mm)

100

0.005

-0.01 -5

0.02 0.01 0 -0.01 -0.02 -5

0

5

azimuth(km) (c) Fig. 8. Effect of orbital measurement systematic error. (a) Effect of orbital measurement systematic error along Y-direction and Z-direction. (b) Effect of orbital measurement systematic error along the X-direction. (c) Range error.

RR | y (η)| ≤ RT 0 where

9

The error of Z (m)

SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR



Ls RT 0

2 σc

σc ≤ |σcx | + σcy + |σcz |

(64) (65)

where σc is the total orbital measurement systematic error along the range direction and is referred to as the range measurement error. Equation (62) shows that the effect along the range contains a constant part and a variable part. Because R R is much smaller than RT 0 —generally R R /RT 0 ≈ 0.01—the amplitude of the constant part is much smaller than σc . Because the synthetic aperture length is several kilometers or tens of kilometers and the range is hundreds of kilometers, (L s /RT 0 )2 is very small. The amplitude of the variable part is much less than σc . That is to say, the orbital measurement systematic error affects the property of the imaging only slightly. Even though the shift caused by the orbital measurement systematic error is quite large, the shift is almost constant, which affects the BP algorithm slightly.

Fig. 8 shows that effect of orbital measurement systematic error (33 m along the X-direction, 33 m along the Y -direction, and 34 m along the Z -direction). Fig. 8(a) is the effect of orbital measurement systematic error along the Y - and Z -direction. The result shows that the orbital measurement systematic error causes a 0.07-m change of Y . Fig. 8(b) is the effect of orbital measurement systematic error along the X-direction. It causes a 0.20-m change of X and almost zero change of Y . Fig. 8(c) is the range error. The maximum error is less than 0.02 mm, which is much less than the wavelength of the L-band and the X-band. Similar to the analysis of the effect of the orbital measurement systematic error for imaging derived from (19), we obtain (69), shown at the bottom of the page, and (70), where θ D is the angle between the satellite and the synchronization receiver, which shows that the orbital measurement systematic error affects the DEM obtained by the stereoscopy bistatic SAR only slightly. Fig. 9 shows the error in DEM caused by the orbital measurement error. We assume that the bistatic system contains 0.01 m measurement error of the synchronization receiver position and the echo receiver position. The result shows that the orbital measurement error affects the precision only slightly. A 100-m orbital system measurement error (33 m along the X-direction, 33 m along the Y -direction, and 34 m along the Z -direction) only introduces 0.5 m error to the DEM. 2) Orbital Measurement Random Error: Assume that the orbital measurement random errors are σx_s , σ y_s , and σz_s in the x-, y-, and z-direction, respectively. Similar to the analysis of the orbital measurement systematic error, we obtain RR σx_s | yx | ≤ R T0 y y ≤ R R σ y_s R T0

(sin θ D − sin θT ) (cos θ R1 − cos θ R2 ) σyc + (cos θ D − cos θT ) (cos θ R1 − cos θ R2 ) σzc RR ≤ σc RT (sin θT + sin θ R1 ) (cos θ R1 − cos θ R2 ) − (cos θT + cos θ R1 ) (sins θ R1 − sin θ R2 ) (sin θ D − sin θT ) (sin θ R1 − sin θ R2 ) σ yc + (cos θ D − cos θT ) (sin θ R1 − sin θ R2 ) σzc RR σz ≈ σc ≤ RT (sin θT + sin θ R1 ) (cos θ R1 − cos θ R2 ) − (cos θT + cos θ R1 ) (sins θ R1 − sin θ R2 )

σy ≈

(66) (67)

(68) (69)

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 10

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

3.5

Similar to the analysis of synchronization receiver measurement error in the y-direction, the effect along the z-direction is presented as

shift along y (mm)

3 2.5 2

yz = yzconst + yz (η) const ≈ σz_syn

 Ls 2 | yz (η)| ≤ σz_syn . RT 0

1.5

yz

1 0.5 0 0

Fig. 10. error.

0.5

error (m)

1

1.5

Shift of Y -maximum caused by the orbital measurement random

RR | yz | ≤ R

T0

σz_s .

(70)

Equations (66), (67), and (70) show that the effect of y is much smaller than σx_s , σ y_s , and σz_s . That is to say, the orbital measurement random error affects the imaging property slightly. But comparing with the effect of the orbital measurement systematic error, because R R /RT 0 = (L s /RT 0 )2 , the orbital measurement random error influences the imaging property much more seriously than the orbital measurement systematic error. Because the orbital measurement random error does not affect the image position, it does not affect the precision of the stereoscopy bistatic SAR. Fig. 10 shows the change of Y -maximum shift caused by the orbital random measurement error. The result shows that a 1.5-m orbital measure random error introduces a 3.5-mm error, close to 1/10 wavelength of the X-band. Comparing with the orbital measurement systematic error, a 100-m total orbital system measurement error only introduces a 0.02-mm variable part of the Y shift. D. Error of the Receiver Location The positions of the synchronization receiver and the echo receiver are measured by a GPS device. The precision of the GPS is limited, which brings errors into the imaging and stereoscopy bistatic SAR. 1) Synchronization Receiver: Assume that the synchronization receiver position measurement error is σ y_syn in  the y-direction. y A and y A represent the real synchronization receiver position and the measurement synchronization receiver position with measurement error, respectively y A = y A + σ y_syn .

(71)

Assume that the imaging position shift caused by the synchronization receiver measurement error is y y ; similar to the analysis above (72)

y y = y yconst + y y (η) sin θ D y y ≈ (73) const sin θ + sin θ σ y_syn T R (x s − x T ) vη y y (η) ≈ sin θ R sin θT σ y_syn (sin θ + sin θ )2 RT 0 RT 0 T R 

Ls 2 ≤ σ y_syn . (74) RT 0

(75) (76) (77)

The synchronization receiver position measurement error along the x-direction causes an imaging shift both along the x- and y-directions. Similar to the analysis of orbital measurement systematic error in the x-direction, the synchronization receiver position measurement error is presented as x s + ηv − x A σx_syn R D (η; x T , yT , z T )

 x B − xT x s + ηv − x T + =−

x RT (η; x T , yT , z T ) R R (x T , yT , z T ) 

y B − yT ys − y T +

yx . (78) − RT (η; x T , yT , z T ) R R (x T , yT , z T ) Based on (49) x s + ηv − x A x s + ηv − x A σx_syn ≈ σx_syn R D (η; x T , yT , z T ) RT (η; x T , yT , z T ) x s + ηv − x T = σx_syn RT (η; x T , yT , z T ) xT − x A + σx_syn . (79) RT (η; x T , yT , z T ) Equation (79) shows that x and σx_syn are both fast variation term of variation η, so (80)

x = −σx_syn x B − xT xT − x A − R (η; x T , yT , z T ) R R (x T , yT , z T ) σx_syn . (81)

yx = − T y − y B − yT yT s + RT (η; x T , yT , z T ) R R (x T , yT , z T ) Then similar to the analysis above, we obtain

yx = yxconst + yx (η) x B − xT yx ≈ − R R (x T , yT , z T ) σx_syn const sin θT + sin θ R

 Ls 2 | yx (η)| ≤ σx_syn . RT 0

(82) (83) (84)

So the total synchronization receiver measurement error along the range presented as

y = yx + y y + yz = yconst + y (η) (85) | yconst | ≈ σsyn (86)

2 Ls | y (η)| ≤ σsyn (87) RT 0 where σsyn = σx _syn + σ y _syn + σz _syn

(88)

with σsyn being the total synchronization receiver location measurement error along the range direction and referred to as the range measurement error.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

11

6.5871 6.5871

0

5

azimuth(km) (a)

-1

1

-2 0

0.45

shift along y (mm)

2

0.1

0.2

0.3

0.4

0.5

0.6

The error of Z (m)

6.5872

6.5871 -5

0 0.7

The error of the measurement error (m) 0.4

Fig. 12. Error of DEM caused by synchronization receiver position measurement error.

0.35

0.3

0.25 -5

0

5

azimuth(km) (b) 0.15

Range error (mm)

0

6.5872

The error of Y (m)

shift along y (m)

6.5872

0.1 0.05 0 -0.05 -0.1 -5

0

5

azimuth(km) (c) Fig. 11. The effect synchronization receiver location. (a) Effect of synchronization receiver measurement error along Y- and Z-directions. (b) Effect of synchronization receiver measurement error along the X-direction. (c) Range error.

Equation (85) shows that y contains a constant part and a variable part. The amplitude of the constant part is similar to σsyn . That is to say, synchronization receiver position measurement error will change the imaging position. Although the shift caused by the synchronization receiver position measurement error is large, the shift is almost constant. Because the synthetic aperture length is several kilometers or tens of kilometers and the range is hundreds of kilometers, (L s /RT 0 )2 is very small. The amplitude of the variable part is much smaller than σsyn . That is to say, the synchronization receiver position measurement error affects the property of the imaging only slightly.

Similar to the analysis of the orbital system measurement error derived from (19), we obtain (90) and (91), shown at the bottom of the page. Clearly, the high estimation error is similar to the synchronization receiver position measurement error. Fig. 11 shows the 10-m synchronization receiver position measurement error (3 m along the X-direction, 3 m along the Y -direction, and 4 m along the Z -direction). Fig. 11(a) shows the effect of synchronization receiver measurement error along the Y - and Z -directions. The result shows that the orbital measurement systematic error causes a 6.60-m change of Y . Fig. 11(b) shows the effect of synchronization receiver measurement error along the X-direction. It causes a 3-m change of X and a 0.35-mm change of Y . Fig. 11(c) is the range error. A 10-m synchronization receiver position measurement error only causes less than 0.15 mm range error, which affects the imaging quality only slightly. Fig. 12 shows the error of DEM caused by synchronization receiver position measurement error. The result shows that a 0.6-m synchronization receiver position measurement error will bring about a 1.56-m error to DEM. 2) Echo Receiver: Assume that the echo receiver measurement error is σ y_echo in the y-direction. y B and y B represent the real echo receiver position and the measurement echo receiver position with measurement error, respectively y B = y B + σ y_echo .

(89)

Assume the image position shift caused by the echo receiver measurement error is y y . Similar to the analysis above

y y = y yconst + y y (η) sin θ R y y ≈ const sin θ + sin θ σ y_echo T

(92) (93)

R

σy ≈

sin θ D (cos θ R1 − cos θ R2 ) σ y_syn + cos θ D (cos θ R1 − cos θ R2 ) σz_syn ≈ σsyn (sin θT + sin θ R1 ) (cos θ R1 − cos θ R2 ) − (cos θT + cos θ R1 ) (sins θ R1 − sin θ R2 )

(90)

σz ≈

sin θ D (sin θ R1 − sin θ R2 ) σsyn_y + sin θ D (sin θ R1 − sin θ R2 ) σsyn_z ≈ σsyn (sin θT + sin θ R1 ) (cos θ R1 − cos θ R2 ) − (cos θT + cos θ R1 ) (sins θ R1 − sin θ R2 )

(91)

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 12

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Similar to the analysis of the echo receiver location measurement error in the y-direction, the effect along the z-direction presented as (95)

x B − xT R R (x T , yT , z T )

yx = − σx_echo . (100) ys − y T y B − yT + RT (η; x T, yT, z T ) R R (x T, yT, z T ) Then

4.2327 -5

0

5

azimuth(km) (a)

1 0.5 0 -0.5 -1 -5

0

5

azimuth(km) (b) 0.03 0.025 0.02 0.015 0.01 0.005 -5

0

5

azimuth(km) (c) Fig. 13. The effect caused by 10m echo receiver position measurement error. (a) Effect of echo receiver position measurement error along Y- and Z-directions. (b) Effect echo receiver position measurement error along X-direction. (c) Range error.

(101) (102) (103)

So the total echo receiver position measurement error along the range presented as (104) (105) (106)

where σecho = σx_echo + σ y_echo + σz_echo

4.2327

shift along y (mm)

(97)

(99)

y = yx + y y + yz = yconst + y (η) | yconst | ≈ σecho

 Ls 2 | y (η)| ≤ σecho RT 0

4.2327

1.5

Equation (98) shows that x is a fast variation term of variation η, and σx_echo is slow variation term of variation η so

yx = yxconst + yx (η) x B − xT yx ≈ − R R (x T , yT , z T ) σx_echo const sin θT + sin θ R

 Ls 2 | yx (η)| ≤ σx_echo . RT 0

4.2327

(96)

The echo receiver position measurement error along the x-direction causes an image shift both along the x- and y-directions. Similar to the analysis of orbital measurement systematic error in the x-direction, the echo receiver position measurement error presented as x B − xT σx_echo R R (x T , yT , z T )

 x s + ηv − x T x B − xT =− +

x RT (η; x T , yT , z T ) R R (x T , yT , z T ) 

y B − yT ys − y T +

yx . (98) − RT (η; x T , yT , z T ) R R (x T , yT , z T )

x = 0

4.2327

range error (mm)

yz = yzconst + yz (η) yz ≈ σz_echo const

 Ls 2 | yz (η)| ≤ σz_echo . RT 0

4.2327

shift along y (m)

y y (η) ≈ sin θT sin θ R (x s − x T ) vη σ y_echo (sin θ + sin θ )2 RT 0 RT 0 T R 2

Ls ≤ σ y_echo . (94) RT 0

(107)

with σecho being the total echo receiver location measurement error along the range direction and referred to ad the range measurement error. The influence of the echo position measurement error is the same as that of the synchronization receiver position

measurement error along the range direction, but the echo position measurement error along the x-direction does not cause an image shift along the azimuth direction. Similar to the analysis of the orbital system measurement error derived from (19), we obtain (112) and (113), shown at the bottom of the next page. Because θ R1 is similar to θ R2 , the denominator is close to 0, so the precision of the echo position measurement seriously affects the precision of stereoscopy bistatic SAR   σ y ≈ RT 0 σecho_1 + σecho_2 RR  RT 0  |σz | ≈ σecho_1 + σecho_2 . RR

(108) (109)

Fig. 13 shows the 10-m echo receiver position measurement error (3 m along the X-direction, 3 m along the Y -direction, and 4 m along the Z -direction). Fig. 15(a) is the effect of echo receiver position measurement error along the Y - and Z -directions. The result shows that the echo receiver position measurement error causes a 4.23-m change of Y . Fig. 13(b) is the effect echo receiver position measurement error along the

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

The effect of the measurement error 0

-0.05

-0.1

-0.1

-0.2

-0.15

-0.3

-0.2 0

0.002 0.004 0.006 0.008

0.01 0.012 0.014 0.016 0.018

The error of Z (m)

The error of Y (m)

0

-0.4 0.02

The error of the measurement error(m) Fig. 14. Error of DEM caused by echo receiver position measurement error.

X-direction. It causes zero change of X and 0.33-mm change of Y . Fig. 13(c) is the range error. A 10-m synchronization receiver position measurement error only causes less than 0.025 mm range error, which affects the imaging quality only slightly. Fig. 14 shows the error of DEM caused by the orbital measurement error. The result shows that a 0.01-m measurement error will bring about a 0.3-m error to DEM. The ratio is more than 20. So the precision of the echo receiver position measurement seriously affects the precision of DEM. E. Transmission Line Time Delay Error For the ground receiver subsystem, the signal received by synchronization antenna and the echo received by echo antenna are sampled at the same analog-to-digital converter (ADC). And the antennas are connected to the ADC using transmission lines. So there are time delays for transmitting the signal from the synchronization antenna to the ADC or from the echo antenna to the ADC. The length of the transmission

σ y ≈

|σz | ≈

13

line from the synchronization antenna to the ADC is different from the length of the transmission line from the echo antenna to the ADC. So the length of each transmission line must be measured. The measurement error brings an error to the imaging and stereoscopy bistatic SAR processing. Assume that the time delay of the synchronization receiver is T A and the time delay of the echo receiver is TB S A (τ, η) = Wr (τ −[R D (η) /c+T A ]) WaT (x s1 (η)−x A ) ×Wa R (x s1 (η)−x A ) exp{−j 2π f 0 [R D (η)/c+T A ]c} × exp{ j π K r (τ − [R D (η) /c + T A ])2 }

(110)

S B (τ, η; x T , yT , z T ) = σ (x T , yT , z T )×Wr (τ −[R B (η; x T , yT , z T )/c + TB ]) ×WaT (η − ηc ; x T , yT , z T ) Wbi (x T , yT , z T ) × exp {− j 2π f 0 [R B (η; x T , yT , z T ) /c + TB ]} × exp{ j π K r (τ − [R B (η; x T , yT , z T )/c + TB ]/c)2 }. (111) Carrying out the same operations, we can get a formulation similar to (10) S (τ, η)    = σ (x T , yT , z T ) pr τ − R (η; x T , yT , z T ) /c + Tdelay ×Wa (x s (η) − x A ) Wbi (x T , yT , z T ) Wa (x s (η) − x T )    × exp − j 2π f 0 R (η; x T , yT , z T ) /c + Tdelay (114) Tdelay = TB − T A .

(115)

Assuming that the imaging position shift caused by the time delay is y, similar to the previous analysis, we get

y = yconst + y (η) (119) 1 cTdelay | yconst | ≈ (120) sin θT + sin θ R sin θT (x s − x T ) vη | y (η)| ≈ cT delay RT RT (sin θT + sin θ R )2

sin θ R1 (cos θT + cos θ R2 ) σ y_echo_1 (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 ) cos θ R1 (cos θT + cos θ R2 ) σz_echo_1 − (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 ) sin θ R2 (cos θT + cos θ R1 ) σ y_echo_2 + (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 ) cos θ R2 (cos θT + cos θ R1 ) σz_echo_2 + (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 ) sin θ R1 (sin θT + sin θ R2 ) σ y_echo_1 (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 ) cos θ R1 (sin θT + sin θ R2 ) σz_echo_1 − (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θ T + sin θ R2 ) (cos θT + cos θ R1 ) sin θ R2 (sin θT + sin θ R1 ) σ y_echo_2 + (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 ) cos θ R2 (sin θT + sin θ R1 ) σz_echo_2 + (sin θT + sin θ R1 ) (cos θT + cos θ R2 ) − (sins θT + sin θ R2 ) (cos θT + cos θ R1 )

(112)

(113)

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 14

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

TABLE II S IMULATED S PACEBORNE R ADAR PARAMETERS

≤

Ls RT

2

cTdelay .

(121)

Equation (116) shows that the effect of y contains a constant part and a variable part. The amplitude of the constant part is similar to cTdelay. That is to say, a different transmission time delay will change the imaging position. Although the shift caused by the different transmission time delay error is large, the shift is almost constant. Because the synthetic aperture length is several kilometers or tens of kilometers and the range is hundreds of kilometers, (L s /RT )2 is very small. The amplitude of the variable part is much smaller than cTdelay. That is to say, the transmission time delay error affects the property of the imaging only slightly Tdelay_1 = TB_1 − T A

(122)

Tdelay_2 = TB_2 − T A .

(123)

Equations (124) and (125), shown at the bottom of the page, show that the high estimation is affected by the transmission time delay. If the sign of Tdelay_1 is same as that of Tdelay2 , the effect of the transmission line time delay is reduced. But if the sign of the Tdelay_1 is different from that of Tdelay_2 , the effect of the transmission line time delay is enhanced. We assume Tdelay_1 = −Tdelay_2 .

(124)

Then, we obtain RT cTdelay_1 RR RT cTdelay_1 . σz ≈ RR

σy ≈

The error of Z (m)



Parameter Value 9.6 300 1000 3477 7.2

0

The error of Y (m)

Simulation Parameters Carrier frequency (GHz) Signal bandwidth (MHz) Sample rate (MHz) Pulse repetition frequency (Hz) Satellite velocity (km/s)

The effect of the measurement error 0

(125) (126)

So the effect of transmission line time delay is very serious. Fig. 15 shows the error of DEM caused by the transmission line error. The result shows that a 0.02-m measurement error will bring a 0.8-m error to DEM. The ratio is more than 40. So the precision of the transmission line error seriously affects the precision of DEM. IV. S IMULATION R ESULTS In this section, simulations and real data experiments are carried out to verify the proposed theoretical analysis. The

-0.5 0

-1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

The error of the measurement error(m) Fig. 15.

Error of DEM caused by transmission line error. TABLE III E XPERIMENT B ISTATIC SAR PARAMETERS System Parameters

System Value

Carrier frequency (GHz) Signal bandwidth (MHz) Sample rate (MHz) Pulse repetition frequency

1.3/9.6 62/300 266/1000 2000/3477

simulation parameters are listed in Table II and the experimental parameters are listed in Table III. Fig. 16 is the processed result of the simulation data and Fig. 17 is the experimental result using TerraSAR-X as the transmitter subsystem. Those results are used as reference results to compare with other results with measurement error. Fig. 18 is the experimental result of the stereoscopy bistatic SAR using space-based L-band SAR as the transmitter subsystem. The receiver subsystem is fixed on a hill, located at the upper right in Fig. 18. The stereoscopy bistatic configuration is the double-pass single-receiver configuration shown in Fig. 3(a). Fig. 18(a) is the imaging result. Fig. 18(b) is the result of mapping the DEM information on the SAR image. Fig. 18(c) is the result of mapping the DEM information on the optical image. A. Scene Average Height Estimation Error Using the simulation parameter list in Tables II and III, The simulation is carried out with a 30-m scene height estimation error for the far target to verify the proposed theoretical analysis. Real data result with a 30-m scene height estimation error is also analyzed. Fig. 19 is the processed result with 30-m scene height estimation error of the simulated data. Fig. 19(a) is the

cos θ R1 cTdelay_1 − cos θ R2 cTdelay_2 (sin θT + sin θ R1 ) (cos θ R1 − cos θ R2 ) − (cos θT + cos θ R1 ) (sins θ R1 − sin θ R2 ) sin θ R1 cTdelay_1 − sin θ R2 cTdelay_2 σz ≈ (sin θT + sin θ R1 ) (cos θ R1 − cos θ R2 ) − (cos θT + cos θ R1 ) (sins θ R1 − sin θ R2 )

σy ≈

(124) (125)

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

15

The focus result 0

8

azimuth (m)

6

-5

4 -10 2 -15

0 -2

-20

-4 -25 -6

(a)

-9006 -9004 -9002 -9000 -8998 -8996 -8994 -8992

range (m)

150

(a) 4

-20

2

-40

0

-60

-2

-80 -8988

-8986

-8984

-8982

-8980

-8978

-8976

-8974

-8972

angle

amplitude (dB)

The focus result along range 0

100

-4 -8970

0

4

-20

2

-40

0

-60

-2

angle

amplitude (dB)

range (m) The focus result along azimuth

0

(b) 150

-80 -8

-6

-4

-2

0

2

4

6

8

-4 10

azimuth (m)

(b) Fig. 16. Processed result of the simulated data. (a) Amplitude contour of the compressed result. (b) Profile along range direction. (c) Profile along azimuth direction.

100

0

(c) Fig. 18. Experiment result of the stereoscopy bistatic SAR. (a) Imaging result. (b) Result mapping the DEM information on the SAR image. (c) Result mapping the DEM information on the optical image.

Fig. 17.

Processed result of the real data using the X-band (TerraSAR-X).

amplitude contour of the compressed result. Fig. 19(b) is the amplitude profile of compressed result. Fig. 19(c) is the angle

profile of compressed result. The upper figure is the profile along the range direction, and lower figure is the profile along the azimuth direction. The blue line is the compressed result without scene height estimation, and the red line is the compressed result with scene height estimation. Those compressed results show that the scene height estimation error only brings a shift along the y-direction and the shift value is similar to the scene height estimation error. The imaging property is almost

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 16

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

The focus result 0

8

azimuth (m)

6

-5

4 -10 2 -15

0 -2

-20

-4 -25 -6

-9025

-9020

-9015

-9010

range (m) (a) The focus result along range

amplitude (dB)

0

-20

-40

-9020

-9010

-9000 -8990 range (m) The focus result along azimuth

0

amplitude (dB)

(a) The result without error The result with error

-8980

-8970

The result without error The result with error

-20

-40

-6

-4

-2

0 azimuth (m)

2

4

6

8

(b) The focus result along range angle (rad)

5

The result without error The result with error

0

-5 -9030

(b) -9020

-9010

-9000 -8990 -8980 range (m) The focus result along azimuth

angle (rad)

5

-8970

-8960

The result without error The result with error

0

-5 -8

-6

-4

-2

0 2 azimuth (m)

4

6

8

10

(c) Fig. 19. Processed result with 30-m scene height estimation error using the simulated data. (a) Amplitude contour of the compressed result. (b) Amplitude profile of compressed result. (c) Angle profile of compressed result.

unaffected. The shift along the Y -direction is 18 m, which is similar to the result of the theoretical analysis. Fig. 20 shows the imaging result with 50-m scene height estimation error. Comparing with Fig. 17, the imaging quality is almost the same. Fig. 20(b) shows the difference between the imaging result with and without the 50-m scene height estimation error. The imaging result without error is in red, and the imaging result with error is in green. If the image with and without error is the same, the combination result will be yellow. The combination result shows that the image with and without the scene height estimation error is almost yellow. That is to say, the imaging results with and without the error are almost the same. In order to show the detail, a part of Fig. 20(b) is enlarged and shown in Fig. 20(c). The figure shows that the scene height estimation error only brings a shift along the y-direction and the imaging property is almost unaffected.

(c) Fig. 20. Imaging result with 50-m scene height estimation error using the experimental data. (a) Imaging result with 50-m scene height estimation error. (b) Result comparison with and without 50-m scene height estimation error. (c) Partial result comparison.

The simulation result and the result obtain from the presented bistatic experiment verified the proposed theoretical analysis. And we can conclude that the scene height estimation error causes an imaging shift along the range direction and that the target near the receiver shifts larger than the target

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

17

The effect of trigger delay

The effect of trigger delay 80

Without trigger delay With trigger delay Error

60 40

Amplitude

20 0

0

500

1000

1500

2000

2500

3000

3500

4000

40 20 0

4500

Without trigger delay With trigger delay Error

60

0

500

1000

Range position The effect of trigger delay

-20

1600

1700

1800

1900

2000

2100

2200

2300

2400

Amplitude (dB)

Amplitude (dB)

3500

4000

4500

Without trigger delay With trigger delay Error

-20

-30 1500

2500

1600

1700

0

0

-20

Without trigger delay With trigger delay Error 1970

1980

1990

2000

2010

2020

2030

2040

2050

1900

2000

2100

2200

2300

2400

2500

0

5

-40 2060

Range position (a)

Angle (rad)

5

1800

Range position The effect of trigger delay Amplitude(dB)

Angle (rad)

3000

-10

Range position The effect of trigger delay

Fig. 21.

2500

0

Without trigger delay With trigger delay Error

-10

-5 1960

2000

Range position The effect of trigger delay

0

-30 1500

1500

-20

0

-5 1960

Without trigger delay With trigger delay Error 1970

1980

1990

2000

2010

2020

2030

2040

2050

Amplitude(dB)

Amplitude

80

-40 2060

Range position (b)

Effect of trigger delay with the simulated data. (a) Effect of a 32-point trigger delay. (b) Effect of a 128-point trigger delay.

far from the receiver; however, the imaging quality is only affected slightly.

B. Trigger Delay of the Synchronization Receiver In order to verify the proposed theoretical analysis of the trigger delay, we cut off the first several data of received signal both of the synchronization channel and of the echo channel and use the signal of the synchronization channel as the match filter to compress the echo to carry out the range compression. The simulation with the trigger delay is also applied to verify the proposed theoretical analysis. Fig. 21(a) shows the simulation results with a 32-point trigger delay and Fig. 21(b) shows the simulation results with a 128-point trigger delay. The total transmitted pulse has 2161 points. The results show that the trigger delay only affects the amplitude. The result also shows that the loss of more points affects the amplitude more, whereas the maximum value position and phase at the maximum value position are not affected by the trigger delay. Compared to Fig. 7, the simulation result verified the theoretical analysis that the trigger delay only affects the amplitude of the main lobe and does not shift the position of the main lobe. The trigger delay affects the phase of the main lobe only slightly. In this simulation, losing 128 points from 2161 points only causes error of the phase in the main lobe, but the phase at the peak value position is not affected.

Fig. 22(a) and (b) shows the results of the 32- and 128point trigger delay. The upper figure is the amplitude. The red line is the compressed result with the trigger delay, the blue line is the compressed result without the trigger delay, and the black line is the error caused by the trigger delay. The middle figure is the error of the angle. The lower figure is a part of the amplitude. The results show that the trigger delay affects the compressed result only slightly. The simulation results and the results obtained from the bistatic experiments verified the proposed theoretical analysis. Thus, we can conclude that the loss of the first several chirp signal data only slightly affects the result of the imaging using BP algorithm, which is an advantage because we can use the data received by the synchronization receiver to compress the echo data obtained by the echo receiver in the range direction. While using a general chirp signal to compress the echo receiver in the range direction, the trigger delay of the synchronization receiver will introduce a shift T /Tr of the maximum position in range direction, which seriously affects the result. C. Error of the Orbital Measurement In the simulation, we assume the satellite movement along the X-direction, 100-m orbital measurement systematic error (33 m along the X-direction, 33 m along the Y -direction, and 34 m along the Z-direction), and ±1-m the orbital measurement random error. We also add those orbital measurement

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 18

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

5

The effect of trigger delay

15

Without trigger delay With trigger delay Error

10 5

0.5

1 Range Position

1.5

2 x 10

Error of Angle (rad)

0.01

Amplitude

8

x 10

5

4

Error

1.5 x 10

0

0

0.5

1 Range Position

4

0

x 10

5

1.5

2 x 10

4

The effect of trigger delay

6

Without trigger delay With trigger delay

4

Error

2 0

600

800

1000 1200 Range Position

1400

1600

(a) Fig. 22.

4

0.02

2

2

-2 400

2 x 10

0.04

8 Without trigger delay With trigger delay

1.5

0.06

The effect of trigger delay

6

1 Range Position

0.08

Amplitude

Error of Angle (rad)

0.02

1 Range Position

0.5

The effect of trigger delay

0.03

0.5

0

0.1

0.04

0

Without trigger delay With trigger delay Error

4

The effect of trigger delay

0

The effect of trigger delay

0 -5

0

5

5

0 -5

x 10

10

Amplitude

Amplitude

15

x 10

-2 400

600

800

1000 1200 Range Position

1400

1600

(b)

Effect of trigger delay with the experimental data. (a) Effect of a 32-point trigger delay. (b) Effect of a 128-point trigger delay.

errors to the precise orbit of the satellite in the experimental data to verify the proposed theoretical analysis. 1) Orbital Measurement Systematic Error: Fig. 23 shows the processed result with 100-m orbital measurement systematic error. Fig. 23(a) is the amplitude contour of the compressed result. Fig. 23(b) is the amplitude profile of the compressed result. Fig. 23(c) is the angle profile of the compressed result along the range and azimuth direction, respectively. The blue line is the compressed result without 100-m orbital measurement systematic error, and the red line is the compressed result with 100-m orbital measurement systematic error. The results show that the orbital measurement systematic error only brings a shift of the image, and that the shift value is much smaller than the orbital measurement systematic error. Fig. 23(b) shows that the shift along the azimuth direction is more serious than the shift along range direction with the same error, which supports our theoretical analysis. The imaging property is almost unaffected, but the phase is affected seriously. Fig. 24 is the imaging result with 100 m orbital measurement systematic error. Comparing with Fig. 17, the imaging quality is almost the same. Fig. 24(b) shows the difference between the imaging result with 100 m orbital measurement systematic error. The imaging result without error is in red, and the imaging result with error is in green. The combination

result shows that the imaging result with and without the error is almost same. Fig. 24(c) is one part of Fig. 24(b) to show the detail of the comparison. The figure shows that the 100-m orbital measurement systematic error introduces a slight shift. The imaging property is almost unaffected. 2) Orbital Measurement Random Error: Fig. 25 shows the processed result with ±1-m orbital measurement random error. Fig. 25(a) is the amplitude contour of the compressed result. Fig. 25(b) is the amplitude profile of the compressed result. Fig. 25(c) is the angle profile of the compressed result along the range and the azimuth direction, respectively. The blue line is the compressed result without error and the red line is the compressed result with error. The results show that the orbital measurement random error affects the imaging property, but the influence of the main lobe is very slight. The imaging position and the phase of the main lobe are only slightly affected. Fig. 26(a) is the imaging result with ±1-m orbital measurement random error. Comparing with Fig. 17, the imaging property is almost the same. Fig. 26(b) shows the difference between the imaging result with and without ±1-m orbital measurement random error. The imaging result without error is in red, and the imaging result with error is in green. The combination result shows that the imaging result with and without the error is almost same. Fig. 26(c) is one part of

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

19

The focus result 0

8 6

-5

azimuth (m)

4 -10 2 -15

0 -2

-20

-4 -25 -6

(a)

-9006 -9004 -9002 -9000 -8998 -8996 -8994 -8992

range (m) (a) The focus result along range amplitude (dB)

0

The result without error The result with error

-20

-40

-9020

-9010

-9000 -8990 range (m) The focus result along azimuth

amplitude (dB)

0

-8980

-8970

The result without error The result with error

-20

-40

-6

-4

-2

0 azimuth (m)

2

4

6

8

(b)

(b) The focus result along range angle (rad)

5

The result without error The result with error

0

-5 -9030

-9020

-9010

-9000 -8990 -8980 range (m) The focus result along azimuth

angle (rad)

5

-8970

-8960

The result without error The result with error

0

-5 -8

-6

-4

-2

0 2 azimuth (m)

4

6

8

10

(c) Fig. 23. Processed result with 100-m orbital measurement systematic error using the simulated data. (a) Amplitude contour of the compressed result. (b) Amplitude profile of compressed result. (c) Angle profile of compressed result.

Fig. 26(b). The figure shows that the error of the ±1-m orbital measurement random error affects the imaging property and imaging position only slightly. The simulation results and the results obtained from the bistatic experiment verified the proposed theoretical analysis. And we can conclude that both the orbital measurement systematic error and the orbital measurement random error only slightly affect both the imaging results using the BP algorithm. That is also the advantage of using the synchronization signal

(c) Fig. 24. Imaging result with 100-m orbital measurement systematic error of the experimental data. (a) Imaging result with 100-m orbital measurement systematic error. (b) Result comparison with and without 100-m orbital measurement systematic error. (c) Ppartial result comparison.

as the match filter to compress the echo data in the range compression process. Using this method, the requirement of the measurement precision can be reduced, which is very useful for the real-time imaging applications. The precise orbital measurement information cannot be obtained in reasonable time. It takes a lot time to transmit the orbital information from the satellite to the station. However, the proposed method can

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 20

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

The focus result 0

8

azimuth (m)

6

-5

4 -10 2 -15

0 -2

-20

-4 -25 -6

(a) -9008 -9006 -9004 -9002 -9000 -8998 -8996 -8994 -8992

range (m) (a) The focus result along range

amplitude (dB)

0

The result without error The result with error

-20

-40

-9020

-9010

-9000 -8990 range (m) The focus result along azimuth

amplitude (dB)

0

-8980

-8970

The result without error The result with error

-20

-40

-6

-4

-2

0 azimuth (m)

2

4

6

8

(b)

(b) The focus result along range

angle (rad)

5

The result without error The result with error

0

-5 -9030

-9020

-9010

-9000 -8990 -8980 range (m) The focus result along azimuth

angle (rad)

5

-8970

-8960

The result without error The result with error

0

-5 -8

-6

-4

-2

0 2 azimuth (m)

4

6

8

10

(c) Fig. 25. Imaging result with ±1m orbital measurement random error of the simulated data. (a) Amplitude contour of the compressed result. (b) Amplitude profile of compressed result. (c) Angle profile of the compressed result.

image the data with only coarse orbital information. Several hundred meters of orbital measurement error only causes a shift of the image and the imaging quality is affected only slightly. D. Error of the Receiver Location In this simulation, we assume a satellite moving along the X-direction, 10-m synchronization receiver location measurement error (3 m along the X-direction, 3 m along the Y -direction, and 4 m along the Z -direction) and 10-m echo receiver location measurement error. We also add those loca-

(c) Fig. 26. Imaging result with ±1-m orbital measurement random error of the experimental data. (a) Imaging result with ±1-m orbital measurement random error. (b) Result comparison with and without ±1-m orbital measurement random error. (c) Partial result comparison.

tion measurement errors to the precise location measurement of the receiver in the experimental data to verify the proposed theoretical analysis. 1) Synchronization Receiver: Fig. 27(a) is the processed result with 10-m synchronization receiver position measurement error. Fig. 27(b) is the amplitude profile of the compressed result. Fig. 27(c) is the angle profile of the compressed result along the range the azimuth direction, respectively. The blue line is the compressed result without error, and the red

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

The focus result 0

10

azimuth (m)

8

-5

6

-10

4 -15 2 -20 0 -25

-2

-4 -9004

-9002

-9000 -8998

-8996 -8994

-8992 -8990

range (m) (a) The focus result along range

amplitude (dB)

0 The result without error The result with error -20

-40

-9020

-9010

-9000 -8990 range (m) The focus result along azimuth

-8980

-8970

amplitude (dB)

0 The result without error The result with error -20

-40

-6

-4

-2

0 azimuth (m)

2

4

6

8

(b) The focus result along range

angle (rad)

5

The result without error The result with error

0

-5 -9030

-9020

-9010

-9000 -8990 -8980 range (m) The focus result along azimuth

angle (rad)

5

-8970

-8960

The result without error The result with error

0

-5 -8

-6

-4

-2

0 2 azimuth (m)

4

6

8

10

(c) Fig. 27. Imaging result with 10-m synchronization receiver position measurement error of the simulated data. (a) Amplitude contour of the compressed result. (b) Amplitude profile of compressed result. (c) Angle profile of compressed result.

line is the compressed result with error. The results show that the synchronization receiver position measurement error introduces a shift both along both the y- and x-directions. Comparing the shift caused by orbital measurement error, the synchronization receiver position measurement error is much more serious, but the precision of the synchronization receiver position measurement is much higher than the precision of the orbital measurement. The imaging property is almost unaffected, but the phase is affected seriously.

21

Fig. 28(a) is the imaging result with 10-m synchronization receiver position measurement error. Comparing with Fig. 17, the imaging property is almost the same. Fig. 28(b) shows the difference between the imaging result with and without 10-m synchronization receiver position measurement error. The imaging result without error is in red, and the imaging result with error is in green. The combination result shows that the imaging result with and without the error is almost the same. Fig. 28(c) is one part of the Fig. 28(b). The figure shows that the error of the 10-m synchronization receiver position measurement error brings an obvious shift, comparing with 100-m orbital measurement error, but the imaging property is almost unaffected. However, the precision of the synchronization receiver position measurement is much higher than the orbital measurement. In our experiment, the precision of GPS is 5 mm and the precision of the orbital measurement is larger than 1 m. 2) Echo Receiver: Fig. 29(a) is the processed result with 10-m echo receiver position measurement error. Fig. 29(b) is the amplitude profile of the compressed result. Fig. 29(c) is the angle profile of the compressed result along the range and azimuth direction, respectively. The blue line is the compressed result without error, and the red line is the compressed result with error. The results show that the echo receiver position measurement error only brings a shift along the y-direction. Comparing the shift caused by orbital measurement error, the echo receiver position measurement error is much more serious, but the precision of the echo receiver position measurement is much higher than the precision of the orbital measurement. The imaging property is almost unaffected, but the phase is affected seriously. Fig. 30(a) is the imaging result with 10-m echo receiver position measurement error. Comparing with Fig. 17, the imaging property is almost the same. Fig. 30(a) shows the difference between the imaging result with and without 10-m echo receiver position measurement. The imaging result without error is in red, and the imaging result with error is in green. The combination result shows that the imaging result with and without the error is almost same. Fig. 30(a) is one part of the Fig. 30(a). The figure shows that the error of the 10-m echo receiver position measurement error brings about an obvious shift, but the imaging property is almost unaffected. Comparing with the effect of the synchronization receiver location measurement error, the shift along the azimuth of the echo receiver location measurement is much less than that of the synchronization receiver location measurement error with the same error, which is the same as in the theoretical analysis. The simulation and real data results verified the proposed theoretical analysis. And we conclude that both the synchronization receiver position measurement error and the echo receiver position measurement error affect the imaging property using BP algorithm only slightly, but both of them introduce a shift of the image, which is much more serious than the shift caused by the orbital measurement error. The location measurement error of the synchronization receiver causes larger shift than that of the echo receiver.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 22

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

The focus result 0

8

azimuth (m)

6

-5

4 -10 2 -15

0 -2

-20

-4 -25 -6

(a) -9005

-9000

-8995

-8990

range (m) The focus result along range

amplitude (dB)

0

The result without error The result with error

-20

-40

-9020

-9010

-9000 -8990 range (m) The focus result along azimuth

amplitude (dB)

0

-8980

-8970

The result without error The result with error

-20

-40

(b)

-6

-4

-2

0 azimuth (m)

2

4

6

8

The focus result along range

angle (rad)

5

The result without error The result with error

0

-5 -9030

-9020

-9010

-9000 -8990 -8980 range (m) The focus result along azimuth

angle (rad)

5

Fig. 28. Imaging result with 10-m synchronization receiver position measurement error of the experimental data. (a) Imaging result with 10-m synchronization receiver position measurement error. (b) Result comparison with and without 10-m synchronization receiver position measurement error. (c) Partial result comparison.

E. Measurement Error of the Transmission Line Length Though the synchronization and echo receiver are colocated and part of the same receiver subsystem, each receiver uses a different antenna. The antennas are connected to the receiver using different transmission lines. We only measure the positions of the antennas’ phase center. Though the synchronization correction is carried out before the experiment,

-8960

The result without error The result with error

0

-5 -8

(c)

-8970

-6

-4

-2

0 2 azimuth (m)

4

6

8

10

Fig. 29. Imaging result with 10-m echo receiver position measurement error of the simulated data. (a) Amplitude contour of the compressed result. (b) Amplitude profile of compressed result. (c) Angle profile of compressed result.

there is also error of the synchronization correction. That error is referred to as the transmission line length error. In order to verify the proposed analysis, we add the 3-m transmission line length measurement error to the real experimental data. We also simulate the effect of the measurement error of the transmission line length with 3-m error. Fig. 31(a) is the processed result with 3-m transmission line difference. Fig. 31(b) is the amplitude profile of the compressed result. Fig. 31(c) is the angle profile of the compressed result along the range and the azimuth direction, respectively. The blue line is the compressed result without error, and the red line is the compressed result with error. The results show that the echo receiver position measurement error

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

23

The focus result 0

8

azimuth (m)

6

-5

4 -10 2 -15

0 -2

-20

-4 -25 -6

(a) -9005

-9000

-8995

-8990

range (m) (a) The focus result along range

amplitude (dB)

0

The result without error The result with error

-20

-40

-9020

-9010

-9000 -8990 range (m) The focus result along azimuth

amplitude (dB)

0

(b)

-8980

-8970

The result without error The result with error

-20

-40

-6

-4

-2

0 azimuth (m)

2

4

6

8

(b) The focus result along range

angle (rad)

5

The result without error The result with error

0

-5 -9030

-9020

-9010

-9000 -8990 -8980 range (m) The focus result along azimuth

angle (rad)

5

-8970

-8960

The result without error The result with error

0

-5 -8

-6

-4

-2

0 2 azimuth (m)

4

6

8

10

(c)

(c) Fig. 30. Imaging result with 10-m echo receiver position measurement error of the experimental data. (a) Imaging result with 10-m echo receiver position measurement error. (b) Result comparison with and without 10-m echo receiver position measurement error. (c) Partial result comparison.

only brings a shift along the y-direction. The imaging property is almost unaffected. Fig. 32(a) is the imaging result with a 3-m transmission line difference. Comparing with Fig. 17, the imaging property is almost the same. Fig. 32(b) shows the difference between the imaging result with and without 100-m orbital system

Fig. 31. Imaging result with 3 m transmission line difference of the simulated data. (a) Amplitude contour of the compressed result. (b) Amplitude profile of compressed result. (c) Angle profile of compressed result.

measurement error. The imaging result without error is in red, and the imaging result with error is in green. The combination result shows that the imaging result with and without the error is almost same. Fig. 32(c) is one part of the Fig. 32(b). The figure shows that the error of the 3-m transmission line difference introduces a little shift, but the imaging property is almost unaffected. The simulation and real data results verified the proposed theoretical analysis. We can that the measurement error of the transmission line affects the imaging property using BP algo-

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 24

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

measurement precision of the transmission line is very high; in the presented experiment the precision is 10 mm. V. C ONCLUSION

(a)

The simulations and real bistatic experimental results verified the proposed theoretical analysis. The scene height estimation error, trigger delay, transmitter position error, receiver position error, and transmission line length measurement error affected quality of imaging only slightly. All of these measurement errors caused an image shift along the range direction. The synchronization receiver position measurement error caused the image shift along the azimuth direction. The scene height estimation error, trigger delay, transmitter position error, and synchronization receiver position measurement error affected the precision of DEM obtained by stereoscopy bistatic SAR. However, the echo receiver position measurement error and transmission line length measurement error seriously affected the precision of DEM obtained by stereoscopy bistatic SAR. Luckily, the measurement precision of the echo receiver position and length of the transmission line can be very satisfactory. R EFERENCES

(b)

(c) Fig. 32. Imaging result with 3-m transmission line difference of the experimental data. (a) Imaging result with 3-m transmission line difference. (b) Result comparison with and without 3-m transmission line difference. (c) Partial result comparison.

rithm only slightly, but introduces a shift in the y-direction, which is much more serious than the shift caused by the orbital measurement error. The measurement error of the transmission line seriously affects the precision of DEM. However, the

[1] S. Reuter, F. Behner, H. Nies, O. Loffeld, D. Matthes, and J. Schiller, “Development and experiments of a passive SAR receiver system in a bistatic spaceborne/stationary configuration,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2010, pp. 118–121. [2] R. Wang, O. Loffeld, H. Nies, A. M. Ortiz, I. Walterscheid, T. Espeter, J. Klare, and J. H. G. Ender, “Focusing results and analysis of advanced bistatic SAR experiments in spaceborne or airborne/airborne or stationary configurations,” in Proc. 8th Eur. Conf. Synthetic Aperture Radar, Jun. 2010, pp. 1042–1045. [3] S. Duque, P. Lopez-Dekker, J. C. Merlano, and J. J. Mallorqui, “Bistaic SAT tomography: Processing and experiment results,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2010, pp. 154–157. [4] S. Duque, P. Lopez-Dekker, J. J. Mallorqu, A. Y. Nashashibi, and A. T. M. Patel, “Experimental results with bistatic SAR tomography,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., vol. 2. Jul. 2009, pp. II-37–II-40. [5] S. Duque, P. Lopez-Dekker, J. J. Mallorqu, and J. C. Merlano, “Repeatpass interferometry using a fixed-receiver and ERS-2/ENVISAT as transmitters of opportunity,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2009, pp. 246–249. [6] S. Duque, P. Lopez-Dekker, and J. J. Mallorqui, “Single-pass bistatic SAR interferometry using fixed-receiver configurations: Theory and experimental validation,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 6, pp. 2740–2749, Jun. 2010. [7] Y. Wang, X. Zhang, W. Li, and J. Shi, “A new bistatic-based sparse linear array 3D imaging SAR model,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2008, pp. III-463–III-466. [8] L. Rui, J. Xiong, and Y. Huang, “Analysis of bistatic SAR frequency synchronization,” in Proc. Int. Conf. Commun., Circuits Syst. Proc., vol. 1. Jun. 2006, pp. 380–383. [9] C. Sun, L. Zhou, D. Zhang, G. Lu, and W. Chen, “Analysis of phase synchronization errors based on distributed small satellite SAR system,” in Proc. 7th Int. Symp. Antennas, Propag. EM Theory, Oct. 2006, pp. 1–4. [10] Z. Li, D. Zeng, T. Long, W. Wang, and C. Hu, “Analysis of time synchronization errors in bistatic SAR,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Sep. 2008, pp. 407–411. [11] P. L. Dekker, J. J. Mallorqui, P. S. Morales, and J. S. Marcos, “Phase synchronization and doppler centroid estimation in fixed receiver bistatic SAR systems,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 11, pp. 3459–2471, Nov. 2008. [12] W.-Q. Wang and J. Cai, “Antenna directing synchronization for bistatic synthetic aperture radar systems,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 307–310, Jan. 2010.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. SHAO et al.: ERROR ANALYSIS OF BISTATIC IMAGING AND STEREOSCOPY USING SAR

[13] Y. Zhang, D. Liang, and Z. Dong, “Analysis of time and frequency synchronization errors in spaceborne parasitic InSAR system,” in Proc. IEEE Int. Conf. Geosci. Remote Sens. Symp., Aug. 2006, pp. 3047–3050. [14] M. Antoniou, Z. Zeng, L. Feifeng, and M. Cherniakov, “Experimental demonstration of passive BSAR imaging using navigation satellites and a fixed receiver,” IEEE Geosci. Remote Sens. Lett., vol. 9, no. 3, pp. 477–481, May 2012. [15] F. H. Wong, I. G. Cumming, and Y. L. Neo, “Focusing bistatic SAR data using the nonlinear chirp scaling algorithm,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 9, pp. 2493–2505, Sep. 2008. [16] Y. L. Neo, F. H. Wong, and I. G. Cumming, “Processing of azimuthinvariant bistatic SAR data using the range doppler algorithm,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 1, pp. 14–21, Jan. 2008. [17] I. Walterscheid, J. H. G. Ender, A. R. Brenner, and O. Loffeld, “Bistatic SAR processing using an omega-k type algorithm,” in Proc. IEEE Int. Conf. Geosci. Remote Sens. Symp., vol. 2. Jul. 2005, pp. 1064–1067. [18] Y. Hongtao, Z. Yong-shun, and Z. Lili, “UWB LFMCW radar imaging based on dechirp processing,” Modern Radar, vol. 27, no. 7, pp. 39–41, Jul. 2005. [19] R. Wang, Y. K. Deng, O. Loffeld, H. Nies, I. Walterscheid, T. Espeter, J. Klare, and H. G. J. Ender, “Processing the azimuth-variant bistatic SAR data by using monostatic imaging algorithms based on twodimensional principle of stationary phase,” IEEE Trans. Geosci. Remote Sens, vol. 49, no. 10, pp. 3504–3520, Oct. 2011. [20] C. Dai, X. Zhang, and J. Shi, “Range cell migration correction for bistatic SAR image formation,” IEEE Geosci. Remote Sens. Lett., vol. 9, no. 1, pp. 124–128, Jun. 2012. [21] Y. Ding and D. C. Munson, “A fast back-projection algorithm for bistatic SAR imaging,” in Proc. Int. Conf. Image Process., vol. 2. Oct. 2002, pp. II-449–II-452. [22] P.-O. Frölind and L. M. H. Ulander, “Evaluation of angular interpolation kernels in fast back-projection SAR processing,” in IEE Proc. Radar, Sonar Navigat., vol. 153, no. 3, pp. 243–249, Jun. 2006. [23] J. Chen, J. Xiong, Y. Huang, and J. Yang, “Research on a novel fast backprojection algorithm for stripmap bistatic SAR imaging,” in Proc. 1st Asian Pacific Conf. Synthetic Aperture Radar, Nov. 2007, pp. 622– 625. [24] L. M. H. Ulander, H. Hellsten, and G. Stenstrom, “Synthetic-aperture radar pro-cessing using fast factorized back-projection,” IEEE Trans. Aerosp. Electron. Syst., vol. 39, no. 3, pp. 760–776, Jul. 2003. [25] M. R. Cassola, P. Prats, G. Krieger, and A. Moreira, “Efficient timedomain focussing for general bistatic SAR configurations: Bistatic fast factorised backprojection,” in Proc. 8th Eur. Conf. Synthetic Aperture Radar, Jun. 2010, pp. 1–4. [26] X. Zhang, X. Zhang, J. Shi, and L. Zhe, “GPU-based parallel back projection algorithm for the translational variant BiSAR imaging,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2011, pp. 2841–2844. [27] G. I. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA, USA: Artech House, Jan. 2005.

25

Robert Wang (M’07–SM’12) received the B.S. degree in control engineering from the University of Henan, Kaifeng, China, in 2002, and the Dr. Eng. degree from the Graduate University of Chinese Academy of Sciences, Beijing, China, in 2007. He joined the Center for Sensorsystems (ZESS), University of Siegen, Siegen, Germany, in 2007. He has been involved in the TerraSAR-X/PAMIR hybrid bistatic SAR experiment, the PAMIR/stationary bistatic SAR experiment, PAMIR/stationary bistatic SAR experiment with non-synchronized oscillators, the 3D/4D SAR tomography for high-resolution information extraction and monitoring earth’s dynamics, and the millimeter-wave FMCW SAR data processing. In addition, he has been involved in some SAR projects for Fraunhofer-FHR. Since 2011, he has been a Research Fellow with the Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences (IECAS), where he was funded by the “100 Talents Programme of The Chinese Academy of Sciences.” He has authored more than 90 papers since 2003, of which more than 30 are peer-reviewed and wellknown journal papers. He has contributed to invited sessions on bistatic SAR at the European Conference on Synthetic Aperture Radar (EUSAR) in 2008 and 2010. He authored a tutorial, Results and Progresses of Advanced Bistatic SAR Experiments, presented at the European Radar Conference 2009 and co-authored a tutorial entitled Progress in Bistatic SAR Concepts and Algorithms, presented at EUSAR2008. He has been chosen as Session Chair at EUSAR2012. His current research interests include monostatic and bistatic SAR imaging, multibaseline for monostatic and bistatic SAR interferometry, high-resolution spaceborne SAR systems and data processing, airborne SAR motion compensation, FMCW SAR systems and millimeterwave SAR systems. He is a Co-Principal Investigator (PI) for Helmholtz-CAS Joint Research Group in the areas of space-borne microwave remote sensing for prevention and forensic analysis of natural hazards and extreme events since 2012.

Yun Kai Deng (M’11) received the M.S. degree in electrical engineering from the Beijing Institute of technology, Beijing, China, in 1993. He joined the Institute of Electronics, Chinese Academy of Sciences (IECAS), in 1993, where he worked on antenna design, microwave circuit design, and spaceborne/airborne SAR technology. He has been the Leader of several spaceborne/airborne SAR programs and developed some key technologies of spaceborne/airborne SAR. Currently, he is a Research Scientist, a member of the scientific board, and the Director of Spaceborne Microwave Remote Sensing System Department, IECAS. He has authored more than 100 papers since 2002, of which more than 40 are peer-reviewed and well-known journal papers. His current research interests include spaceborne/airborne SAR technology for advanced modes, multifunctional radar imaging, and microwave circuit design. He has been the Principal Investigator for Helmholtz-CAS Joint Research Group in the areas of space-borne microwave remote sensing for prevention and forensic analysis of natural hazards and extreme events since 2012.

Yue Liu received the B.S. degree in electronic engineering and information science from the University of Science and Technology of China (USTC), Hefei, China, in 2007, and the Ph.D. degree from the Graduate University of Chinese Academy of Sciences (GUCAS), Beijing, in 2012. She continued her research with the Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing. Her current research interests include CW SAR technology and InSAR tech-

Yunfeng Shao received the Bachelors degree from Shanghai Jiaotong University, Shanghai, China, in 2009. He is currently pursuing the Ph.D. degree with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing, China. His current research interests include bistatic SAR imaging algorithm, stereoscopy bistatic SAR, bistatic InSAR, and TomoSAR processing. nology.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 26

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Runpu Chen received the Bachelors degree from Xidian University, Xi’an, China, in 2009. She is currently pursuing the Ph.D. degree with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing, China. Her current research interests include SAR interferometric techniques, with a focus on multitemporal InSAR, persistent scatterer interferometry (PSI), tomography SAR, SqueeSAR and their applications on nature hazards and urban monitoring.

Gang Liu was born in Shandong, China, on May 15, 1986. He received the B.S. degree in electronic and information engineering from Sichuan University, Chengdu, China, in 2009. He is currently pursuing the Ph.D. degree in electronic and information engineering with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing, China. His current research interests include interferometric synthetic aperture radar signal processing.

Timo Balz (M’09) was born in Stuttgart, Germany, in 1974. He received the Diploma degree (Dipl.Geogr.) in geography and the Doctoral degree (Dr.Ing.) in aerospace engineering and geodesy from the Universitaet Stuttgart, Stuttgart, in 2001 and 2007, respectively. He was a Research Assistant with the Institute for Photogrammetry, Universitaet Stuttgart, from 2001 to 2007. From 2004 to 2005, he was a Visiting Scholar with Wuhan University, Wuhan, China. From 2008 to 2010, he was a Post-Doctoral Research Fellow with the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (LIESMARS), Wuhan University. Since 2010, he has been an Associate Professor for Radar Remote Sensing with LIESMARS. His current research interests include SAR simulation, surface motion estimation with SAR, computer visualization, SAR image interpretation, and radargrammetry. Mr. Balz serves as Associate Editor for the IEEE G EOSCIENCE AND R EMOTE S ENSING L ETTERS .

Otmar Loffeld (M’05–SM’06) received the Diploma degree in electrical engineering from the Technical University of Aachen, Aachen¸ Germany, in 1982, the Eng.Dr. degree and the Habilitation degrees in digital signal processing and estimation theory in 1986, and 1989, respectively, both from the University of Siegen, Siegen, Germany. He was a Professor of digital signal processing and estimation theory with the University of Siegen. Since then, he gives lectures on general communication theory, digital signal processing, stochastic models and estimation theory and synthetic aperture radar. He is author of two textbooks on estimation theory. His current research interests include multi sensor data fusion, Kalman filtering techniques for data fusion, optimal filtering and process identification, SAR processing and simulation, SAR-interferometry, phase unwrapping, and baseline estimation. A recent field of interest is bistatic SAR processing. He became a member of the Center for Sensorsystems (ZESS) which is a central scientific research establishment at the University of Siegen. Since 2005, he has been the Chairman of that Center. He became the Principal Investigator (PI) on baseline estimation for the X-band part of the Shuttle Radar Topography Mission (SRTM), where ZESS contributed to DLR’s baseline calibration algorithms, in 1999. He is PI for interferometric techniques in the German TerraSAR-X mission, and, together with Prof. Ender from FGAN, he is a PI for a bistatic spaceborne airborne experiment, where TerraSAR-X serves as the bistatic illuminator, while FGAN’s PAMIR system mounted on a Transall airplane is used as a bistatic receiver. In 2002, he founded the International Postgraduate Program, Multi Sensorics, and, based on that program, he established the NRW Research School on Multi Modal Sensor Systems for Environmental Exploration and Safety at the University of Siegen in 2008. He is the Speaker and Coordinator of both doctoral degree programs, hosted by ZESS. He is also the University’s Scientif Coordinator for multidimensional and imaging systems. He is a member of the ITG/VDE. Prof. Loffeld was the recipient of the Scientific Research Award of North Rhine-Westphalia (Bennigsen-Foerder Preis) for his works on applying Kalman filters to phase estimation problems, such as Doppler centroid estimation in SAR, and phase and frequency demodulation.