sea surface wind speed estimation based on gnss ... - IEEE Xplore
SEA SURFACE WIND SPEED ESTIMATION BASED ON GNSS SIGNAL MEASUREMENTS Kegen Yu, Chris Rizos and Andrew Dempster School of Surveying and Spatial Information Systems University of New South Wales, Sydney, NSW 2052, Australia (kegen.yu, c.rizos, a.dempster)@unsw.edu.au ABSTRACT In this paper we investigate near sea surface wind speed estimation using GNSS (Global Navigation Satellite System) signals. A low-altitude airborne experiment was conducted recently using a UNSW-owned light aircraft over the coast of Sydney. Both direct and reflected signals were captured via a zenith-looking antenna and a nadir-looking antenna respectively. The logged IF data bits were processed to generate delay waveforms and delay-Doppler waveforms. Using the measured waveforms and the theoretical ones, the wind speed can be estimated through waveform fitting. The processed waveforms associated with eight satellites were employed to estimate the wind speed. A four-step method is proposed to perform the waveform fitting. The results show that similar estimation accuracy can be achieved using signals transmitted from satellites with low or high elevation angles. It is demonstrated that the estimation accuracy of the wind speed is around 1 m/s. Further the incorrect encoding of some quantized data bits in a software receiver is investigated. Index Terms— Sea surface wind speed estimation, GNSS direct and reflected signal, delay waveform, delayDoppler waveform, low-altitude airborne experiment 1. INTRODUCTION The Information about the sea surface conditions is very useful for a range of services. For instance, the safety of ocean transport and ocean fishery can be enhanced so that tragic ship accidents can be avoided or greatly reduced. Also, with accurate information about the sea state appropriate measures can be taken to significantly reduce the economical loss due to flooding, either caused by strong local wind or by powerful swells, especially in coastal areas. Sea surface wind and sea state information can be retrieved through different approaches. Typically, the weather conditions of coastal area are monitored by coastal weather observation stations such as using off-the-shelf wind speed and direction estimation equipment and the Waverider buoys. Large-scale weather conditions monitoring and
978-1-4673-1159-5/12/$31.00 ©2012 IEEE
forecasting is usually carried out by various weather satellites launched and owned by different countries. GNSS reflectometry (GNSS-R) is another potential approach that can be exploited to monitor the wind and wave conditions of the vast ocean surface. The GNSS signals are a free resource, which are available continuously and globally. Such a concept of GNSS-based remotely sensing geophysical parameters was originally proposed by Martin-Neira [1]. Although significant advances have been made over the past two decades [2-9], there are few real GNSS-R based applications at the present time. However, with continuous research and development undertaken by the relevant research community and industry, it would be envisaged that GNSS-R will become a mature technology and play a complementary role in the earth observation. The focus of this paper is on the sea surface wind speed estimation using data collected during a low-altitude airborne experiment. The estimation makes use of the model of correlation powers derived in [2] and the model of sea surface wave spectrum developed in [3]. In particular, a four-step procedure is proposed to estimate the wind speed using model fitting. Direct and reflected signals transmitted from eight GNSS satellites were received and employed for wind speed estimation. It is observed that in the case where the aircraft flight height is around 3 kilometres there is no clear relationship between the estimation accuracy and the satellite elevation angles which are greater than a specific value such as 20 degrees. Nevertheless, further studies with much more samples are needed to investigate such a relationship for higher flight altitudes especially in the case of a spaceborne platform, or when a different estimation approach is applied. Further, a problem of the encoding of the IF data in a software receiver is addressed. That is, in the 2-bit quantisation the {-1} bits and the {-3} bits were swapped. It is observed that such incorrect encoding can degrade the signal-to-noise ratio of the delay waveforms considerably, although the impact on the wind speed estimation is negligible when the cut-off power level of the delay waveform is set at a high value.
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2. LOW-ALTITUSE AIRBORNE EXPERIMENT The airborne experiment was carried out by a UNSW-owned light aircraft as shown in Figure 1 flying off the coast of Sydney on 4 November 2011. The equipment used for the data logging consists of the software receiver for generating the IF data bits, the RHCP zenith-looking antenna for receiving the direct signals, the LHCP nadir-looking antenna for receiving the reflected signals, the low noise amplifier (LNA), and the laptop for operation and data storage. Figure 2 shows the receiver, the antennas, and the LNA, which were secured in the aircraft.
Wind Gust (m/s)
Figure 3. Two observation stations and the short flight track segemnt. 8 6 4
Wind Speed (m/s)
2
Figure 1. Light aircraft used for conducting the experiment.
North Head Norah Head 1
2
3
4 5 Local Time (pm)
6
7
6
4 North Head Norah Head 2
1
2
3
4 5 Local Time (pm)
6
7
Figure 4. Wind speed and gust recorded at North Head Station and Norah Head Station on 4 November 2011. Figure 2. Receiver, LNA, RHCP antenna and LHCP antenna.
3. WIND SPEED ESTIMATION 3.1. A Problem with the Software Receiver The NordNav receiver was used for the data logging during the experiment. The 2-bit quantization scheme was used so that the output data bits are within {3, 1, -1, -3}. It was observed that there was an encoding problem with the receiver, i.e. incorrectly encoding the data bits {-1} with {3} and vice versa. Figure 5 shows the bit pattern of the originally collected data bits and that after correcting the wrong encoding. Such an incorrect 2-bit quantization encoding scheme is actually equivalent to a 1.5-bit quantization scheme. As a result, certain performance degradation would be incurred. This problem was resolved and the data were corrected. Time domain plot
Point A Point B Norah Head
Amplitude
0
-2 0.005 4
x 10
0.01 0.015 Time (ms) Histogram
0
4
2
0 -4
-2
0 Bin
2
0.005
0.01 0.015 Time (ms) Histogram
4
x 10
Number in bin
North Head 53.360 47.639 65.295
0
0
Number in bin
Norah Head 16.351 19.310
2
-2
Table 1. Distances (units in km) between the Observation Stations and the two end points on the small flight track segment.
Point B 6.403
Time domain plot
2
Amplitude
Figure 3 shows the experimental location and the short flight track segment between Point A and Point B with duration of 100 seconds. Also shown are the two closest weather observation stations, the Norah Head Station and the North Head Station. The distances between the end points of the track and the Stations are listed in Table 1. The wind speed and gust observed in the afternoon are shown in Figure 4 and the wind direction was basically east southeast (ESE) (not shown). These data were provided by Australian Government Bureau of Meteorology. The flight duration of the 100 seconds corresponds to the vertical dashed line. It can be seen that at this duration the wind speed measured at Norah Station was 4.2 m/s, while it was 4.7 m/s at North Head Station. The wind speeds at Point A and Point B should be between these two speeds but closer to that at Norah Head Station. The sea surface can be treated as welldeveloped since the wind had blown the surface continuously for a few hours and the variation of the wind speed and direction was not very large. As a result the corresponding theory can be employed to perform the wind parameter estimation.
4
4
2
0 -4
-2
0 Bin
2
4
Figure 5. Bit statistics of IF data logged via the Nordnav receiver (left) ; bit statistics of the dat after swapping the {-1} with {-3} bits.
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Table 2 shows the elevation angles of eight GPS satellites whose direct and reflected signals were received by the software receiver via both the zenith-looking antenna and the nadir-looking antenna. The delay waveforms and the delay-Doppler waveforms associated with the eight satellites were produced and Figure 6 shows the waveforms of the satellite PRN#28. The coherent integration time was set at 1 millisecond and the non-coherent integration time was equal to 0.5 seconds. That is, the results were produced by averaging 500 waveforms of 1 millisecond. It is observed that over the period of 0.5 seconds the code phase of the signals can vary significantly up to by 16 samples equivalent to one code chip. Thus, when performing the non-coherent integration, the phase variation must be taken into account. Variation in the Doppler frequency is also observed but it is negligible over a period of a few seconds. It can be seen that on the top of the delay-Doppler waveforms the signals are spread over two or more code chips, resulting from the roughness of the sea surface. The spreading of the signals over time can be more clearly observed from the delay waveforms. It is this spread on the trailing edge of the delay waveform that the sea surface wind speed can be estimated and this will be discussed in the next subsection. Table 2. Elevation angles of the eight satellites.
Satellite PRN# Elevation (deg) Satellite PRN# Elevation (deg)
13 65.42 10 35.35
7 60.51 19 34.78
8 44.89 28 26.30
23 35.94 3 23.55
It is worth investigating the impact of the incorrect encoding of {-1} and {-3} data bits as mentioned in section 3.1. Figure 7 shows the delay waveforms of the reflected signals associated with satellite PRN#8. It can be clearly observed that the performance improved after correcting the {-1} bits with the {-3} bits. The noise floor in this case was reduced by about 0.8 dB, approximately 7% of the maximal signal power. From such a decrease in the noise floor, it may be predicted that the decrease in the noise floor or the increase
in the signal-to-noise ratio would be more significant when a higher-level quantization, such as the 3-bit or 4-bit quantization is used. Also, it can be seen that the two delay waveforms are nearly identical when the signal power is above -8 dB. That is, in the case where only the waveform with a power greater than -8 dB is used, the swapping of the {-1} bits and {-3} bits will actually not produce any impact on wind retrieval provided that only the waveform shape is employed. 0 original after swapping
-2
Correlation Power (dB)
3.2. Delay Waveform and Delay-Doppler Waveform
-4 -6 -8 -10 -12 -14 446
447
448
449 450 451 CA Code Phase (Chip)
452
3.3. Near Sea Surface Wind Speed Estimation The wind speed estimation is based on the model fitting method using the model derived in [2]. Figure 8 shows the five theoretical delay waveforms corresponding to five different wind speeds (3, 4, 5, 6, and 7 m/s) and the measured delay waveform associated with satellite PRN#13 which has the largest elevation angle. Note that in Figure 8 and the delay waveform in Figure 6, the time axis t=0 is arbitrary. The measured waveform is produced through coherent integration of 1-millisecond IF signals and then non-coherent integration of 1000 such 1-millisecond waveforms. It can be seen that the measured waveform has a good match with the theoretical waveform of wind speed 4 m/s, producing the wind speed estimate of 4 m/s, which is a good estimate of the real wind speed. It is observed that the theoretical waveforms in this case are insensitive to the wind direction. Further investigation is required to find out why such an outcome occurred.
590
3
589
2
588
1
Correlation Power (dB)
5 6 Doppler (kHz)
581
10
580
8
Normalised Correlation Power (dB)
4
C/A Code Phase (chip)
C/A Code Phase (chip)
5
591
6
579
4
578
2
577 5 6 Doppler (kHz)
10
454
Figure 7. Impact of swapping the {-1} and {-3} bits of the IF signals when the correlation powers are normalized.
0 592
453
reflected direct
-2 -3 -4 -5 -6 -7 -8 0
5
2.5 m/s 3 m/s 3.5 m/s 4 m/s 4.5 m/s measured
-1
0.2
0.4
0.6 0.8 1 1.2 Time (C/A code chip)
1.4
1.6
Figure 8. Wind speed estimation through matching the waveforms.
0 -5 0
2 4 6 Time (C/A code chip)
8
Figure 6. Delay waveforms and Delay-Doppler waveforms of direct and reflected GNSS signals.
This is just an illustrative example to show how the wind speed is estimated. In practice, a mathematical approach will be employed to automatically produce estimation solutions. Regarding this model-matching approach, a certain number
2589
of theoretical waveforms are produced and a cost function is defined. The theoretical waveform with the minimal cost function is then selected and the corresponding wind speed is the estimate of the real wind speed. The cost function can be defined as the sum of the squared difference between the theoretical and measured waveforms. However, this method requires the alignment of the two waveforms so that the difference between the two waveforms is minimized. Alternatively, a slope-based method proposed in [2] can be employed. However, as observed in Figure 8, it is rather difficult to distinguish the slopes of neighboring curves related to different wind speeds. Here a four-step procedure is proposed to perform the waveform fitting to estimate the wind speed: 1) interpolating both the measured and theoretical waveforms without changing the original data; 2) selecting the cut-off correlation power to retain the waveform above certain power lever so that the slope of the trailing edge does not change abruptly; 3) calculating the areas of the interpolated waveforms above the cut-off power and calculating the area difference between the measured waveform and each of the theoretical waveforms; and 4) selecting the theoretical waveform that produces the minimum area difference and taking the corresponding wind speed as the estimate. Figure 9 shows the individual wind speed estimates using signals related to the eight satellites. The data were collected at Point A and one second of the data were processed to generate the results. The horizontal axis corresponds to the eight satellites and the first satellite (PRN#13) has the largest elevation angle, while the eighth satellite (PRN#3) has the smallest one. The average of the eight wind speed estimates is 4.04 m/s, which is close to the wind speed at the Norah Head Observation Station. It is difficult to see the relationship between the estimation performance and the elevation angles from such a small number of samples. Much more samples are needed to obtain useful observations.
Wind Speed Estimates (m/s)
ACKNOWLEDGEMENTS The authors would like to acknowledge that this research work was carried out for the SAR Formation Flying Project which was funded by the Australian Space Research Program (ASRP) and for the ARC Discovery Project DP0877381 (Environmental Geodesy: Variations of Sea Level and Water Storage in the Australian Region). The authors would also like to thank their colleagues Mr. Peter Mumford, Mr. Greg Nippard, Prof. Jason Middleton and Dr. Eamonn Glennon for conducting the airborne experiments. REFERENCES [1] Martín-Neira, M.,“A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry,” ESA J., vol. 17, pp. 331–355, Dec. 1993. [2] Zavorotny, V.U., Voronovich, A.G., “Scattering of GPS signals from the ocean with wind remote sensing application”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, No. 2, pp. 951-964, 2000. [3] Elfouhaily, T,, Chapron, B,, Katsaros, K,, Vandemark, D., “A unified directional spectrum for long and short wind-driven waves”, Journal of Geophysical Research, Vol. 102, No. C7, pp. 15781-15796, 1997. [4] Garrison, J.L., Komjathy, A., Zavorotny, V.U. and Katzberg, S.J., “Wind speed measurement using forward scattered GPS signals”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 40, No. 1, pp. 5065, 2002. [5] Lowe, S.T., Zuffada, C., Chao, Y., Kroger, P., Young, L.E. and LaBrecque, J.L., “5-cm-precision aircraft ocean altimetry using GPS reflections,” Geophysical Research Letters, Vol. 29, No. 10, pp. 13751375, 2002. [6] Gleason, S.T., Hodgart, S., Sun, Y., Gommenginger, C., Mackin, S., Adjrad, M and Unwin, M., “Detection and processing of bistatically reflected GPS signals from low Earth orbit for the purpose of ocean remote sensing”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 43, No. 6, pp. 1229-1241, 2005.
5
4
3
[7] Rius, A., Cardellach, E. and Martin-Neira, M., “Altimetric analysis of the sea-surface GPS-reflected signals”, IEEE Transactions on Geoscience and Remote Sensing, Vol.48, No. 4, pp. 2119-2127, 2010.
2
1
0 1
from eight satellites were utilized to estimate the wind speed individually. Estimation accuracy of around 1 m/s was achieved by using signals transmitted from either lowelevation or high-elevation satellites. A problem of incorrectly encoding the quantized data bits within a software receiver was also investigated.
individual estimates wind speed at Norah Head wind speed at North Head 2
3
4 5 Satellites
6
7
8
Figure 9. Wind speed estimates using signals transmitted at eight satellites.
[8] Martin-Neira, M., D’Adddio, S., Buck, C, Floury, N. and PrietoCerdeira, R., “The PARIS ocean altimeter in-orbit demonstrator”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 49, No. 6, pp. 2209-2237, 2011.
4. CONCLUSIONS In this paper GNSS-R based wind speed estimation was investigated using the data collected during a low-altitude airborne experiment. A simple but reliable four-step delaywaveform fitting method was proposed. Signals transmitted
2590
978-1-4673-1159-5/12/$31.00 ©2012 IEEE
forecasting is usually carried out by various weather satellites launched and owned by different countries. GNSS reflectometry (GNSS-R) is another potential approach that can be exploited to monitor the wind and wave conditions of the vast ocean surface. The GNSS signals are a free resource, which are available continuously and globally. Such a concept of GNSS-based remotely sensing geophysical parameters was originally proposed by Martin-Neira [1]. Although significant advances have been made over the past two decades [2-9], there are few real GNSS-R based applications at the present time. However, with continuous research and development undertaken by the relevant research community and industry, it would be envisaged that GNSS-R will become a mature technology and play a complementary role in the earth observation. The focus of this paper is on the sea surface wind speed estimation using data collected during a low-altitude airborne experiment. The estimation makes use of the model of correlation powers derived in [2] and the model of sea surface wave spectrum developed in [3]. In particular, a four-step procedure is proposed to estimate the wind speed using model fitting. Direct and reflected signals transmitted from eight GNSS satellites were received and employed for wind speed estimation. It is observed that in the case where the aircraft flight height is around 3 kilometres there is no clear relationship between the estimation accuracy and the satellite elevation angles which are greater than a specific value such as 20 degrees. Nevertheless, further studies with much more samples are needed to investigate such a relationship for higher flight altitudes especially in the case of a spaceborne platform, or when a different estimation approach is applied. Further, a problem of the encoding of the IF data in a software receiver is addressed. That is, in the 2-bit quantisation the {-1} bits and the {-3} bits were swapped. It is observed that such incorrect encoding can degrade the signal-to-noise ratio of the delay waveforms considerably, although the impact on the wind speed estimation is negligible when the cut-off power level of the delay waveform is set at a high value.
2587
IGARSS 2012
2. LOW-ALTITUSE AIRBORNE EXPERIMENT The airborne experiment was carried out by a UNSW-owned light aircraft as shown in Figure 1 flying off the coast of Sydney on 4 November 2011. The equipment used for the data logging consists of the software receiver for generating the IF data bits, the RHCP zenith-looking antenna for receiving the direct signals, the LHCP nadir-looking antenna for receiving the reflected signals, the low noise amplifier (LNA), and the laptop for operation and data storage. Figure 2 shows the receiver, the antennas, and the LNA, which were secured in the aircraft.
Wind Gust (m/s)
Figure 3. Two observation stations and the short flight track segemnt. 8 6 4
Wind Speed (m/s)
2
Figure 1. Light aircraft used for conducting the experiment.
North Head Norah Head 1
2
3
4 5 Local Time (pm)
6
7
6
4 North Head Norah Head 2
1
2
3
4 5 Local Time (pm)
6
7
Figure 4. Wind speed and gust recorded at North Head Station and Norah Head Station on 4 November 2011. Figure 2. Receiver, LNA, RHCP antenna and LHCP antenna.
3. WIND SPEED ESTIMATION 3.1. A Problem with the Software Receiver The NordNav receiver was used for the data logging during the experiment. The 2-bit quantization scheme was used so that the output data bits are within {3, 1, -1, -3}. It was observed that there was an encoding problem with the receiver, i.e. incorrectly encoding the data bits {-1} with {3} and vice versa. Figure 5 shows the bit pattern of the originally collected data bits and that after correcting the wrong encoding. Such an incorrect 2-bit quantization encoding scheme is actually equivalent to a 1.5-bit quantization scheme. As a result, certain performance degradation would be incurred. This problem was resolved and the data were corrected. Time domain plot
Point A Point B Norah Head
Amplitude
0
-2 0.005 4
x 10
0.01 0.015 Time (ms) Histogram
0
4
2
0 -4
-2
0 Bin
2
0.005
0.01 0.015 Time (ms) Histogram
4
x 10
Number in bin
North Head 53.360 47.639 65.295
0
0
Number in bin
Norah Head 16.351 19.310
2
-2
Table 1. Distances (units in km) between the Observation Stations and the two end points on the small flight track segment.
Point B 6.403
Time domain plot
2
Amplitude
Figure 3 shows the experimental location and the short flight track segment between Point A and Point B with duration of 100 seconds. Also shown are the two closest weather observation stations, the Norah Head Station and the North Head Station. The distances between the end points of the track and the Stations are listed in Table 1. The wind speed and gust observed in the afternoon are shown in Figure 4 and the wind direction was basically east southeast (ESE) (not shown). These data were provided by Australian Government Bureau of Meteorology. The flight duration of the 100 seconds corresponds to the vertical dashed line. It can be seen that at this duration the wind speed measured at Norah Station was 4.2 m/s, while it was 4.7 m/s at North Head Station. The wind speeds at Point A and Point B should be between these two speeds but closer to that at Norah Head Station. The sea surface can be treated as welldeveloped since the wind had blown the surface continuously for a few hours and the variation of the wind speed and direction was not very large. As a result the corresponding theory can be employed to perform the wind parameter estimation.
4
4
2
0 -4
-2
0 Bin
2
4
Figure 5. Bit statistics of IF data logged via the Nordnav receiver (left) ; bit statistics of the dat after swapping the {-1} with {-3} bits.
2588
Table 2 shows the elevation angles of eight GPS satellites whose direct and reflected signals were received by the software receiver via both the zenith-looking antenna and the nadir-looking antenna. The delay waveforms and the delay-Doppler waveforms associated with the eight satellites were produced and Figure 6 shows the waveforms of the satellite PRN#28. The coherent integration time was set at 1 millisecond and the non-coherent integration time was equal to 0.5 seconds. That is, the results were produced by averaging 500 waveforms of 1 millisecond. It is observed that over the period of 0.5 seconds the code phase of the signals can vary significantly up to by 16 samples equivalent to one code chip. Thus, when performing the non-coherent integration, the phase variation must be taken into account. Variation in the Doppler frequency is also observed but it is negligible over a period of a few seconds. It can be seen that on the top of the delay-Doppler waveforms the signals are spread over two or more code chips, resulting from the roughness of the sea surface. The spreading of the signals over time can be more clearly observed from the delay waveforms. It is this spread on the trailing edge of the delay waveform that the sea surface wind speed can be estimated and this will be discussed in the next subsection. Table 2. Elevation angles of the eight satellites.
Satellite PRN# Elevation (deg) Satellite PRN# Elevation (deg)
13 65.42 10 35.35
7 60.51 19 34.78
8 44.89 28 26.30
23 35.94 3 23.55
It is worth investigating the impact of the incorrect encoding of {-1} and {-3} data bits as mentioned in section 3.1. Figure 7 shows the delay waveforms of the reflected signals associated with satellite PRN#8. It can be clearly observed that the performance improved after correcting the {-1} bits with the {-3} bits. The noise floor in this case was reduced by about 0.8 dB, approximately 7% of the maximal signal power. From such a decrease in the noise floor, it may be predicted that the decrease in the noise floor or the increase
in the signal-to-noise ratio would be more significant when a higher-level quantization, such as the 3-bit or 4-bit quantization is used. Also, it can be seen that the two delay waveforms are nearly identical when the signal power is above -8 dB. That is, in the case where only the waveform with a power greater than -8 dB is used, the swapping of the {-1} bits and {-3} bits will actually not produce any impact on wind retrieval provided that only the waveform shape is employed. 0 original after swapping
-2
Correlation Power (dB)
3.2. Delay Waveform and Delay-Doppler Waveform
-4 -6 -8 -10 -12 -14 446
447
448
449 450 451 CA Code Phase (Chip)
452
3.3. Near Sea Surface Wind Speed Estimation The wind speed estimation is based on the model fitting method using the model derived in [2]. Figure 8 shows the five theoretical delay waveforms corresponding to five different wind speeds (3, 4, 5, 6, and 7 m/s) and the measured delay waveform associated with satellite PRN#13 which has the largest elevation angle. Note that in Figure 8 and the delay waveform in Figure 6, the time axis t=0 is arbitrary. The measured waveform is produced through coherent integration of 1-millisecond IF signals and then non-coherent integration of 1000 such 1-millisecond waveforms. It can be seen that the measured waveform has a good match with the theoretical waveform of wind speed 4 m/s, producing the wind speed estimate of 4 m/s, which is a good estimate of the real wind speed. It is observed that the theoretical waveforms in this case are insensitive to the wind direction. Further investigation is required to find out why such an outcome occurred.
590
3
589
2
588
1
Correlation Power (dB)
5 6 Doppler (kHz)
581
10
580
8
Normalised Correlation Power (dB)
4
C/A Code Phase (chip)
C/A Code Phase (chip)
5
591
6
579
4
578
2
577 5 6 Doppler (kHz)
10
454
Figure 7. Impact of swapping the {-1} and {-3} bits of the IF signals when the correlation powers are normalized.
0 592
453
reflected direct
-2 -3 -4 -5 -6 -7 -8 0
5
2.5 m/s 3 m/s 3.5 m/s 4 m/s 4.5 m/s measured
-1
0.2
0.4
0.6 0.8 1 1.2 Time (C/A code chip)
1.4
1.6
Figure 8. Wind speed estimation through matching the waveforms.
0 -5 0
2 4 6 Time (C/A code chip)
8
Figure 6. Delay waveforms and Delay-Doppler waveforms of direct and reflected GNSS signals.
This is just an illustrative example to show how the wind speed is estimated. In practice, a mathematical approach will be employed to automatically produce estimation solutions. Regarding this model-matching approach, a certain number
2589
of theoretical waveforms are produced and a cost function is defined. The theoretical waveform with the minimal cost function is then selected and the corresponding wind speed is the estimate of the real wind speed. The cost function can be defined as the sum of the squared difference between the theoretical and measured waveforms. However, this method requires the alignment of the two waveforms so that the difference between the two waveforms is minimized. Alternatively, a slope-based method proposed in [2] can be employed. However, as observed in Figure 8, it is rather difficult to distinguish the slopes of neighboring curves related to different wind speeds. Here a four-step procedure is proposed to perform the waveform fitting to estimate the wind speed: 1) interpolating both the measured and theoretical waveforms without changing the original data; 2) selecting the cut-off correlation power to retain the waveform above certain power lever so that the slope of the trailing edge does not change abruptly; 3) calculating the areas of the interpolated waveforms above the cut-off power and calculating the area difference between the measured waveform and each of the theoretical waveforms; and 4) selecting the theoretical waveform that produces the minimum area difference and taking the corresponding wind speed as the estimate. Figure 9 shows the individual wind speed estimates using signals related to the eight satellites. The data were collected at Point A and one second of the data were processed to generate the results. The horizontal axis corresponds to the eight satellites and the first satellite (PRN#13) has the largest elevation angle, while the eighth satellite (PRN#3) has the smallest one. The average of the eight wind speed estimates is 4.04 m/s, which is close to the wind speed at the Norah Head Observation Station. It is difficult to see the relationship between the estimation performance and the elevation angles from such a small number of samples. Much more samples are needed to obtain useful observations.
Wind Speed Estimates (m/s)
ACKNOWLEDGEMENTS The authors would like to acknowledge that this research work was carried out for the SAR Formation Flying Project which was funded by the Australian Space Research Program (ASRP) and for the ARC Discovery Project DP0877381 (Environmental Geodesy: Variations of Sea Level and Water Storage in the Australian Region). The authors would also like to thank their colleagues Mr. Peter Mumford, Mr. Greg Nippard, Prof. Jason Middleton and Dr. Eamonn Glennon for conducting the airborne experiments. REFERENCES [1] Martín-Neira, M.,“A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry,” ESA J., vol. 17, pp. 331–355, Dec. 1993. [2] Zavorotny, V.U., Voronovich, A.G., “Scattering of GPS signals from the ocean with wind remote sensing application”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, No. 2, pp. 951-964, 2000. [3] Elfouhaily, T,, Chapron, B,, Katsaros, K,, Vandemark, D., “A unified directional spectrum for long and short wind-driven waves”, Journal of Geophysical Research, Vol. 102, No. C7, pp. 15781-15796, 1997. [4] Garrison, J.L., Komjathy, A., Zavorotny, V.U. and Katzberg, S.J., “Wind speed measurement using forward scattered GPS signals”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 40, No. 1, pp. 5065, 2002. [5] Lowe, S.T., Zuffada, C., Chao, Y., Kroger, P., Young, L.E. and LaBrecque, J.L., “5-cm-precision aircraft ocean altimetry using GPS reflections,” Geophysical Research Letters, Vol. 29, No. 10, pp. 13751375, 2002. [6] Gleason, S.T., Hodgart, S., Sun, Y., Gommenginger, C., Mackin, S., Adjrad, M and Unwin, M., “Detection and processing of bistatically reflected GPS signals from low Earth orbit for the purpose of ocean remote sensing”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 43, No. 6, pp. 1229-1241, 2005.
5
4
3
[7] Rius, A., Cardellach, E. and Martin-Neira, M., “Altimetric analysis of the sea-surface GPS-reflected signals”, IEEE Transactions on Geoscience and Remote Sensing, Vol.48, No. 4, pp. 2119-2127, 2010.
2
1
0 1
from eight satellites were utilized to estimate the wind speed individually. Estimation accuracy of around 1 m/s was achieved by using signals transmitted from either lowelevation or high-elevation satellites. A problem of incorrectly encoding the quantized data bits within a software receiver was also investigated.
individual estimates wind speed at Norah Head wind speed at North Head 2
3
4 5 Satellites
6
7
8
Figure 9. Wind speed estimates using signals transmitted at eight satellites.
[8] Martin-Neira, M., D’Adddio, S., Buck, C, Floury, N. and PrietoCerdeira, R., “The PARIS ocean altimeter in-orbit demonstrator”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 49, No. 6, pp. 2209-2237, 2011.
4. CONCLUSIONS In this paper GNSS-R based wind speed estimation was investigated using the data collected during a low-altitude airborne experiment. A simple but reliable four-step delaywaveform fitting method was proposed. Signals transmitted
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