TDoA and RSS Based Extended Kalman Filter for ... - Semantic Scholar
TDoA and RSS based Extended Kalman Filter for Indoor Person Localization Julian Lategahn, Marcel M¨uller, Christof R¨ohrig University of Applied Sciences and Arts in Dortmund, Emil-Figge-Str. 42, 44227 Dortmund, Germany [email protected]
Abstract—Pedestrian localization systems require the knowledge of a users position for manifold applications in indoor and outdoor environments. For this purpose severel methods can be used, such as a Global Navigation Satellite System (GNSS) or Inertial Navigation Systems (INS). Since GNSS are not available in indoor environments or street canyons, in this paper a 802.15.4a network is used to estimate the pedestrian’s position. The used network platform provides the Time Difference of Arrival (TDoA) as well as the Received Signal Strength (RSS). To fuse both measurement types a novel method is implemented which is based on the Extended Kalman Filter (EKF). Due to the low accuracy of RSS it is ignored if the TDoA system performs well. But if the TDoA measurements are affected by multipath propagation or other effects the RSS values are used to identify those situations and to correct the estimated position of the user. To evaluate the algorithm experimental results in two different environments are presented. Index Terms—Person Localization; Indoor; RSS; TDoA; Extended Kalman Filter
I. I NTRODUCTION Localization of human operators is the basis of any Location-Based Service (LBS). LBS provide information or services with respect to the current position. There are many existing applications such as restaurant finders or museum guides, which provide information about an exhibit or lead the way to a certain point of interest. Of course there is a need of an accurate localization in other domains, for example in logistics [1], safety applications or in the field of Ambient Assisted Living (AAL). Outside of buildings Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS) or the European equivalent Galileo, are well suited to solve the positioning problem. There are many applications like car navigation systems, training support for runners and LBS on smartphones as well. In those applications GNSS, due to the accuracy of many meters, are often combined with other localization systems. For example an Inertial Navigation Systems (INS) can be used, which is measuring the users steps and his orientation, or wheel encoders in cars [2]. But inertial techniques need an initial position and cannot provide a long term stability of the position. If the user is in an indoor environment or a deep street canyon where GNSS information is not availible over a long time period, the system supplies only incorrect or no results. In such environments other techniques are needed to compute the users position. In this paper we propose a Wireless Sensor Network (WSN) for the localization. It consists of stationary anchor nodes with
prior known positions and mobile devices, which are attached at the users body [3]. In order to estimate a users position in a WSN there are several techniques to accomplish this goal. An easy way to compute the position is to use the Received Signal Strength (RSS). Most radio receivers in a wireless system have the ability to measure the signal strength. This signal strength can be translated to a distance by using a path loss model, as we do in this paper. Another method is the use of a radio map. Here an offline phase is performed to take RSS measurements at specified points with known positions and stored in a map. In the online phase the current measured RSS values of the user are compared to the saved ones in the map. Due to this relation a user can be localized [4]. Angle of Arrival (AoA) is a different method, which localize users by measuring the direction of the incoming signal. For this purpose special antenna arrays are needed. If some measurements to different anchors are available the current position can be computed using triangulation. Besides to the already introduced techniques, there are a couple of methods based on the signals Time of Flight (ToF). One of them is to measure the Time of Arrival (ToA). While using this method the clocks of all participants must be precisely synchronized. Due to the knowledge of the signals velocity the position can be computed by trilateration. If the synchronization between the anchors and the mobile devices is not possible, the Roundtrip Time of Flight (RToF) can be used instead. Here the system measures the signals flight duration from the mobile device to the anchor and the other way round. This eliminates the clock error but increases the duration per distance measurement. Another method is to measure the Time Difference of Arrival (TDoA). In this approach only the anchors have to be synchronized. Basically there are a few methods to derive TDoA measurements. In this Paper the so called Uplink-TDoA is used. Here the tag broadcasts a signal, which is processed on the anchor nodes. Using multilateration the resulting time differences can be translated to a position. A more detailed overview of the presented methods and their applications is given in [5]. In this paper a combination of Uplink-TDoA and a RSS path loss model is used to estimate a person’s position. To deal with the noisy measurements of both techniques an Extended Kalman Filter (EKF) is employed. We used the nanoPAL RTLS Toolbox provided by Nanotron Technologies in our experiments [6]. The commercial available system confirms
978-1-4673-6187-3/13/$31.00 ©2013 IEEE
Initial Position
the Extended Kalman Filter can be used instead [14]. The EKF linearizes the non-linear system by using a first order Taylor expansion. The non-linear function f translates the state vector x at time step k−1 to the next time step k, while the functionh relates the current state to the measurement zk :
Prediction Phase
Update Phase Fig. 1.
TDoA RSS
Extended Kalman Filter
the IEEE 802.15.4a standard and works in the 2.4 GHz ISM band. IEEE 802.15.4a defines Chirp Spread Spectrum (CSS), which is used by the toolbox, and Ultra Wide Band (UWB) for measuring distances. One drawback of the nanoPAL system in context to the paper is the relatively low resolution of the RSS measurements, which is at 2 dBm. II. R ELATED W ORK Due to the increasing demand for indoor positioning systems, wireless localization is an important research field in the past years. Many published papers deal with different kinds of localization techniques in GNSS and WSN. In [4] a RSS fingerprinting algorithm is presented, which uses a particle filter to estimate the position from a radio map. Because of the limited accuracy of RSS based methods it is useful to make combinations with other techniques. So [7] and [8] use algorithms to fuse ToA respectively TDoA measurements with the signal strength. Disadvantage of the algorithm used in [8] is the non-observance of multipath propagations. Other papers deal with the combination of wireless localization and INS. In [9] a system is presented, which fuses RSS measurements with a step detection, step length estimation and an orientation estimation. This extension increases the accuracy of the system many times over. Similar observations were made in [10] where the authors used a combined UWB/INS System. Due to the popularity of smartphones, which are mostly well equipped with GPS, WiFi and inertial sensors, there are many researchers working on such locating systems as presented in [11]. In many applications it is useful to combine indoor with outdoor localization techniques as the authors did in [12]. Here GPS and RFID is used to achieve a seamless transition between both technologies. III. E XTENDED K ALMAN F ILTER The Kalman Filter, which was first introduced in [13], is a recursive state estimator of a linear dynamic system. The filter handles incomplete and noisy measurement-data by minimizing the mean squared error. If the state transition or the measurement model is modeled by non-linear equations,
xk = f (xk−1 , uk ) + ωk ,
(1)
zk = h(xk ) + νk .
(2)
The random variables ωk and νk represent the noise of the state transition and the measurement. They are assumed to be white, mutually independent and normally distributed with covariances Qk and Rk respectively. The recursive estimation process is governed by a prediction - update cycle as shown in figure 1. The initial position is computed by a multilateration least squares algorithm which is presented in [15]. The state transition function from 1 is assumed to be linear, so it becomes as follows: xk xk−1 (3) = + ωk. yk yk−1 In this novel approach the update phase is splitted into two separate parts. The first one, which is explained more detailed in subsection III-A, includes the TDoA measurements. Due to the higher accuracy compared to the RSS measurements, the model is used as the primary source of location information. In a second step the signal strength is used as a corrector for the TDoA model. If the first step computes an evidently inaccurate estimation, the RSS measurements are additionally used to correct the position. Algorithm 1 shows the principle of the RSS measurement selection. After the state is updated with the TDoA measurement model, every RSS value is checked if a corrupted estimation is indicated. If there is an inconsistency, the RSS measurement is used to correct the estimation. Algorithm 1 Update Phase update state with the TDoA measurement model for all RSS measurements do compute RSS value between tag and current anchor if measured RSS value > computed RSS value then update state with the RSS measurement model end if end for
A. TDoA Measurement Model In the first step of the update phase, the TDoA measurements are used to estimate the position. In an Uplink-TDoA system there are several fixed anchor nodes, with known positions and a well synchronized time basis. The anchors detect the signal and save the time, when the signal arrives. Afterwards all reached anchors forward the timestamp to a central server, where the timestamps are processed to time
A3
T
A1
A2
Fig. 2.
Multilateration
differences t∗,a with respect to a reference anchor t∗ as follows: t∗,a = t∗ − ta
(4)
where t∗ is the ToA measured at the reference anchor and t the one at the ath anchor. The range differences da can be computed as follows: a
da = c t∗,a = (xk − x∗ )2 + (yk − y ∗ )2 + (hk − h∗ )2 − (xk − xa )2 + (yk − y a )2 + (hk − ha )2 (5) where c is the propagation velocity of the signal, xk , yk and hk denote the coordinates of the tag, x∗ , y ∗ and h∗ the reference anchor ones and xa , y a and ha the coordinates at the ath anchor. In this case the height of all participants is assumed to be constant. Each of these equations defines a hyperbola, which intersect in the tag’s position, if the measurements have no noise. This method is called multilateration and needs a least two hyperbolas to compute an unique position. Figure 2 shows a possible constellation of a minimal configuration in a TDoA network. In this case A1 is the reference anchor and A2 respectively A3 are the counterparts. The corresponding measurement vector zkT DoA is defined as follows: zkTDoA = d1
d2
...
dA
T
+ νkTDoA .
(6)
The measurement covariance RTDoA of the random variable νkTDoA is assumed to be constant in every step k. One problem while using a TDoA system is to detect multipath propagations and Non-line-of-Sight (NLOS) measurements. Since there are two time measurements in every computed difference it is difficult to assign the corrupted measurement to a single anchor. In [16] four methods, which handle those situations and discard defective measurements, are presented. In this paper the methods are used as well in order to improve the results. Two of them take advantage of
Fig. 3.
Trilateration
the diversity hardware used in the anchor nodes to exclude measurements. The third one is a simple logical verification. Here TDoA measurements are discarded, if its value exceeds the maximum ToF value between the used anchor nodes. While the last one checks the most likely measurements due to the state and the state covariance estimated in the EKF prediction. B. RSS Measurement Model In the second step of the update phase RSS measurements are utilized to validate the previous. Figure 3 shows the principle of the used algorithm, called trilateration. Therefore at least three distances between a tag and the different anchors are needed in the plane. The resulting distances are used to define circles, which intersect in the tags position. To apply the trilateration with RSS values the signal strength must be translated into distances. In free space the power of a signal decreases proportional inverse quadratic to the distance between anchor and tag. In real applications this model is not applicable, because the signal is affected by several environment dependent effects. The following path loss model is often used to estimate the power of a signal P (da ) received at anchor a at a given distance da : a d (7) P (da ) = P0 − 10np log10 d0 where P0 is the signal power at a short reference distance d0 and np is the path-loss exponent. In order to determine the concrete values a series of measurements has been done. The tag was placed at different distances to an anchor, from 1 m to 20 m with a step size of 1 m. Figure 4 shows the measured RSS values in blue and the fitted path loss model in red. It can be seen that the measurements have an inaccuracy of a few dBm which results in larger distance errors depending on
12
−40
Real Trajectory EKF TDOA EKF TDoA+RSS Anchor
median RSS fitted RSS −45 10
RSS [dBm]
−50 8
−55
y [m]
−60
6
−65 4
−70 0
2
4
6
8 10 12 14 tag−anchor separation [m]
16
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20 2
Fig. 4.
Path-Loss model
the real distance. To use 7 in the EKF da has to be computed by Euclidean distance: d = a
0 −5
0
5
Fig. 5.
(xk − xa )2 + (yk − y a )2 + (hk − ha )2 .
T P (dA ) + νkRSS
(9)
In this case the measurement covariance RkRSS is a varying value. Due to the earlier described selection process of the RSS values in algorithm 1 only measurements are used, which are quite likely improving the position estimation. Thus the measurement covariance Rka,RSS is build as follows:
2 a,RSS −P (da )) Rka,RSS = s b−(z
10
15
20
Outdoor test case
(8)
xk , yk , hk denote the coordinates of the tag and xa , y a , ha the coordinates at the ath anchor. The measurement vector zkRSS consists of all used RSS values: zkRSS = P (d1 ) P (d2 ) . . .
x [m]
(10)
where s is a scaling factor and b is the basis. Both values depend on the environment of the application and were determined experimental. The computation of the variance R in this way ensures that larger differences in z a,RSS − P (da ) leads to a smaler variance and thus a higher belief in the RSS measurements. IV. E XPERIMENTAL R ESULTS For evaluation purposes two test cases in different environments are performed. The first one was realized outdoor next to a wall of an office building. Six anchors were placed at a height of 2 m in a rectangle, which covered an area of 10 by 20 m. In order to communicate among each other and with a central server, every anchor is equipped with Ethernet. The central server provides the TDoA and RSS measurements to a locating engine. To increase the accuracy, each anchor is equipped with two separate transceiver modules. The tag
was attached in front of a person at his chest. He walked a predefined quadratic path within the anchors area. Figure 5 shows the results of the test case. The black curve denotes the real trajectory, while the red and the green ones are the filtered estimations. The wall of the office building was located above to the upper anchors. In this area the TDoA measurements were strongly influenced by multipath propagations of the radio signal. In this part of the figure the red curve, which represents the EKF with TDoA and RSS measurements has a quite better estimate than the reference EKF with only TDoA values. The RSS values can temporary correct the estimation. The error in the position of the combined EKF is usually up to 1 m. The reference filter, however, has an error up to 1.5 m. The second test was performed in a large warehouse during the normal distribution workings. This means that there are lift trucks and stacked goods above a few meters placed within the whole area. This causes more often Non-line-of-Sight measurements in some critical parts of the warehouse. To cover the entire warehouse of approximately 40 by 60 m with a good reception, the number of anchors was increased to eight. The person who walked the predefined track held the tag in his hand during the test case. The real trajectory is represented by the black curve in figure 6. The figure shows the results of the warehouse test case as well. Here again the EKF with TDoA and RSS measurements is displayed in red while the TDoA EKF is represented in green. In the upper part of the area high stacked pallets interrupt the tags radio signal. This causes a poor estimation of the position with only one or two anchors with line of sight. Here initially both EKF variants cannot handle the situation
60
50
Real Trajectory EKF TDOA EKF TDoA+RSS Anchor
y [m]
40
30
20
10
0
0
5
10
15
20
Fig. 6.
x [m]
25
30
35
40
45
Warehouse test case
but if there are a few good RSS measurements the TDoA+RSS EKF can stabilize itself to a good estimation. The remaining trajectory the RSS measurements help steady if the inaccuracy increases while using only TDoA measurements. In comparison to the first test case, the error in the position estimation is increased, due to the more difficult conditions. The filter achieves an accuracy of up to 3 m in the upper area and mostly below 1 m in other parts of the warehouse. V. C ONCLUSION AND F UTURE W ORK In this paper a new fusion method for TDoA and RSS values is presented. In order to obtain position estimates an EKF is employed to combine both measurements. The filter was evaluated in two different environments. It has been shown, that the EKF has a positive influence in certain situations, when the TDoA measurements leads to a poor estimation. But due to the low accuracy and resolution of the RSS measurements the filter cannot improve the results in general. To achieve a larger improvement in the accuracy additional sensors will be used in future studies. An accelerometer and orientation sensors, such as a digital compass or a gyroscope, can lead to a more precise prediction of the filter. The accelerometer will be used to detect steps and the length of the steps as well. Moreover auxiliary information like maps can be helpful. Especially in buildings a map could help to avoid estimations that are not accessible, like positions in the wall. R EFERENCES [1] C. R¨ohrig, C. Kirsch, J. Lategahn, M. M¨uller, and L. Telle, “Localization of Autonomous Mobile Robots in a Cellular Transport System,” Engineering Letters, vol. 20, no. 2, pp. 148–158, 2012.
[2] S. Godha, G. Lachapelle, and Cannon M.E., “Integrated GPS/INS System for Pedestrian Navigation in a Signal Degraded Environment,” Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, pp. 2151–2164, 2006. [3] W. Dargie and C. Poellabauer, Fundamentals of Wireless Sensor Networks: Theory and Practice, ser. Wireless Communications and Mobile Computing. Wiley, 2010. [4] J. Tsuji, H. Kawamura, and K. Suzuki, “ZigBee based indoor localization with particle filter estimation,” in IEEE International Conference on Systems Man and Cybernetics, 2010, pp. 1115–1120. [5] N. Patwari, J. Ash, S. Kyperountas, A. I. Hero, R. Moses, and N. Correal, “Locating the nodes: cooperative localization in wireless sensor networks,” Signal Processing Magazine, vol. 22, pp. 54–69, 2005. [6] Nanotron Technologies GmbH, nanoPAL RTLS Toolbox User Guide, 2nd ed., 2012. [7] A. Lewandowski and C. Wietfeld, “A comprehensive approach for optimizing ToA-localization in harsh industrial environments,” Position Location and Navigation Symposium, pp. 516–525, 2010. [8] D. Zhu and K. Yi, “EKF localization based on TDOA/RSS in underground mines using UWB ranging,” International Conference on Signal Processing, Communications and Computing, pp. 1–4, 2011. [9] J. Schmid, M. V¨olker, T. G¨adeke, P. Weber, and W. Stork, “An Approach to Infrastructure-Independent Person Localization with an IEEE 802.15.4 WSN,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–9. [10] S. Sczyslo, J. Schroeder, S. Galler, and T. Kaiser, “Hybrid localization using UWB and inertial sensors,” IEEE International Conference on Ultra-Wideband, pp. 89–92, 2008. [11] C. Lukianto, C. H¨onniger, and H. Sternberg, “Pedestrian smartphonebased indoor navigation using ultra portable sensory equipment,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–6. [12] L. Johannes, J. Degener, and W. Niemeier, “Set-up of a combined indoor and outdoor positioning solution and experimental results,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–6. [13] R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems,” Transactions of the ASME - Journal of Basic Engineering, vol. 82, no. Series D, pp. 35–45, 1960. [14] A. H. Jazwinski, Stochastic processes and filtering theory. New York: Academic Press, 1970. [15] G. Shen, R. Zetik, and R. Thoma, “Performance comparison of TOA and TDOA based location estimation algorithms in LOS environment,” in 5th Workshop on Positioning, Navigation and Communication, vol. 2008, 2008, pp. 71–78. [16] M. M¨uller, J. Lategahn, and C. R¨ohrig, “Pedestrian Localization using IEEE 802.15.4a TDoA Wireless Sensor Network,” in International Symposium on Wireless Systems, 2012, pp. 23–27.
Abstract—Pedestrian localization systems require the knowledge of a users position for manifold applications in indoor and outdoor environments. For this purpose severel methods can be used, such as a Global Navigation Satellite System (GNSS) or Inertial Navigation Systems (INS). Since GNSS are not available in indoor environments or street canyons, in this paper a 802.15.4a network is used to estimate the pedestrian’s position. The used network platform provides the Time Difference of Arrival (TDoA) as well as the Received Signal Strength (RSS). To fuse both measurement types a novel method is implemented which is based on the Extended Kalman Filter (EKF). Due to the low accuracy of RSS it is ignored if the TDoA system performs well. But if the TDoA measurements are affected by multipath propagation or other effects the RSS values are used to identify those situations and to correct the estimated position of the user. To evaluate the algorithm experimental results in two different environments are presented. Index Terms—Person Localization; Indoor; RSS; TDoA; Extended Kalman Filter
I. I NTRODUCTION Localization of human operators is the basis of any Location-Based Service (LBS). LBS provide information or services with respect to the current position. There are many existing applications such as restaurant finders or museum guides, which provide information about an exhibit or lead the way to a certain point of interest. Of course there is a need of an accurate localization in other domains, for example in logistics [1], safety applications or in the field of Ambient Assisted Living (AAL). Outside of buildings Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS) or the European equivalent Galileo, are well suited to solve the positioning problem. There are many applications like car navigation systems, training support for runners and LBS on smartphones as well. In those applications GNSS, due to the accuracy of many meters, are often combined with other localization systems. For example an Inertial Navigation Systems (INS) can be used, which is measuring the users steps and his orientation, or wheel encoders in cars [2]. But inertial techniques need an initial position and cannot provide a long term stability of the position. If the user is in an indoor environment or a deep street canyon where GNSS information is not availible over a long time period, the system supplies only incorrect or no results. In such environments other techniques are needed to compute the users position. In this paper we propose a Wireless Sensor Network (WSN) for the localization. It consists of stationary anchor nodes with
prior known positions and mobile devices, which are attached at the users body [3]. In order to estimate a users position in a WSN there are several techniques to accomplish this goal. An easy way to compute the position is to use the Received Signal Strength (RSS). Most radio receivers in a wireless system have the ability to measure the signal strength. This signal strength can be translated to a distance by using a path loss model, as we do in this paper. Another method is the use of a radio map. Here an offline phase is performed to take RSS measurements at specified points with known positions and stored in a map. In the online phase the current measured RSS values of the user are compared to the saved ones in the map. Due to this relation a user can be localized [4]. Angle of Arrival (AoA) is a different method, which localize users by measuring the direction of the incoming signal. For this purpose special antenna arrays are needed. If some measurements to different anchors are available the current position can be computed using triangulation. Besides to the already introduced techniques, there are a couple of methods based on the signals Time of Flight (ToF). One of them is to measure the Time of Arrival (ToA). While using this method the clocks of all participants must be precisely synchronized. Due to the knowledge of the signals velocity the position can be computed by trilateration. If the synchronization between the anchors and the mobile devices is not possible, the Roundtrip Time of Flight (RToF) can be used instead. Here the system measures the signals flight duration from the mobile device to the anchor and the other way round. This eliminates the clock error but increases the duration per distance measurement. Another method is to measure the Time Difference of Arrival (TDoA). In this approach only the anchors have to be synchronized. Basically there are a few methods to derive TDoA measurements. In this Paper the so called Uplink-TDoA is used. Here the tag broadcasts a signal, which is processed on the anchor nodes. Using multilateration the resulting time differences can be translated to a position. A more detailed overview of the presented methods and their applications is given in [5]. In this paper a combination of Uplink-TDoA and a RSS path loss model is used to estimate a person’s position. To deal with the noisy measurements of both techniques an Extended Kalman Filter (EKF) is employed. We used the nanoPAL RTLS Toolbox provided by Nanotron Technologies in our experiments [6]. The commercial available system confirms
978-1-4673-6187-3/13/$31.00 ©2013 IEEE
Initial Position
the Extended Kalman Filter can be used instead [14]. The EKF linearizes the non-linear system by using a first order Taylor expansion. The non-linear function f translates the state vector x at time step k−1 to the next time step k, while the functionh relates the current state to the measurement zk :
Prediction Phase
Update Phase Fig. 1.
TDoA RSS
Extended Kalman Filter
the IEEE 802.15.4a standard and works in the 2.4 GHz ISM band. IEEE 802.15.4a defines Chirp Spread Spectrum (CSS), which is used by the toolbox, and Ultra Wide Band (UWB) for measuring distances. One drawback of the nanoPAL system in context to the paper is the relatively low resolution of the RSS measurements, which is at 2 dBm. II. R ELATED W ORK Due to the increasing demand for indoor positioning systems, wireless localization is an important research field in the past years. Many published papers deal with different kinds of localization techniques in GNSS and WSN. In [4] a RSS fingerprinting algorithm is presented, which uses a particle filter to estimate the position from a radio map. Because of the limited accuracy of RSS based methods it is useful to make combinations with other techniques. So [7] and [8] use algorithms to fuse ToA respectively TDoA measurements with the signal strength. Disadvantage of the algorithm used in [8] is the non-observance of multipath propagations. Other papers deal with the combination of wireless localization and INS. In [9] a system is presented, which fuses RSS measurements with a step detection, step length estimation and an orientation estimation. This extension increases the accuracy of the system many times over. Similar observations were made in [10] where the authors used a combined UWB/INS System. Due to the popularity of smartphones, which are mostly well equipped with GPS, WiFi and inertial sensors, there are many researchers working on such locating systems as presented in [11]. In many applications it is useful to combine indoor with outdoor localization techniques as the authors did in [12]. Here GPS and RFID is used to achieve a seamless transition between both technologies. III. E XTENDED K ALMAN F ILTER The Kalman Filter, which was first introduced in [13], is a recursive state estimator of a linear dynamic system. The filter handles incomplete and noisy measurement-data by minimizing the mean squared error. If the state transition or the measurement model is modeled by non-linear equations,
xk = f (xk−1 , uk ) + ωk ,
(1)
zk = h(xk ) + νk .
(2)
The random variables ωk and νk represent the noise of the state transition and the measurement. They are assumed to be white, mutually independent and normally distributed with covariances Qk and Rk respectively. The recursive estimation process is governed by a prediction - update cycle as shown in figure 1. The initial position is computed by a multilateration least squares algorithm which is presented in [15]. The state transition function from 1 is assumed to be linear, so it becomes as follows: xk xk−1 (3) = + ωk. yk yk−1 In this novel approach the update phase is splitted into two separate parts. The first one, which is explained more detailed in subsection III-A, includes the TDoA measurements. Due to the higher accuracy compared to the RSS measurements, the model is used as the primary source of location information. In a second step the signal strength is used as a corrector for the TDoA model. If the first step computes an evidently inaccurate estimation, the RSS measurements are additionally used to correct the position. Algorithm 1 shows the principle of the RSS measurement selection. After the state is updated with the TDoA measurement model, every RSS value is checked if a corrupted estimation is indicated. If there is an inconsistency, the RSS measurement is used to correct the estimation. Algorithm 1 Update Phase update state with the TDoA measurement model for all RSS measurements do compute RSS value between tag and current anchor if measured RSS value > computed RSS value then update state with the RSS measurement model end if end for
A. TDoA Measurement Model In the first step of the update phase, the TDoA measurements are used to estimate the position. In an Uplink-TDoA system there are several fixed anchor nodes, with known positions and a well synchronized time basis. The anchors detect the signal and save the time, when the signal arrives. Afterwards all reached anchors forward the timestamp to a central server, where the timestamps are processed to time
A3
T
A1
A2
Fig. 2.
Multilateration
differences t∗,a with respect to a reference anchor t∗ as follows: t∗,a = t∗ − ta
(4)
where t∗ is the ToA measured at the reference anchor and t the one at the ath anchor. The range differences da can be computed as follows: a
da = c t∗,a = (xk − x∗ )2 + (yk − y ∗ )2 + (hk − h∗ )2 − (xk − xa )2 + (yk − y a )2 + (hk − ha )2 (5) where c is the propagation velocity of the signal, xk , yk and hk denote the coordinates of the tag, x∗ , y ∗ and h∗ the reference anchor ones and xa , y a and ha the coordinates at the ath anchor. In this case the height of all participants is assumed to be constant. Each of these equations defines a hyperbola, which intersect in the tag’s position, if the measurements have no noise. This method is called multilateration and needs a least two hyperbolas to compute an unique position. Figure 2 shows a possible constellation of a minimal configuration in a TDoA network. In this case A1 is the reference anchor and A2 respectively A3 are the counterparts. The corresponding measurement vector zkT DoA is defined as follows: zkTDoA = d1
d2
...
dA
T
+ νkTDoA .
(6)
The measurement covariance RTDoA of the random variable νkTDoA is assumed to be constant in every step k. One problem while using a TDoA system is to detect multipath propagations and Non-line-of-Sight (NLOS) measurements. Since there are two time measurements in every computed difference it is difficult to assign the corrupted measurement to a single anchor. In [16] four methods, which handle those situations and discard defective measurements, are presented. In this paper the methods are used as well in order to improve the results. Two of them take advantage of
Fig. 3.
Trilateration
the diversity hardware used in the anchor nodes to exclude measurements. The third one is a simple logical verification. Here TDoA measurements are discarded, if its value exceeds the maximum ToF value between the used anchor nodes. While the last one checks the most likely measurements due to the state and the state covariance estimated in the EKF prediction. B. RSS Measurement Model In the second step of the update phase RSS measurements are utilized to validate the previous. Figure 3 shows the principle of the used algorithm, called trilateration. Therefore at least three distances between a tag and the different anchors are needed in the plane. The resulting distances are used to define circles, which intersect in the tags position. To apply the trilateration with RSS values the signal strength must be translated into distances. In free space the power of a signal decreases proportional inverse quadratic to the distance between anchor and tag. In real applications this model is not applicable, because the signal is affected by several environment dependent effects. The following path loss model is often used to estimate the power of a signal P (da ) received at anchor a at a given distance da : a d (7) P (da ) = P0 − 10np log10 d0 where P0 is the signal power at a short reference distance d0 and np is the path-loss exponent. In order to determine the concrete values a series of measurements has been done. The tag was placed at different distances to an anchor, from 1 m to 20 m with a step size of 1 m. Figure 4 shows the measured RSS values in blue and the fitted path loss model in red. It can be seen that the measurements have an inaccuracy of a few dBm which results in larger distance errors depending on
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the real distance. To use 7 in the EKF da has to be computed by Euclidean distance: d = a
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(xk − xa )2 + (yk − y a )2 + (hk − ha )2 .
T P (dA ) + νkRSS
(9)
In this case the measurement covariance RkRSS is a varying value. Due to the earlier described selection process of the RSS values in algorithm 1 only measurements are used, which are quite likely improving the position estimation. Thus the measurement covariance Rka,RSS is build as follows:
2 a,RSS −P (da )) Rka,RSS = s b−(z
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(8)
xk , yk , hk denote the coordinates of the tag and xa , y a , ha the coordinates at the ath anchor. The measurement vector zkRSS consists of all used RSS values: zkRSS = P (d1 ) P (d2 ) . . .
x [m]
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where s is a scaling factor and b is the basis. Both values depend on the environment of the application and were determined experimental. The computation of the variance R in this way ensures that larger differences in z a,RSS − P (da ) leads to a smaler variance and thus a higher belief in the RSS measurements. IV. E XPERIMENTAL R ESULTS For evaluation purposes two test cases in different environments are performed. The first one was realized outdoor next to a wall of an office building. Six anchors were placed at a height of 2 m in a rectangle, which covered an area of 10 by 20 m. In order to communicate among each other and with a central server, every anchor is equipped with Ethernet. The central server provides the TDoA and RSS measurements to a locating engine. To increase the accuracy, each anchor is equipped with two separate transceiver modules. The tag
was attached in front of a person at his chest. He walked a predefined quadratic path within the anchors area. Figure 5 shows the results of the test case. The black curve denotes the real trajectory, while the red and the green ones are the filtered estimations. The wall of the office building was located above to the upper anchors. In this area the TDoA measurements were strongly influenced by multipath propagations of the radio signal. In this part of the figure the red curve, which represents the EKF with TDoA and RSS measurements has a quite better estimate than the reference EKF with only TDoA values. The RSS values can temporary correct the estimation. The error in the position of the combined EKF is usually up to 1 m. The reference filter, however, has an error up to 1.5 m. The second test was performed in a large warehouse during the normal distribution workings. This means that there are lift trucks and stacked goods above a few meters placed within the whole area. This causes more often Non-line-of-Sight measurements in some critical parts of the warehouse. To cover the entire warehouse of approximately 40 by 60 m with a good reception, the number of anchors was increased to eight. The person who walked the predefined track held the tag in his hand during the test case. The real trajectory is represented by the black curve in figure 6. The figure shows the results of the warehouse test case as well. Here again the EKF with TDoA and RSS measurements is displayed in red while the TDoA EKF is represented in green. In the upper part of the area high stacked pallets interrupt the tags radio signal. This causes a poor estimation of the position with only one or two anchors with line of sight. Here initially both EKF variants cannot handle the situation
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but if there are a few good RSS measurements the TDoA+RSS EKF can stabilize itself to a good estimation. The remaining trajectory the RSS measurements help steady if the inaccuracy increases while using only TDoA measurements. In comparison to the first test case, the error in the position estimation is increased, due to the more difficult conditions. The filter achieves an accuracy of up to 3 m in the upper area and mostly below 1 m in other parts of the warehouse. V. C ONCLUSION AND F UTURE W ORK In this paper a new fusion method for TDoA and RSS values is presented. In order to obtain position estimates an EKF is employed to combine both measurements. The filter was evaluated in two different environments. It has been shown, that the EKF has a positive influence in certain situations, when the TDoA measurements leads to a poor estimation. But due to the low accuracy and resolution of the RSS measurements the filter cannot improve the results in general. To achieve a larger improvement in the accuracy additional sensors will be used in future studies. An accelerometer and orientation sensors, such as a digital compass or a gyroscope, can lead to a more precise prediction of the filter. The accelerometer will be used to detect steps and the length of the steps as well. Moreover auxiliary information like maps can be helpful. Especially in buildings a map could help to avoid estimations that are not accessible, like positions in the wall. R EFERENCES [1] C. R¨ohrig, C. Kirsch, J. Lategahn, M. M¨uller, and L. Telle, “Localization of Autonomous Mobile Robots in a Cellular Transport System,” Engineering Letters, vol. 20, no. 2, pp. 148–158, 2012.
[2] S. Godha, G. Lachapelle, and Cannon M.E., “Integrated GPS/INS System for Pedestrian Navigation in a Signal Degraded Environment,” Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, pp. 2151–2164, 2006. [3] W. Dargie and C. Poellabauer, Fundamentals of Wireless Sensor Networks: Theory and Practice, ser. Wireless Communications and Mobile Computing. Wiley, 2010. [4] J. Tsuji, H. Kawamura, and K. Suzuki, “ZigBee based indoor localization with particle filter estimation,” in IEEE International Conference on Systems Man and Cybernetics, 2010, pp. 1115–1120. [5] N. Patwari, J. Ash, S. Kyperountas, A. I. Hero, R. Moses, and N. Correal, “Locating the nodes: cooperative localization in wireless sensor networks,” Signal Processing Magazine, vol. 22, pp. 54–69, 2005. [6] Nanotron Technologies GmbH, nanoPAL RTLS Toolbox User Guide, 2nd ed., 2012. [7] A. Lewandowski and C. Wietfeld, “A comprehensive approach for optimizing ToA-localization in harsh industrial environments,” Position Location and Navigation Symposium, pp. 516–525, 2010. [8] D. Zhu and K. Yi, “EKF localization based on TDOA/RSS in underground mines using UWB ranging,” International Conference on Signal Processing, Communications and Computing, pp. 1–4, 2011. [9] J. Schmid, M. V¨olker, T. G¨adeke, P. Weber, and W. Stork, “An Approach to Infrastructure-Independent Person Localization with an IEEE 802.15.4 WSN,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–9. [10] S. Sczyslo, J. Schroeder, S. Galler, and T. Kaiser, “Hybrid localization using UWB and inertial sensors,” IEEE International Conference on Ultra-Wideband, pp. 89–92, 2008. [11] C. Lukianto, C. H¨onniger, and H. Sternberg, “Pedestrian smartphonebased indoor navigation using ultra portable sensory equipment,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–6. [12] L. Johannes, J. Degener, and W. Niemeier, “Set-up of a combined indoor and outdoor positioning solution and experimental results,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–6. [13] R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems,” Transactions of the ASME - Journal of Basic Engineering, vol. 82, no. Series D, pp. 35–45, 1960. [14] A. H. Jazwinski, Stochastic processes and filtering theory. New York: Academic Press, 1970. [15] G. Shen, R. Zetik, and R. Thoma, “Performance comparison of TOA and TDOA based location estimation algorithms in LOS environment,” in 5th Workshop on Positioning, Navigation and Communication, vol. 2008, 2008, pp. 71–78. [16] M. M¨uller, J. Lategahn, and C. R¨ohrig, “Pedestrian Localization using IEEE 802.15.4a TDoA Wireless Sensor Network,” in International Symposium on Wireless Systems, 2012, pp. 23–27.
