Positioning Enhancement with Double Differencing and ... - CiteSeerX

Positioning Enhancement with Double Differencing and DSRC Nima Alam, Asghar Tabatabaei Balaei, Andrew G Dempster University of New South Wales, Australia

BIOGRAPHY Nima Alam is pursuing his PhD in the field of “Vehicular Positioning Enhancement with DSRC” in the School of Surveying & Spatial Information Systems at the University of New South Wales commencing Feb. 2009. He achieved a Bachelor degree in Telecommunication Systems from Sharif University of Technology, Tehran, Iran, in 1998. He obtained his Masters degree in Control Systems in 2000 from the same university. He has been involved in a variety of projects in the automotive industry including industrial robotics, moving robots, factory automation, machine vision, GPS navigation, and fleet management between 2000 and 2008. Asghar Tabatabaei has a BE (1997) and MEngSc (2000) in Electrical Engineering from Sharif University of Technology, Tehran, Iran and PhD (2008) in global navigation satellite interference from the University of New South Wales, Sydney, Australia where he has also worked as a post doctoral research fellow in the School of Surveying and Spatial Information Systems. He is currently an associate lecturer in the Electrical Engineering and Telecommunication department of UNSW. Andrew Dempster is Director of Research in the School of Surveying and Spatial Information Systems at the University of New South Wales. He has a BE and MEngSc from UNSW and a PhD from University of Cambridge. He was system engineer and project manager for the first GPS receiver developed in Australia in the late 80s and has been involved in satellite navigation ever since. His current research interests are in satellite navigation receiver design and signal processing, and new location technologies. ABSTRACT Global Navigation Satellite Systems (GNSS) are comprehensively used for navigation in vehicular environments. However, the limited accuracy of GNSS for civilian use makes it unsuitable for some safety applications such as collision avoidance. Cooperative positioning in vehicular networks is a relatively new concept for positioning enhancement in a group of vehicles capable of communicating with each other. In addition to data communication, estimation of the distance between the nodes of a vehicular network is one the most challenging issues in cooperative positioning. Radio ranging methods such as Received Signal Strength (RSS),

Time of Arrival (TOA), and Time Difference of Arrival (TDOA) are the most common techniques which are referred to in the literature for distance estimation without considering the poor accuracy of these methods for positioning accuracy improvement purposes, especially in vehicular environments. In this article, two methods for positioning enhancement and distance estimation are proposed that do not rely on common radio ranging techniques. The independence from radio ranging is one of the main contributions of this work. The proposed techniques are solely based on communicating data among the vehicular network nodes through Dedicated Short Range Communication (DSRC). The proposed solutions are suitable for suburbs and open space areas such as highways with less multipath error and at least four common visible satellites. The key idea is elimination of common errors of pseudorange estimates among the nodes of the vehicular network in a cluster of vehicles or between vehicles and roadside units. This looks similar to Differential GPS (DGPS) but the approach is different. The other advantage of the proposed methods is the low minimum possible number of participating nodes required by the algorithms, which is useful for saving communications bandwidth. Some experiments were conducted to verify the performance of the proposed algorithms. Results for the two methods, tested in static situations, show gains of 50%-65% for distance estimation depending on the level of multipath error and 55% for position estimation in a low multipath environment. INTRODUCTION Position data is a fundamental basis of many systems in civilian, military, and industry applications. Vehicular applications are some of the most demanding systems for accurate position data. Global Navigation Satellite Systems such as GPS [1] are the most comprehensive systems used for localization. While car navigation systems, among the vehicular applications, operate based on GPS, other emerging applications in vehicular networks cannot use it. For example, the limited accuracy of GPS signals does not meet the requirements of safety-related applications such as collision avoidance. In addition to DGPS [1] which is used for positioning accuracy improvement, some innovative approaches have been presented in recent years for positioning accuracy enhancement within vehicular networks, based on communicating data among the nodes of the network. This concept is called Cooperative Positioning (CP). An

overview of CP techniques and radio ranging in wireless sensor networks is carried out in [2, 3]. One of the important factors in cooperative positioning is the communication between nodes of the network for sharing data. Addressing the safety issues and other potential applications in vehicular environments, the U.S. Federal Communication Commission has assigned a bandwidth of 75MHz from 5.85GHz to 5.925GHz for Dedicated Short Range Communication (DSRC), specifically for reliable, fast, and short range communication, up to 1000 m, between vehicles or a vehicle and roadside infrastructure [4, 5]. Another important parameter in CP algorithms is the distance between the nodes of the network. Received RSS, TOA, and TDOA are the most common techniques considered for radio ranging [6] in CP algorithms. An omission in most related literature is the study of shortcomings and limitations of each method, especially when considering vehicular networks. Achieving the ranging accuracy required or assumed for CP algorithms is mostly impossible using existing techniques. For example, RSS, a simple and cost effective method of ranging, is often assumed as the distance estimation technique in cooperative localization algorithms, while the accuracy of this vulnerable method is not sufficient for most applications [7]. An overview of the challenges in radio ranging with DSRC is discussed in [8]. One of the main contributions of this paper is distance estimation without using radio ranging for the purpose of CP. Also, the presented CP algorithm relies only on data communication between the vehicle and a road side unit as a reference beacon. Cooperative positioning has been considered for both localization and positioning accuracy improvement. In some methods such as those presented in [9-14], position data of the nodes are available and accuracy improvement is achieved with cooperative positioning. The methods presented in [15-17] use some GPS-equipped or known position nodes, as beacons, for localizing the other nodes. In the methods presented in this article, all nodes have GPS receivers and an open space environment is considered, for example a suburban highway. Also four common satellites are assumed to be visible for the nodes participating in CP. It is assumed that DSRC is used for communication between the nodes. Two scenarios are investigated.

Figure 1. One beacon and one vehicle with DSRC communication and four common visible satellites

In the second scenario, depicted in figure 2, the vehicles are equipped with GPS receiver but the reference beacon with known accurate position is not available. In this situation, the CP algorithm provides the distance between the nodes with a better accuracy than GPS provides. This range estimation can be used for other CP algorithms which are based on distances between the nodes and also for collision avoidance.

Figure 2. Two vehicles with DSRC communication and four common visible satellites

In the sequel, the new CP and ranging algorithms are presented followed by defining the required data, to be communicated through DSRC. Simulations and their results are presented. Finally, some experiments and their results are discussed followed by the conclusion of this article. CP AND RANGING ALGORITHMS

In the first scenario, depicted in figure 1, one node is a fixed beacon with a GPS receiver and an accurate known position. The other node is a vehicle equipped with a GPS receiver. These two nodes can communicate through DSRC. In this situation, the CP algorithm provides the relative position of the vehicle to the reference node. Knowing the reference node’s accurate position, the absolute position of the vehicle can be obtained with accuracy better than for GPS.

The main idea behind the methods presented here is the elimination of those GPS errors which are common in the vicinity of each node in a vehicular environment. This is aimed to be achieved by sharing some data between the nodes through DSRC and some processing. As a result, the positioning or distance estimation is viable with a better accuracy than for standalone GPS. This approach looks like that of DGPS but the presented method is different from DGPS in the content of communicated data between

the nodes and the applied algorithm. Also it seems similar to the “float solution” of RTK [18] in equations but the difference here is the unique solution with four satellites because we do not consider phase ambiguity, which is involved in career phase-based positioning.

Scenario 1- CP with Reference Node Consider a reference node with a GPS receiver and an accurate known position as “Node a” and a GPS-equipped vehicle as “Node b”. Figure 3 shows the situation. For simplicity of illustration, only one of the four common satellites is depicted in this figure. As can be seen, the vectors from nodes a and b to the ith satellite are called , the distances between the nodes and ith satellite and and , and the vector between two nodes is . are Considering the Cartesian Earth-Centered Earth-Fixed (ECFE) coordinate system [1], position vectors of the ith satellite, nodes a, and node b are defined as , , .

(3) Replacing Eq. (2) in Eq. (3) results in: (4) As can be seen in Eq. (4), common errors between the nodes are removed in the Single-Difference. Considering another satellite, for example jth satellite, the DoubleDifference [18] of pseudoranges between ith and jth satellite and the nodes is calculated as: (5) Eq. (2) can be written for jth satellite too. Replacing from Eq. (2) in Eq. (5) results in: (6) As can be seen in Eq. (6), the errors due to the receivers’ clocks are eliminated in Double Differencing. The remaining error is the effect of the receivers’ noise and multipath. There is: (7) Reconsidering figure 3, due to the geometry of the satellite , , and the relative position of the nodes ( can be considered to be parallel, giving [1]: and (8)

Figure. 3. One beacon, one vehicle, and one of four common visible satellites

is the angle between and and “T” where represents the transpose operator. Eq. (8) can be rewritten for the jth satellite: (9)

There is: , , ,

| |

| | | |

Replacement of Eq. (8) and Eq. (9) in Eq. (6) results in: (1)

and are the estimated pseudoranges between the If nodes and the ith satellite, then [1]:

(10) If there are four common satellites visible at both nodes, numbered 1 to 4, the following equation can be produced: (11)

(2) where: where is the result of common ranging error sources in the vicinity of the nodes. Ionospheric delay, Tropospheric delay, satellite clock stability, and Ephemeris prediction and are the most important of these error sources. are the receiver clock errors in the nodes, c is the speed of and are the ranging errors due to receiver light, and noise and multipath. These errors are independent for two nodes. Now the Single-Difference [18] of pseudoranges between the ith satellite and the nodes a and b is calculated:

,

,

(12)

In Eq. (11), L can be calculated based on pseudoranges and Eq. (5), Φ can be calculated from the position of the reference beacon and satellites, and the uncertainty of is the result of receiver noise and multipath errors. From Eq. (12):

(13) Now, the first scenario is formulated. If the vehicle, node b, receives the estimated pseudoranges and the position of reference node a through DSRC, it can estimate its relative position to the reference beacon and from Eq. (1) its coordinates in Cartesian ECEF can be calculated. Moreover, the reference beacon can be aware of the vehicle’s position if the vehicle transmits its estimated pseudoranges to the reference node through DSRC. Regarding Eq. (13) the estimation is:

Now we find the distance between the nodes based on the available data. Once this distance is estimated, it can be used in a variety of CP algorithms which are based on distances between the nodes, eliminating the necessity for common radio ranging techniques, and also for collision avoidance. From Eq. (1) there is: √

(17)

Replacing

from Eq. (13) results in:

(14) 2

and the estimation error is: (15) As can be seen in Eq. (15), the estimation error is due to receiver noise and multipath. Now, is defined for evaluation of the estimation performance against standalone GPS positioning error: ∑ where

, is the covariance of

(16)

where: (19) Replacing from Eq. (12) in Eq. (19) results in: (20) where: 2 2 2

.

Scenario 2- Ranging with Data Communication In this scenario, there is not any reference node and both nodes a and b are vehicles with four visible satellites in common and position data with GPS accuracy. Figure 4 shows the situation with one satellite.

(18)

2 2 2 1 1 1

(21)

and: ·

cos

(22)

where “.” is the inner product operator. Due to the geometry of the situation, the parameters in the right side of the Eq. (22) can be replaced by the estimated vectors and distances based on GPS position of the nodes. ′

cos

· ′

(23)

where:

Figure 4. Two vehicles and one of four common visible satellites

In this situation, using the GPS-based position of the nodes and ignoring the resulting error in calculation of Φ, estimation of the relative position vector by Eq. (14) is again possible. But the point is that the relative vector is useless in enhancement of absolute positioning accuracy of the nodes because both nodes only have an accuracy level supplied by standalone GPS.

′

′

,

′

′

′

,

′

(24)

and ′ is the position vector of node a in the Cartesian ECEF coordinate system available from the GPS receiver. Calculating using Eq. (21), the estimation of distance r from Eq. (18) is possible. Taylor expansion of Eq. (18) results in: √

(25)

Regarding Eq. (25), the distance r can be estimated by:

√

(26)

and the error of estimation is: (27)

corresponding pseudorange noise (PRN) code of the satellites. If the node is a vehicle, it broadcasts its ID, the time, the pseudoranges of the visible satellites, and corresponding PRN of the satellites. Figure 5 shows a diagram of data which are communicated.

As can be seen, in this case the estimation error depends on and decreases as distance increases.

Double Differencing Error Mitigation Regarding Eq. (11), the remaining errors in DoubleDifferencing are multipath and receiver noise. Mitigating the impact of the uncertainty vector, , before applying Double-differences to the presented algorithms improves the performance of CP or distance estimation. For this, evaluation of covariance is essential. Let Z be defined as a vector with elements of multipath and receivers noise for two nodes and four common visible satellites: Ζ

(28)

as the Assuming independency of the entries in Z and standard deviation of these, the covariance matrix of Z is: (29) where I is an identity matrix. Considering Eq. (7) and (12) there is: Ζ

(30)

where: 1 1 1

1 1 1

1 1 0 0 0 0

Now, the covariance of 2

0 0 1 1 0 0

0 0 0 0 1 1

(31)

is:

2 1 1 1 2 1 1 1 2

(32)

This covariance matrix can be used to design filters, e.g. a Kalman filter, for mitigating the effect of on derived Double-Differences based on pseudoranges. This way, the performance of the proposed algorithms increases.

Figure 5. Broadcast data from each node through DSRC

In this figure, PRN#i and PR#i are the PRN and pseudorange of the ith visible satellite respectively. Time tags are provided by GPS time. If a reference node is available in the network, absolute positioning of other nodes is possible. If there is not any reference node, distances between the nodes can be estimated. SIMULATIONS AND RESULTS For simulating the presented methods, a snapshot of real positions of GPS satellites in the vicinity of a surveyed point in the University of New South Wales, Kensington campus, have been considered. The surveyed point is assumed as the reference node in the first scenario and as node a in the second. In both scenarios, node b has been simulated with a random point in the vicinity of node a in various distances of 10, 50,100, 200, and 300 m. The maximum distance in the simulation is considered to be 300 m, which is the effective range of DSRC [19]. The standard deviation of receiver noise and multipath errors, , is varied between 0.1 to 10 m with 0.1 m steps. For each combination of and distance, 5000 trials were run. MATLAB version 7.7.0.471(R2008b) was used for simulations. For simulating the error of GPS positioning, the standard deviation of , , is considered to be 7.5 m : [1] and

DATA COMMUNICATION The required data for CP in a vehicular network is communicated through DSRC which has a limited bandwidth. Considering this limitation, using as few packets for CP as possible is very important. In the proposed methods, each node broadcasts some data which help other nodes estimate their position or distance to the others. If the node is a reference node, it broadcasts its ID, its absolute position in ECEF coordinate system, the time, the pseudoranges of the visible satellites, and

(33) and (34) where PDOP is Position Dilution of Precision [1]. For the CP using a reference node, at first the performance of the proposed algorithm is compared with GPS when the

distance between the reference node and the vehicle is 50 m. Figure 6 shows the result.

algorithm actually degrades performance in comparison to the standalone method in areas with high multipath errors. Evaluating the second scenario and its proposed algorithm for distance estimation, the errors of the presented algorithm and GPS-based distance estimation at a distance of 50 m between two nodes is depicted in figure 8. As can be seen, the proposed method accuracy is better than GPS over the spanned . For a better evaluation of is defined as distance the proposed algorithm, describes the estimation error elimination factor. performance of proposed method in percent. 1

Figure 6. Performance of the presented CP method and GPS

100

(36)

where is the standard deviation of the error described by Eq. (27) and is the standard deviation of GPS-based distance estimation error.

As can be seen, performance of the proposed algorithm is better than GPS for low levels of multipath and receiver noise errors. This enhancement in positioning decreases as these errors increase. The other point is the degraded performance of proposed method compared to GPS at higher levels of . For a better evaluation of the presented CP method of the is defined as the CP error elimination first scenario, factor. Regarding the Eq. (16) and Eq. (34) describes the performance of the proposed method in percent. 1

100

(35)

means less position estimate error compared to Higher GPS positioning. This parameter has been evaluated for different distances between two nodes. Figure 7 shows the result.

Figure 8. Performance of the presented distance estimation method and GPS-based distance estimation

Higher means less distance estimate error compared to has been evaluated in different GPS-based ranging. distances of 10, 50,100, 200, and 300 m. Figure 9 shows the results.

Figure. 7. Performance of the proposed CP algorithm

As can be anticipated from Eq. (15), the performance curve is the same for different distances. The negative value of for higher indicates that the proposed

Figure 9. Performance of the presented distance estimation method for different distances

As can be seen and was expected from Eq. (27), the proposed algorithm results in better accuracy for higher

distances. The other point is degradation of performance with increasing pseudorange error due to multipath and receiver noise. Moreover, the poor performance of the results proposed method at lower distances and higher in negative , which shows its failure in these conditions. While time-based ranging methods are technically very difficult for implementation in vehicular networks because of the required synchronization among the nodes, RSS is the radio ranging method most considered in such environments. Comparing the performance of this ranging technique with RSS, the accuracy of estimation can be considered. According to [8], RSS ranging may result in 100% error depending on the accuracy of path loss model [20] while the algorithm proposed here can eliminate more than 80% of GPS-based distance estimation in low multipath conditions.

enhancement of positioning accuracy which is actually degradation. This result is justifiable in the environments with higher levels of multipath error. Figure 11 compares the accuracy of the GPS-based distance estimation and the presented algorithm in the first experiment. As can be seen, the proposed method of distance estimation has better performance than GPS.

EXPERIMENTAL RESULTS For verification of the proposed methods, two experiments, in static situations, were run at the University of New South Wales, Kensington campus. In these experiments, NORDNAV receivers were used as two nodes for receiving the GPS signals. Recorded data including pseudoranges, satellite positions, users’ position, and time were processed off-line. The pseudorange-based Double-Differences were filtered before applying them to the proposed methods to increase the performance. In the conducted experiments, a Kaman filter was used for smoothing Double-Differences. For the first experiment two nodes a and b, of a distance of 51.38 m, were placed on the roof and in front of the EE building respectively. Both points had been surveyed accurately. Because of the buildings around node b, a high level of multipath error and hence a lower performance were expected. Data for each receiver were recorded for a period of time. The results of applying this recorded data to the presented algorithms are depicted in figures 10 and 11. The position error is the distance between real and estimated position of node b. The distance error is the difference of the real distance and estimated distance between two nodes. In the figures showing the experimental results, the GPS curves are based on position estimates which are directly provided by the NORNAV receivers. CP curves are results of applying the pseudoranges, provided by NORDNAV module, to the proposed algorithms. As can be seen in figure 10, the performance of the proposed algorithm is lower than GPS-based positioning. An enhancement factor, similar to Eq. (35), can be defined based on RMSE (Root Mean Squared Error): ̂

1

100

(37)

and are RMSE of the estimated position by where the proposed method and GPS respectively. Replacing the values, shown in figure 10, in Eq. (37) results in ̂ = -11%

Figure 10. Experimental performance of the presented positioning method for a distance of 51.38 m between the nodes

Figure 11. Experimental performance of the presented distance estimation method for a distance of 51.38 m between the nodes

An enhancement factor, similar to Eq. (36), can be defined here: ̂

1

100

(38)

where and are RMSE of the estimated distance by proposed method and GPS-based distance estimation respectively. Replacing the values, shown in figure 11, in Eq. (38) results in ̂ =50% enhancement of distance estimation accuracy. Comparing the results of position and distance estimation for the first experiment shows improved performance for the proposed distance estimation method, compared to standalone GPS, while the position estimation accuracy is lower than GPS. This can be explained by referring to the simulation results and considering figures 6 and 8 (or 7 and 9). As is shown in

these figures, for higher levels of multipath and receiver noise, the proposed method of distance estimation may outperform the GPS-based distance estimate even when the position estimation algorithm has lower performance than standalone GPS. In the second test, both nodes, a and b, were on the roof of EE building at two accurately surveyed points. In this test, the distance between the nodes was 11.10 m. The difference between the conditions for the two experiments is the lower level of multipath error due to the position of node b. For this, better performance of the proposed algorithms was expected in the second test. Data from the receivers were recorded for a period of time. The results of applying the recorded pseudoranges to the proposed algorithms are depicted in figures 12 and 13.

Figure 12. Experimental performance of the presented positioning method for a distance of 11.10 m between the nodes

The position error is the distance between the real and estimated position of node b. As can be seen in figure 12, the proposed CP method results in a better accuracy compared to GPS. Using Eq. (37), the enhancement of ̂ =55% is achieved. Figure 13, compares the accuracy of GPS-based distance estimation and the presented algorithm in the second experiment. Replacing the values, indicated in figure 13, in Eq. (38) results in ̂ =65% enhancement of distance estimation accuracy. As was expected, the proposed techniques have a better performance in the second experiment due to the lower level of multipath error. CONCLUSION Two methods of positioning and distance estimation, based on vehicular communication with DSRC, were proposed. Both algorithms are suitable for environments with low multipath error. Suburban highways and open space roads are appropriate environments for implementation of these algorithms. The assumption of four common visible satellites in the vicinity of a cluster of vehicles is viable in such environments. One of the main aspects of the proposed methods is the elimination of the necessity for radio ranging techniques such as RSS, TOA, and TDOA. Achievable ranging accuracy with these methods, especially in a vehicular environment, is mostly not enough to help CP algorithms. The presented ranging method is based on data communication and can be used for different CP algorithms for enhancement of positioning in a vehicular network with GPS availability.

Figure 13. Experimental performance of the presented distance estimation method for a distance of 11.10 m between the nodes

The other advantage of the presented methods is the minimum possible number of participating nodes. This is also an advantage as it helps to save the limited bandwidth of DRSC. Some experiments were conducted for verification of the proposed methods. The results show the enhancement of positioning and ranging compared to that of standalone GPS. The proposed algorithms can be used for instant positioning enhancement and ranging based on available data at each time interval. As future work, using dynamic models and optimized estimators, such as a Kalman Filter, for increasing the performance of these algorithms and expansion to dynamic experiments are intended. REFERENCES

The basic idea of these solutions is similar to that underpinning DGPS but the approach is different. One advantage of the proposed techniques, if compared to DGPS, is the use of existing (future) infrastructure.

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