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Relative Positioning Enhancement in VANETs: A Tight Integration Approach Nima Alam, Asghar Tabatabaei Balaei, and Andrew G. Dempster, Senior Member, IEEE

Abstract—Position information is a fundamental requirement for many vehicular applications such as navigation, intelligent transportation systems (ITSs), collision avoidance, and locationbased services (LBSs). Relative positioning is effective for many applications, including collision avoidance and LBSs. Although Global Navigation Satellite Systems (GNSSs) can be used for absolute or relative positioning, the level of accuracy does not meet the requirements of many applications. Cooperative positioning (CP) techniques, fusing data from different sources, can be used to improve the performance of absolute or relative positioning in a vehicular ad hoc network (VANET). VANET CP systems are mostly based on radio ranging, which is not viable, despite being assumed in much of the literature. Considering this and emerging vehicular communication technologies, a CP method is presented to improve the relative positioning between two vehicles within a VANET, fusing the available low-level Global Positioning System (GPS) data. The proposed method depends on no radio ranging technique. The performance of the proposed method is verified by analytical and experimental results. Although the principles of the proposed method are similar to those of differential solutions such as differential GPS (DGPS), the proposed technique outperforms DGPS with about 37% and 45% enhancement in accuracy and precision of relative positioning, respectively. Index Terms—Cooperative positioning (CP), dedicated shortrange communication (DSRC), tight integration, vehicular ad hoc network (VANET).

I. I NTRODUCTION

R

EAL-TIME position information is required for many vehicular applications such as intelligent transportation systems (ITSs), navigation, and location-based services (LBSs). Global Navigation Satellite Systems (GNSSs), such as the Global Positioning System (GPS), are the most comprehensive positioning tools that can be considered for these applications. However, the limited accuracy and availability of GNSSs [1] must be improved to meet the requirements of positionbased applications in vehicular ad hoc networks (VANETs) [2]. Communication-based positioning enhancement, which can be termed “cooperative positioning (CP),” is a family of techManuscript received December 14, 2011; revised March 4, 2012 and May 21, 2012; accepted June 13, 2012. The Associate Editor for this paper was C. T. Chigan. N. Alam and A. G. Dempster are with the Australian Centre for Space Engineering Research, University of New South Wales, Sydney, NSW 2052, Australia (e-mail: [email protected]; [email protected]). A. Tabatabaei Balaei is with the Department of Electrical Engineering and Telecommunication, University of New South Wales, Sydney, NSW 2052, Australia (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TITS.2012.2205381

niques for improving the relative positioning between at least two points. Some conventional CP methods are differential GPS (DGPS) [1], real-time kinematic (RTK) positioning [3], satellite-based augmentation systems (SBASs), ground-based augmentation systems (GBASs) [1], and assisted GPS [4]. The achievable performance of these methods depends on many parameters, including the number of common visible satellites, dynamics of the users, and the level of uncorrelated errors, such as receiver noise and multipath. The high level of multipath and frequent GPS signal blockage in urban areas degrades the efficiency—even prevents the functionality—of these CP methods for VANETs. Tackling these issues, a new class of vehicular CP methods that relies on vehicle–vehicle or vehicle–infrastructure communication, ranging/range-rating between the nodes, and a fusion algorithm has emerged. Some examples of range-based CP methods are presented in [5]–[10]. In these techniques, the distance between the nodes is assumed to be estimated using some radio ranging techniques, including time of arrival (TOA), time difference of arrival (TDOA), and received signal strength (RSS). The complexity of timebased ranging techniques and inaccuracy of the RSS method in the vehicular environment is not well acknowledged in the literature, and practical implementation of those CP methods with radio ranging is a big challenge [11]. Avoiding the complexities and challenges of radio ranging in vehicular environments, we proposed a range-rate-based vehicular CP using Doppler shift of the signal, which is used for vehicular communication [12]. In [13]–[17], other examples of range-rate-based CP are proposed. Although the viability of Doppler-based CP methods in the vehicular environment is more promising, there is another limit to the functionality of these techniques. This is the requirement for a minimum relative motion between the participating vehicles to generate an observable Doppler shift. For example, in the Doppler-based CP in [12], the CP technique is defined only for a vehicle and its neighbors traveling in on-coming lanes. There is another class of CP techniques, without ranging or range rating, that can avoid the complexities of rangebased CP methods and the limits of range-rate-based CP. Some examples are presented in [18]–[21]. Each of these methods has some limits or shortcomings, which prevents them from being effectively applicable in a vehicular environment. In [18], the nodes must move very slowly, i.e., below 10 km/h. In [19], the latency of the system may be up to a few seconds, which is not reliable for vehicular applications, particularly at high speeds. The method proposed in [20] is essentially DGPS, but uncorrelated GPS errors such as multipath are not considered.

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However, multipath is a dominant error in urban areas and cannot be removed using differential approaches [1]. In [21], the method proposed is not experimentally verified, and the data fusion algorithm employed may not be fast enough for real-time positioning. In this paper, avoiding radio ranging and range rating, a CP method is proposed for relative positioning, which fuses low-level GPS data, i.e., pseudoranges. In this method, GPS pseudoranges are shared among the participating vehicles. Each vehicle estimates its relative position to the neighbors fusing the local GPS observations and those of the neighbors, which can be received through vehicular communication. The idea behind the proposed technique is similar to differential positioning principles, but two more advantages are the main contributions of this work, i.e., 1) elimination of the infrastructure costs, which are required for conventional systems such as DGPS; 2) achieving higher performance in relative positioning, compared to DGPS by eliminating the errors induced by infrastructure nodes. Experimental results show about 37% and 45% improvement over DGPS in the accuracy and precision of relative positioning, respectively. In Section II, the problem and solution approach are explained. Section III investigates the performance of the adopted approach to develop the CP technique. Section IV details the estimator of the proposed CP method. In Section V, the experimental results are discussed, the performance of the proposed system is evaluated, and the viability of the proposed method is verified. In Section VI, the nominated communication medium is explained. Section VII summarizes the contributions of this work and future steps. II. P ROBLEM D EFINITION AND S OLUTION A PPROACH Assume a number of vehicles in a VANET that have GPS receivers and can communicate with each other. In addition, assume that GPS signal coverage is sufficient in the area and that the vehicles can observe at least four common GPS satellites. This is a requirement for the proposed method and will be detailed later. Due to this requirement, the proposed method is not suitable for dense urban areas where the chance of observing four common satellites by the vehicles is low. The ultimate goal is that each vehicle can estimate its relative position to the neighbors using a data fusion algorithm that is fed by local GPS observations and those of the neighbors received through vehicle–vehicle communication. Two cases are explained and compared. In one case, Fig. 1, we assume that there is a DGPS reference station in the area. This station broadcasts DGPS corrections, and vehicles estimate their absolute position using GPS signals and DGPS corrections. Then, the vehicles communicate their absolute position estimates to other vehicles, so that each vehicle can calculate its position relative to its neighbors, differencing the absolute positions. We call this approach DGPS-based relative positioning for the rest of this paper. In the second case, i.e., our proposal, we assume that no DGPS reference station and correction message is available (see Fig. 2). The problem is to find a CP method that can provide

Fig. 1.

Relative positioning using DGPS-based position estimates.

Fig. 2.

Tight integration CP for relative positioning using low-level GPS data.

relative positioning among the vehicles using vehicle–vehicle communication, without any infrastructure node. In addition, the proposed method must perform better than case 1, i.e., DGPS-based relative positioning. As will be explained later, this CP technique will be implemented fusing low-level GPS data, pseudoranges, which are shared among the vehicles. We call this a tight integration CP. Each vehicle will use pseudorange data to estimate its position relative to its neighbors. The proposed solution will eliminate those GPS errors that are common for all vehicles in the data fusion process. These errors are due to the ionosphere, troposphere, GPS satellite orbit errors, and satellite clock drifts. In DGPS, these errors are broadcast by reference stations as correction messages. Then, each vehicle considers these correction messages to remove the common errors from the observed pseudoranges and improve its standalone position estimates. In [1], the pseudorange observable in a GPS receiver, which is called node k, is explained as ρik (t) = Rki (t) + cδk (t) + cδ i (t) + εi (t) + ζki (t)

(1)

where t is the time; ρik is the code pseudoranges between node k and satellite i; Rki is the distance between node k and satellite i; c is the speed of light; δk is the clock error of receiver k; δ i is the clock error of satellite i; εi is the error due to ionosphere, troposphere, and orbit of satellite i; and ζki is

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very long distance between the satellites and earth, the relative vectors between vehicles and each satellite can be assumed to be parallel. In addition, the unit vector to each satellite is effectively the same for all vehicles in a vicinity of tens of kilometers due to the long distance between the satellites and the vehicles (more than 20 000 km). We have  i Rk − Rli = uTi rkl (4) Rkj − Rlj = uTj rkl Fig. 3.

Relative geometry of two vehicles and two satellites.

the effect of thermal noise in receiver k and multipath error of satellite i. In (1), the satellite clock error is the same for all receivers. The error from the ionosphere, troposphere, and satellite orbit is also the same for all receivers in a vicinity of tens of kilometers [1]. These errors can be eliminated through differencing the observations of any pair of GPS receivers k and l, which observe a common satellite. The clock error of the receivers can also be removed if two common satellites can be observed by the receivers. Double differencing is a technique for removing the receivers’ clock errors and correlated errors of the GPS observations by two receivers and two satellites. In [3], the double differencing operation for observation X in nodes k and l from satellites i and j is defined as follows: ij (t) = Xki (t) − Xli (t) − Xkj (t) + Xlj (t). Xkl

(2)

Substituting (1) in (2), the double difference of the pseudoranges for nodes k and l and satellites i and j at time t is ij ij ρij kl (t) = Rkl (t) + ζkl (t).

(3)

As can be seen, the correlated errors between two nodes, the clock error of the receivers, and the clock error of the satellites are eliminated in (3). The pseudorange double difference is equal to that of ranges to satellites plus the effect of uncorrelated errors, which cannot be removed by differencing. Double differencing can be used for relative positioning. For example, in RTK GPS, the double difference of GPS carrier phases is used for precise positioning [3]. Of course, this method cannot yet be deployed for vehicular positioning due to the vulnerability of phase measurements to the high dynamics of vehicles and frequent signal blockage and multipath in urban areas. Another example is the method proposed in [22], which uses a combination of double differenced pseudoranges and carrier phases for relative positioning between two airplanes for collision avoidance purposes. For our problem, we try to find relative position estimates between the vehicles using (3). The left side of (3) is formed based on observed pseudoranges. In ij is the residual of uncorrelated errors that are the right side, ζkl not removed by double differencing. This will be treated as obij should be decomservation noise. For relative positioning, Rkl posed in terms of relative positions between the receivers. Fig. 3 shows two vehicles, i.e., k and l, and a pair of satellites i and j. In this figure, ui is the unit vector from node k (or l) to satellite i, and uj is the unit vector from node k (or l) to satellite j. Assuming that rk and rl are the position vectors of vehicles k and l, respectively, rkl = rl − rk is the relative position vector between node k and node l. As explained in [3], due to the

where T is the transpose operator. Considering (2) and (4), the double difference of the distances between the vehicles and satellites is ij (t) = [ui (t) − uj (t)]T rkl (t). Rkl

(5)

Substituting (5) in (3) leads to ij ui (t) − uj (t)]T rkl (t) + ζkl (t). ρij kl (t) = [

(6)

In (6), for each node, the left side is known from local observations and received data through vehicular communication. The unknown relative position and the observation noise are in the right side. The unit vectors can be accurately calculated using the standalone GPS-based position estimates because unit vectors are effectively the same for all points in the vicinity of the vehicles, due to the great distance to the satellites. For a 3-D solution, three incidences of equation are required to estimate relative position between vehicles k and l, i.e., rkl . Before presenting the detailed design of the CP technique, a performance analysis is discussed in Section III. This analysis is independent of the proposed CP method and investigates the potential achievable performance adopting the tight integration approach and that of DGPS. The results of this analysis also provide insights into the design of the tight integration CP algorithm. III. G ENERAL P ERFORMANCE A NALYSIS To analyze and compare the performances of the adopted solution approach and DGPS, the Cramer–Rao Lower Bound (CRLB) [23] of these methods is investigated. CRLB is the best achievable covariance of error by an unbiased estimator. The comparison of the CRLBs helps predict which technique will perform better. We expect experimental results to comply with CRLB analysis. CRLB is the inverse of Fisher Information Matrix (FIM) [23]. The FIM is calculated as  T    ∂ ln (p(Z|θ)) ∂ ln (p(Z|θ))  (7) IZ (θ) = E θ  ∂θ ∂θ where Z is the observation vector of a system; θ is the state vector of that system; p is the conditional probability density function (pdf) of Z, conditional on the value of θ; and E{·} is the expected value operator. A. CRLB of the Tight Integration Approach To calculate the CRLB, we consider a general condition with m common visible satellites and n vehicles, which broadcast their observed GPS pseudoranges. Thus, each vehicle can

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fuse its observed pseudoranges and those of n − 1 neighbors received through vehicular communication. Assuming that vehicle 1 is the target vehicle and performs CP to estimate its relative position to all neighbors T θn = [ r12

Zn = ζn =

[ ρ12 12 12 [ ζ12

T T · · · r1n ]

··· ···

ρ1m 12 1m ζ12

(8) ··· ···

ρ12 1n 12 ζ1n

··· ···

T ρ1m 1n ] 1m T ζ1n ]

(9) (10)

are the state, observation, and noise vectors, respectively, and we have Z n = Hn θ n + ζ n where

⎡

respectively. Equation (21) represents the CRLB of the proposed CP system with n participating vehicles. Considering (12) and (18), it can be concluded that CRLB is a function of pseudorange errors and location of the visible satellites.

U O · · · · · · ⎢ O U O · · · . .. .. .. Hn = ⎢ ⎣ .. . . .  O · · · · · · O ⎡ T ⎤ u1 (t) − uT2 (t) ⎢ uT1 (t) − uT3 (t) ⎥ ⎥ .. U (t) = ⎢ ⎣ ⎦ .

(11)

DGPS-based relative positioning (Fig. 1) is conducted by each vehicle subtracting its DGPS-based absolute position estimate and that of a neighbor that is received through vehicular communication. Thus, the CRLB of the DGPS-based absolute positioning is considered first. For vehicle k, the state vector can be defined as θk = [ rk

⎤ 

O O ⎥ .. ⎥ (12) . ⎦ U (m−1)(n−1)×3(n−1)

cδk ]

(22)

where rk is the absolute position vector, and δk is the clock error of the vehicle. According to [1], using the Taylor expansion, the vector of the observed pseudoranges by vehicle k can be presented in linear form, i.e.,

(13)

Zk = H  θk + ζk

(23)

]T Zk = [ ρ1k · · · ρm ⎤ k ⎡ T u1 1 ⎢ .. ⎥ H  = ⎣ ... .⎦ uTm 1

(24)

where

uT1 (t) − uTm (t) and O is a (m − 1) × 3 zero matrix. To calculate p(Zn |θn ), the covariance of Zn is required. Equation (11) can be reformulated as Zn = Hn θn + An ζˆn

B. CRLB of DGPS-Based Relative Positioning

(14)

ζk = [ ζk1

···

ζkm ]T .

(25) (26)

where (15) ζˆn = [ ζ11 · · · ζ1m · · · ζn1 · · · ζnm ]T ⎡ ⎤ A −A O · · · · · · O ⎢ A O −A O · · · O ⎥ .. .. .. .. ⎥ .. An = ⎢ (16) ⎣ ... . . . . . ⎦ A O · · · · · · O −A (m−1)(n−1)×mn with O being a (m − 1) × m zero matrix, and A = [ 1(m−1)×1

−I(m−1)×(m−1) ] .

(17)

1 in A represents a matrix with subscripted dimensions and all entries being 1. Assuming independence of the error of observed pseudoranges and σρ as the standard deviation (STD) of pseudorange errors, the covariance of Zn is n = σρ2 An ATn .

(18)

Assuming a Gaussian pdf for pseudorange errors, we have   exp −12 (Zn −Hn θn )T −1 n (Zn −Hn θn )  p(Zn |θn ) = . (19) (2π)(m−1)(n−1)/2 det(n ) Substituting (19) in (7) and simplifying, FIM and CRLB are represented by IZn = HnT −1 n Hn −1  −1 CCP = IZn = HnT −1 n Hn

(20) (21)

For DGPS, we assume that common errors have already been removed from the pseudorange observations (24). Thus, the observation noise (26) includes uncorrelated errors such as multipath and receiver noise, which cannot be removed by DGPS [1]. Common errors among the receivers lead to bias in position estimates. Thus, σρ can be considered as the STD of the uncorrelated errors of pseudoranges at the DGPS base station and DGPS receiver, and the √ STD of the corrected pseudoranges at the DGPS receiver is 2σρ . Considering this and assuming a Gaussian distribution for errors, the conditional pdf of observation is   exp − 4σ1 2 (Zk − H  θk )T (Zn − Hn θn ) ρ √ p (Zk |θk ) = . 2 πσρ (27) Substituting (27) in (7) and simplifying Ik =

1 (H T H  )−1 2σρ2

Ck = 2σρ2 H T H 

(28) (29)

represent the FIM and CRLB of the DGPS-based absolute position estimates of vehicle k, respectively. As mentioned before, vehicle k calculates the relative position to vehicle l by differencing its DGPS-based absolute position and that of vehicle l. Thus, due to the independence

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Fig. 4.

Performance of the tight integration approach over 24 hours.

Fig. 5. Performance of the tight integration approach for different numbers of vehicles.

of positioning errors of different vehicles, the CRLB of DGPSbased relative positioning is CDGPS = 2Ck = 4σρ2 H T H  .

5

(30)

Now, (21) and (30) can be used to analyze and compare the performance of the proposed CP approach and DGPS-based relative positioning. C. Evaluation of CRLBs To investigate performance, the visible GPS satellites in the vicinity of the test area are monitored using data logged by the GNSS base station at the University of New South Wales (UNSW), Sydney, Australia. The number of visible GPS satellites at the base station varies between 7 and 12 over 24 hours. For calculating the performance based on CRLB, the following distance root mean square (drms) error parameters are defined for the tight integration approach and DGPS-based relative positioning, respectively:  (31) T Idrms = CCP (1, 1) + CCP (2, 2)  (32) DGPSdrms = CDGPS (1, 1) + CDGPS (2, 2). First, using the data logged at the UNSW GNSS base station, the performance of the tight integration approach is calculated over 24 hours for different numbers of common visible GPS satellites m. When there is more than one possible combination of GPS satellites, the average of the performance from different combinations is considered. For now, the number of participating vehicles is assumed to be n = 10, which is an arbitrary number. In addition, the STD of pseudorange errors is considered to be σρ = 3 m. This value is set with regard to the observations by the GPS receivers used for the experiments, when located in a fixed known position. Fig. 4 shows the behavior of T Idrms . As can be seen, the performance increases for higher numbers of common visible satellites. In addition, the performance fluctuates over time due to varying positions of the satellites. Before comparing with DGPS, the effect of the number of

participating vehicles in the tight integration approach is investigated. For this, n is varied between 2 and 20, and for each condition, the average of T Idrms over 24 hours is considered. σρ = 3 m is considered as previously given. Fig. 5 shows the performance for different numbers of vehicles and visible satellites. As can be seen, the performance is independent of the number of participating vehicles. This behavior is different from the general attitude of range or range-rate-based CP systems in which increasing the number of vehicles improves the performance [24]. The reason is the lack of intervehicle range or range-rate data. In range/range-rate-based CP techniques, adding one vehicle to the system is equivalent to adding one set of GNSS data (for the case that GNSS is available) plus some range or range-rate data between the added vehicle and its neighbors. However, in the proposed tight integration approach, adding a vehicle to the system only adds a set of GNSS data with relevant uncertainties. Here, we conclude that the target vehicle in the proposed tight integration approach can manage to optimize the computational burden of CP. The target vehicle receives GPS pseudorange data from the neighbors. Due to the independence of the performance from the number of neighbors, the target vehicle has different choices to fuse data. It can form several parallel CP engines for each neighbor. This results in matrixes with low dimensions and low computational burden for each engine. However, the number of parallel CP engines increases. Another strategy is to form a single CP engine for all neighbors, which results in big matrixes and higher computational burden. A combined approach is also possible to divide the neighbors among a certain number of CP engines. Investigating more details of this issue is not of interest in this paper. It is considered to be future work. However, we adopt the first approach to develop our CP algorithm, which is considering each neighbor in a separate CP engine. Now, considering two vehicles for CP, the expected performance of the tight integration approach and DGPS-based relative positioning is investigated. For this, the relevant parameters defined by (31) and (32) are calculated for n = 2 and different numbers of visible satellites. σρ = 3 m is considered

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forms a separate CP engine for each neighbor. To estimate the relative position of a neighbor, a Kalman filter is considered for the process and observation models, as presented in θ(t + τ ) = F θ(t) + Gγ γ(t)

(34)

Z(t) = H(t)θ(t) + ζ(t)

(35)

respectively, where τ is the observation period, θ is the state vector, F is the state transition model, Gγ is the process noise model, γ is the Gaussian relative acceleration noise with the STD σγ and zero mean along each axis, Z(t) is the observation vector, H(t) is the observation model, and ζ is the observation noise. Assuming vehicle k to be the target vehicle, the state vector for relative positioning to vehicle l is defined as   rkl (t) θ(t) = (36) vkl (t) Fig. 6. Performance of (left) the tight integration approach and (right) DGPSbased relative positioning. TABLE I AVERAGE P ERFORMANCE OVER 24 H OURS

where vkl is the relative velocity between the vehicles. This definition leads to     I3×3 τ I3×3 0. 5τ 2 I3×3 F = , Gγ = (37) O3×3 I3×3 τ I3×3 where O is a matrix with all zero entries, and I is the identity matrix. The process noise covariance Q is   0. 25τ 4 I3×3 0. 5τ 3 I3×3 Q = σγ2 Gγ GTγ = σγ2 . (38) 0. 5τ 3 I3×3 τ 2 I3×3

as previously given. Fig. 6 shows the results. As can be seen, the tight integration approach shows an improvement over DGPSbased relative positioning. This is generally sensible because the uncorrelated errors of the receivers are not removed through differencing. In DGPS-based relative positioning, these errors enter the system from three receivers (i.e., two vehicles and one base), whereas, for the proposed method, there are only two receivers. Table I summarizes the average drms for two approaches and different numbers of satellites and relative improvement over DGPS using   Avg. T Idrms × 100. (33) μCRLB = 1 − Avg. DGPSdrms According to Table I, we can expect about 30% improvement over DGPS using the tight integration approach when the number of common visible satellites is more than 4. IV. T IGHT I NTEGRATION C OOPERATIVE P OSITIONING T ECHNIQUE In Section II, a tight integration approach based on double differences was proposed. A general performance analysis was conducted in Section III to illustrate the superiority of tight integration over DGPS for relative positioning. In this section, an estimator is explained for tight integration CP for relative positioning between the vehicles. Equation (6) relates the relative position of two vehicles to double differences of observed GPS pseudoranges. Considering the results of the previous section, here we assume that the target vehicle

Assuming that a normal condition for driving (no skidding, no severe shaking, etc.) σγ is considered to be of low value 0.1 m/s2 , for the proposed method, the observation vector for m common visible satellites is T ρ1m kl (t) ]

···

Z(t) = [ ρ12 kl (t)

(39)

and according to (35) and (6), there is H(t) = [ U (t)

O(m−1)×3 ]

(40)

and the observation noise is 12 ζ(t) = [ ζkl (t)

···

1m ζkl (t) ]T .

(41)

To calculate the covariance of the observation noise, (41) is reformulated as ζ = [A

−A ] [ ζk1

···

ζkm

ζl1

···

ζlm ]T .

(42)

Assuming the independence of pseudorange errors, there is  = [A

−A ][ A

−A ]T σρ2

(43)

which leads to  = 2σρ2 AAT .

(44)

The value of σρ can be estimated based on the measurements when the receiver antenna is located in a known position. Provided at least four common satellites are visible at nodes k and l, the initial state of the system can be estimated using (6). Having F , Gγ , H, , and Q, the required parameters for

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Fig. 7.

Test site and path (original photo from Google Map).

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Fig. 8. Number of observed GPS satellites by the vehicles.

Kalman filtering are provided and the observations (39) can be fed to the filter for relative positioning. The performance of the proposed method will be compared with that of DGPS-based relative positioning. DGPS-based relative position estimate is the difference of the DGPS-based absolute position of the target vehicle and that of its neighbor. To calculate DGPS absolute position estimates, a standard method, using a Kalman filter, will be used after applying the DGPS corrections to the observed pseudoranges [1]. The DGPS Corrections are calculated using the observations of the GNSS base station at UNSW. V. E XPERIMENTAL R ESULTS To evaluate the presented CP method, a test case was set up including two vehicles equipped with single-band GPS receivers (i.e., one NordNav and one u-blox AEK-4T) and laptops for data logging. The vehicles were driven along different roads near UNSW with different speeds and sufficient GPS satellite coverage for about 45 min. The pseudoranges and corresponding GPS time tags observed by the receivers were logged during the experiment. For evaluation purposes, the real position of the vehicles, with cm level of accuracy, was logged using a Leica 1200 RTK GPS rover in each vehicle. The performance of RTK GPS is limited by the high mobility of vehicles, particularly in urban areas. Because of this, the more accurate position of the vehicles was not logged for the whole 45 min. The longest continuous useful observation time with RTK GPS fixes was 12 min, and this is used to evaluate the proposed method. Fig. 7 shows the test site and the corresponding route traveled during 12 min. As can be seen, the route includes a combination of straight and curvy sections to improve the credibility of the evaluation of the proposed system. The UNSW base station is located in this figure. This station continuously logs the GNSS observations. Its observations during our test are used to provide DGPS corrections. The vehicles were driven at different speeds, relative speeds, and distances. The maximum speed was 80 km/h, the maximum relative speed was 34 km/h, and the maximum distance between them was 78 m. Fig. 8 shows the number of observed GPS satellites at each vehicle during the test. At the UNSW base station, the signals from the highest possible number of visible satellites (11 or 12 satellites) in the area were acquired. As can be seen,

Fig. 9. Relative positioning error for CP and DGPS.

the GPS receiver in vehicle 1 has better performance in acquiring the satellites. For short-term lost signals, 1 to 2 epochs, the corresponding innovation in the Kalman filter is set to zero, and the relevant entry of the observation covariance  is set to a very large number to represent mathematical infinity. To evaluate the performance of the proposed CP method, the error of position estimates is defined as rkl (t) − rkl (t) er (t) = ˆ

(45)

where rˆkl is the estimated relative position. This error is calculated for the proposed method and DGPS. The root mean square (rms) and STD of er is used to define the achieved improvement over DGPS, i.e.,   RMS(er |CP ) μa = 1 − × 100 (46) RMS(er |DGPS )   STD(er |CP ) × 100. (47) μp = 1 − STD(er |DGPS ) Parameter μa indicates the improvement in bias of the error (accuracy), and μp shows the enhancement in the noise of error (precision). Fig. 9 compares the performance of the proposed CP method with that of DGPS. Table II summarizes all results. As can be seen, the proposed CP method outperforms DGPS. In addition, the performance achieved for each method and

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TABLE II E XPERIMENTAL R ESULTS (CP AND S TANDALONE AND DGPS E RRORS )

Fig. 10. Relative positioning error and speed.

improvement complies with the results of Section III. Another point is important here. The performance of DGPS is not on the order of submeters in the vehicular environment of this experiment. This is due to considerable multipath error in vehicular and urban areas and receiver noise that are not removed through differencing. Now, the impact of the speed of the vehicles on the performance of positioning is investigated. To do this, the positioning error is characterized for different absolute and relative speeds. For this, the range between the minimum and maximum of absolute and relative speeds are divided into ten speed bins. The average of relative positioning error is calculated for each bin. For absolute speed, the average of the speeds of the two vehicles at each time is considered. Fig. 10 shows the effect of speed on the performance. As can be seen, the error of the proposed method and that of DGPS is lower at high and low speeds. The reason is that, at high speeds, the vehicles have been in highways without surrounding buildings. Thus, multipath error is lower. In addition, the difference of performances decreases for higher speeds. The very low speeds belong to a top floor open space car park without surrounding obstacles. This situation results in low multipath as well. The middle speeds belong to urban streets with some buildings and trees around. Thus, the multipath error is higher. For relative speed, the error increases at higher relative speeds. Higher relative speed is for the urban streets where the pattern of speed in two vehicles is independent due to traffic conditions and stopping at traffic lights. However, on highways, both vehicles had a similar speed around the average speed of the traffic. VI. C OMMUNICATION AND C OMPUTATION The assumed medium for vehicular communication is dedicated short range communication (DSRC) [25]. DSRC is a medium with 75-MHz bandwidth, at 5.9 GHz, as described

in the IEEE802.11p standard, which is dedicated to vehicle– vehicle and vehicle–infrastructure communication. The nominal communication range is about 1000 m under line-of-sight conditions. DSRC has basically seven channels, each with 10-MHz bandwidth. It is assumed that one of these channels can be used for the presented CP method and vehicles share their GPS-based data, communicating through that channel. In the proposed CP algorithm, the bandwidth of DSRC is not a concern because the considered broadcast data, i.e., the pseudoranges of the visible satellites, need a bandwidth that is much lower than the bandwidth of DSRC channels (10 MHz), even if the update rate is a few per second. For instance, with regard to [26], less than 150 bytes of data is required to transmit the pseudoranges and carrier phases of ten satellites observed by a dual-band receiver. The required data rate for the proposed method is less than this, as only a single band is used for the proposed technique, and the GPS carrier phase is not communicated. Moreover, according to [27], the maximum number of neighbors in the DSRC range in typical moving heavy traffic is about 35. Thus, considering the necessary data rate for each vehicle to run the proposed CP method, it seems that DSRC bandwidth is far beyond the requirements of the international standard for GNSS real-time data exchange. The computational burden of the proposed method is not a challenge for implementation. The double difference approach provides a linear state-space model, and there is no iterative step, such as absolute positioning, to estimate the relative position. The process of relative position estimation does not depend on communication after the vehicle receives a packet from its neighbor. This means that, after receiving a packet from a neighbor, the CP algorithm can be locally run and can estimate the relative position within a known period. VII. C ONCLUSION A CP method has been presented for relative positioning in VANETs adopting a tight integration approach. The method is based on fusing low-level GPS data, i.e., pseudoranges, from the participating vehicles. The system is functional with at least four common visible satellites for the vehicles. Applying real logged data from a vehicular field test, the achieved enhancement in the accuracy and precision of relative positioning over DGPS is about 37% and 45%, respectively. Another advantage of the proposed technique, compared with the majority of vehicular CP methods, is the independence of intervehicle radio ranging methods such as RSS, TOA, and TDOA. These methods are very problematic in VANETs and not as accurate as assumed in the literature. Multipath error degrades the performance of the conventional differential positioning methods, e.g., DGPS. Although the proposed method has a differential approach in principle, eliminating the reference station, which is required to broadcast corrections for DGPS, was a key factor for superiority of the proposed method over DGPS-based relative positioning. Regarding a typical maximum number of the possible neighbors for a vehicle in VANET and the required data rate for GNSS data exchange, it is concluded that the bandwidth of a DSRC channel is enough for the proposed system.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. ALAM et al.: RELATIVE POSITIONING ENHANCEMENT IN VANETs: A TIGHT INTEGRATION APPROACH

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[23] H. L. V. Trees, Detection, Estimation, and Modulation Theory. New York: Wiley-IEEE, 2003. [24] N. Alam, A. T. Balaei, and A. G. Dempster, “Performance boundaries for cooperative positioning in VANETs,” presented at the Int. Global Navigation Satellite Systems Symp., Sydney, Australia, 2011. [25] Amendment of the Commission’s Rules Regarding Dedicated ShortRange Communication Services in the 5.850–5.925 GHz Band (5.9 GHz Band), 2002. [26] Y. Heo, T. Yan, S. Lim, and C. Rizos, “International standard GNSS realtime data formats and protocols,” presented at the Int. Global Navigation Satellite Systems Symp., Surfers Paradise, Australia, 2009. [27] J. Yao, A. T. Balaei, N. Alam, M. Efatmaneshnik, A. G. Dempster, and M. Hassan, “Characterizing cooperative positioning in VANET,” presented at the IEEE Wireless Communications and Networking, QuintanaRoo, Mexico, 2011.

Nima Alam received the B.E. degree in telecommunication systems and the M.Eng.Sc. degree in control systems from Sharif University of Technology, Tehran, Iran, in 1998 and 2000, respectively, and the Ph.D. degree in vehicular positioning enhancement using dedicated short-range communication from the University of New South Wales (UNSW), Sydney, Australia, in 2012. He is currently a Research Associate with the Australian Centre for Space Engineering Research, UNSW. From 2000 to 2008, he was involved in a variety of projects in the automotive industry, including industrial robotics, automated guide vehicles, factory automation, machine vision, and Global Positioning System navigation. In 2010 and 2011, he was a Consultant with the National ICT Australia TruckOn project and Future Logistics Living Laboratory.

Asghar Tabatabaei Balaei received the B.E. and M.Eng.Sc. degrees in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1997 and 2000, respectively, and the Ph.D. degree in global navigation satellite interference from the University of New South Wales (UNSW), Sydney, Australia, in 2008. He has been a Postdoctoral Research Fellow with the School of Surveying and Spatial Information Systems, UNSW, working in the area of cooperative positioning systems. He is currently an Associate Lecturer with the Department of Electrical Engineering and Telecommunication, UNSW, as well as a Researcher with the National ICT Australia.

Andrew G. Dempster (M’92–SM’03) received the B.E. and M.Eng.Sc. degrees from the University of New South Wales (UNSW), Sydney, Australia, in 1984 and 1992, respectively, and the Ph.D. degree in efficient circuits for signal processing arithmetic from the University of Cambridge, Cambridge, U.K., in 1995. He is currently the Director of the Australian Centre for Space Engineering Research, UNSW. He is also the Director of Research with the School of Surveying and Spatial Information Systems and the Director of Postgraduate Research of the Faculty of Engineering. He is the holder of six patents. His current research interests are satellite navigation receiver design and signal processing, as well as new location technologies. Dr. Dempster was a System Engineer and Project Manager for the first Global Positioning System receiver developed in Australia in the late 1980s and has been involved in satellite navigation ever since.