Ieeepro techno solutions 2013 ieee embedded project relative positioning enhancement

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 1, MARCH 2013 47
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 location-
based 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 short-
range communication (DSRC), tight integration, vehicular ad hoc
network (VANET).
I. INTRODUCTION
REAL-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 applica-
tions. However, the limited accuracy and availability of GNSSs
[1] must be improved to meet the requirements of position-
based applications in vehicular ad hoc networks (VANETs) [2].
Communication-based positioning enhancement, which can be
termed “cooperative positioning (CP),” is a family of tech-
Manuscript received December 14, 2011; revised March 4, 2012 and
May 21, 2012; accepted June 13, 2012. Date of publication July 10, 2012; date
of current version February 25, 2013. 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: nima.alam@unsw.edu.au; a.dempster@unsw.edu.au).
A. Tabatabaei Balaei is with the Department of Electrical Engineering and
Telecommunication, University of New South Wales, Sydney, NSW 2052,
Australia (e-mail: asghart@unsw.edu.au).
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 time-
based 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 range-
based 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.
1524-9050/$31.00 © 2012 IEEE

48 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 1, MARCH 2013
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 position-
ing, respectively.
In Section II, the problem and solution approach are ex-
plained. 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 exper-
imental 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. PROBLEM DEFINITION AND SOLUTION APPROACH
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 satel-
lites. 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 observ-
ing 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 com-
municate their absolute position estimates to other vehicles, so
that each vehicle can calculate its position relative to its neigh-
bors, 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 imple-
mented 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 correc-
tion 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
ρi
k(t) = Ri
k(t) + cδk(t) + cδi
(t) + εi
(t) + ζi
k(t) (1)
where t is the time; ρi
k is the code pseudoranges between
node k and satellite i; Ri
k is the distance between node k
and satellite i; c is the speed of light; δk is the clock error of
receiver k; δi
is the clock error of satellite i; εi
is the error due
to ionosphere, troposphere, and orbit of satellite i; and ζi
k is

ALAM et al.: RELATIVE POSITIONING ENHANCEMENT IN VANETs: A TIGHT INTEGRATION APPROACH 49
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:
Xij
kl(t) = Xi
k(t) − Xi
l (t) − Xj
k(t) + Xj
l (t). (2)
Substituting (1) in (2), the double difference of the pseudor-
anges for nodes k and l and satellites i and j at time t is
ρij
kl(t) = Rij
kl(t) + ζij
kl(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 uncorre-
lated 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
the right side, ζij
kl is the residual of uncorrelated errors that are
not removed by double differencing. This will be treated as ob-
servation noise. For relative positioning, Rij
kl should be decom-
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
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
Ri
k − Ri
l = uT
i rkl
Rj
k − Rj
l = uT
j rkl
(4)
where T is the transpose operator. Considering (2) and (4), the
double difference of the distances between the vehicles and
satellites is
Rij
kl(t) = [ui(t) − uj(t)]T
rkl(t). (5)
Substituting (5) in (3) leads to
ρij
kl(t) = [ui(t) − uj(t)]T
rkl(t) + ζij
kl(t). (6)
In (6), for each node, the left side is known from local ob-
servations 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 pre-
senting the detailed design of the CP technique, a performance
analysis is discussed in Section III. This analysis is indepen-
dent 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. GENERAL PERFORMANCE ANALYSIS
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
IZ(θ) = E
∂ ln (p(Z|θ))
∂θ
T
∂ ln (p(Z|θ))
∂θ
θ (7)
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

fuse its observed pseudoranges and those of n − 1 neigh-
bors received through vehicular communication. Assuming that
vehicle 1 is the target vehicle and performs CP to estimate its
relative position to all neighbors
θn = [ rT
12 · · · rT
1n ]T
(8)
Zn = [ ρ12
12 · · · ρ1m
12 · · · ρ12
1n · · · ρ1m
1n ]T
(9)
ζn = [ ζ12
12 · · · ζ1m
12 · · · ζ12
1n · · · ζ1m
1n ]T
(10)
are the state, observation, and noise vectors, respectively, and
we have
Zn = Hnθn + ζn (11)
where
Hn =
⎡
⎢
⎢
⎣
U O · · · · · · O
O U O · · · O
...
...
...
...
...
O · · · · · · O U
⎤
⎥
⎥
⎦
(m−1)(n−1)×3(n−1)
(12)
U(t) =
⎡
⎢
⎢
⎣
uT
1 (t) − uT
2 (t)
uT
1 (t) − uT
3 (t)
...
uT
1 (t) − uT
m(t)
⎤
⎥
⎥
⎦ (13)
and O is a (m − 1) × 3 zero matrix. To calculate p(Zn|θn),
the covariance of Zn is required. Equation (11) can be refor-
mulated as
Zn = Hnθn + An
ˆζn (14)
where
ˆζn = [ ζ1
1 · · · ζm
1 · · · ζ1
n · · · ζm
n ]T
(15)
An =
⎡
⎢
⎢
⎣
A −A O · · · · · · O
A O −A O · · · O
...
...
...
...
...
...
A O · · · · · · O −A
⎤
⎥
⎥
⎦
(m−1)(n−1)×mn
(16)
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 = σ2
ρAnAT
n . (18)
Assuming a Gaussian pdf for pseudorange errors, we have
p(Zn|θn) =
exp −1
2 (Zn −Hnθn)T −1
n (Zn −Hnθn)
(2π)(m−1)(n−1)/2 det( n)
. (19)
Substituting (19) in (7) and simplifying, FIM and CRLB are
represented by
IZn = HT
n
−1
n Hn (20)
CCP = I−1
Zn = HT
n
−1
n Hn
−1
(21)
respectively. Equation (21) represents the CRLB of the pro-
posed 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.
B. CRLB of DGPS-Based Relative Positioning
DGPS-based relative positioning (Fig. 1) is conducted by
each vehicle subtracting its DGPS-based absolute position esti-
mate 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 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.,
Zk = H θk + ζk (23)
where
Zk = [ ρ1
k · · · ρm
k ]T
(24)
H =
⎡
⎢
⎣
uT
1 1
...
...
uT
m 1
⎤
⎥
⎦ (25)
ζk = [ ζ1
k · · · ζm
k ]T
. (26)
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
p (Zk|θk) =
exp − 1
4σ2
ρ
(Zk − H θk)T
(Zn − Hnθn)
2
√
πσρ
.
(27)
Substituting (27) in (7) and simplifying
Ik =
1
2σ2
ρ
(H T
H )−1
(28)
Ck = 2σ2
ρH T
H (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 po-
sition to vehicle l by differencing its DGPS-based absolute
position and that of vehicle l. Thus, due to the independence

Fig. 4. Performance of the tight integration approach over 24 hours.
of positioning errors of different vehicles, the CRLB of DGPS-
based relative positioning is
CDGPS = 2Ck = 4σ2
ρH T
H . (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:
TIdrms = CCP(1, 1) + CCP(2, 2) (31)
DGPSdrms = CDGPS(1, 1) + CDGPS(2, 2). (32)
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 combina-
tion 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 TIdrms.
As can be seen, the performance increases for higher num-
bers 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
Fig. 5. Performance of the tight integration approach for different numbers of
vehicles.
participating vehicles in the tight integration approach is inves-
tigated. For this, n is varied between 2 and 20, and for each
condition, the average of TIdrms 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 de-
tails 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 per-
formance of the tight integration approach and DGPS-based
relative positioning is investigated. For this, the relevant pa-
rameters defined by (31) and (32) are calculated for n = 2 and
different numbers of visible satellites. σρ = 3 m is considered

Fig. 6. Performance of (left) the tight integration approach and (right) DGPS-
based relative positioning.
TABLE I
AVERAGE PERFORMANCE OVER 24 HOURS
as previously given. Fig. 6 shows the results. As can be seen, the
tight integration approach shows an improvement over DGPS-
based 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
μCRLB = 1 −
Avg. TIdrms
Avg. DGPSdrms
× 100. (33)
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. TIGHT INTEGRATION COOPERATIVE
POSITIONING TECHNIQUE
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 differ-
ences of observed GPS pseudoranges. Considering the results
of the previous section, here we assume that the target vehicle
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) = Fθ(t) + Gγγ(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
θ(t) =
rkl(t)
vkl(t)
(36)
where vkl is the relative velocity between the vehicles. This
definition leads to
F =
I3×3 τI3×3
O3×3 I3×3
, Gγ =
0. 5τ2
I3×3
τI3×3
(37)
where O is a matrix with all zero entries, and I is the identity
matrix. The process noise covariance Q is
Q = σ2
γGγGT
γ = σ2
γ
0. 25τ4
I3×3 0. 5τ3
I3×3
0. 5τ3
I3×3 τ2
I3×3
. (38)
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
Z(t) = [ ρ12
kl (t) · · · ρ1m
kl (t) ]T
(39)
and according to (35) and (6), there is
H(t) = [ U(t) O(m−1)×3 ] (40)
and the observation noise is
ζ(t) = [ ζ12
kl (t) · · · ζ1m
kl (t) ]T
. (41)
To calculate the covariance of the observation noise, (41) is
reformulated as
ζ = [ A −A ] [ ζ1
k · · · ζm
k ζ1
l · · · ζm
l ]T
. (42)
Assuming the independence of pseudorange errors, there is
= [ A −A ][ A −A ]T
σ2
ρ (43)
which leads to
= 2σ2
ρAAT
. (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

Fig. 7. Test site and path (original photo from Google Map).
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. EXPERIMENTAL RESULTS
To evaluate the presented CP method, a test case was set
up including two vehicles equipped with single-band GPS re-
ceivers (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 correspond-
ing 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 observa-
tions. 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 satel-
lites 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. 8. Number of observed GPS satellites by the vehicles.
Fig. 9. Relative positioning error for CP and DGPS.
the GPS receiver in vehicle 1 has better performance in acquir-
ing 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
er(t) = ˆrkl(t) − rkl(t) (45)
where ˆrkl is the estimated relative position. This error is calcu-
lated 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.,
μa = 1 −
RMS(er|CP)
RMS(er|DGPS)
× 100 (46)
μp = 1 −
STD(er|CP)
STD(er|DGPS)
× 100. (47)
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

TABLE II
EXPERIMENTAL RESULTS (CP AND STANDALONE AND DGPS ERRORS)
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 perfor-
mance 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. COMMUNICATION AND COMPUTATION
The assumed medium for vehicular communication is ded-
icated 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 nomi-
nal 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. CONCLUSION
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. Apply-
ing real logged data from a vehicular field test, the achieved
enhancement in the accuracy and precision of relative position-
ing 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 conven-
tional 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 neigh-
bors 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.

The performance of the proposed method does not depend on
the number of participating vehicles. Thus, the computational
burden of the proposed method can be optimized by managing
the number of CP engines and the neighbors processed at each
engine. This will be considered as future work.
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M. Hassan, “Characterizing cooperative positioning in VANET,” pre-
sented at the IEEE Wireless Communications and Networking, Quintana-
Roo, Mexico, 2011.
Nima Alam received the B.E. degree in telecommu-
nication systems and the M.Eng.Sc. degree in con-
trol 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 Telecommunica-
tion, 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.

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