Improved Vehicle Positioning in Urban

Environment through Integration of GPS and

Low-Cost Inertial Sensors

Pavel Davidson, Jani Hautamäki, Jussi Collin, and Jarmo Takala

Department of Computer Systems, Tampere University of Technology

P.O.Box 553, FIN-3310, Finland

BIOGRAPHY

Pavel Davidson received his MSc in aerospace

engineering from Technion, Israel Institute of

Technology in 1996. From 1996 until 2006 he was

employed with Israel Aircraft Industries, Tricom

Technologies, and Spirit Corp. His main research

interest is in navigation including multi-sensor

integration and GIS. Currently he is a PhD

candidate at Tampere University of Technology

(TUT).

Jani Hautamäki is studying towards MSc degree at

the Department of Computer Systems at TUT. His

area of specialization is programming of embedded

systems.

Jussi Collin is a senior research scientist at TUT. He

received his Dr. Tech. degree from TUT in 2006.

The topic of his dissertation was: Investigations of

Self-Contained Sensors for Personal Navigation. His

current research topic is sensor-aided navigation

systems.

Jarmo Takala received his MSc and Dr. Tech.

degrees from TUT in 1987 and 1999, respectively.

Currently he is Professor of Computer Engineering

at TUT. His research interests are digital signal

processing and parallel architectures for DSP

INTRODUCTION

Accurate and continuous position calculation is a

key task for vehicle navigation and telematics

applications. In most portable car navigation and

telematics devices, the position is calculated based

only on GPS data. However, in urban canyons

stand-alone GPS suffers signal masking and

reflections of the signal from buildings, large

vehicles, and other reflective surfaces. Driving tests

in such metropolises as Hong Kong, Tokyo, and

New York show that the chance of receiving four

GPS satellites required for navigation can be as low

as 20% of total driving time [1]. Even when four or

more satellites are available, strong multipath effect

might cause a positioning error of more than 100 m.

In order to obtain uninterrupted navigation data in

urban environment, GPS data can be augmented

with a complementary navigation system that can

work continuously in any type of urban environment

[2]–[4]. This is known as an integrated navigation

system. This article presents such an integrated

GPS/DR (Dead Reckoning) navigation system. We

consider a DR configuration consisting of one gyro

for directional measurements and 3D accelerometer.

Both the gyro and accelerometers satisfy the

requirements for mass market portable consumer

devices: low cost, light weight, and low power

consumption. An odometer is not used in the

proposed system as it requires additional car

installation; this system is intended mainly for

portable devices such as mobile phones, GPS-based

peripherals, and handheld GPS navigation devices.

This paper shows how GPS data can be augmented

with DR sensor data using an Extended Kalman

Filter (EKF) to achieve the required navigation

performance in urban environment. In the proposed

system, the DR sensors are calibrated when GPS is

available. If GPS signal is not available or GPS

position accuracy suffers from multipath, the

calibrated DR sensors are used to determine the

position of the vehicle. Field tests with real-time

prototype show that the proposed method improves

vehicle positioning performance in high multipath

signal environment and during short GPS signal

outages.

Figure 1. Typical urban environment in downtown

Calgary, Canada.

1 INTEGRATION CONCEPT

The proposed car navigation system includes

different types of navigation sensors and

technologies. Our concept of data fusion from

multiple sensor technologies is illustrated in Fig. 2.

This methodology comprises several stages of data

processing:

− Inertial sensors data for stop detection;

− Inertial sensor data for position, velocity and

heading computations (DR computations);

− Calibration of inertial sensors when vehicle is

stationary;

− Integrated GPS/DR navigation solution;

The hardware parts of our navigation system are the

shaded boxes. The above concept of integrating

GPS and inertial sensors will be explained and

represented mathematically in chapter 3.

2 DESCRIPTION OF REAL-TIME

PROTOTYPE

To evaluate the performance of our integrated

GPS/DR navigation system, a real-time prototype

was built. One Analog Devices ADXRS150 yaw-

rate gyro [5], and VTI Technologies SCA3000 3D

accelerometer [6] were selected as the dead

reckoning sensors to augment IT03 L1 GPS receiver

by Fastrax [7], which is based on the Atheros

chipset [8]. The inertial sensors are mounted on a

separate sensor board which is connected to the

Fastrax IT03 evaluation kit via SPI bus available on

I/O card terminal connectors as shown in Fig. 3.

Sensor Parameter

Compensation

Multi-Sensor Data Fusion

(Extended Kalman Filter)

Coordinate

Transformation

Matrix Computation

ψσσσσψ ,,,,,,, VENEN VPP

3D Accelerometer

Stop Detection

Module

Gyro

GPS

Figure 2. Conceptual description of the navigation

information sources and data flow for our portable

car navigation system.

This evaluation kit allows convenient real-time data

fusion between the GPS and inertial sensors. In this

arrangement the GPS receiver is the core of the

system and is responsible for both making its own

measurements, and for time tagging of the inertial

sensor measurements. The integrated GPS/DR

solution is computed at rate of 5 Hz and represented

in NMEA 0183 format.

3 INTEGRATION OF GPS AND DR

Kalman filtering

The real-time data fusion algorithm employs an

extended Kalman filter (EKF) to combine computed

GPS position, velocity, and heading with the

acceleration and heading rate measurements

provided by the 3D accelerometer and heading gyro.

The EKF uses the values of the filter states to

predict the future states through a dynamic model

Figure 3. Evaluation kit hardware. GPS receiver

chip is located below the sensor board.

which is based on dead reckoning equations to

estimate position, velocity, and heading. The

dynamic model is given by

( )

==

=

ω

ψ

ψ

ψ

L

E

N

a

V

V

xfV

P

P

xsin

cos

&

&

&

&

& (1)

where NP , EP are the vehicle north and the east

positions, ψ is the vehicle heading, ω is the

measured heading rate, V is the speed over ground,

La is the measured vehicle acceleration in the

longitudinal direction. The vehicle frame

longitudinal acceleration is calculated by

transforming three-dimensional acceleration vector

measured by accelerometers in the sensor frame into

vehicle frame and calculating projection of the

transformed vector on vehicle’s longitudinal axes. It

also includes the effect of gravitational forces

because of unknown road grade. It is defined as

ngbaa LTL +⋅++= θ (2)

where Ta is the true vehicle longitudinal

acceleration, g is the gravitational constant, θ is the

road grade, Lb is the longitudinal acceleration error

and n is a wideband accelerometer noise. To

properly model accelerometer and gyro

measurement errors and unknown road grade, the

state vector is augmented with two additional states:

δω gyro bias, and aδ acceleration bias and

misalignment (including unknown road grade) as

follows:

[ ]TEN awVPPx δδψ= . (3)

The Kalman filter covariance propagation is given

by

( ) ( ) ( ) ( ) ( )kkkkPkkkPT Γ+ΦΦ=+ ||1 (4)

where Φ is a discrete equivalent of the continuous

transition matrix F and Γ is a discrete equivalent

of the process noise power spectral density matrix.

Since the dynamic model is nonlinear, it has to be

linearized with respect to the state variables. The

linearization is performed around the previously

estimated values such that the continuous transition

matrix F takes the following form:

−

−

−

=

a

g

T

T

V

V

F

/100000

0/10000

010000

100000

00cossin00

00sincos00

ψψ

ψψ

. (5)

The states for the gyroscope and acceleration

measurement errors were modeled as the first order

Gauss-Markov processes with time constants Tg and

Ta respectively. The values of these time constants

and driving noise parameters are the tuning

parameters of the Kalman filter. They can be

derived from the accelerometer and gyro random

walk and output noise characteristics. These values

can be adjusted to approximate the Allan Variance

plot of correlated noise in averaging time range we

are interested.

Since only one heading gyro is used, the road tilt

influence on horizontal acceleration measurements

cannot be separated from the actual vehicle

acceleration. Nevertheless if the driving noise and

time constant in Gauss-Markov process are chosen

correctly the total acceleration measurement error

including road tilts can be approximated quite well

by this model. Compared to the bias error and

unknown road tilts, the effect of the scale factor

error is relatively small. Therefore, they are not

included in the state vector. The EKF state vector is

a 6-state vector.

It was verified by numerous road tests that when

GPS signals are available the integration algorithm

for GPS+MEMS sensor measurement is robust to

sensors bias variations and to moderate road tilts.

The Kalman filter propagation of the state and

covariance is done with approximately 10 Hz rate.

This sampling rate guarantees no degradation for

vehicles in regular urban dynamic environment. A

10 Hz propagation rate allows for a first order

approximation of the continuous transition matrix

F by its discrete equivalent Φ = I+F∆t, where I is

identity matrix and ∆t is sampling period.

The observation vector is calculated by taking the

difference between GPS and DR corresponding

positions and velocities, and in some cases heading.

The measurement update can take the following

forms:

− vehicle position, velocity and heading;

− vehicle position and velocity;

− velocity only, in the case of the zero

velocity update;

The position accuracy of a single-frequency L1 GPS

receiver is approximately 10 m in the horizontal axis

and 15 m in the vertical axis. A single-frequency L1

GPS receiver determines velocity based on the

Doppler shift of the GPS carrier wave. The velocity

accuracy in the horizontal axis can reach 2–5 cm/s

and in the vertical axis 4–10 cm/s 1σ standard

deviation of the stochastic errors [9]. The accuracy

of GPS depends heavily on satellite geometry and

multipath errors. In this project, the update rate of

the GPS receiver was set to 1 Hz to reduce the

amount of computations in the processor. The GPS

velocity measurements can be also used to

determine vehicle heading. If there is no vehicle

sideslip, the heading can be calculated as

( )north

GPS

east

GPSGPS VV /arctan=ψ (6)

where east

GPSV,

north

GPSV

are the east and north GPS

velocity measurements, respectively. The standard

deviation of the heading error can be approximated

by [12]

( ) ( ) GPSGPSGPS VV /δσψσ = . (7)

The GPS heading GPSψ is calculated only when a

vehicle has sufficient speed. This threshold is

determined empirically and here a threshold of 2.5

m/s was used.

Alignment and calibration

In order to assist GPS with the gyro and

accelerometers, initialization procedures have to be

completed: initial alignment and calibration. The

initial alignment procedure includes horizontal

alignment based on the accelerometers outputs, yaw

angle estimation using horizontal components of

vehicle velocity, and azimuth alignment using

external heading information. The initial calibration

includes estimation of the accelerometer bias and

misalignment, and also calibration of the gyroscope

bias.

The horizontal alignment includes the estimation of

the sensor frame orientation with respect to the

pseudo vehicle frame [2]. The pseudo vehicle frame

can be defined as: X axis corresponds to

longitudinal axis of vehicle, Z axis corresponds to

vertical axis of the local level, and Y axis completes

the triad. When vehicle is stationary the outputs

from the horizontal accelerometers are caused by the

tilt of the sensor frame with respect to the local

horizon and accelerometer biases. This effect can be

compensated in the following manner

=

z

y

x

S

V

a

a

a

D

g

0

0

(8)

where xa , ya , za are measured accelerations in

sensor frame, g is the gravitational acceleration and S

VD is a coordinate transformation matrix from

sensor frame S to pseudo-vehicle frame V.

Horizontal alignment gives two Euler angles for

transformation matrix S

VD .

In reality the alignment is usually performed in a

place which is tilted with respect to the local

horizon by some small angle. In this case, the

transformation matrix S

VD will include this

misalignment error which in turn will result in errors

when calculating the projection of the acceleration

vector on vehicle’s longitudinal axes. However, this

misalignment error can be estimated quite

accurately when DR computed velocity is compared

with GPS velocity. Therefore, the detrimental effect

of misalignment error can be reduced when the

vehicle’s longitudinal acceleration is compensated

with the estimated misalignment error.

The yaw angle between sensor frame and vehicle

frame can be estimated when vehicle is accelerating

with constant direction [2] using the following

kinematic relation:

=

H

x

H

y

V

Varctanγ (9)

where H

xV , H

yV are the horizontal components of

vehicle velocity. The calculation of the yaw angle

gives the third angle necessary for computation of

the transformation matrix S

VD .

The moments when vehicle is stationary can be also

used for estimation of gyroscope bias error. In this

case, the changes in heading are caused only by

heading gyro bias. Therefore, the process of gyro

bias estimation is straightforward. A real-time

estimation algorithm can be based, for example, on

recursive least squares method.

In our navigation system, both the alignment and

calibration are implemented in real-time and can be

performed at any time when vehicle is stationary. It

takes about 20 seconds to complete all these

procedures in fully automatic mode. There is no

Figure 4. Magnitude of the acceleration vector. Red

dots show the acceleration (mg) during detected

stop vs. time (min).

need for the user to take any special actions. During

and after the alignment the portable navigation

device has to be fixed into a cradle. The system has

the capability to re-initialize alignment and

calibration parameters at any time when it is not

moving. The need for re-computation of alignment

parameters may arise due to change in orientation of

the device during the drive which can be detected by

the algorithm. This change in orientation can affect

the gyro scale factor. The need for re-computation

of accelerometer and gyro calibration parameters is

caused by changes of accelerometer and gyro bias

mainly due to temperature variations.

Stop detection module

The stationary state is detected by a stop detection

module based on accelerometer information. Our

stop detection algorithm is based on the analysis of

the vehicle acceleration measured by the

accelerometers and its variance. When GPS signals

are available the velocity computed by a GPS

receiver can be also used.

Since this algorithm has to be independent of the

mounting angle of the device, the original

measurements at time kt from three accelerometers,

( )kx ta , ( )ky ta , ( )kz ta , in sensor frame are

transformed to a acceleration vector, ( )ktar

, since

the norm of acceleration vector does not depend on

the angles to which the device is mounted [11].

A typical example of the magnitude of measured

acceleration vector during a test drive is shown in

Fig. 4. Vehicle acceleration in horizontal plane

depends significantly on the movement of the

vehicle including road imperfections,

Figure 5. Mean quadratic deviation calculated in

(10). Vertical axis is in logarithmic scale and time

in minutes. The dashed line is the decision

threshold. Red dots above the decision line are due

to the time lag.

measurement bias, and noise [10]. As it can be seen

from the curve, during a complete stop the variance

of the signal is noticeably smaller since it contains

only the gravitational acceleration, accelerometer

noise, and engine vibrations. The bias drift over

short time is negligible. The sampling frequency of

accelerometer in this example was 100 Hz.

During complete stops the variance of ar

does not

exceed certain threshold which can be found during

short initial learning phase. The mean and variance

of ar

during complete stop, sµ and 2

sσ ,

respectively, are computed and stored.

The real-time implementation of this algorithm is

based on the analysis of accelerometer data inside

time window of predefined length. The time

window length is one of the design parameters in

this algorithm and usually chosen as 0.6–1.0 sec.

Then the mean quadratic deviation of the

acceleration samples from �� inside this time

window is calculated as

( )∑=

−=N

k

skn xN 1

21µσ (10)

where ( )kk taxr

= is the magnitude of accelerations

at time kt , ( ) ( ) ( ) ( )[ ]Tkzkykxk tatatata =r

, and

N is the number of samples inside the time window.

The decision about vehicle being moving or

stationary is made based on computed deviation,

nσ , and variance of ar

, 2

sσ ; when sn p σσ ⋅< ,

we

17 18 19 20 21 22 23800

850

900

950

1000

1050

1100

1150

1200

17 18 19 20 21 22 23

101

102

Figure 6. Tampere road test. Position computed by

DR navigation system during 30 sec GPS outage is

shown by black dots. Map source –

OpenStreetMap.org

assume complete stop. The parameter p was chosen

empirically based on the results of drive tests.

This algorithm can work in all types of vehicles and

has the ability to adapt to different conditions during

short learning phase when GPS is available. The

real-time version of stop detection algorithm

employs the probabilistic approach. It analyses the

accelerometers data within a moving window.

Unlike the algorithm described in [10] where stops

are reliably detected only after 15 sec delay, our

algorithm detects stops almost immediately.

4 EXPERIMENTAL RESULTS

Our portable car navigation system was tested in

road tests in urban environment that included

tunnels, parking garages, urban canyons, and road

interchanges. Typical performance during these road

tests is presented in this section.

The first experiment is driving test in Tampere,

Finland, shown in Fig. 6. The 30 sec GPS outage

was created artificially by unplugging the GPS

antenna from the receiver. The position computed

by our combined GPS/DR navigation system is

shown by green dots. When GPS signals are not

available the navigation system continues to

compute vehicle position, velocity, and heading

using MEMS gyro and accelerometers. Black dots

for the trajectory on the map correspond to the dead-

reckoned position when GPS signals are not

available. Magenta dots correspond to the trajectory

Figure 7. Portland tunnel road test. The tunnel is

about 300 m long. The first GPS fix after the tunnel

was 4 sec after car exit the tunnel.

computed by DGPS. Since DGPS position error is

only about 0.2 m, we consider this position our

reference trajectory. The direction of car motion is

shown by the arrow. This test shows that the

combined GPS/DR solution provides significant

improvement; accurate position, velocity, and

heading information were available even in the

absence of GPS signal. After 30 sec GPS outage the

position error did not exceed 20 m.

Figure 7 displays the system positioning

performance during driving test in Portland, OR that

included a 300 m long tunnel. It should be noted

that there are no GPS signals in the tunnel. Magenta

dots correspond to the standalone GPS receiver

position measurements. Green crosses for the

trajectory on the map correspond to the combined

GPS+MEMS computed position. Black dots

correspond to the dead-reckoned solution when GPS

signals were not available. The first GPS position

fix was received approximately 4 sec after car

passed the tunnel making the total GPS outage about

18 sec. The error of GPS+MEMS computed position

at that time was less than 20 m. The first GPS

measurements after the tunnel have a quite large

position error, about 30 m. This test shows that the

combined GPS+MEMS solution provides

significant improvement; accurate position, velocity,

and heading information were available even in the

absence of GPS signal.

Figure 8 displays the test route in Portland, OR

downtown drive test. This test route included high-

Figure 8. Portland urban canyon test. This test

route goes between tall buildings. In some places

GPS position error caused by multipath is about 35

m.

multipath urban canyon environment in the vicinity

of high-rise buildings. In some places, GPS position

error caused by multipath was about 35 m. This test

shows improvements of the combined GPS+MEMS

system performance in high-multipath environment,

which is explained by the ability of the combined

GPS+MEMS algorithm to filter out GPS position

and velocity outliers.

5 CONCLUSIONS

This paper has shown that low-cost inertial sensors

can significantly improve GPS positioning by

continuing to output position during short GPS

outages with sufficient accuracy for most of car

navigation applications. The integrated

GPS+MEMS system has also demonstrated

improvement of position and velocity accuracy in

high multipath urban canyon environment and the

ability to provide continuous output of the vehicle

heading even when vehicle is not moving. This is

useful if we apply the map-matching algorithm. This

device does not require any installation in the

vehicle. It works in all vehicles and can be easily

transferred between vehicles. Finally, it should be

noted that our design is suitable for portable

navigation devices since the cost, size, and power

consumption of inertial sensors meet the

requirements for mass market consumer electronics.

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