7B-4-6 
accuracy. In fact, an integrated DGPS/DR 
system is an accurate and reliable positioning 
system which can be used for vehicle 
tracking and navigation purposes, see Mar and 
Leu (1996). 
3.2 Resulting System Model 
For a vehicle moving at low speed, the 
velocities can be considered as slowly- 
varying or constant and therefore modeled by 
lst-order Markov random processes.. 
Moreover, the dynamic model of the moving 
vehicle is given by 
p = v 
j. 
h 
v = -4-v + ti 
(8) 
where p is vehicle’s position, v is velocity of 
the vehicle and 7] is a zero-mean Gaussian 
white noise process. Let the integrated 
DGPS/DR system be described by the 
following state-space model: 
vehicle’s position, (v x , v y ) is 
vehicle’s velocity in the horizontal 
plane, 8 tu is the GPS receiver clock 
offset, 8 lru is the GPS receiver clock 
offset drift, £ is the gyro drift rate 
error and B is the odometer scale error. 
The state matrix A(t) is a sparse matrix which 
can be written: 
A = 
A, 
0 
0 
0 0 
a 2 0 
0 A 3 
0 0 1 0 
0 0 0 1 
0 o -p v 0 
0 0 0 -p v 
^2 
0 1 
P GPS 
0 
1 
x(t) - A • x{t) + w(t) (9) 
where 
x(t) = [x,y,v x ,v y ,8 m ,8 n ,e,B] T 
(10) 
and w(t) is assumed to be white measurment 
noise. The components (x,y) denotes the 
where fi v and fi GPS is time 
correlation coefficients. The 
measurement equation is written 
p l m = R l +8 tu +V l (11)