7B-4-5 
vehicle antenna due to trees, buildings, hills, 
bridges, etc. To solve this problem, DR 
techniques can be used to position the vehicle 
for short periods of time until the GPS signals 
are re-acquired. The DR system designed for 
this purpose, consists of a low-cost wheel 
odometer and a piezoelectric gyro. The 
objective of using an integrated DGPS/DR 
system is to provide almost continuous position 
information of the vehicle. Figure 1 shows the 
block diagram of the integrated system. 
3.1 Dead-Reckoning 
The wheel odometer NAQ-1 is a distance 
sensor. The number of electric pulses from 
the sensor counts the rotations of the 
vehicle wheel. The piezoelectric gyro EVN- 
05 is basically a direction sensor. The 
voltage output from the gyro represents the 
rate of turn (deg/s), which has a nominal 
value 2.5 V when the rate of turn is zero. 
The maximum angular velocity that can be 
measurement by the gyro is ±90 deg/s. 
The odometer and the gyro are used to 
measure the displacement vector of the 
vehicle. The two-dimensional planar position 
can be expressed as 
fc-i 
x t= x a + X 5 ; COS0 « (5) 
i=0 
fc-1 
y t =>’o + S S . sin0 / (6) 
/=0 
where (x k ,y k ) is the vehicle’s 
position at time t k decomposed in a 
horizontal reference system, ( jc 0 , y 0 ) 
is the initial vehicle’s position at time 
t 0 , 5, is the traveled distance of the 
vehicle between time t i and time t i+l , 
and 6 i is the absolute heading 
between time t i and time t M . The 
relative heading co i is defined as the 
difference between two continuous 
absolute headings. If the relative 
headings co i at epochs t i (i-0, 1, ..., 
k) are given , then the vehicle’s 
absolute heading 9 k at epoch t k can 
be written as 
0*=Ì>, (7) 
1=0 
For DR systems the errors will 
accumulate very quickly with time. 
Hence, the positioning accuracy 
decreases with the traveled distance of 
the vehicle. Therefore, a DR navigation 
system requires periodic updating of a 
DGPS system in order to give sufficient