7B-4-8 
multiplications significantly. For instance, the 
matrix product <&(k)P(k / k)Q> T (k) corresponds to 
1024 multiplications where only 112 multiplications 
is required for implementation. 
4. Experimental Results 
To compare the positioning accuracy of the 
stand alone DGPS receiver with the 
smoothing algorithm of Section 2.2, a fixed 
control point was chosen. The position for 
the control point was measured for 40 
minutes and the positioning accuracy was 
analyzed an presented in Table 2. 
Table 2. Positioning accuracy for 
standard DGPS and the code pseudorange 
algorithm based on carrier phase 
measurements. 
Smoothing 
North 
East 
I 
Algorithm 
error ( 1 a) 
error ( 1 a) 
da) 
No 
4.53 m 
3.90 m 
5.97 m 
Yes 
2.15 m 
1.70 m 
2.74 m 
The effect of exploiting the sparse structure 
of the matrices (removing the zero elements 
when implementing the EKF) is illustrated 
on a PC 486 with 50 MHz clock frequency. 
Table 3 shows the computational time of 
the 8-state EKF for the two cases. 
Table 3. Comparison of the 
computational time for a 8-state EKF. 
EKF exploiting 
the sparse 
structure of the 
system matrices 
Computation 
time for each step 
No 
63 ms 
Yes 
31ms 
5. Conclusions 
In urban and tree-covered areas, the 
GPS signal can be blocked. This will 
affect the accuracy of the vehicle 
navigation system. To solve this 
problem, an integrated DGPS/DR 
vehicular navigation system based on 
an 8-state extended Kalman filter is 
proposed. It is shown that the 
computational loads can be 
significantly reduced by exploiting 
the structural properties of the system 
matrices when implementing the 
Kalman filter. This is due to the 
sparse structure of the matrices. 
Moreover, multiplications with zeros 
should be avoided. This can reduce 
the computational time with about 50 
percent.