Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 477

Table 9.2 Data Received from a GPS Measurement

Parameter Value

Time 250,812.171875 seconds

Satellite position (ECEF)
x
y
z

− 11,095,241m

− 3,414,814m

23,488,864m

Satellite velocity
& x

&

91.63 m/s

y
&

− 294.00 m/s

3.70 m/s

z

Pseudorange measurement 23,049,952m

Pseudorange rate measurement 16.952 m/s

Pseudorange deviation 7m

Pseudorange rate deviation 0.05 m/s

time of the GPS measurement. In our example, the history buffer contains the value
(1,527,397; 4,486,699; 4,253,850) for the position before and after the GPS mea-

surement time because the vehicle was parked during the initialization. Thus, the
interpolated value will be (1,527,397;

−

4,486,699; 4,253,850). Using (9.5), the
measurement matrix is formulated as shown here:

−

~

r =−=− x x 11095 241 , , − 1527 397 , , =− 12 622 638 , ,

x s ν

ui

~

( )

r = y −=− y 3 414 814 , , −− 4 486 699 , , = 1071885 , ,

y s ν ui

~

r =−= z z 23 488 864 , , − 4 253 850 , , = 19 235 014 , ,

z s ν

ui

~ ~~~ 2 2 2

r = r + r + r = 2 3 031841 , ,

x y z

~
~

r
r

x

010

()

H t =

~
~

1

r
r

0

x

0 1

12 622 63 8

23 031841

, ,

− 0 1 0

, ,

=

12 622 638
23 031841

, ,

0 − 01

, ,

− 0548 . 0 1 0

=

0 − 0548 . 0 1

Extrapolate the Error Covariance Matrix and Add in the Process Noise
It can be shown that with a

∆ t = 1 second and using the 1-step state transition matrix

t − , the first extrapolated covariance P () can be calculated as follows: