Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 480

The current clock bias ( t u ) can be calculated by using the initial clock bias of 0
and adding the clock drift for 1 second. Assuming an equivalent drift rate, ct u

&

,of10

& ∆

m/s, the clock bias at this first iteration is ct + ct t = 010 10. Thus, the range + =

u u

observation is

~

()

OBS r =− r r

m

~

=− ρ

23 031841

r + ct

cor u

= , , − 23 049 952 , , + 10

=− 18 101 ,

Next, we compute the observed range rate, which is the LOS component of the
satellite's range rate minus the user's range rate. To determine the LOS component,
a LOS vector is formulated as follows:

xx
r

−

− 11095 241 1527 397

23 031841

, , − , ,

sv

LOS =

ui

= =− 0 . 548

~

x

, ,

( )

− 3 414 814 4 486 699

23 031841

, , − − , ,

yy
r

−

sv

LOS =

ui

= = − 00465 .

~

y

, ,

z − z

23 488 864 4 253 850
23 0318

, , − , ,

LOS =

sv ui

= = 0835 .

~

z

r , , 41

The estimated range rate, ~

r , is

~

&

( ) ( ) ( )

r = LOS x & − x & + LOS y & − & y + LOS z & − & z

x sv y sv z sv

ui ui ui

( ) ( ) ( )

=− 05 . 48 9163 . −+ 00 . 00465 . − 29401 . −− 00 . 0835 370 . . − 0 0 .

=− 6081 . ms

The observed error of range rate is

~

&

()

& &

OBS r =− r r

m

~

&

( )

&

&

=− r ρ

608

− ct

cor u

( )

=− .

.

− − 552 − 10

= 5012

and the observation vector is thus

− 18 101

5012

,

()

y t 1 =

.

The predicted observation, Hx () t $ () t

− , is calculated to be zero since the current 1

estimate of the error state is zero.

00
00

.
.

() ()

$

Hx t t

−

=

1 1