Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 484

9.2.4.7 Code Loop Aiding
As mentioned in Section 9.2.1, code loop aiding is the most commonly exercised
option. To gain additional insight into the operation of an aided code loop, let us
return to Figure 9.11 and consider the decomposition of the aided range delay esti-
mate, ρ est , in terms of an INS component and a GPS component:

[ ] [ ]

() ( ) () ( ) ()

Ps = K sKP s ssKP s + + + (9.11)

est c c rcvr c INS

Equation (9.11) is an expression for a classic complementary filter in the frequency
(i.e., Laplace) domain, in that it represents the combination of a lowpass filter oper-
ation on receiver information with a highpass filter operation on INS information.
Thus, as the bandwidth of the receiver is reduced (i.e., K c is reduced, or the loop's
time constant is increased), the aided loop is constructing an estimate of the range
delay based largely on simply integrating the INS velocity from the estimated range
delay when the loop was unaided. Thus, in the limit, as K c approaches zero, the
loop's estimated range delay is completely determined from the INS behavior since
the onset of aiding. This observation should assist in understanding some of the
problems that are encountered when attempting to process the estimated range
delay in a conventional Kalman filter design. These problems are discussed in [11].
Consider the aided code loop, including the Kalman filter operation, depicted in
Figure 9.12, referred to in the discussion that follows as a partitioned design . The
estimated range delay,

ρ est , is used to close the code loop, with its filter represented
as the gain K c as before; it is also used as a code phase measurement input to the
Kalman filter. The Kalman filter generates an estimate of the INS velocity error v est ,

which is used to correct the INS velocity. The “known” satellite velocity v s is then
subtracted from the corrected INS velocity and projected along the LOS (repre-
sented by the unit vector u ) to the satellite tracked by this loop. Based on the comple-
mentary filter model derived for the aided code loop model, the utility of the Kalman
filter correction when aided can be questioned. In fact, the aided configuration can
become unstable as the bandwidth is lowered below the effective bandwidth of the
Kalman filter [11, 12]: This is also driven by the fact that there are two loop filters.

δ

I
Q

δρ

Receiver
correlator

Code loop
detector

K c

Code loop
filter ρ est

v s
− −

v

+

+

+

Code loop
NCO

u T

INS

−

(For each channel)

δ v est

Kalman filter

Figure 9.12 Partitioned tracker/navigator block diagram.