Global Positioning System Reference
In-Depth Information
The first, the code loop itself, is using a very low gain ( K c ) closure; the second loop
closure is through the Kalman filter. The Kalman filter, expecting to receive mea-
surements corrupted by uncorrelated measurement error, is processing measure-
ments whose error is strongly correlated in time. This is a classical filter-modeling
problem and contributes to the potential for instability.
A number of approaches can be used to stabilize the aided code loop [12]. Two
of the more straightforward include simply turning off the Kalman filter corrections
to the INS while the loop is aided and reducing the effective bandwidth of the
Kalman filter (i.e., reducing its gains) to be less than the lowest bandwidth that the
code loop itself (determined by the lowest value used for K c ) can achieve. The refer-
enced analysis [12], which represents the Kalman filter as a fixed gain Butterworth
filter (to enable conventional stability analysis), motivates the frequency domain
interpretation in Figure 9.13. Stability problems generally arise when the Kalman
filter effective bandwidth exceeds the code loop bandwidth, as illustrated in Figure
9.13(b).
The aided code loop depicted in Figure 9.12 is referred to as a partitioned design
because the tracking loop and navigation filter are considered separate func-
tions—the bandwidth of the tracking loop can be varied as a function of sensed
SNR, but it is independent of the Kalman filter operation. In the next section, the
navigation and tracking functions will be considered a single, integrated function,
which will lead to a receiver aiding formulation that has been referred to as
ultratight integration .
9.2.4.8 Integrated Tracking/Navigation Functions
Figure 9.14 provides a block diagram of the so-called integrated tracker/navigator,
also referred to in the literature as ultratight or deeply integrated . The very first rec-
ognition of the benefits of this level of integration occurred in [13]. In that paper,
the essential observation is made that the optimal estimators for navigation and sig-
nal tracking differ only in their coordinates (i.e., that a best estimator for position,
velocity, and clock phase and frequency error should be equivalent to a best estima-
Kalman
filter
Kalman filter
gain
gain
Code loop
Code loop
BB
c
<
BB
K
<
K
c
Frequency
Frequency
(a)
(b)
Figure 9.13
Aided code loop frequency domain perspective: (a) “safe” and (b) “dangerous” con-
ditions.
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