Global Positioning System Reference
In-Depth Information
bandwidth. As the host vehicle performs highly dynamic maneuvers near threshold
tracking conditions, the ultratightly coupled design increases the aided bandwidth
just enough to maintain lock. Even though the Kalman filter of the partitioned
design similarly correctly models the clock g sensitivity (its model is identical to that
of the integrated design), its tracking loop does not adapt in recognition of this error
source. The ultratightly coupled design thus affords another dimension of band-
width adaptivity. More generally, the improvements of the integrated design can be
understood by observing that its bandwidth adapts to everything that is modeled by
the Kalman filter, including INS quality and clock dynamics. The maturity of the
simulations used in [13] for the comparative evaluations was questionable in that
the receiver motion and satellite geometry were limited to a plane; however, more
thorough and detailed evaluations have been reported fairly recently [18] and
confirm the fundamental conclusions of this very early paper.
Given the potential performance improvements reported in [13], it is natural to
ask why it has taken so long (i.e., more than 20 years) for the ultratightly coupled
design to gain wide acceptance (it was at least considered in a succeeding generation
design to [1] by Rockwell-Collins). The reason for its delay in recognition as a wor-
thy design approach may in part be cultural: not many individuals are skilled in
both the art of Kalman filtering and receiver design. A more technical reason for the
lack of acceptance is some of the significant modeling issues for the ultratightly cou-
pled design, two of which can be addressed here. The first technical issue is the mod-
eling of the code loop nonlinearity by the Kalman filter; the second is loss of lock
detection. The code loop model embedded in the Kalman filter is quite important,
especially as the loop thresholds are approached. Ignoring the nonlinear nature of
the detector generally leads to performance degradations. A quasi-linear or describ-
ing function-based [19] approach is preferred, where the representation of the
detector gain or the associated assigned error variance to the code phase measure-
ment depend on the input SNR. As the SNR is lowered, the quasi-linear gain
approach calculates a probability that the detector may be operating outside of its
linear range—denoted p l in the following equation—and weights the gain in this
region (often zero) by the probability in computing a quasi-linear gain:
(
)
K
=−
1
p
K
+
p K
q
l
l
l
n
where K l is the detector gain in the linear range, and K n is the detector gain in the
nonlinear range of the detector. The probabilities are evaluated using the uncer-
tainty, embedded in the filter's covariance matrix, projected along the LOS to the
satellite that is tracked. Thus, as loss-of-lock conditions are approached, the inte-
grated design recognizes the limited utility of each code phase measurement: in the
limit as the effective detector gain become zero, it is using only INS information to
close the code loop.
Finally, loss-of-lock becomes difficult for either the partitioned or integrated
designs as threshold conditions are approached. This is fundamentally because all
parameters that can be used to assess lock (see Section 5.11.2) are unreliable.
Sophisticated approaches based on hypothesis testing and parallel filter operations
can be considered. Such approaches, for the one or more receiver channels close to
threshold, consider the lock state unknown and process the receiver ouputs with
parallel filters—one assuming the channel (or channels) is (are) in lock, the other
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