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Chapter 5 / Missile State Observer
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5.10.3 Serial Measurement Processing and Linearity
Independent measurements in non-linear systems are best processed serially
with scalar inversion. This avoids a computationally intensive matrix
inversion that is prone to numerical inaccuracies. Serial processing is
equivalent to parallel processing for independent measurements however,
the intermediate state update provides an opportunity to improve the filter
linearisation between measurements that can be a source of filter instability.
Miller [M.10] showed that processing angular measurements before range data,
with interim re-linearisation, improved tracking performance, virtually
eliminating measurement linearisation errors. This improves the EKF
tendency to overestimate its ability to derive cross-range data from range
measurements that can lead to serious performance degradation, Park [P.6] .
5.10.4 Measurement Delays
The time between taking a measurement and its application due to
communication and processing delays must be accounted for in high
bandwidth systems. Using time stamped measurements these delays are
accurately known and easily compensated for, as described in §5.10.2.
5.10.5 Measurement Range Traps
Thresholds can be applied to measurements according to known physical
and dynamic characteristics of the missile or sensor. Missile lateral
acceleration and angular rate measurements exceeding their capability are
ignored and the filter is propagating until a valid measurement is available.
5.10.6 Measurement Consistency Traps
If the difference between successive measurements is inconsistent with their
trend, accepted noise levels, and sensor capabilities, they must be discarded.
Consistency traps are apply to parameters with low rates of change. For
example, checks on target LOS rate derived from ground radar target angles
to ensure that it is consistent with the expected capability of the target.
5.10.7 Divergence Traps and Innovation Thresholds
If the expected state error is consistently less than the true rms state error,
and growing smaller, the filter is divergent. If the expectations are simply
constant and do not match the true rms error the filter is ill-conditioned, a
less serious problem. The simplest test is to compare the measurement
innovations with their expected √variance. This is the Mahalanobis distance
(PIM) of §22.13.16 a chi-squared metric that measures how well the
covariance is tuned to the measurements,
PI
2
M
: =
∆Z
T
⋅
5-28
T −1
( H ⋅ C ⋅ H + R ) ⋅ ∆Z
Equation 5.10-1