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Chapter 5 / Missile State Observer
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However, care is needed when quoting absolute (PIE) values as a filter can
be well conditioned even if the condition number is large. For tracking
λMAX tends to be dominated by the position error normal to the LOS, and
λMIN by range-rate errors. Daum shows that the conditioning number is a
sensitive indicator that increases markedly before [C] diagonal thresholds
and process noise can take effect.
Two avenues of research linked to observability are of interest. Ohtsuka [O.3]
shows that general observability is improved by maximising the information
in each measurement update,
PI
OBS
5-31
T T ( Φ ⋅ H ⋅ ⋅ Φ )
: = det H
Equation 5.10-12
PN is probably the most enduring of the missile guidance laws however, it
actively minimises observability by establishing an early constant velocity
collision course. Song [S.6] shows that adding terms to the guidance law that
cause the LOS to oscillate improves state observation and hence
performance. Although their conclusions are self-evident, mechanisation of
algorithms to enhance observability is interesting, particularly when states
are added to the observer to actively estimate sensor errors.
5.11 Missile State Observer Simulator
The target and missile state observers are placed in context within the
overall simulation structure in Figure 6-1, where they are referred to as the
“embedded simulators”. The numbers associated with particular functions
shown in this figure represent the order in which they are performed.
IMM_CONTROL and FF_CONTROL control the target and missile
observer functions respectively, as shown in Figure 5-7. These controllers
are activated by DX_CONTROL at 10 Hz and 400 Hz when the state
integrator loop controller INDEXI is 1 - see Figure 8-7. The target state
observer is initialised by module I_MM as described in §4.4, with the
missile observer inhibited. Once initialisation is complete the target track
and covariance information is up-linked to the missile where module I_FF
initialises the missile state observer and loads IMM target information.
Individual IMM filters are selected by setting individual bits of control
IMM_TP as shown in Figure 5-7. When a single filter is selected, IMM
combination and re-initialisation is suspended and the filter output is
delivered to the missile observer via the up-link module. Each filter
propagates its own states and covariances using either a conventional EKF,
Iterated EKF, or second order filter formulation.
U_GB_RADAR_T is activated if new radar measurements are ready for
processing, and each measurement is processed serially with intermediate
re-linearisation. The IMM pre- and post-measurement combined states and