Adaptive algorithms for state estimation are currently of tremendous
interest. Such estimation techniques have particular military usefulness
in automatic gunfire control systems. The conventional Kalman filter,
developed by Kalman and Bucy, optimally solves the state estimation
problem concerning linear systems with Gaussian disturbance and error
processes. The maneuvering target tracking problem generally involves
nonlinear system properties as well as non-Gaussian disturbance processes.
The study presented here explores several solutions. to this problem.
An adaptive state estimator centered about the familiar Kalman
filter has been developed for applications in three-dimensional maneuvering
target tracking. Target maneuvers are modeled in a general
manner by a semi-Markov process. The semi-Markov modeling is based on
very intuitively appealing assumptions. Specifically, target maneuvers
are randomly selected from a range (possibly infinite) of maneuver commands.
The selected command is sustained for a random holding time
before another command is selected. Dynamics of the selection and holding
process may be stationary or time varying. By incorporating the
semi-Markov modeling into a Baysian estimation scheme, an adaptive state
estimator can be designed to identify the particular maneuver command
influencing the target. The algorithm has the distinct advantages of
requiring only one Kalman filter and non-growing computer storage requirements.
Several techniques of implementing the adaptive algorithm have been
developed. The merits of rectangular and spherical modeling have been
explored. Most importantly, the planar discrete level semi-Markov algorithm,
originally developed for sonar applications, has been extended
to a continuum of levels, as well as extended to three-dimensional
tracking.
The developed algorithms have been fully evaluated by computer
simulations. Emphasis has been placed on computational burden as well as
overall tracking performance. Results are presented that show.that the
developed estimators largely eliminate severe tracking errors that occur
when more simplistic target models are incorporated.
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