A Practical Filter for Systems With Unknown Parameters

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Abstract
This paper deals with the problem of a practical filter for discrete-time, dynamic systems with unknown parameters whose variation cannot be estimated in advance. The modeling errors caused by unknown parameters clearly degrade the filter performance and sometimes lead to divergence of estimation errors. Divergence is said to occur when the calculated covariance of estimation errors becomes very small comparing with the actual covariance. A practical filter that modifies the calculated covariance is developed as a technique for controlling the divergence. This is done by testing whether or not the actual residual at each stage is likely to have come from the calculated distribution, and the calculated covariance is modified when the test is rejected. The numerical results of digital simulation indicate that divergence of estimation errors is observed when the a priori information for dynamic systems is in error and that the divergence is prevented by the proposed filter.

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