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In many signal processing applications of Kalman filter (KF) and its variantsand extensions, accurate estimation of extreme states is often of greatimportance. When the observations used are uncertain, however, KF suffers fromconditional bias (CB) which results in consistent under- and overestimation ofextremes in the right and left tails, respectively. Recently, CB-penalized KF,or CBPKF, has been developed to address CB. In this paper, we present analternative formulation based on variance-inflated KF to reduce computation andalgorithmic complexity, and describe adaptive implementation to improveunconditional performance. For theoretical basis and context, we also provide acomplete self-contained description of CB-penalized Fisher-like estimation andCBPKF. The results from 1-dimensional synthetic experiments for a linear systemwith varying degrees of nonstationarity show that adaptive CBPKF reduces rootmean square error at the extreme tail ends by 20 to 30% over KF whileperforming comparably to KF in the unconditional sense. The alternativeformulation is found to approximate the original formulation very closely whilereducing computing time to 1.5 to 3.5 times of that for KF depending on thedimensionality of the problem. Adaptive CBPKF hence offers a significantaddition to the dynamic filtering methods for general application in signalprocessing when accurate estimation of extremes is of importance.

Adaptive Conditional Bias-Penalized Kalman Filter for Improved Estimation of Extremes and its Approximation for Reduced Computation