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

TL;DR

This paper introduces an adaptive, variance-inflated Kalman filter variant that reduces bias in extreme state estimation, improves accuracy, and decreases computational complexity for signal processing applications.

Contribution

It proposes a new adaptive, variance-inflated Kalman filter formulation that approximates the original bias-penalized method while reducing computation and enhancing extreme state estimation.

Findings

Reduces root mean square error at extremes by 20-30%

Approximates original bias-penalized filter closely

Decreases computation time to 1.5-3.5 times KF

Abstract

In many signal processing applications of Kalman filter (KF) and its variants and extensions, accurate estimation of extreme states is often of great importance. When the observations used are uncertain, however, KF suffers from conditional bias (CB) which results in consistent under- and overestimation of extremes in the right and left tails, respectively. Recently, CB-penalized KF, or CBPKF, has been developed to address CB. In this paper, we present an alternative formulation based on variance-inflated KF to reduce computation and algorithmic complexity, and describe adaptive implementation to improve unconditional performance. For theoretical basis and context, we also provide a complete self-contained description of CB-penalized Fisher-like estimation and CBPKF. The results from 1-dimensional synthetic experiments for a linear system with varying degrees of nonstationarity show that adaptive CBPKF reduces root mean square error at the extreme tail ends by 20 to 30% over KF while performing comparably to KF in the unconditional sense. The alternative formulation is found to approximate the original formulation very closely while reducing computing time to 1.5 to 3.5 times of that for KF depending on the dimensionality of the problem. Adaptive CBPKF hence offers a significant addition to the dynamic filtering methods for general application in signal processing when accurate estimation of extremes is of importance.