A robust empirical bayes approach to the adaptive Kalman filter

Abstract

This work addresses a long-standing need to create a mathematically credible and consistent foundation for adaptive Kalman filtering. Since the original breakthrough by Kalman and Bucy in 1960, it has been recognized that some practical applications of their work require supplementary algorithms, not provided by the original derivation. In particular, algorithms are required to "adapt" the filter's gain element when encountering insufficient or incorrect knowledge of the required statistical parameters. The open literature of Kalman filtering contains many presentations of "Adaptive Kalman" algorithms. However, satisfying first-principles approaches for justifying such algorithms appear lacking. Without a consistent, rational foundation, the adaptive Kalman filter has remained an ad hoc development.