A Kalman-filtering derivation of simultaneous input and state estimation

Abstract

Simultaneous input and state estimation algorithms are studied as particular limits of Kalman filtering problems. This admits interpretation of the algorithm properties and critical analysis of their claims to being partly model-free and to providing unbiased estimates. A disturbance model, white noise of unbounded variance, is provided and the bias feature is shown to be a geometric projection property rather than probabilistic in nature. As a consequence of this analysis, the algorithm is connected, in the stationary case, to Algebraic Riccati equation computations for the gains, estimate covariances and filter frequency response.