Retrospective Cost Adaptive Unknown Input Observers with Application to State and Driver Estimation in the Ionosphere-Thermosphere.

Abstract

The classical Kalman filter is the optimal state estimator for linear systems under white process and sensor noise with zero mean and finite second moments. In addition, the Kalman filter accommodates the presence of a known, deterministic input. In practice, however, the deterministic input may not be known exactly, and this error can be viewed as a component of the process noise. However, this approach may be too conservative and can lead to bias when the unknown input has a nonzero ``mean'' value. Consequently, a more direct approach is to extend the estimator to include an estimate of the unknown input.

In this work, we consider an unknown input observer based on retrospective cost optimization, where the unknown input is estimated by first minimizing a retrospective cost function, and then updating an adaptive feedback system using recursive least squares. The retrospective cost method is a minimal modeling approach that is applicable to both minimum- and nonminimum-phase systems.

Since the retrospective cost observer relies on recursive least squares to update an adaptive feedback system, a novel sliding window, variable regularization recursive least squares algorithm is developed and investigated. In contrast to classical recursive least squares algorithms, the sliding window recursive least squares algorithm does not lose its ability to adapt, and does not become unstable when the data lose persistency.