A decision-directed rapid estimation of states for systems subject to unknown input sequences

Abstract

Sufficient conditions for convergence of standard Kalman filter estimating the states of a system subject to unknown inputs have been postulated and proved; and the limit of signal to noise ratio under which the proposed scheme will not be advantageous, have been derived. The scheme has been applied to the development of an obstacle detection algorithm for the proposed Mars rover, and a simultaneous Bayesian estimate of states and inputs is derived to point direction for future improvement of the presently suboptimal input estimation.

This Thesis describes a decision directed adaptive discrete filter for rapid estimation of states for systems subject to unknown input sequences, from noisy observations. Divergence of Kalman filter is a foreseen possibility when the states of a partially or incorrectly known system are being estimated. Therefore, possible divergence is prevented by modeling the uncertainties in the system as a finite sequence of unknown inputs and incorporating Bayes decision rule to detect the inputs. The scheme is applicable to arbitrary inputs of known form. In case of inputs with known evolution, a state augmented approach is presented to make the estimation near-optimal. However, due to the bank of four, three-stage filtered estimates being calculated simultaneously, the scheme is applicable subject to the availability of sufficient computation capabilities