Optimal State Estimation and its Application to Inertial Navigation System Control

Abstract

The behaviour of most functions in practical situations can always — at least approximately — be described by a finite-dimensional system of differential equations. The theory of optimal state estimation deals with the minimum error-variance reconstruction of the functions from a limited information in a noisy environment. The solution approach, algorithm and stability properties for the linear Gaussian estimation problem are reviewed. A general and typical way for the design of a suboptimal estimation algorithm with special regard to system properties and realization requirements is shown for the technical problem of the error estimation of an aided inertial navigation system. According to the closedloop system requirement of high accuracy in a noisy environment the considerations about the estimator design are extended to the design of simple, (sub-) optimal controllers. A comparison to the optimal estimation accuracy shows the efficiency of proposed output feedback controller design procedure in this technical example.