Adaptive State Variable Estimation Using Robust Smoothing

摘要

The development of a conventional Kalman filter is based on a full knowledge of system a prior information. A problem of concern is that associated with determining the estimates of the state variables of a system from observation data when a full knowledge of some a prior system information is unknown. The information includes a knowledge of noise statistics, system forcing functions, and descriptions of system dynamics. This paper addresses only one of the important aspects of the above problem: state variable estimation in the absence of knowledge about deterministic system forcing functions. A robust estimation concept for weighting certain elements of the Kalman gain and covariance matrices is presented. Robust statistical procedures are used to smooth estimates of the state variables once the estimates are determined by an adaptive Kalman filter. The weights for the elements of the Kalman gain and covariance matrices are functions of the sample means and sample variances of the innovations sequence. A primary application of the techniques presented in this paper is that of determining the estimates of position, velocity, and acceleration of a maneuvering body in three-dimensional space from observed data collected by a remote sensor tracking the maneuvering body.