Adaptive State Variable Estimation Using Robust Smoothing

Abstract

The development of a conventional Kalman filter is based on full knowledge of system parameters, noise statistics, and deterministic forcing functions. This work addresses the problem of known system parameters and unknown noise statistics and deterministic forcing functions. A robust estimation technique for weighting certain elements of the Kalman gain and covariance matrices is given. These weights are functions of sample means and variances of the residual (innovations) sequence. Robust statistical procedures are employed to smooth the estimates given by the adaptive Kalman filter. An application to a simple linear system is given, however, primary application would be to the estimation of position, velocity, and acceleration for a maneuvering body in three dimensional space based on observed data collected by a remote sensor tracking the maneuvering body.