Robust estimation of covariance matrices

Abstract

Data manipulations which increase the robustness and accuracy of estimators of covariance parameters by using the innovations correlation approach are considered. The procedures are especially useful for improving estimates of process-noise covariance parameters for slowly varying systems when measurement noise is large. The innovations correlate covariance estimation technique developed by P.R. Belanger (1974) is extended to the case where process noise is weak in magnitude compared to measurement noise. Belanger's method exploits the linear relationship between the desired noise covariance parameters and the correlations of the innovation sequence of a suboptimal Kalman filter to formulate a least-squares algorithm. The estimates of the process-noise covariance parameters are improved by low-pass prefiltering and downsampling the data before applying the least-squares innovations correlation algorithm. Results for a single-output, linear time-invariant system are stated, and the subsequent analysis treats only this case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>