Receding Horizon Least Squares Estimator with Application to Estimation of Process and Measurement Noise Covariances

This paper presents a noise covariance estimation method for dynamical models with rectangular noise gain matrices. A novel receding horizon least squares criterion to achieve high estimation accuracy and stability under environmental uncertainties and experimental errors is proposed. The solution to the optimization problem for the proposed criterion gives equations for a novel covariance estimator. The estimator uses a set of recent information with appropriately chosen horizon conditions. Of special interest is a constant rectangular noise gain matrices for which the key theoretical results are obtained. They include derivation of a recursive form for the receding horizon covariance estimator and iteration procedure for selection of the best horizon length. Efficiency of the covariance estimator is demonstrated through its implementation and performance on dynamical systems with an arbitrary number of process and measurement noises.