Study of Mean Square Errors of Receding Horizon Unbiased FIR Filters

This work considers the statistical properties of the receding horizon unbiased filter with finite impulse response. Our approach is based on analysis of proposed new representations for the filter mean square error (MSE) during sliding windows. We focus on developing algorithms for selecting the optimal length of the sliding window in sense of minimum of the MSE trace. The main idea is to construct asymptotic approximation of the MSE trace for large finite values of the sliding window size. This allows to evaluate the impact of different parameters on the estimation error and find the optimal length of the sliding window. If only ranges for noises matrices are specified, we propose an adaptive version of its evaluation in the learning cycle.