Covariance Analysis of the Receding Horizon Optimal FIR Filter

In this paper, we study properties of the receding horizon optimal FIR (RHOFIR) filter. The used approach based on analysis its error covariance matrix (ECM). Our contributions are as follows. First, the monotonicity and convergence of the ECM with increasing the horizon size of the sliding window (SW) are established. One important consequence of obtained results is that the ECM trace of the RHOFIR filter does not reach its lower bound (a steady state) on compact sets. This allows formulating a rule for selecting a horizon size of the SW determining a moment when the ECM trace enters a neighborhood of the steady state. Second, an upper bound is obtained for the decomposition of the ECM into two terms in which one of them does not depend on the noise of the dynamics. This makes it is possible to specify an estimate for the horizon size of the SW using information only about the noise intensity of the measurements. Third, an error sensitivity analysis to the dynamics and measurements noises of the ECM is carried out.