Back-and-forth nudging moving horizon estimation for discrete-time linear systems

In this paper, we propose a novel moving horizon estimation algorithm for discrete-time linear systems with a limited number of measurements. Motivated by the idea of the back-and-forth nudging algorithm, we design the back-and-forth nudging in time moving-horizon estimation method by deploying two moving horizon estimators that move backward and forward iteratively. Based on a finite number of measurements, the proposed algorithm can be used for moving-horizon state estimation with guaranteed convergence. By using the proposed method, we show that the norm of the state estimation error is upper bounded by a sequence that converges to its steady-state in finite-time (i.e., using a finite number of measurements), provided that suitable parameters are selected. The unbiasedness properties and comparison results with the conventional (forward-in-time) moving horizon estimation are discussed. The effectiveness of the proposed approach is validated through a numerical example.