FIR system identification with set-valued and precise observations from multiple sensors

Abstract

This paper considers the system identification problem for FIR (finite impulse response) systems with set-valued and precise observations received from multiple sensors. A fusion estimation algorithm based on some suitable identification algorithms for different types of observations is proposed. In particular, least square method is chosen for FIR systems with precise observations, while empirical measure method and EM algorithm are chosen for FIR systems with set-valued observations in the cases of periodic and general system inputs, respectively. Then, the quasi-convex combination estimator (QCCE) fusing the two different estimators by a linear combination with appropriate weights is constructed. Furthermore, the convergence properties are theoretically analyzed in terms of strong consistency and asymptotic efficiency. The fused estimator QCCE is proved to achieve the Cramer-Rao (CR) lower bound asymptotically under periodic inputs. Extensive numerical simulations validate the superiority of the fusion estimation algorithm under both periodic and general inputs.