Filtering and prediction for discrete systems with unknown input using nonparametric algorithms

Abstract

The paper addressed the filtering and prediction problems with using nonparametric algorithms for discrete stochastic systems with unknown input. The designed algorithms are based on combining the Kalman filter and nonparametric estimator. The optimal properties of the explored algorithms are proved. Examples are given to illustrate the usefulness of the proposed approach.

State Estimation for Linear Discrete-Time Systems with Unknown Input Using Nonparametric Technique

“…In this paper, fo r d iscrete linear stochastic systems with the known control input, an unknown input and parameters the algorith m with use of the Kalman filtering and nonparametric estimators is proposed. This aproach generalizes the result of the paper [7]. The examp les are given to illustrate the properties of the proposed algorithms in co mparison with the algorith ms used the LSM -estimator.…”

“…However, formu las (3) Applying the mathematical induction, as in [7], we obtain the estimator of the unknown input…”