Robust Recursive Least-Squares Predictor with Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties

This paper presents, in Theorem 1, the robust recursive least-squares (RLS) prediction and filtering algorithm for the signal and the nominal system state (SS). The algorithm uses cross-covariance (CC) information between the nominal and degraded SS, as well as auto-covariance (AC) information for the degraded SS, both expressed in semi-degenerate kernel forms. The algorithm also utilizes the observation matrices for the system and the degraded system, as well as the variance of the white Gaussian observation noise (WGON). A recursive algorithm for the prediction error variance function of the robust RLS predictor in Theorem 1 is presented. Based on the robust RLS prediction and filtering algorithm in Theorem 1, Theorem 2 presents the robust RLS Wiener prediction and filtering algorithm. This algorithm utilizes the corresponding system and observation matrices in both nominal and degraded systems, the cross-variance (CV) function between the nominal SS and the degraded SS, the auto-variance (AV) function of the degraded SS, and the variance of the WGON. A numerical simulation example illustrates the efficacy of the robust RLS prediction and filtering algorithm proposed in Theorem 1. The proposed robust predictor and filter demonstrate improved estimation accuracy compared to the existing RLS predictor and filter, which use covariance information.