Design of RLS Wiener estimators from randomly delayed observations in linear discrete-time stochastic systems

Abstract

This paper presents the design of a new recursive least-squares (RLS) Wiener filter and fixed-point smoother based on randomly delayed observed values by one sampling time in linear discrete-time wide-sense stationary stochastic systems. The mixed observed value y( k) consists of the past observed value y ¯ ( k - 1 ) by one sampling time with the probability p( k) and of the current observed value y ¯ ( k ) at time k with the probability 1 − p( k). It is assumed that the delayed measurements are characterized by Bernoulli random variables. The observation y ¯ ( k ) is given as the sum of the signal z( k) and the white observation noise v( k). The RLS Wiener estimators explicitly require the following information: (a) the system matrix for the state vector; (b) the observation matrix; (c) the variance of the state vector; (d) the delayed probability p( k); (e) the variance of white observation noise v( k).