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

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).