Design of RLS Wiener Smoother and Filter from Randomly Delayed Observations in Linear Discrete-Time Stochastic Systems

This paper presents the new algorithm of the recursive least-squares (RLS) Wiener fixed-point smoother and filter based on the randomly delayed observed values by one sampling time in linear discretetime wide-sense stationary stochastic systems. The observed value ) (k y consists of the observed value ) 1 (  k y with the probability ) (k p and of ) (k y with the probability ). ( 1 k p  It is assumed that the delayed measurements are characterized by Bernoulli random variables. The observation ) (k y is given as the sum of the signal ) ( ) ( k Hx k z  and the white observation noise ) (k v . The RLS Wiener estimators use the following information: (a) the system matrix for the state vector ) (k x ; (b) the observation matrix ; H (c) the variance of the state vector ); (k x (d) the delayed probability ); (k p (e) the variance of white observation noise ); (k v (f) the input noise variance of the state equation for the augmented vector ) (k V related with the observation noise