SUMMARY
The purpose of this paper is to design the recursive least-squares (RLS) Wiener fixed-point smoother and filter in linear discrete-time descriptor systems. The signal process is observed with additional observation noise. The observed value is randomly delayed by multiple sampling intervals or has the possibility of uncertainty that the observed value does not include the signal and contains the observation noise only. It is assumed that the probability of the observation delay and the probability that the observation does not contain the signal are known. The delayed or uncertain measurements are characterized by the Bernoulli random variables. The characteristic of this paper is that the RLS Wiener estimators are proposed from the randomly delayed, by multiple sampling intervals, or uncertain observations particularly for the descriptor systems in linear discrete-time stochastic systems.