RLS Wiener Filter and Fixed-Point Smoother with Randomly Delayed or Uncertain Observations in Linear Discrete-Time Stochastic Systems
Abstract
Seiichi Nakamori
This paper designs the recursive least-squares (RLS) Wiener fixed-point smoother and filter from randomly delayed observed values by multiple sampling times or uncertain observations in linear discrete-time stochastic systems. The observed value is generated in terms of the delayed observed values or uncertain observed values. In the case of the observed value with delay or without delay, their probabilities are assigned. Here, each observation includes signal plus white observation noise. Related to the uncertain observed value with delay or without delay, the probability that the observation consists of only observation noise is allocated, according to the time delayed or not delayed. It is assumed that the delay and uncertain measurements are characterized by the Bernoulli random variables. The RLS Wiener estimators use the following information. (1) The system matrix. (2) The observation matrix. (3) The variance of the state vector. (4) The probabilities concerned with the delayed observation and the uncertain observation. (5) The variance of white observation noise.
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