Discrete linear recursive smoothing for systems with uncertain observations

The least-squares smoothing estimate for discrete linear systems with uncertain observations is investigated. The observations may contain noise alone, and the uncertainty in the observations is governed by a binary switching sequence
\gammak
, where
\gammak
may be regarded as a mixture process and is specified by a conditional probability distribution. Examples of such systems are found in multichannel data links with random interruptions, and such mixture sequences can also serve as models for a communication channel with multiplicative noise.