Fixed-Lag Smoothing Algorithm under Non-independent Uncertainty

This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2, 2)element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels. key words: filtering, fixed-lag smoothing, covariance information, uncertain observations