Fixed-interval Smoother with Non-independent Uncertainty using Covariance Information

S. Nakamori (Japan), R. Caballero, A. Hermoso, J. Linares, and M.I. Sánchez (Spain)


Estimation. Statistical modelling. Covariance Information.Uncertain Observations. Conditional Probability


This paper treats the least mean-squared error linear filtering and fixed-interval smoothing problems of a discrete-time signal from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli random variables, for the case of white observation noise. It is assumed that the autocovariance function of the signal is expressed in a semi-degenerate kernel form. The estimators do not use the state-space model but only covariance information about the signal and the observation noise, the probability that signal exists in observed values and the (2, 2)-element of the conditional probability matrices of the sequence which describes the uncertainty in the observations. The algorithms are applied for estimating signals which can be transmitted through one or two channels.

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