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Recursive fixed-point smoothing algorithm from covariances based on uncertain observations with correlation in the uncertainty. (English) Zbl 1157.65314
Summary: We consider the least-squares linear estimation problem of a discrete-time signal from noisy observations in which the signal can be randomly missing. The uncertainty about the signal being present or missing at the observations is characterized by a set of Bernoulli variables which are correlated when the difference between times is equal to a certain value $$m$$. The marginal distribution of each one of these variables, specified by the probability that the signal exists at each observation, as well as their correlation function, are known. A linear recursive filtering and fixed-point smoothing algorithm is obtained using an innovation approach without requiring the state-space model generating the signal, but just the covariance functions of the processes involved in the observation equation.

##### MSC:
 65C60 Computational problems in statistics (MSC2010) 62M20 Inference from stochastic processes and prediction 62G05 Nonparametric estimation
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##### References:
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