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Fixed-Point, Fixed-Interval and Fixed-Lag Smoothing Algorithms from Uncertain Observations Based on Covariances
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2004/12/01
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
filtering, fixed-point smoothing, fixed-interval smoothing, fixed-lag smoothing, covariance information, uncertain observations,
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This paper treats the least-squares linear filtering and smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables. Using an innovation approach we obtain the filtering algorithm and a general expression for the smoother which leads to fixed-point, fixed-interval and fixed-lag smoothing recursive algorithms. The proposed algorithms do not require the knowledge of the state-space model generating the signal, but only the covariance information of the signal and the observation noise, as well as the probability that the signal exists in the observed values.