Fixed-Point, Fixed-Interval and Fixed-Lag Smoothing Algorithms from Uncertain Observations Based on Covariances

Seiichi NAKAMORI
Raquel CABALLERO-AGUILA
Aurora HERMOSO-CARAZO
Josefa LINARES-PEREZ

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A    No.12    pp.3350-3359
Publication Date: 2004/12/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
filtering,  fixed-point smoothing,  fixed-interval smoothing,  fixed-lag smoothing,  covariance information,  uncertain observations,  

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Summary: 
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.