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Least-squares linear estimation of signals from observations with Markovian delays. (English) Zbl 1231.65018

Assuming no signal equation is available, and that the delay is modeled by a homogeneous discrete-time Markov chain to capture the dependence between delays, the authors study the least-squares linear estimation problem of a signal based on randomly delay measurements. The signal estimation is addressed assuming that the covariance functions of the process are known and the covariance function of the signals expressed in a semi-degenerated kernel form. The proposed recursive filtering and fixed-point smoothing algorithms are obtained using an innovation approach. A numerical simulation example is included.

MSC:

65C60 Computational problems in statistics (MSC2010)
65C40 Numerical analysis or methods applied to Markov chains
60J22 Computational methods in Markov chains
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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