## 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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### References:

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