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**Quadratic estimation of multivariate signals from randomly delayed measurements.**
*(English)*
Zbl 1084.94001

Summary: This paper discusses the least-squares quadratic estimation problem of a multivariate discrete signal, from noisy measurements which can be delayed by one sampling period. The delay in the observations is assumed to be random and the probability of a delay in each measurement is known. The quadratic recursive estimation algorithm, which uses only the delay probabilities and the moments (up to fourth-order) of the signal and noise-measurement, is derived from a linear estimation algorithm for a suitably defined augmented system.

### MSC:

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

93E10 | Estimation and detection in stochastic control theory |

93E24 | Least squares and related methods for stochastic control systems |

37M10 | Time series analysis of dynamical systems |

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\textit{S. Nakamori} et al., Multidimensional Syst. Signal Process. 16, No. 4, 417--438 (2005; Zbl 1084.94001)

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### References:

[9] | P. Wu, E.E. Yaz, and K.J. Olejniczak, ”Harmonic Estimation with Random Sensor Delay,” Proceedings of the 36th International Conference on Decision & Control, 1997, pp. 1524–1525. |

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