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**Linear unbiased state estimation under randomly varying bounded sensor delay.**
*(English)*
Zbl 0944.93029

The paper is about estimating the state of a plant from noise contaminated measurements which, in addition, are subject to a random delay. The authors show that in suitable dimensions the situation can be modelled as a discrete-time time-varying linear stochastic system with additive white noise (plant model) together with a read-out map,
\[
y(k)= C(k)[x(k), x(k-1)]^*+ D(k)[W(k), W(k- 1)]^*,
\]
which is perturbed by an independent white noise \(\{W(k)\}\) and for which, in addition, the matrices \(C(k)\) and \(D(k)\) are random (independent of the white noise processes) reflecting the random delay.

In this form the problem is about designing linear estimators for discrete-time linear system with additive and parametric noise. The authors derive the matrices \(K(k)\) and \(G(k)\) which determine the estimator \[ \widehat x(k+1)= K(k)\widehat x(k)+ G(k)y(k+ 1), \] to satisfy the requirements of unbiasedness and minimum variance for the estimation error \(x(k)-\widehat x(k)\).

In this form the problem is about designing linear estimators for discrete-time linear system with additive and parametric noise. The authors derive the matrices \(K(k)\) and \(G(k)\) which determine the estimator \[ \widehat x(k+1)= K(k)\widehat x(k)+ G(k)y(k+ 1), \] to satisfy the requirements of unbiasedness and minimum variance for the estimation error \(x(k)-\widehat x(k)\).

Reviewer: V.Wihstutz (Charlotte)

### MSC:

93E10 | Estimation and detection in stochastic control theory |

93C55 | Discrete-time control/observation systems |

93B07 | Observability |

93E11 | Filtering in stochastic control theory |

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\textit{E. Yaz} and \textit{A. Ray}, Appl. Math. Lett. 11, No. 4, 27--32 (1998; Zbl 0944.93029)

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### References:

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