## 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 $$x(k)-\widehat x(k)$$.

### 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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### References:

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