:SMART

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This paper is concerned with a recursive state estimation of the system which includes distributed and/or multiple pure delays. The overall system equation of this problem is a multi-dimensional linear difference equation of high-order. First the state estimation problem for this distributed-delay model is formulated. Starting from a postulated linear estimator, a recursive suboptimal filter equation is derived. It is shown that by the filter developed in this paper the delay terms can be easily handled without reducing the multi-dimensional high-order system equation to a conventional larger dimensional first-order system equation. In the case that there is no delay terms in the overall system, the filter algorithm developed in this paper is consistent with the Kalman filter. A numerical example is included.
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