Optimal filtering of random processes with aggregation of observations at different time points

Problem statement. In problems of optimal filtering of random processes, an increase in the accuracy of the estimate is associated with an increase in the volume of observations and (or) the availability of additional information about the estimated parameter. In this article, in order to improve the accuracy of the estimation, it is proposed to provide a time separation (relative delay) of the observation results at the input of the meter. Such separation is possible by using spatial separation of the meters, or by using a multipath delay line at the input of the meter. In both cases, mutually delayed values of the measured parameter will be observed at the input of the multi-channel meter. It is not possible to apply traditional methods of Markov theory to obtain an optimal estimate of the mutually delayed values of the Markovian process, since collectively these mutually delayed values will not have the Markovian property.

Goal. Improving the accuracy of filtering random processes.

Results. To solve this problem, the article suggests using the optimal filtering method for inter-delayed Markovian processes, the essence of which lies in the fact that at each moment of time, not individual values of the Markovian process are evaluated, but its entire trajectory over a limited time interval longer than the maximum delay in the observation channels. As a result of the research, an optimal algorithm for the operation of a multichannel meter has been synthesized. Using a specific example, the analysis of the possibility of its implementation and the quality of its work is carried out.