RECURSIVE LINEAR FILTERING OF THE RANDOM DYNAMIC FIELDS UNDER A PRIORI UNCERTAINTY

The task of filtering random dynamic fields is relevant for a number of applications. To solve it, one can use a statistical approach based on the Kalman filter theory. Because of large dimension of the images, this leads to complicated equations and requires large computational costs, which makes it difficult to solve the problem in real time. Instead of statistical, it is suggested to use a deterministic approach based on the recursive least-squares technique. It is assumed that the field model, its covariance characteristics, as well as the model and characteristics of the measurement results are a priori given. To obtain recursive filter equations the loss function is used, which consists of two parts. The first one is the quadratic residual functional of the solution with weight in the form of an inverse covariance measurement matrix. The second one is a quadratic functional of the difference between the current estimation and its extrapolation to the next time point. As a result, an optimal filtering algorithm is obtained in an explicit form, which can be realized in real time with significantly less computational costs compared to the Kalman filter. An equation for the variance of filtering errors is obtained, that allows estimating the accuracy of the proposed filter and its comparison with the accuracy of the Kalman filter. An example of using the proposed methodology is given. 

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