Diffuse Initialization of Kalman Filter

The behavior of Kalman filter is studied at interpretation of unknown initial conditions as the random variables having a covariance matrix proportional to large positive parameter. The developed approach allows one to express characteristics of the filter in an analytic form, to explain a phenomenon of divergence and propose a limiting estimation algorithm which is independent of large initial parameter leading to divergence. As the application there were considered two problems: filtering with a sliding window and a parameter estimation of separable regression. The received results are illustrated by example of training a radial basic neural network.