Accurate optimal filtering formula in a nonstationary piecewise-linear parameter estimation problem

A parameter is estimated which is piecewise-Iinear in tne nonstationary equation of the process observed in discrete time with Gaussian uncorrelated measurement errors. Closed recurrent equations are found for sufficient statistics as are formulae for a posteriori characteristics of the parameter. The limit form of these characteristics and filtering equations are investigated with infinitely large a priori variances of the components of the vector parameter.