Filtering algorithm with a piecewise-polynomial description of signals taking account of their continuity and level constraint

A new method for constructing Kalman-type filters is proposed, which, in addition to classical models of stochastic processes generated by a white noise, also uses a more universal piecewise-polynomial description of signals with consideration of their continuity and smoothness, allowing observing constraints on their level. On the one hand, the description makes it possible to avoid difficulties of filter adjustment in the lack of complete information about the signal probabilistic properties. On the other hand, the method proposed is more general as compared to the traditional spline approximation as it allows using information about the level of the nonstochastic component (and/or its derivatives), taking proper account of the structure and parameters of the stochastic components. The solution is obtained in recursive form.