The use of piecewise-continuous dynamic systems in filtering problems

The paper is concerned with filtering and obtaining the derivatives of a signal observed with noises with incomplete a priori data on their statistical characteristics. A sufficiently simple, in terms of hardware, nonlinear filter is proposed that is described by differential equations with piecewise-continuous right-hand parts. The filter is shown to feature the property of adapting to noise parameters changes in an unpredictable way. The operation of the filter is analyzed by approximate methods.