The paper is devoted to the analytical substantiation of a new approach to the processing of signals representing a collection of some piecewise linear signals under conditions of a priori uncertainty about its parameters. The results of computer simulation fully confirm the main theoretical results and allow us to conclude that the new method is highly efficient in processing piecewise linear signals under conditions of a priori uncertainty about the useful signal function and the statistical characteristics of the additive noise component. The developed method makes it possible to reduce the dispersion of the additive noise component up to 10 times, however, as the dispersion of the noise increases, the efficiency decreases.