Investigating errors when forecasting processes with uncertain dynamics and observation noise by the self-adjusting brown's zero-order model

Abstract

This paper reports a study into the errors of process forecasting under the conditions of uncertainty in the dynamics and observation noise using a self-adjusting Brown's zero-order model. The dynamics test models have been built for predicted processes and observation noises, which make it possible to investigate forecasting errors for the self-adjusting and adaptive models. The test process dynamics were determined in the form of a rectangular video pulse with a fixed unit amplitude, a radio pulse of the harmonic process with an amplitude attenuated exponentially, as well as a video pulse with amplitude increasing exponentially. As a model of observation noise, an additive discrete Gaussian process with zero mean and variable value of the mean square deviation was considered. It was established that for small values of the mean square deviation of observation noise, a self-adjusting model under the conditions of dynamics uncertainty produces a smaller error in the process forecast. For the test jump-like dynamics of the process, the variance of the forecast error was less than 1 %. At the same time, for the adaptive model, with an adaptation parameter from the classical and beyond-the-limit sets, the variance of the error was about 20 % and 5 %, respectively. With significant observation noises, the variance of the error in the forecast of the test process dynamics for the self-adjusting and adaptive models with a parameter from the classical set was in the range from 1 % to 20 %. However, for the adaptive model, with a parameter from the beyond-the-limit set, the variance of the prediction error was close to 100 % for all test models.