Filter Estimator Based on the Probability Distribution

In this paper, we propose a model of a parameter estimator filter for Black Box-type Stochastic Systems (BBSS), that is, only its inputs and outputs are known; considering its intrinsic properties observed in the second probability moment, in which the probability has the description of a specific distribution function relative to the random variables and the law of large numbers, allowing the stochastic system to be described with a Gaussian Distribution Function (GDF) and its linear transformation core in the Taylor series. Commonly, all estimates are assumed in the Second Moment of Probability (SMP) with equiprobable conditions, but in this case, a specific description of the Probability Distribution Function (PDF) is considered a priori, which is a contribution to the theory of digital filtering in estimation for signal reconstruction. The simulation of the parameter estimation is carried out for a given reference signal, maintaining the stability of the system in discrete time, and a comparison is made between the estimator based on the SMP and the PDF to observe the level of convergence, where the PDF approach has a better performance respect to the SMP one.