A $m$-dimensional stochastic estimator

Abstract

This paper shows the development of a optimal stochastic estimator for a black-box system in a $m$-dimensional space, observing noise with an unknown dynamics model. The results are based in state space, described by a discrete stochastic estimator and noise characterization. The proposed result gives an algorithm to construct diagonal form for the state space system. It is a new technique for a instrumental variable tool, and a diagonalization process avoiding the calculation of pseudo-inverse matrices is presented with a linear computational complexity $O(j)$ and $j$ as the diagonal matrix dimension. The results show that it is possible to reconstruct the observable signal with a probability approximation.