Estimación-identificación como filtro digital integrado: descripción e implementación recursiva

The digital filter theory with identification process allows knowing internal states dynamics, with respect to a reference system, commonly considered as a black box or base system. This gives the identifier its input and output signals as essential information; so that the identifier is formed by identification actions. The actions developed by the identifier consider the transition matrix "described by the exponential function respect to internal parameters for the unknown black box reference system", identifying states delayed, with gain matrix "formatted by correlation convergence error" and the innovation process "build by the output base system noise and the identification result." Unfortunately, in the black box concept the internal parameters have the same problem, which means, neither observed nor transition matrix, because it is a description function depicted exponentially. Thus, the identifier structure considers that the transition matrix is an essential problem. This paper proposes the estimator as internal parameter descriptor "this is a technique required to describe the internal gains with respect to the black box system" thus generating the transition matrix. With respect to the gain matrix, the identification error "expressed by a second probability moment in recursive forms" affects the identifier as an adaptive algorithm. This allows having a sufficient convergence rate. The filter is built with two actions: estimator and identifier, this considers the adaptive properties with respect to the gain and dynamically adjusts the identifier convergence levels, observed in simulation results.