Filtro estimador por deconvolución y pseudoinversa: descripción e implementación recursiva
Filter Estimator by Deconvolution and Pseudoinverse: Recursive Description and Implementation
Consuelo Varinia García Mendoza1 y José de Jesús Medel Juárez2
1 Escuela Superior de Cómputo, Instituto Politécnico Nacional, México. varinia400@hotmail.com
]]> 2 Centro de Investigación en Computación, Instituto Politécnico Nacional, México. jjmedelj@yahoo.com.mx
Article received on 10/09/2013.
Accepted on 21/10/2013.
Resumen
En este trabajo se presenta un filtro estimador con base al modelo matricial de deconvolución utilizando a la pseudoinversa como proceso de filtrado, con el cual es posible conocer la dinámica interna del modelo tipo caja negra con respuesta lineal, y con evolución invariante en el tiempo. Se presenta la descripción recursiva del filtro por deconvolución y pseudoinversa considerando: a) la convolución en diferencias finitas, b) el filtro por deconvolución y pseudoinversa, c) la descripción recursiva del funcional del error y d) las condiciones de estabilidad a cubrir por el estimador tomado en cuenta los criterios de Lyapunov. De manera ilustrativa, se presenta una simulación utilizando MatLab®.
Palabras clave: Deconvolución, pseudoinversa de una matriz, funcional del error, filtro estimador recursivo, estabilidad de Lyapunov.
Abstract
]]> In this paper we present a filter estimator based on deconvolution matrix model using the pseudoinverse as a filtering process, which permits to know the internal dynamics of a black-box model with linear response and time-invariant evolution. We present a recursive description of the filter by deconvolution and pseudoinverse considering a) convolution in finite differences, b) the filter by deconvolution and pseudoinverse, c) recursive description of error functional, and d) stability conditions to be covered by the estimator taking into account the Lyapunov criteria. To illustrate the description, a MATLAB® simulation is presented.Keywords: Deconvolution, pseudoinverse of a matrix, error functional, recursive filter estimator, Lyapunov stability.
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