Estimation of parameters using the deconvolution and the pseudoinverse: description and recursive implementation

This work presents a parameter estimator in recursive form based in deconvolution matrix model as a discrete filter process, in which is possible to know the internal convolution dynamics respect to black box with time invariant lineal answer. Extending the convolution process to a period conformed by a group of intervals where the system doesn't change, allows the approximation to matrix description in base to the real system, giving their inputs and outputs in the same period, generating a multivariable description, without change the context holding its invariance conditions, needs the pseudoinverse estimation, because observe in it singularities and inversion problems. In the same way the dispersion measures respect to the reference, considering the trace as the reference matrix as its estimated, described by the mean square error, Decibels and Bode, all of its developed in recursive form, allowing to link between its immediate past states to consume the minimal computational resources. The stability conditions evolved required estimator, considered in this case the Lyapunov Criteria. In illustrative sense, develop us the simulation in where the extended matrixes are non square form and bounded temporally into time interval, considering time invariant conditions respect to bounded input, having a recursive estimator as a final result. In this work concluded considering that the deconvolution as an estimator is a tool required for non square systems invariant in the time.