State-space adaptive filtering based balanced realization

Abstract

Balanced realizations are attractive candidates for state-space adaptive filter structures due to low parameter sensitivity. Since the balanced realization minimizes the ratio of maximum-to-minimum eigenvalues of the Grammian matrices, this property may lead to an adaptive filter exhibiting good noise rejection. Thus a balanced realization would seem an appropriate choice for the structure of an adaptive filtering algorithm. This paper focuses on answering the research question how does one use discrete-time Lyapunov equations such that, upon adjusting the parameters, the terms in the system matrices vary in such a way that the solutions for the controllability and observability Grammian matrices are always diagonal and equal Here, using an alternative to the finite impulse response coefficients as the adaptive filter parameters, a state-space adaptive filtering based balanced realization is proposed for output-error minimization. The algorithm is in internally balanced realization. Simulation results show that the balanced structure yields good noise rejection compared with the controllable canonical form in steady-state. The simulation results from the experiments imply that the approach is able to reduce the fluctuation in steady-state compared with the controllable canonical structure under the same scenarios.