Blind Filtering and Separation Using a State‐Space Approach
Andrzej S Cichocki, Шун-ичи Амари · 2002
The state-space description of dynamical systems is a powerful and flexible generalized model for blind separation and deconvolution or more generally for filtering and separation. There are several reasons why the state-space models are advantageous for blind separation and filtering. Although transfer function models in the Z-domain or the frequency domain are equivalent to the state-space models in the time domain for any linear, stable time-invariant dynamical system, using transfer function directly it is difficult to exploit internal representation of real dynamical systems. The main advantage of the state-space description is that it not only gives the internal description of a system, but there are various equivalent canonical types of state-space realizations for a system, such as balanced realization and observable canonical forms. In particular, it is possible to parameterize some specific classes of models, which are of interest in applications. In addition, it is relatively easy to tackle the stability problem of state-space systems using the Kalman filter. Moreover, the state-space model enables a much more general description than the standard finite impulse response (FIR) convolutive filtering models discussed in Chapter 9. In fact, all the known filtering models, such as the AR, MA, ARMA, ARMAX and Gamma filtering could also be considered as special cases of flexible state-space models. In this chapter, we briefly review adaptive learning algorithms based on the natural gradient approach and give some perspective and new insight into multiple-input multiple-output blind separation and filtering in the state-space framework.