Adaptive filtering and identification
Jiří Jan · Institution of Engineering and Technology eBooks · 2000
In the previous chapter, when designing restoration filters which should provide optimal estimates of original signals based on their observed noisy and distorted versions, we used explicit information obtained by a priori identification of signal-source properties. Alternatively, the stationary signal-source parameters could also be estimated from the signal itself providing that a suitable signal-generation model has been introduced. Consequently, it is possible to design an optimal or suboptimal restoration system; in the case of stationary processes, the system is, or aims at, a time-invariant filter, such as the classical Wiener filter. Nevertheless, if the filter is to work in an unknown environment (either because the identification is impossible or the environment is time varying in an unpredictable way), it must be capable of adapting to such a situation. We shall therefore deal in this chapter with adaptive filters that are able to learn from a given environment, i.e. they are capable of providing the necessary information estimates of the needed quantities in the course of their work, with out any a priori information. It is then possible to expect that such filters will be able to react (with a certain delay) even to changes in environmental properties and thus to also process signals generated by nonstationary processes. Adaptive filters can be designed as filters with infinite or finite impulse response. General recursive filters (ARMA-type filters) promise naturally, in principle, better estimates. Their basic disadvantage is that they may become unstable in the course of adaptation; thus, complicated precautions in the adaptation mechanisms are needed to prevent parameter-adjustment leading to instability. We shall therefore limit ourselves in this book to common nonrecursive FIR adaptive filters (e.g. MA type) which are always stable.