Stochastic learning automata and adaptive IIR filters

Abstract

It is well known that gradient search fails in adaptive IIR filters because their error surfaces may be multimodal. In this paper, a new learning approach is presented to overcome the problem. Instead of applying conventional deterministic methods to optimise the filter coefficients, intelligent learning techniques are used. Specifically stochastic learning automata are considered. They have a well established mathematical foundation and global optimisation capability. It is shown that the latter capability can be utilised fruitfully to search the multimodal error surfaces. Three learning automata based approaches are developed. The first scheme uses a single automaton to search the parameter space, a second scheme employs a co-operative team of automata and the final approach incorporates a hybrid strategy combining both gradient search and learning automaton. Computer simulation results are presented to illustrate and compare the performances in a system identification application. It is found that they are all capable of achieving global convergence under different conditions, including insufficient filter order and/or input colouration. Stability during adaptation can be maintained. The paper concludes with a discussion on the use of learning automata in adaptive signal processing and the directions for future research.