An adaptive neural fuzzy filter and its applications

A new kind of nonlinear adaptive filter, the adaptive neural fuzzy filter (ANFF), based upon a neural network's learning ability and fuzzy if-then rule structure, is proposed in this paper, The ANFF is inherently a feedforward multilayered connectionist network which can learn by itself according to numerical training data or expert knowledge represented by fuzzy if-then rules, The adaptation here includes the construction of fuzzy if-then rules (structure learning), and the tuning of the free parameters of membership functions (parameter learning), In the structure learning phase, fuzzy rules are found based on the matching of input-output clusters, In the parameter learning phase, a backpropagation-like adaptation algorithm is developed to minimize the output error, There are no hidden nodes (i.e., no membership functions and fuzzy rules) initially, and both the structure learning and parameter learning are performed concurrently as the adaptation proceeds, However, if some linguistic information about the design of the filter is available, such knowledge can be put into the ANFF to form an initial structure with hidden nodes, Two major advantages of the ANFF can thus be seen: 1) a priori knowledge can be incorporated into the ANFF which makes the fusion of numerical data and linguistic information in the filter possible; and 2) no predetermination, like the number of hidden nodes, must be given, since the ANFF can find its optimal structure and parameters automatically. Moreover, in contrast to traditional fuzzy systems where the input-output spaces are partitioned as grid type causing the combinatorial growing of fuzzy rules as the input-output dimensions increase, irregular partitions are done in the ANFF according to the distribution of training data so fewer fuzzy rules will be generated, To demonstrate the performance of the ANFF, two applications, the nonlinear channel equalization and the adaptive noise cancellation, are simulated, Efficiency and advantages of the ANFF are verified by these simulations and comparisons.