Recursive adaptive filter design using an adaptive genetic algorithm

An adaptive genetic algorithm for determining the optimum filter coefficients in a recursive adaptive filter is presented. The algorithm does not use gradient techniques and thus is appropriate for use in problems where the function to be optimized is non-unimodal or non-quadratic, such as the mean-squared error surface in a recursive adaptive filter. The mechanisms of the algorithm are inspired by adaptive processes observed in nature. After an initial set of possible filters is randomly selected, each filter is mapped to a binary string representation. Selected bit strings are then transformed using the operations of crossover and mutation to build new "generations" of filters. The probability of selecting a particular bit string to modify and/or replicate for the next "generation" is inversely proportional to its estimated mean-squared error value. Hence, the process not only examines new filter coefficient values, but also retains the advances made in previous "generations". Computer simulations of the algorithm\´s performance on unimodal and bimodal error surfaces are presented.