Comparative Study of Conventional and Genetic Algorithms in Adaptive Signal Processing and Control

A comparative study is made of genetic algorithms and conventional numeric methods for the purpose of filter optimization in a class of adaptive stochastic systems known as trackers. With this example, the bridging of the gap between the standard numeric algorithms (NA) used conventionally as optimum seeking tool, and the more flexible genetic algorithms (GA) is demonstrated. The need for using NA or GA is associated with uncertainty in covariances of the noises driving a reference signal model (RSM) (a shaping filter) and a controlled plant (CP). All the work findings have been made on the basis of experimental data obtained with the help of a specially designed software product. GAs in the work are based on one kind of fitness function associated with the so called “Statistical Orthogonality Principle”, which expresses uncorreletedness of a residual and its sensitivity function as the necessary and sufficient condition for the mean square residual (MSR) to attain its minimum. To generate a proper residual (i. e., the residual that is available and whose MSR is minimal at the optimal system parameters), the Auxiliary Performance Index (API) is exploited. As the conventional NAs to attain the minimal MSR, Robbins-Monroe procedure and Least Square method are used. Case studies of influences on the GA behavior of some other fitness functions would be one possible direction for further research. Studies on comparison of GAs and other NAs useful for identification of the optimal system parameters and based not only on the API approach, are in sight, as well.