Research On Adaptive Filter Design Based On Optimization Algorithms And Their Applications

Adaptive filtering theory is one of the focuses of signal processing and widely used. The adaptivefilter is composed of filtering structure, performance and adaptive algorithm. This paper focuses onthe adaptive algorithm, including the LMS algorithm and adaptive genetic algorithm.Firstly, based on the analysis of the LMS algorithm from the aspects of principle, performance andinfluencing factors, this paper simulates and states that the traditional LMS algorithm hascontradictions among fixed step size, convergence rate and steady-state error. By comparing andanalyzing several typical improved variable step size algorithms, of which this paper proves theadvantages and disadvantages respectively.Then, based on the autocorrelation function of the error signal, which can eliminate theuncorrelated noise’s impact, three improved algorithms are put forward. The first improved algorithmtakes advantage of the second power and the forgetting factor of the autocorrelation function of theerror signal to adjust the step size factor; the second improved algorithm proposes a mathematicalfunction that has the same characteristics with the adjustment principle of variable step size algorithmto adjust the step size factor; the third improved algorithm transforms the versiera function to make itsfunction characteristic accord with the adjustment principle of variable step size LMS algorithm.Then the improved algorithms are applied to the system identification. By compared in differentexperimental conditions, indicate that the adaptive filter based on improved variable step size LMSalgorithms achieves an obviously improvement in the convergence rate, time-varying system trackingability and steady-state offset error etc.At last, the paper introduces the principle of adaptive genetic algorithm, summarizes the existingimproved methods of crossover and mutation probability, and therefor puts forward the improvedcrossover and mutation probability algorithm. Then combining which with the parallel selectionmethod and optimal retention strategy, is proposed and applied to the design of passive power filtersimulation model. The simulation results indicate that compare with the traditional engineering designmethods, the new adaptive genetic algorithm’s improvement results is more obvious and effective onthe optimization goals of investment, capacity of reactive power compensation and filtering effect.