A modified simplex based direct search optimization algorithm for adaptive transversal FIR filters

In this paper, a novel modified optimization algorithm is presented, which combines Nelder-Mead (NM) method with a gradient-based approach. The well-known Nelder Mead optimization technique is widely used but it suffers from convergence issues in higher dimensional complex problems. Unlike the NM, in this proposed technique we have focused on two issues of the NM approach, one is shape of the simplex which is reshaped at each iteration according to the objective function, so we used a fixed shape of the simplex and we regenerate the simplex at each iteration and the second issue is related to reflection and expansion steps of the NM technique in each iteration, NM used fixed value of $$, that is, $$ = 1 for reflection and $$ = 2 for expansion and replace the worst point of the simplex with that new point in each iteration. In this way NM search the optimum point. In proposed algorithm the optimum value of the parameter $$ is computed and then centroid of new simplex is originated at this optimum point and regenerate the simplex with this centroid in each iteration that optimum value of $$ will ensure the fast convergence of the proposed technique. The proposed algorithm has been applied to the real time implementation of the transversal adaptive filter. The application used to demonstrate the performance of the proposed technique is a well-known convex optimization problem having quadratic cost function, and results show that the proposed technique shows fast convergence than the Nelder-Mead method for lower dimension problems and the proposed technique has also good convergence for higher dimensions, that is, for higher filter taps problem. The proposed technique has also been compared with stochastic techniques like LMS and NLMS (benchmark) techniques. The proposed technique shows good results against LMS. The comparison shows that the modified algorithm guarantees quite acceptable convergence with improved accuracy for higher dimensional identification problems.