A hybrid gradient‐based and differential evolution algorithm for infinite impulse response adaptive filtering

Abstract

SUMMARYGlobal optimization algorithms (GO) had been applied to solve the adaptive infinite impulse response filtering problem, which is known to have multimodal error surface under certain conditions. However, although GO may be able to search multimodal surfaces, they have certain disadvantages. They may not converge to any minimum point, the convergence speed is reduced as the solution vectors move closer, and tracking ability for non‐stationary environment is lacking. The traditional gradient descent method does not have these limitation but is not able to search multimodal surfaces. In this work, we propose a hybrid algorithm combining gradient descent and differential evolution (DE) for adapting the coefficients of infinite impulse response adaptive filters. DE is run in a block‐based manner. The coefficient vector with the lowest error surface value (the best member) of the current block is updated via gradient descent for the duration of the next block. Thus combining the ability to search multimodal surface of DE and fast local search of gradient descent. As with all GO, global search capacity is gradually lost as the coefficient vectors converge together. Thus, re‐initialization is also incorporated into the hybrid algorithm to provide continuous global search capacity for non‐stationary environment. All the coefficient vectors except the best member are re‐initialized when the normalized mean Euclidean distance between each pair of vectors falls below a threshold value. Simulation results show that the proposed algorithm achieves better solution quality and convergence speed than classic DE and GO for stationary and non‐stationary environments. Copyright © 2013 John Wiley & Sons, Ltd.