Abstract
In the field of signal processing such as system identification, the affine projection algorithm (APA) is extensively implemented. However, running such algorithms in a non-Gaussian scenario may degrade its performance, since the second-order moment cannot extract all information from the signal. To prevent performance degradation of the algorithm in system identification tasks, we propose a novel APA based on least mean fourth (LMF) algorithm. The new algorithm, namely affine projection least mean fourth algorithm (APLMFA) is based on the high-order error power (HOEP) criterion and as such, can achieve improved performance. We also provide a convergence analysis for APLMFA. Numerical simulation results verify the presented APLMFA achieves smaller steady-state error as compared with the state-of-the-art algorithms.
Highlights
System identification is a means of modeling an unknown system only via input-output relationship, which is a fundamental of signal processing and control science [1]–[5]
(1) A novel affine projection algorithm (APA) is proposed based on least mean fourth (LMF) algorithm for system identification problem and acoustic echo cancelation (AEC) system, which is derived by taking the minimum dispersion method
It can be seen from this figure, the smaller interval corresponds to lower noise process and as such, the proposed affine projection least mean fourth algorithm (APLMFA) has the smallest excess MSE (EMSE) with distribution interval [−1, 1]
Summary
System identification is a means of modeling an unknown system only via input-output relationship, which is a fundamental of signal processing and control science [1]–[5]. The least mean fourth (LMF) algorithm is a celebrated algorithm based on HOEP criterion, which is proposed by Walach and Widrow in 1984 [38] Such algorithm is derived by taking the advantages of the fourth power of the error signal, and is superior to the LMS algorithm in non-Gaussian scenarios. (1) A novel APA is proposed based on LMF algorithm for system identification problem and AEC system, which is derived by taking the minimum dispersion method. The a priori error (i) is employed to replace the a posteriori error p(i) during weight adaptation This approximation is widely applied to the derivation of the APA-based algorithms, and the similar method can be found in [44]. The APA requires NP + P2 + 2N + 2P memory requirements, and the proposed algorithm has reduced memory requirements when compared to the APA
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