This paper addresses the stability issues of the leastmeanabsolutethird (LMAT) algorithm using the normalization based on the third order in the estimation error. A novel robust normalized leastmeanabsolutethird...
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This paper addresses the stability issues of the leastmeanabsolutethird (LMAT) algorithm using the normalization based on the third order in the estimation error. A novel robust normalized leastmeanabsolutethird (RNLMAT) algorithm is therefore proposed to be stable for all statistics of the input, noise, and initial weights. For further improving the filtering performance of RNLMAT in different noises and initial conditions, the variable step-size RNLMAT (VSSRNLMAT) and the switching RNLMAT (SWRNLMAT) algorithms are proposed using the statistics of the estimation error and a switching method, respectively. The filtering performance of RNLMAT is improved by VSSRNLMAT and SWRNLMAT at the expense of affordable computational cost. RNLMAT with less computational complexity than other normalized adaptive filtering algorithms, can provide better filtering accuracy and robustness against impulsive noises. The steady-state performance of RNLMAT and SWRNLMAT in terms of the excess mean-square error is performed for theoretical analysis. Simulations conducted in system identification under different noise environments confirm the theoretical results and the superiorities of the proposed algorithms from the aspects of filtering accuracy and robustness against large outliers.
In this paper, a novel kernel adaptive filter, based on the leastmeanabsolutethird (LMAT) loss function, is proposed for time series prediction in various noise environments. Combining the benefits of the kernel me...
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In this paper, a novel kernel adaptive filter, based on the leastmeanabsolutethird (LMAT) loss function, is proposed for time series prediction in various noise environments. Combining the benefits of the kernel method and the LMAT loss function, the proposed KLMAT algorithm performs robustly against noises with different probability densities. However, an important limitation of the KLMAT algorithm is a trade-off between the convergence rate and steady-state prediction error imposed by the selection of a certain value for the learning rate. Therefore, a variable learning rate version (VLR-KLMAT algorithm) is also proposed based on a Lorentzian function. We analyze the stability and convergence behavior of the KLMAT algorithm and derive a sufficient condition to predict its learning rate behavior. Moreover, a kernel recursive extension of the KLMAT algorithm is further proposed for performance improvement. Simulation results in the context of time series prediction verify the effectiveness of the proposed algorithms.
As one of adaptive filtering algorithms based on the high order error power (HOEP) criterion, the leastmeanabsolutethird (LMAT) algorithm outperforms the leastmean square (LMS) algorithm in terms of the convergenc...
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As one of adaptive filtering algorithms based on the high order error power (HOEP) criterion, the leastmeanabsolutethird (LMAT) algorithm outperforms the leastmean square (LMS) algorithm in terms of the convergence performance. However, the choice range of its step-size is dependent on the power of the input signal. To overcome this shortcoming, a new normalized LMAT (NLMAT) algorithm is presented in this paper. The proposed algorithm has a good anti-jamming capability against the impulsive noise via assigning a upper-bound to the square of the feedback error in the weight update rule. Moreover, the range of the step-size is derived in detail to guarantee the stability of the proposed algorithm in the mean and mean-square senses. Furthermore, the performance of the proposed algorithm is analyzed in terms of the steady-state mean square deviation (MSD) and mean square error (MSE) as well as computational complexity. Simulation results in the context of system identifications illustrate that the proposed algorithm performs much better than the existing algorithms in various noise environments, with a fast convergence rate, low steady-state error and good tacking capability. (c) 2014 Elsevier B.V. All rights reserved.
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