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A bias‐compensated normalised least mean square (BCNLMS) algorithm with variable step size (denoted as BCVNLMS) is developed in this work to improve the accuracy and convergence speed for the three‐phase power system (TPPS) frequency estimation in circumstance of the noise and harmonic interference. Taking into account the problem of bias estimation caused by the mixed noises in the acquisition signal of the TPPS, the NLMS algorithm with an unbiased criterion (called BCNLMS) was employed to compensate the bias and improve the estimate accuracy. Furthermore, an adaptive variable step scheme is also incorporated into the BCNLMS algorithm to improve the convergence speed and stability during the process of adaptively frequency estimation. The experimental results show that the proposed BCVNLMS algorithm outperforms other well‐known methods for frequency estimation of the TPPS in several scenarios such as severe noise pollution, harmonic interference and frequency mutation. [ABSTRACT FROM AUTHOR]

Summary: Two novel adaptive filtering algorithms based on the mixed square/fourth error criterion are proposed for solving sparse system identification problems. Motivated by the fact that the proportionate update scheme can enhance the tracking ability of the system, we develop a proportionate least mean square/fourth (PLMS/F) algorithm in this paper. Combining the proportionate update scheme and the LMS/F algorithm, the proposed PLMS/F algorithm shows superiority for non‐Gaussian noise environments. Moreover, to further improve the performance of the PLMS/F algorithm in the noisy input cases, a bias‐compensated PLMS/F algorithm is developed by incorporating an unbiased criterion to compensate the bias caused by input noises. Simulation results in the context of the sparse system identification framework demonstrate that the proposed PLMS/F and bias‐compensated PLMS/F algorithms can achieve excellent identification performance in terms of steady‐state misalignment and convergence speed under noisy input and non‐Gaussian output noise environments. [ABSTRACT FROM AUTHOR]

The quantised kernel least mean square (QKLMS) is a simple yet efficient online learning algorithm, which reduces the computational cost significantly by quantising the input space to constrain the growth of network size. The QKLMS considers only the input space compression and assumes that the desired outputs of the quantised data are equal to those of the closest centres. In many cases, however, the outputs in a neighbourhood may have big differences, especially when the underlying system is disturbed by impulsive noises. Such fluctuation in desired outputs may seriously deteriorate the learning performance. To address this issue, a simple online method is proposed to smooth the desired signal within a neighbourhood corresponding to a quantisation region. The resulting algorithm is referred to as the QKLMS with desired signal smoothing. The desirable performance of the new algorithm is confirmed by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]