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Motivated by the need for robust frequency estimation for both balanced and unbalanced power system conditions and the fact that most of the existing techniques perform poorly in the presence of external interferences, a more noise‐resilient widely linear least mean kurtosis (WL‐LMK) algorithm is proposed that uses both the magnitude and phase angle errors for online estimation of three‐phase power system frequency. The proposed method makes use of the full second‐order information within the complex‐valued system voltage through Clarke's αβ transformation and the concept of augmented complex statistics and WL modelling. The effectiveness of the proposed scheme is verified through simulation studies of synthetic signals and experimental data. [ABSTRACT FROM AUTHOR]

An incremental least‐mean M‐estimate algorithm is proposed for distributed network, which minimises a robust M‐estimator‐based cost function against impulsive noise via the gradient descent method. Moreover, based on the same frame for implementation, an incremental distributed least‐mean p‐power algorithm is presented for combating impulsive noise. Simulations verify the superiority of the proposed algorithms in the presence of impulsive noise relative to some existing incremental distributed algorithms. [ABSTRACT FROM AUTHOR]

A new class of bias‐compensated affine‐projection‐like (APL) algorithms is proposed, in which a bias‐compensation vector is derived to eliminate the bias caused by the noisy input. In addition, a new estimation method for the input noise variance is proposed which does not require the input–output noise variance ratio in advance. Simulations in a system identification context show that the proposed algorithms achieve significant improvements in steady‐state misalignment as compared with the conventional APL algorithms. [ABSTRACT FROM AUTHOR]

Proposed is an L0 norm constraint set‐membership affine projection algorithm with coefficient vector reuse, which is derived by minimising a differentiable cost function that utilises the L0 norm of the updated weight vector as well as the sum of the squared Euclidean norms of the differences between the updated weight vector and past weight vectors. In addition, a power estimate method is introduced to eliminate the effect of the fluctuation of the output error on the step size. Simulations on sparse system identifications demonstrate that the proposed algorithm achieves a lower steady‐state misalignment than the existing algorithms in a high background noise environment. [ABSTRACT FROM AUTHOR]

A variable step‐size distributed incremental normalised least mean square (DINLMS) algorithm is proposed, in which the time‐varying step‐size of each node in the distributed network is obtained by minimising a posterior estimation error at that node. It overcomes the drawback that fast convergence rate with high steady‐state misalignment or low steady‐state misalignment with slow convergence rate, which always exists in the traditional DINLMS. The simulation results show that the proposed algorithm could achieve a better performance. [ABSTRACT FROM AUTHOR]

For echo cancellation, a memory improved proportionate M‐estimate affine projection algorithm (MIP‐MAPA) is proposed in which the M‐estimator‐based cost function containing the weighting matrix is minimised as the cost function and an efficient recursive implementation is applied according to the memory of the previous step‐size control matrices. A test on echo cancellations under an impulsive noise environment showed that the proposed MIP‐MAPA achieves improvement in steady‐state misalignment compared with existing algorithms. [ABSTRACT FROM AUTHOR]