An Augmented Complex-Valued Least-Mean Kurtosis Algorithm for the Filtering of Noncircular Signals

Diffusion ACNSAF Algorithm for Secure Distributed Estimation Under Complex-Valued Attacks

“…where o(n) is a complex-valued doubly second order noncircular white Gaussian process with σ 2 o = 1 andσ 2 o = 0.8. Another benchmark noncircular signal is the Ikeda signal (nonlinear and with coupled states), given by [38]…”

Novel quaternion‐valued least‐mean kurtosis adaptive filtering algorithm based on the GHR calculus

“…To this end, we will analyse the steady-state performance of the proposed QLMK algorithm by following the same steps in [33,34,45,[47][48][49][50]. Primarily, we assume that the proposed QLMK algorithm is convergent.…”

“…Primarily, the sufficient convergence condition in the sense of the MSE can be defined as [34,45,47,49,50] 0…”

“…On the other hand, to further enhance the performance of some important engineering applications [35][36][37][38][39][40][41][42][43][44][45], adaptive filtering algorithms based on high-order statistics have been proposed in the real and complex domains. One of the most popular high-order statistics-based adaptive filtering algorithms is the least mean kurtosis (LMK) algorithm [35].…”

“…The cumulants with order higher than two in this cost function are identically zero. For this reason, the kurtosis based cost function provides the possibility that the algorithm is convergent independent of the Gaussian measurement noise [35,36,44,45]. According to the central limit theorem [36], the probability density function of the measurement noise consisting of the independent sources shows a Gaussian behaviour.…”