Mengüç E.C.2019-08-012019-08-0120181751-9675https://dx.doi.org/10.1049/iet-spr.2017.0340https://hdl.handle.net/11480/1642A novel quaternion-valued least-mean kurtosis (QLMK) adaptive filtering algorithm is proposed for three- and fourdimensional processes by using the recent generalised Hamilton-real (GHR) calculus. The proposed QLMK algorithm based GHR calculus minimises the negated kurtosis of the error signal as a cost function in the quaternion domain, thus provides an elegant way to solve a trade-off problem between the convergence rate and steady-state error. Moreover, the proposed QLMK algorithm has naturally a robust behaviour for a wide range of noise signals due to its kurtosis-based cost function. Furthermore, the steady-state performance of the proposed QLMK algorithm is analysed to obtain convergence and misadjustment conditions. The comprehensive simulation results on benchmark and real-world problems show that the use of this cost function defined by the quaternion statistics in the proposed QLMK algorithm allows us to process quaternion-valued signals and thus, significantly enhances the performance of the adaptive filter in terms of both the steady-state error and the convergence rate, as compared with the quaternion-valued least-mean-square algorithm based on the recent GHR calculus. © 2018, The Institution of Engineering and Technology.eninfo:eu-repo/semantics/closedAccessArticle12448749510.1049/iet-spr.2017.03402-s2.0-85047822307Q2WOS:000437313800013Q3