Quaternion kernel recursive least-squares algorithm

Various kernel-based algorithms have been successfully applied to nonlinear problems in adaptive filters over the last two decades. In this paper, we study a kernel recursive least squares (KRLS) algorithm in the quaternion domain. By the generalized Hamilton-real calculus method, we can apply the kernel trick to calculate the quaternion KRLS filter. In order to show the feasibility of the proposed algorithm, firstly we investigate the quaternion recursive least squares (QRLS) algorithm, and simulations show that the proposed QRLS algorithm has the same steady error as that of the closed-form solution; Secondly, we generalize the QRLS algorithm to the quaternion KRLS algorithm, theoretical analysis show the convergence, and simulations are described demonstrating the performance of the proposed algorithm.