Recursive Constrained Adaptive Algorithm Under q-Rényi Kernel Function

In this brief, we proposed a recursive constrained maximum $q$ - $\text{R}\acute {\text e}$ nyi kernel (RCMqR) adaptive filtering algorithm, which is derived via introducing a $q$ - $\text{R}\acute {\text e}$ nyi kernel function into constrained adaptive algorithm and using $q$ - $\text{R}\acute {\text e}$ nyi kernel function to construct a new cost function and providing its recursive form to create a linear constrained filter. The created RCMqR algorithm can achieve superior performance compared with other conventional algorithms under non-Gaussian noises environment. Theoretical transient mean-square deviation (MSD) of the RCMqR algorithm is presented when the system background noises are Gaussian-noise and non-Gaussian noise, and a sufficient condition has been achieved to make sure RCMqR algorithm converge. Various computer simulations are performed in system identification for the purpose of comparison. The simulation results verified that the theoretical analysis match well with the simulations and the proposed algorithm has better robustness than other algorithms under non-Gaussian impulsive noise.