Research On Kernel Adaptive Filtering Algorithm Under Alpha Stable Distributed Noise

Kernel adaptive filtering algorithm can solve nonlinear filtering problem effectively because of its own characteristics.Non-gaussian noise exists in practical applications,and Alpha stable distribution can be used to model it well.Therefore,the research of kernel adaptive filtering algorithm based on Alpha stable distribution environment has certain practical significance.It is important for cost function in kernel adaptive filtering algorithm.The improvement of cost function is one of the trends of current algorithm research.Firstly,the existing cost function suitable for the algorithm under Alpha stable distribution noise is improved,and the new algorithm guarantees its robustness while improving its convergence performance.Secondly,for the pulse noise environment,a new cost function with robust performance is constructed to ensure a lower steady-state error and a faster convergence rate.Finally,aiming at the network growth problem in the kernel adaptive filtering algorithm,the sparsification is reasonably used to improve the algorithm to ensure the filtering accuracy and reduce the computational complexity of the algorithm.The specific content is divided into the following points:(1)The convergence rate of the kernel least logatithmic absolute difference algorithm is slow.In this thesis,we improve the cost function of this algorithm and propose a kernel least logatithmic absolute difference algorithm based on p norm.Due to the joint action of p norm a and constant,the steepness of the cost function increases so improves the convergence performance of the algorithm.The theoretical analysis and simulation verification of the algorithm are presented.(2)For the nonlinear problem,a new cost function—inverse hyperbolic sine function is constructed in the kernel space,so we obtain the kernel least inverse hyperbolic sine algorithm,and analyze the mean square convergence performance through energy conservation.However,due to its high computational complexity,combined with the quantization method,the "redundant" data is used to judge whether the data is added to the center of the dictionary,and the quantization kernel least inverse hyperbolic sine algorithm,which runs the network growth rate is reduced,thus reducing the computational complexity of the algorithm.(3)The kernel recursive least squares algorithm has fast convergence rate and ideal filtering accuracy,combines it with the inverse hyperbolic sine,so we have a kernel recursive least inverse sine hyperbolic adaptive filtering algorithm.This algorithm inherits the advantages of the kernel recursive least squares algorithm and the inverse hyperbolic sine function,which can achieve excellent performance in nonlinear systems and show good robustness in the pulsed noise environment.However,this algorithm has the problem of network growth,and combines it with the surprise criterion with the mathematical framework,we obtain the kernel recursive least inverse hyperbolic sine algorithm based on the surprise criterion.The algorithm can suppress the network growth and thus reduce the computational complexity of the algorithm.