Research And Application Of Fractional Order Adaptive Filters Based On Chaotic Particle Swarm

Adaptive filter theory,a branch of adaptive signal processing,can automatically and iteratively adjust filter parameters to achieve optimal filtering by satisfying certain criteria.Adaptive filtering algorithms are the core part of adaptive filter design,and therefore their merit determines the performance of adaptive filters.The least mean square(LMS)algorithm and the recursive least squares(RLS)algorithm are two typical adaptive filtering algorithms that are widely used in the fields of image processing,biomedical signals and system identification.The traditional LMS algorithm has the advantages of simplicity,efficiency,high real-time performance and insensitivity to quantization noise of coefficients,but suffers from slow convergence when the number of weights is large.The RLS algorithm can achieve faster convergence,but the calculation is relatively complex and cannot achieve stable convergence in non-stationary signal processing.In contrast,fractional-order calculus,as a generalization of integer order calculus,plays an important role in practical engineering applications.In recent years,scholars have introduced fractional-order calculus into the design of adaptive filtering algorithms and found that fractional-order adaptive filtering algorithms have better filtering performance compared with traditional adaptive filtering algorithms.Therefore,this research investigates the step size factor,forgetting factor,convergence speed,steady-state error and computational complexity of the fractional-order LMS algorithm and fractional-order RLS algorithm,and uses the characteristics of fast convergence and strong global search ability of the chaotic particle swarm algorithm to find the optimal parameters in the fractional-order adaptive filtering algorithm,and then completes the optimal design of the fractional-order adaptive filter.In order to further verify the performance of the fractional-order adaptive filter based on chaotic particle swarm,the revised algorithm is applied to a real speech signal noise reduction process,and the filtering,noise reduction and anti-interference performance of the optimized algorithm are significantly better than that of the traditional adaptive filtering algorithm.The theoretical analysis and simulation results show that the chaotic particle swarm optimization has good optimization capability and can effectively improve the convergence speed of the fractional-order adaptive filtering algorithm,achieving low steady-state error at high convergence speed and effectively reducing the computational complexity of the fractional-order RLS algorithm...