Diffusion Sparse Equal-scale RLS Algorithm With Adaptive Step Sizes

Adaptive filter is a popular research topic in the field of signal processing.It consists of two parts:filter structure and adaptive algorithm.There are many application areas for these adaptive filters as there are many combinations for the different filter structures and adaptive algorithms.At present,the most popular application field of adaptive filter is system identification,which mainly estimates some parameters in the system according to input and output signals.The algorithms most used in system identification are the least mean squares(LMS)algorithm and the recursive least squares(RLS)algorithm and some of their modified algorithms.The sparsity of a system means that only a few coefficients in the system have rela-tively large values,and the rest coefficients are equal or close to zero.In nature,most sys-tems are sparse,such as speech signal and image signal.So when we identify an unknown system,it is usually assumed that the system is sparse.However,the LMS algorithm and RLS algorithm,which are commonly used in system identification,show poor estima-tion performance when identifying a sparse system or sparse systems.Because they are suitable for common systems and cannot take advantage of the sparse characteristics.In recent years,some researchers have made some improvements to the adaptive algorithm to make it suitable for identifying sparse systems.However,all these algorithms have their own shortcomings.By analyzing distributed systems and diffusion RLS algorithm,in this thesis,we study diffusion sparse proportional adaptive RLS algorithm with system sparsity by re-ferring the previous research experience.First of all,in order to improve application of system sparsity,this thesis applies advantages of the diffusion sparse LMS algorithm to the diffusion sparse RLS algorithm.That is to say the sparse penalty term of the diffu-sion sparse RLS algorithm is selected as the regularized form,namely?_Lf(w).And in the performance analysis,the sparse penalty function f(·)is selected as the relatively simple L₁norm and L₀norm form.Secondly,in order to improve the convergence rate of the algorithm,a proportional adaptive coefficient is added to the cost function and recursive formula obtained from the above improvement.It makes the recursive step size of each node at the current moment positively correlated with the estimated value of the node at the previous moment.Finally,the effectiveness of the algorithm is verified by simulation experiments.This coefficient make the recursive step size of each node at the current mo-ment positively correlated with the estimated value of the node at the previous moment.The last step is to verify the effectiveness by taking simulation.The simulation experiment in MATLAB shows that the algorithm proposed in this thesis has a faster convergence rate compared with the LMS algorithm,the RLS algorithm and the diffusion sparse RLS algorithm when identifying sparse systems.