Research On A Class Of Adaptive Algorithms With Exponentiated Error For Sparse System Identification

Digital signal processing has been widely used in many fields,such as communication engineering,medicine,automatic control system.Recently,adaptive filtering,as a branch of digital signal processing,is researched by scholars around the world,which is benefit from itssuitability and filtering.It was developed from linear filtering algorithms,such as Wiener filtering and Kalman filtering,and it is found in system identification,acoustic echo cancellation and image processing.But with the deepening of research,the methods of disciplines are to be quantified.When dealing with some complex signals,the traditional adaptive algorithms can not process these signals efficiently.To meet the needs,the adaptive filter that changes its characteristics has been the one of the most popular ways,so the inherent law will be observed and quantifiedby system identification.Although the traditional least mean square(LMS)algorithm has been widely employed,the impulsive environments will worse the algorithm robustness and convergence speed.To solve the problem,a class of algorithms with exponentiated error cost functions was proposed by C.Boukis,we make improvements on the basis of LE2 and LSE algorithmsby the zero attractors,variable step size and distributed adaptive methodHowever,sparse systems widely exist in practice,there are a large number of zero or very small values in unknown systems.The unknown systems with a few significant values in coefficients have sparse characteristic.For such systems,the traditional adaptive algorithms do not employ sparsity,which have the poor performances.Recently,the zero-attracting sparse penalty algorithms were proposed and achieved improved performance for sparse system identification.Moreover,those algorithms have low computational complexity,the paper dedicated to the research of improved algorithms with exponentiated error cost functions by this methodFirst,the basic principle of adaptive filtering and the basic ideal of LMS,LE2,LSE algorithms and their distributed adaptive algorithms are introduced in this paper.The advantages and disadvantages of the existing LE2 and LSE algorithms are analyzed Employing the characteristic of the zero-attracting sparse penalty algorithm,a reweighted lp-norm constraint least exponentiated square(RLP-LE2)algorithm is proposed in this paper and it tests in various environments.Secondly,LE2 algorithm is based on the least exponential error,but it has a poor robustness under the impulsive environments.The sum of error exponentials algorithm(LSE)given by C.Boukis has a better robustness.However,due to the fixed step of LSE algorithm,it needs to balance convergence rate and steady-stste misadjustment.Benefit from the variable step size,we improve the performance of LSE algorithm with prior error.Moreover,a polynomial variable step-size least sum of error exponentials algorithm based on maximum correntropy criterion(PZA-VSILSE-MCC)is given in this paper,and it has better robustness in non-Gaussian impulse environment.Finally,the distributed algorithms were proposed by Cassio G.Lopes in 2006 have improved the poor performance of adaptive algorithms in the geographical area.In the distributed network,each node can obtain and deal with signals form environment,whose agents are connected in distributed topology.The observed dates from each agentcan be enable to estimate the vector of parameters of the unknown system.To enhance the ability of sparse system identification,an lp-norm constraint distributed least exponentiated square(RLP-DLE2)algorithm and a polynomial variable step-size distributed least sum of error exponentials(PZA-DVSILSE)algorithm are proposed in this paper,which achieves a low steady-state misalignment comparing the performances of this and several exiting algorithms.