Research On System Identification Of Variable Sparseness Based On Adaptive Filtering Algorithm

System identification is one of the most widely popular applications of adaptive filtering.At the same time,system identification research is also a very challenging problem,especially if the system impulse response is still sparse.In non-Gaussian noise,the PLMP has good filtering characteristics for system identification of sparse impulse response.However,in practical applications,the sparseness of the system is not static.The PLMP cannot guarantee the best filtering performance under the time-varying sparsity system.To avoid the reduction of the convergence speed of the existing PLMP algorithm when the sparsity of the system varying,an improved PLMP?IPLMP?algorithm has been proposed,which idea is when the sparseness is small,the LMP plays a leading role;when the system sparsity is large,the PLMP plays a leading role.The IPLMP is well adapted to the environment in which the system sparseness changes.This thesis optimizes the IPLMP from the following three aspects:?1?To improve the sparse rate of the system weight update,this thesis adds thel₁-norm of the weight coefficient to the cost function of IPLMP algorithm,that is,the IPLMP uses thel₁-norm to measure the sparsity of the system,and COST-ZAIPLMP algorithm is obtained.However,thel₁-norm is not an effective measure of sparsity.Since the-law and correntropy induced metric?CIM?are good approximators of thel₀-norm,we have proposed two different IPLMP algorithms,which called COST-RZAIPLMP and COST-CIMIPLMP,respectively.The three algorithms after improving cost function have faster convergence speed and lower steady-state error than the IPLMP algorithm.?2?In order to get a more accurate step factor,for the IPLMP algorithm,the step-size control matrix element with the parameters relating to the sparsity of system uses thel₁-norm of the weight coefficient.two methods of ?-law and CIM are introduced,and two other improved algorithms are obtained,which called-IPLMP and CIM-IPLMP.In order to deeply analyze the two algorithms,the mean and mean square convergences of the ?-IPLMP and CIM-IPLMP are analyzed,and some related theoretical results are also obtained.For sparse systems,the ?-IPLMP and the CIM-IPLMP have better filtering characteristics.?3?Since the IPLMP and CIM-IPLMP need to set the value of the parameter with the system sparsity in advance,the value given in advance does not necessarily adapt to the sparsity of the current system.Introducing time-varying parameters,the IPLMP-?-vary and CIM-IPLMP-?-vary are proposed,which can adjust the algorithm to adjust the degree of system sparsity.In order to reduce the computational load of the CIM-IPLMP,the CIM-IPLMP-TAYLAR is obtained by using the first-order Taylor expansion of the step-size control matrix element in the CIM-IPLMP.The CIM-IPLMP-TAYLAR combines with the time-varying parameters relating to the sparsity of system to obtain the CIM-IPLMP-TAYLAR-?-vary.Simulation results demonstrate the effectiveness of these algorithms.Simulation results show that,in comparison with the LMP and PLMP algorithms,the proposed algorithms can achieve faster convergence rate and better filtering accuracy in the sparsity varying system under non-Gaussian noisy environments.