Theoretical Research On Noise Enhancement In Robust Estimation

In some practical systems,such as radar,sonar,mobile communications,and neural networks,the occurrence of impulsive noise has been reported,which can cause poor performances of processors designed under certain assumptions and make signal extraction,tracking,and recovery difficult.Therefore,it is necessary and meaningful to explore robust statistical methods.In this paper,this thesis studies the positive effects of noise in robust estimation,including the effect on the efficiency and the robustness of robust estimators.Noise enhancement is a general concept of noise benefits based on stochastic resonance,which manifests that noise can improve the performance of nonlinear systems when noise,nonlinear systems and useful signals satisfy a time-scale matching condition.Noise enhancement has been widely studied in the field of information transmission and processing.In this paper,we obtain some important results of noise enhancement in robust estimation,which greatly extend the application of stochastic resonance effects for noise-enhanced signals and information processing.The main research contents and innovations of this paper are as followed:1.For a single robust M-estimator,a discriminant function,elicited from the background noise probability density and the given M-estimator function,provides the condition of existence of the optimal noise.It is proven that the optimal noise,when it exists,is the symmetric dichotomous noise.In the extreme contaminated noise model,we prove that the maximum bias of M-estimators can be reduced by adding extra noise.For an array of identical M-estimators,we demonstrate that for a given estimator function and fixed noise levels,the asymptotic efficiency of the array system is a monotonically increasing function of the M-estimator number.Furthermore,aiming to maximizing the asymptotic efficiency of the array system,the optimal probability density of the added noise is proven to be the solution of a weighted minimum L~2-norm function.Furthermore,the upper bound of the asymptotic efficiency and its corresponding optimal noise probability density are given.2.Using the Parzen-window density estimation technique,we approximate the non-convex optimization problem as a solution of an optimization problem with respect to a non-negative vector under certain constraints.The approximate solution of the additive noise optimal probability density proves the feasibility of the proposed method in various M-estimators with arbitrary parallel array numbers.The simulation results verify the effectiveness of the proposed method.3.The above noise-benefit theory in independent case is extended to the dependent noise environment.The noise-enhanced asymptotic efficiency of robust estimators in colored noise environment is theoretically analyzed.A robust linear combination estimator with noise enhancement under the Bayesian framework is designed.The optimal weighting coefficient setting method and the robust noise level tuning method are given.It is proved that the mean square error of the proposed estimator with the optimal weighting coefficient can be reduced by adding additive noise and shows robustness in the background of various heavy-tailed noise environments.The conclusions of noise enhancement in robust estimation are verified by numerical simulation,which confirm that noise can play a positive role in robust estimation.It provides more practical applications of stochastic resonance and may extend to more practical engineering projects,such as the areas of neural network and machine learning.