Research On Signal Detection And Parameter Estimation For Nonlinear Systems Based On Stochastic Resonance

Noise is usually defined as an unwanted signal or a disturbance to the system,and too much noises will make the performance of detection and estimation deteriorate.For the sake of improving the system performance,various physical and/or electrical methods are utilized to remove the noise or separate it from the useful signal as much as possible.However,the discovery of stochastic resonance(SR)indicates that noise is not necessarily harmful but can play a positive role through nonlinear system in enhancing signal under certain conditions.Signal detection and parameter estimation based on stochastic resonance are also known as noise enhanced signal detection and parameter estimation.The previous researches on noise enhanced detection problems have been heavily focused on to improve the fixed suboptimal detector by adding noise to the system.Furthermore,it has been considered that no additive noise can improve the fixed optimal detector,while it also has ignored that the optimal decision with adding noise to the system may be superior to the original optimal decision without additive noise under the same criterion when the detector is not fixed.On the other hand,the previous studies on noise enhanced parameter estimation problems have mainly included to improve the fixed suboptimal estimators through adding additive noise to the input and explore the possibility of enhancing the optimal linear and the Bayesian estimators by adjusting the additive noise level for various specific quantizers.Nevertheless,no existing work extends the beneficial effect of additive noise on the optimal linear and Bayesian estimations to a more general nonlinear system,or derives the additive noise that achieves the optimal estimation performance.Combined with the analysis above,in order to further enrich the theory of signal detection and parameter estimation based on SR,this thesis not only focuses on the noise enhanced binary composite hypothesis-testing problem under the restricted Neyman-Pearson(NP)criterion,but also investigate the optimal detection performance under the maximum a posteriori(MAP)criterion,the optimal linear and Bayesian estimations based on the minimum mean square error(MMSE)criterion,and the minimum Cramer-Rao lower bound(CRLB)obtained by adding an independent additive noise to the input of a general nonlinear system.The main contents and contributions of this thesis can be summarized as follows:(1)For a binary composite hypothesis-testing problem,a noise enhanced detection model is formulated according to the restricted Neyman–Pearson(NP)criterion when the prior information is partially known in order to improve the performance of a fixed suboptimal detector.Meanwhile,the noise enhanced detection problems under classical NP and Max–min criteria can be viewed as two special cases,and the feasible range of the constraint on the minimum detection probability is given.Under certain condition,the noise enhanced restricted NP problem can be equivalent to a noise enhanced classical NP problem with a different prior distribution,and the corresponding solution is given from this perspective.Furthermore,the relationship between the noise enhanced average detection probability and the constraint on the minimum detection probability is explored.Finally,numerical examples and simulations are provided to illustrate the theoretical results.(2)In order to investigate the performance of the noise enhanced optimal decision obtained by adding additive noise to the system input on the premise of detector is variable,a noise enhanced detection model is established under MAP criterion for a binary hypothesis-testing problem.Firstly,without any constraint,the optimal additive noise that minimizes the error probability and the corresponding optimal detector under MAP criterion are derived.Secondly,two constraints on detection and false-alarm probabilities are introduced to noise enhanced detection model,and the corresponding solutions are searched with and without the randomization between different detectors,respectively.Finally,take sine transform and limiter systems,for examples,to analyze the extent of error probability decreasing obtained via adding noise under different conditions.(3)For the linear minimum mean squared error(LMMSE)estimation problem,to reduce the mean squared error(MSE)between the input parameter and its linear estimator,a noise enhanced LMMSE estimation model is formulated via adding an additive noise to the nonlinear system input.First,when prior information is completely known,the noise enhanced linear estimator that minimizes MSE and the corresponding optimal additive nois are explored.In addition,in the presence of prior information uncertainty,a constrained LMMSE model is established by introducing a constraint on the expected value of the nonlinear system output,and the corresponding algorithms are developed to find the optimal additive noise.Finally,sine transform and multiple thresholds quantizer systems are taken for examples to compare the performance of LMMSE estimators obtained before and after adding additive noise to the input.(4)For the Bayesian estimation problem with the MSE between the parameter and its estimation as a cost function,in order to further improve the estimation performance,a noise enhanced Bayesian estimation model is formulated based on the noise modified nonlinear system output obtained by adding additive noise to the system input,and the optimal additive noise that minimizes MSE of Bayesian estimation is derived.In addition,to investigate the lower limit on MSE of unbias estimation,the optimal additive noise that minimizes CRLB is deduced when the paremeter is a constant or a random variable.Finally,take limiter and sine transform systems,for examples,to compare the MSE of Bayesian estimation and CRLB obtained by adding the two different noises above.