Research On Signal Estimation And Filtering Based On Adaptive Stochastic Resonanc

In the field of signal processing,practical constraints such as broadband occupation and implementation costs are often solved by quantizing the signal,as it reduces the broadband occupation and simplifies the hardware design.At the same time,low precision sensors,e.g.quantizers,offer the advantages of high sampling rates and low cost.However,the quantization of signals also poses some problems,such as loss of data information,degraded system estimation performance,reduced resolution,and the introduction of nonlinear effects into the system.These problems are new challenges for the signal parameter estimation.However,the addition of an appropriate amount of random noise to a non-linear system provides a new approach or a way of thinking for the estimation of signal parameters.This method can also optimize the performance of the system to a certain extent,and has become a hot topic in modern statistical signal processing.Specially,how to find the optimal level or the optimal type of noise is a meaningful and urgent problem to be solved.In this paper,an adaptive stochastic resonance algorithm based on gradient descent and difference is proposed to investigate the benefit of added noise in binary quantizer summing networks and non-linear filtering.The learning algorithm not only adaptively adjusts the weight coefficients,but also adaptively updates the noise level or noise type.However,in some practical problems,the computation of the gradient is too complex or even unsolvable,so we further use the difference to estimate the gradient to form an adaptive stochastic resonance method.This method not only avoids the calculation of derivatives and reduces the computational complexity,but also improves the optimization efficiency of the estimator.A form of stochastic resonance or noise-assisted signal processing is achieved by the above method,which also extends the application of adaptive stochastic resonance to some complex non-linear signal processing tasks.The main research and innovation points are as follows:(i)First,the scalar parameter estimation in binary quantizer summing networks is investigated and an adaptive learning algorithm based on gradient descent and difference is theoretically derived.The algorithm is used to automatically adjust the weight coefficients,artificial additive noise level and the quantizer threshold in the summing network to reduce the mean-square error(MSE)of the estimator,so as to improve the performance of the estimator.The results show that the adaptive stochastic resonance learning algorithm is able to find the optimal non-zero value of the additive noise level,which minimizes the MSE of the estimator.The benefit of the artificial additive noise in the summing network is confirmed.(ii)For Bayesian parameter vector estimation,this paper estimates low precision observation vectors by a difference-based adaptive learning algorithm.Under the assumption that the number of sensors in the vector estimator is sufficiently large,the MSE matrix of the Bayesian parameter vector estimator is derived theoretically.The trace of this matrix is used as the objective function to automatically find the optimal additive noise level in the vector estimator sensors.The results show that,by differentially adapting the additive noise level,the Bayesian vector estimator also benefits from the optimal additive noise and the performance of the optimized estimator is very close to that of a linear minimum MSE estimator based on full precision observations.(iii)A transversal filter is designed based on a binary quantizer summing network model to filter the expected signal form the low precision observations.With a sufficient number of quantizers in the summing network,the filter capability is analyzed by using gradient descent-based and difference-based adaptive learning algorithms,respectively.It is shown that the optimal additive noise level obtained by the two methods can effectively reduce the MSE of the designed filter,reflecting the benefit of the artificial additive noise in non-linear filters.(iv)For single-parameter signal estimation in binary quantizer summing networks,this paper further utilizes the sequential quadratic programming algorithm to adaptively optimize the weight coefficients and the probability density function of the additive noise.The results show that a kind of approximated probability density functions can be found by the SQP method to further reduce the MSE of the designed estimator.