Bayesian Estimator Design And Noise Benefit Research Based On Low-Resolution Observations

In modern signal processing systems,due to practical constraints such as bandwidth occupation,energy supply,and system implementation costs,it is necessary to quantify the analog observation signal before further data processing.The quantization of signal not only reduces the complexity of hardware design,the power consumption of devices and the consumption of communication bandwidth,but also has the advantages of low cost,small physical size,and easy realization of high rate sampling.Despite the above advantages,the quantization of the signal will lose data information,reduce the resolution,reduce the performance of the system,and introduce nonlinear effects into the system,which brings many new challenges to the estimation of signal parameters.In some nonlinear systems,adding an appropriate amount of random noise can optimize the performance of the nonlinear system,which is the phenomenon of stochastic resonance.With the discovery of the phenomenon of aperiodic stochastic resonance and suprathreshold stochastic resonance,the system input is no longer limited to the periodic signal with a single frequency,and stochastic resonance is also not limited to the concept of “resonance”,which is now widely known as “noise benefit” in the field of signal processing.This paper studies the design of Bayesian parameter estimator based on low resolution observations and the noise benefits in distributed Bayesian parameter estimation.This paper first theoretically analyzes the relationship between the Bayesian Cramér-Rao lower bound(BCRB)of the original data and the BCRB of the new data added by artificial noise.At the same time,it is also concluded that the performance of the minimum mean square error(MMSE)estimator constructed based on the new observation data is inferior to the performance of the MMSE estimator designed based on the original data.Although this conclusion is disappointing,the computational complexity of MMSE estimator is large,and it is often difficult to obtain an analytical solution.Therefore,some suboptimal estimators that are easy to design are often used in actual signal estimation problems,and it is also feasible to explore the noise benefits in this way.For random scalar parameter estimation,this paper studies the noise benefits in several Bayesian parameter estimation situations.Based on the observation data of the low precision quantizer,four kinds of Bayesian estimators are designed in this paper,and the optimal distribution of artificial noise is determined for different background noise types to reduce the MSE of parameter estimation.Theoretical analysis shows that the optimal probability distribution of artificial noise in a single sensor is Dirac function,which is the constant deviation constant,and its performance is far inferior to the MMSE estimator designed based on the original data.For the parallel array distributed estimator,it is theoretically proved that the optimal artificial noise distribution of MSE can be reduced instead of the constant bias constant,which is a “bona fide” distribution function that indicates a random vector.For distributed sensors,this paper uses Gaussian kernel density estimation method to convert the nonlinear functional optimization problem of noise probability distribution into a constrained finite dimensional parameter estimation problem.This paper takes MSE as the objective function and uses the sequential quadratic programming algorithm to solve the optimal parameters of the noise distribution,and gives an approximate expression of the optimal noise distribution.The results show that the designed Bayesian estimator can always benefit from the optimal artificial noise and effectively approach the performance of MMSE estimator regardless of whether the thresholds of quantizer are the same in distributed estimation.Aiming at random parameter vector estimation,based on the low-precision observation data of distributed sensors and using the benefits of noise,this paper designs a distributed Bayesian parameter vector estimator,and gives the Bayesian MSE matrix theoretical expression of the estimator.When the number of array sensors is large enough,this paper proposes a low-cost calculation method of Bayesian MSE matrix and the corresponding Bayesian parameter vector estimator.The research results show that by adjusting the noise probability distribution or noise intensity in the estimator,the designed estimator can significantly reduce the Bayesian MSE matrix of random parameter vector estimation.