Research On Line Spectral Estimation Algorithm Based On Approximate Bayesian Inference

This thesis mainly studies an efficient line spectral estimation algorithm based on approximate Bayesian inference.Line spectral estimation refers to the decomposition of frequencies and amplitudes from the complex sinusoidal signals,which is an important basic problem in signal processing applications.According to the degree of dependence on the prearranged grid(composed of discrete frequency values),line spectral estimation algorithms can be systematically divided into three categories: on-grid method,off-grid method and grid-less method.The approximate Bayesian inference is the use of the prior probability and likelihood probability inference process of posterior probability,and then this posterior probability can be used to estimate the hidden parameters or forecasting data,this method not only can output point estimation,and also can output the distribution information,so in this thesis,the approximate Bayesian inference is used to solve the line spectral estimation problem,design a new algorithm combining on-grid and grid-less method.Firstly,in order to simplify the problem of line spectrum estimation,a sparse modeling method is proposed in this thesis.A series of activators are introduced to control the sparsity of the model,and the model order solving in line spectrum estimation is transformed into activators sequence estimation.Then,the Bayesian method is used to evaluate the linear spectrum estimation problem,and the prior probabilities are assumed for all parameters to be estimated respectively.In order to consider the influence of the ADC(analog to digital converter),a non-Gaussian transition probability is used to describe the nonlinear distortion caused by it.Based on prior probability and likelihood probability inferring posterior probability,there are classical approximate inference algorithms: Generalized Approximate Message Passing(GAMP)and Bilinear Generalized Approximate Message Passing(BiG-AMP).However,in the line spectrum estimation problem,because of the correlation in the model,these two algorithms are not applicable.Therefore,on the basis of these two algorithms,this thesis designs an inference algorithm which is a mixture of on-grid method and grid-less method.Among them,GAMP and Belief Propagation(BP)work together to solve the posterior probability of the remaining parameters in the given line spectrum estimation.The grid-less method reregards the frequency parameters as unknown,and estimates all unknown parameters using BiG-AMP,BP and Expectation maximization(EM)algorithm.In the hybrid inference algorithm proposed in this thesis,the grid-less method provides a initialization function for the grid-less method,so as to avoid the phase ambiguity that may occur in the grid-less method.At the same time,the grid-less method performs inference and estimation as the main part of the algorithm,eliminating the spectrum leakage problem commonly encountered in the grid-less method.In addition,unlike the previous work,the proposed algorithm does not only retain the point estimates of the parameters,but performs a complete Bayesian processing by estimating the posterior probability density function of the parameters and calculating the expectations.Therefore,the uncertainty of the parameter estimates can be captured and operated.In addition,this thesis also analyzes and discusses the proposed algorithm from the aspects of information theory,methodology,convergence and complexity,and demonstrates the innovation and superiority of the proposed algorithm.Simulation results under different performance indexes show that the performance of the proposed algorithm is better than that of the existing methods,and is very close to the Cramer-Rao bound(CRB)of a unbiased estimator.Moreover,the algorithm has strong robustness and keeps good performance under the nonlinear distortion caused by the ADC.