Joint Detection And Estimation Of Wideband Signals Based On MCMC Methods

At present, a common approach to wideband signal processing is to sample the spectrum of the incoming signals at each sensor to form an array of narrowband signals. Having done that, algorithms developed for the narrowband model can be used to solve wideband signal processing problems. This transformation process has high complexity, always causes transformation error, and the operation is big, which results in the wideband signal processing methods have poor real time performance and low estimation precision. As a result, based on the low bandpass signal reconstruction theory, a novel wideband model structure is developed, which is applicable to both the wideband and the narrowband signal. By introducing the Markov Chain Monte Carlo (MCMC) method into the Bayesian parameter estimation theory, jointly model order detection and DOA estimation method is proposed in this paper. The main results of this thesis are summarized as follows:1. A novel wideband model structure is developed based on bandpass signal reconstruction theory, which is more exact and more applicable. In additon, the interpolation matrix is extended, which avoids estimating the DOA in advance. The model proposed is applicable to wideband signals, narrow band signals, correlated signasl and incorrelated signals.2. Based on the Bayesian maximum posterior probability estimation, jointly model order detection and DOA estimation method is proposed. In the Bayesian approach, the number and DOA of signals are assumed random variables, one starts with the prior distribution function of the parameter from which one can obtain its posterior distribution function using Bayes'formula. Then, the desired posterior distribution function including the number and ISD (inter-sensor delay, which is aroused by the same signal arriving at the different sensor in different time) can be get.3. Markov Chain Monte Carlo (MCMC) methods are studied deeply, which have widespread applications in Bayesian parameter estimation. The Monte Carlo methods are reviewed, including the basic theories of Markov Chain Monte Carlo and different sampling procedures, like Metropolis-Hastings (M-H) algorithm, Gibbs sampler, and reversible jump sampler. The dependent Markov chain and random walks sampling methods are emphasized. In addition, the combing strategies of different sampling methods are introduced. In order to improve the convergence speed and estimation precision, on the basis of the mixture strategy, a hybrid MCMC method combing the dependent Markov chain and the adaptive random walks sampling methods is proposed, and a hybrid sampling algorithm based on RJMCMC method are proposed.4. By introducing the hybrid RJMCMC method into the Bayesian maximum posterior probability estimation, the problem of operation is resolved. We first assume that the number of signals impinging onto the array is given, we propose to use a hybrid MCMC sampler to estimate the inter-sensor delays. In simulation, kinds of signals including wideband, narrowband, correlated and incorrelated signals are used to analyze the performance of the method developed. Simulation results show that the method also has good estimation with small snapshots. Finally, we consider the case where the number of signal is unknown. The hybrid RJMCMC method is used to jointly estimate the number of model order and the DOA. Simulation results demonstrate that the probability of an error in detection of the model order tends to diminish toward zero, and the mean squared error of inter-sensor delay approaches CRLB closely with moderate number of snapshots N and elements M with increasing SNR values.