Study On The New Methods Of High-Resolution Direction Finding Based On Monte Carlo Methods

High-resolution multi-source direction finding is always a hot research area in array signal processing. The breakthrough of this technique is greatly meaningful in many research fields such as sonar, radar, geology, biomedical engineering and so on. Especially the underwater acoustic high-resolution multi-source direction finding technique is the key to underwater defence and ocean exploration. Sponsored by the National Natural Science Foundation of China, Specialized Research Fund for the Doctoral Program of Higher Education and other research projects, Bayesian high-resolution methods are thoroughly studied in this thesis. Also in order to reduce the computation of Bayesian method, Monte Carlo method is combined with Bayesian methods, the new methods of direction finding based on Monte Carlo method are studied.The new progresses and main results are summarized as follows:1. Bayesian high-resolution direction finding method is thoroughly studied.Bayesian high-resolution direction finding method is introduced first. Bayesian spectrum analysis technique and Bayesian maximum a posterior estimator are presented. By comparison of two methods in theory and performance, it is proved that the theory of the latter method is relatively simple and also its performance is better. The Bayesian maximum a posterior estimator is studied next in detail. Simulation results show the performance of Bayesian Maximum a posterior DOA Estimator (BM DOA Estimator) is excellent, and also it can estimate the coherent sources, perform better than MLE, especially in low SNRs. But the computation of BM DOA Estimator is very large. It requires multidimensional grid search, and the computational burden increases exponentially with the dimension. Therefore its new fast algorithm is very necessary.2. Bayesian maximum a posterior DOA estimator based on Gibbs sampling (GSBM) is further investigated.In order to reduce the computation of BM DOA Estimator, Markov Chain Monte Carol (MCMC) methods are applied and Bayesian Maximum a posterior DOA Estimator based on Gibbs Sampling (GSBM) is given. GSBM is studied further based on previous work. GSBM needn't multidimensional search and hence reduces the computation obviously. Simulation results demonstrate that GSBM not only keeps the good performance of original BM method, better than MLE, MUSIC and MiniNorm; but also reduces the computation complexity of original BM from O(LK) to O(K×J×Ns).3. Maximum likelihood DOA estimator based on importance sampling (ISMLE) is proposed.Maximum Likelihood DOA Estimator (MLE DOA Estimator) requires multidimensional search to produce great computation. To solve this problem, classical Monte Carlo methods is combined with MLE and the Maximum Likelihood DOA Estimator Based on Importance Sampling (ISMLE) is proposed. The theoretical derivation of ISMLE is presented, especially for the choice of Importance Function (IF). Simulation results show ISMLE not only keeps the good performance of MLE, catching the CRB in high SNRs, performs better than MUSIC and MiniNorm in low SRNs; but also reduces the computation complexity of MLE from O(LK) to O(K×H).4. Bayesian maximum a posterior DOA estimator based on importance sampling (ISBM) is proposed.Classical Monte Carlo methods are applied to BM DOA estimator to reduce the computational burden. Bayesian Maximum a posterior DOA Estimator based on Importance Sampling (ISBM) is proposed. The theoretical derivation of ISBM is presented. Simulation results show that ISBM not only keeps the performance of original BM method, better than MLE, MUSIC, and MiniNorm; but also reduces the computation complexity of original BM method from O(LK) to O(K×H), obviously reduces the computation. Also the research results show that the computation of ISBM is similar as GSBM, but the performance of ISBM is better than GSBM. Therefore ISBM a more efficient computation method for BM DOA estimation.