The Low Complexity Stochastic Maximum Likelihood Algorithm Based On Intelligent Optimization

Spatial spectrum estimation(referred to as DOA)is an important research topic in sensor array signal processing,which has wide applications in communication systems,military,biomedical engineering and so on.The Stochastic Maximum Likelihood(SML)algorithm is one of the most important solving methods for DOA because it has the best performance in theory.However,the estimation of SML generally involves of a multi-dimensional nonlinear optimization problem.As a result,its computational complexity is rather high and it is hard to apply this technique into real-time systems.To reduce the computational complexity of SML estimation,we proposed two low-complexity spatial spectrum estimation algorithms based on SML.The main research work is as follows:Firstly,considering the high computational complexity of SML,we proposed a low complexity improved PSO algorithm.This algorithm has the following steps.1)We firstly obtain the closed solution of Estimation of Signal Parameters via Rotational Invariance Techniques(ESPRIT)to pre-estimate the DOA,in addition,we compute the current Signal Noise Ratio(SNR)of the system as well as the Cramer-Rao Bound(CRB)of the SML;2)According to the pre-estimated DOA and current CRB,we then determine a small specific initialized space which is closed to the optimal solution of SML;3)Modify the inner factor and let the particles converge to the global solution of SML.Since these particles are already very close to the solution of SML,they will converge quickly.As a result,the computational complexity can be greatly reduced compared with the original PSO algorithm,thus,the proposed method achieves significant merit of convergence speed.Secondly,to reduce the computational complexity moreover,we explored a low complexity membrane computing algorithm for SML estimation.First of all,we divide the whole searching space into several basic membranes and a surface membrane.In each basic membrane,the PSO algorithm is adopted to find the local solution.Through the evolution rule and communication mechanism of each membrane,all the local solutions are collected into the surface membrane and finally we use the artificial bee colony optimization algorithm to get the global solution.The feature of this algorithm can be parallel and distributed computing.Therefore,it is also more efficient compared with our improved PSO algorithm.At last,we demonstrate the efficiency of the two proposed algorithms through simulations.we compare our proposed algorithm with other techniques such as original PSO algorithm under the pre-condition that the DOA estimation accuracy are the same.In our simulation,the number of particles and iteration times of our improved PSO algorithm is about one fifth of that of the conventional PSO algorithm.The calculation time of the improved PSO algorithm is only about one tenth of that of the conventional PSO algorithm.For the proposed membrane computing algorithm,the calculation time is about one eleventh of that of the conventional PSO algorithm.As a result,our proposed two algorithms greatly reduce the computational complexity of SML,in addition,the real-time effect is remarkable.