Research On Parameter Estimation Algorithms For Array Signals Under Low Signal-to-Noise Ratio And Small Sample Size

The increasing popularity and rapid development of electronic warfare poses challenges for array signal processing in complex electromagnetic environments.In particular,with the growing demand for accurate source enumeration and high-precision direction finding under non-ideal signal conditions,classical source enumeration methods represented by Information Theoretical Criterion(ITC)and traditional direction-finding methods based on subspace theory have exposed their limitations,posing serious bottlenecks for development of array parameter estimation.Over the past few years,the significant advancements in computational intelligence especially the extensive investigation into granular computing and machine learning,has provided a strong impetus for addressing the limitations of traditional methods used in array parameter estimation.This,in turn,has created new prospects for advancing both the theory and application of array signal processing.Granular computing is a methodology that abstracts and models data as higher-level computational units,facilitating the analysis of data distribution features and correlations.It enables tackling intricate problems with uncertainties.Although granular computing has been explored in areas like data mining and pattern recognition,its incorporation into array signal processing,particularly in regards to source enumeration,has been largely overlooked.For this reason,the main research focus of this dissertation is on combining the benefits of granular computing in solving uncertainty problems and source enumeration in scenarios with low Signal-to-Noise Ratio(SNR)and small sample size.Machine learning is a data-driven approach to signal analysis and processing.It involves the extraction of patterns and rules from sample data,which are then utilized for the classification and prediction of new data sets.Recent research has achieved certain results in the application of machine learning to Direction-of-Arrival(DOA)estimation,addressing shortcomings of traditional methods in adapting to adverse signal environments.In this dissertation,the emphasis is on further improving the adaptability of direction-finding methods to low SNR and small sample data,while also reducing computational complexity.The dissertation employs granular computing,machine learning and subspace analysis to tackle the challenges of source enumeration and direction finding in low SNR and small sample size scenarios.The primary contributions and innovative aspects of this research are as follows:1.To address the urgent need for accurate estimation of the number of sources under low SNR and limited sample size conditions,we propose a source enumeration method based on fuzzy information granulation.To distinguish signal eigenvalues and noise eigenvalues that overlap with each other,the eigenvalue sequence of the sample covariance matrix is treated as a numerical sequence.Under the constraints of justifiable granularity and well-articulated semantics,interval information granules are constructed based on this sequence.The inherent distribution characteristics of each sample eigenvalue are explored and analyzed,according to which a rough boundary between signal eigenvalues and noise eigenvalues is determined to obtain an initial estimation result of the number of sources.Then,an encodingdecoding mechanism based on the fuzzy C-means algorithm is applied to refine the rough partitioning result.The distribution property of each eigenvalue is described into a prototype matrix and a membership matrix.By minimizing decoding error,the membership of those eigenvalues at the classification boundary between signal eigenvalues and noise eigenvalues is determined.Ultimately,the precise estimation result of the number of sources is reflected through the optimal membership matrix.Theoretical analysis and simulation results verify that the proposed approach proves to be capable of precisely estimating the number of sources,with a high probability of success under low SNR and limited sample size conditions.Its performance is superior to traditional methods based on the ITC and the Gerschgorin disk criterion.Moreover,the method exhibits robustness to changes in the number of array antennas and the angular separation between sources,effectively meeting the demand of accurate source enumeration for array parameter systems.2.To deal with the issue of performance degradation or failure of subspace-based DOA methods under low SNR and small sample size conditions,a signal subspace reconstruction method based on quantum-behaved particle swarm optimization(QPSO)is proposed.Firstly,the theoretical expression of the signal subspace is derived using subspace theory.Subsequently,the DOA problem in low SNR and inadequate sample data is transformed into a multivariate optimization problem to improve the orthogonal relationship between subspaces.Finally,the QPSO with global search capability is utilized to solve this problem.Compared to traditional subspace decomposition-based methods,the proposed method considers the signal subspace reconstruction and the optimization of orthogonal relationship,resulting in higher precision in DOA estimation.The method is also easy to implement with fewer manually controlled parameters.3.In an effort to address the issues of inadequate adaptability and performance deterioration observed in convectional model-driven DOA algorithms,this dissertation presents a DOA estimation technique based on Auto Encoder(AE)and Kernel Extreme Learning Machine(KELM),which is suitable for low SNR and small sample sizes.During data preprocessing stage,AE is used to extract features of directions of arrival(DOA)contained in the real and imaginary parts of upper triangular elements of the sample covariance matrix(SCM),establish a nonlinear mapping relationship between DOAs and SCM,and form an effective feature dataset.In neural network training and testing phase,a kernel function is introduced into Extreme Learning Machine(ELM)to improve the training efficiency,called Kernel Extreme Learning Machine(KELM).A single hidden-layer feedforward network(SLFN)is trained by combining effective feature datasets and KELM.The trained SLFN can serve as a DOA estimator to solve direction finding problem under low signal-to-noise ratio and small sample size.Simulation experiments show that compared to traditional direction finding methods which is model-driven,the proposed method has strong adaptability to low signal-to-noise ratio and small sample size scenarios.