基于临界特征值的 MDL 信源数欠估计分析方法

摘要

针对最小描述长度准则下的信源数欠估计问题，提出了一种基于临界特征值的欠估计分析方法，通过对信源数估计算法进行分析，给出了临界特征值的求解表达式及唯一性证明。相比现有方法，临界特征值方法可对不同漏检数下的欠估计边界进行预测，并评估阵列参数对信源数估计性能的影响。为解决大漏检数下的临界特征值的求解复杂问题，提出了一种近似方法，分析了近似误差的影响因素。仿真数值实验结果表明，临界特征值方法可准确描述算法在不同漏检数下的欠估计边界，为基于信息论准则的信源数估计算法提供了一种新的具有普适性的分析手段。%A method based on critical eigenvalues was proposed to evaluate the underestimation problem of source enumeration under the minimum description length (MDL)criterion.The uniqueness of critical eigenvalues was proved and their solution expression was presented with the analysis of the enumeration algorithm.It was shown that the critical eigenvalue method can predict the boundary of underestimation for different numbers of undetected sources and evaluate the influences of array parameters on the performance of source enumeration,compared with the existing methods.An approximation method was proposed to reduce the calculation complexity of solving critical eigenvalues under the condition of large numbers of undetected sources and the factors affecting the approximation errors were also analyzed.Simulation results indicated that the critical eigenvalue method can exactly describe the boundary of underestimation of source enumeration.The results provided a new analysis tool for other source enumeration methods based on information criteria.