基于最大期望算法的多时变信号DOA估计方法

当多个辐射源同时存在并交替发射信号时,接收数据间相互交错,且多个数据间并无显性关联,无源合成阵列每一次测量仅能获取来波的频率、幅度与相位等数据信息。为了同时、高效地实现多个参数的联合估计,提出采用最大期望算法进行估计多个时变信号参数估计的新方案,将一个高维多参数优化问题分解成多个并行的低维问题进行求解。该方法主要包含求解期望值步骤和期望值最大化两个步骤。求解期望值步骤主要建立接收信号与其辐射源的对应关系,即信号分选,而期望值最大化步骤采用最大似然方法估计辐射源的入射角信息。这两个步骤相互迭代,交替进行辐射源信号的分选与测向。同时,还推导出无源合成圆阵相位差数据的最大似然方法进行入射角的精确估计的闭合形式解,并通过接收信号的复数响应进行相位模糊解算,并推导出测向精度的理论下限。最后,通过数值仿真结果验证了该方法的有效性。

DOA estimation of multiple time-varying signals with expectation-maximization algorithm

When multiple sources coexist during a rotating period,the emitting signals from these sources are interleaved and hence implicitly related,since only frequency,magnitude and phase difference can be obtained in each sample.In order to realize the joint estimation of multiple parameters simultaneously and efficiently,this paper proposes a new scheme to estimate the parameters of multiple time-varying signals using maximum expectation algorithm.A high-dimensional multi-parameter optimization problem is decomposed into several parallel low-dimensional problems for solving.The method mainly consists of two steps:solving expected value and maximizing expected value.The expected value step mainly establishes the correspondence between the received signal and the radiation source,that is,signal sorting,while the expected value maximization step uses the maximum likelihood method to estimate the incident Angle information of the radiation source.The two steps are iterated each other,and the separation and direction finding of the radiation source signal are carried out alternately.In this paper,the closed form solution of the maximum likelihood method for the passive synthetic circular array phase difference data is derived for the exact estimation of the incident Angle,and the phase fuzzy solution is calculated by the complex response of the received signal,and the theoretical lower limit of the direction finding accuracy is also derived.Finally,the effectiveness of the proposed method is verified by numerical simulation.