基于半参数椭球模型的MIMO雷达融合检测问题研究

Multiple-input multiple-output (MIMO) radar, as a new radar system, has played an important role in the national defense strategy. With the worsening of the electromagnetic environment, conventional parametric models as well as their established detection theory, cannot cope with the heterogeneous and uncertain non-Gaussian clutter environment that may vary from station to station in a MIMO radar system. Our project is centering on the fusion-based detection problem of MIMO radar in a complex clutter environment. First, we propose to model the clutter by a semi-parametric elliptical matrix model. A substantial advantage of our model compared to the earlier parametric modelling is that it provides a more precise description of the complex clutter background. Then, we will introduce the group of transformations to reflect the model parameters and distribution types, and then, set out to establish the theoretical system of statistical inference induced by the group invariance under a semi-parametric model. This theory aims at studying invariant tests and distribution-free estimations. Moreover, the interplay of the group invariance with fully CFARness and with distribution-freeness will be studied in the semi-parametric case. From these theoretical results, we will develop a synthetic approach to design fusion-based fully CFAR adaptive detection algorithms for the MIMO radar in a complex clutter environment. Additionally, a knowledge-aided technique will be further exploited to improve the performance of the resulting algorithms. Our intended theoretical achievements in this project, including the inference theory on group invariance under a semi-parametric model and the design philosophy of fully CFAR detectors, may enrich and perfect the existing MIMO radar theory. Also, they are expected to create a new direction for the research and development of adaptive detection and estimation.

MIMO雷达作为新兴的雷达体制，在未来国防建设中有重要作用。随着电磁环境的恶化，传统的参数模型及其检测理论已难以应对非均匀、非高斯、不确定且分站有差异的MIMO雷达杂波环境。本项目围绕复杂杂波环境中的MIMO雷达融合检测问题展开研究：首先提出用半参数的椭球矩阵模型来建模MIMO雷达杂波，该模型相比参数模型，对复杂杂波环境有更强的描述能力；进而引入变换群来描述模型参数和分布函数的变化机制，构建半参数椭球矩阵模型的群不变统计推断理论体系，包括不变检验和分布自由估计；最后，通过分析群不变性与完全CFAR性质、分布无关性的内在联系，给出有完全CFAR性质的集中式和分布式融合检测算法设计方案，并有效地利用知识辅助进一步提升检测能力。本项目研究中建立的系统性算法设计理念和原创性基础理论体系，不仅丰富和完善了MIMO雷达理论，还将为自适应检测研究开辟新的方向。

项目研究复杂环境下的雷达及MIMO雷达融合检测问题。针对非均匀非高斯场景下的雷达研究，提出了一些创新性的建模、融合及检测方法和理论。主要包括：1）研究复杂杂波在多通道多单元的联合特征，提出“复值多变量椭球等高矩阵分布族”的杂波模型，建立了相应的极大不变框架，得到了半参数模型下三种CFAR性质基于不变性的充分条件，提出了新的完全CFAR自适应检测算法；2）基于信息几何理论，研究了椭球分布流形的黎曼几何结构，导出了椭球分布散度矩阵的几何度量，提出了矩阵型数据的内在融合度量，并应用于雷达数据的融合检测中；3）在各种具体场景下，如低秩杂波、多径反射、子空间检测等，研究带先验的目标检测问题的不变检测理论，设计出新的知识辅助雷达、MIMO雷达检测算法。在本项目资助下，课题组共发表SCI论文7篇，其中5篇是由项目负责人以第一作者/通讯作者发表在IEEE Transactions on Signal Processing上；发表EI会议论文6篇；申请专利3项。顺利完成了项目研究任务，达到甚至超出计划书中规定的研究成果指标。项目研究成果具有理论意义和应用价值，促进了数学、统计学和信息科学的交叉融合研究。