基于信息几何和高维统计分析的多传感器目标检测与跟踪融合研究

With the wide applications and rapid developments of multi-sensor technology, and the significantly increased abilities to access the data, we are facing the more complicated environments and processing objects as well as the higher requirements on the information quality. In this project, for some intrinsic features in target information processing, such as nonlinearity, non-Gaussianity, uncertainty and high dimensionality, we will adopt and develop the advanced mathematical and statistical theories and approaches to research the detection and tracking problem of complicated targets in complicated stochastic dynamical systems, and the information fusion problem for multi-sensor systems. It is expected that to solve some basic and key problems on the theoretical research and engineering applications in information fusion field. The details are listed as follows: 1) Using the variational Bayesian filtering, we will study the state estimation and tracking of targets and the corresponding fusion algorithms for nonlinear, non-Gaussian stochastic dynamical systems; 2) By modeling the statistical manifolds for distributed multi-sensor systems, we will research the distributed estimation fusion problem in the general frame of information geometry so as to develop more efficient fusion algorithms; 3) By researching the statistical and geometric models of multiple objects having complicated structure, and developing the spectral theory of high-dimensional random matrices involving sample covariance matrices, we will provide some more efficient detection and classification algorithms for complicated targets. Through the research of this project, we will provide some new theoretical bases, ideas and methods for related research areas. The achievements of this project can promote the development of related interdisciplines, and match the requirements of the development of high technology and defense modernization.

随着多传感器技术广泛应用和迅速发展，获取数据的能力显著提升，人们越来越多地面对更加复杂的环境和处理对象，对信息质量的需求日益提高。本项目针对多源信息融合中非线性、非高斯、不确定和高维度等诸多特性，利用和发展信息几何以及高维统计分析的理论和方法，研究复杂随机系统中复杂目标的检测、跟踪及其融合理论与算法，解决理论研究与工程应用领域中几项基本而又关键的问题。包括：通过变分贝叶斯滤波研究非线性、非高斯随机动态系统中目标状态估计、跟踪及融合理论和方法；研究分布式系统统计流形，在更一般框架下获得估计融合优化模型及算法；研究复杂结构目标的统计和几何模型，通过高维随机矩阵的谱理论，获得高维特征复杂目标的高效检测或分类理论和算法。项目将为相关领域的研究提供新的理论基础、思路和方法，促进学科发展，适应高科技及国防现代化建设的紧迫需求。

项目研究多传感器复杂随机系统目标检测、跟踪及其融合中几个基本而重要的问题。我们利用和发展信息几何、高维统计推断的理论和方法，提出一些创新性方法，获得了几项新理论、新方法以及相应的有效算法。主要包括：1）研究结构复杂目标观测的统计模型，提出了距离扩展目标的不变自适应检测新理论和算法，发展了IEEE汇刊上最近的一些不变检验理论，提出具有恒虚警率等优良性质的不变检测器；2）基于信息几何提出分布式估计融合一种新框架，建立分布式估计统计流形以及流形上的估计融合优化模型，并开发出相应的优化算法，获得的估计融合在均方误差意义下比现有算法更优；3）对于高维信号的检测和估计问题，研究涉及的高维随机矩阵统计性质，在较一般条件下对多种结构化协方差矩阵提出收缩估计等方法，进而获得信号处理和数据处理中优良的检测器或估计器；4）针对非线性、非高斯、含未知输入等不确定随机动态系统，提出多种不同条件下的目标状态稳健估计和滤波算法。在本项目资助下，我们在包括国际著名的IEEE Transactions on Signal Processing等国内外期刊发表论文16篇，在国际信息融合大会和中国信息融合大会文集发表会议论文10篇，其中SCI收录9篇，EI收录11篇，顺利完成了项目研究任务，实现了预期研究目标。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深入交叉与融合。