基于方差奇异和带反馈的连续动态系统多传感器估计融合研究

In order to adapt to the rapid development of modern high-tech, economy, society, military and other fields, it is urgent for us to solve the problems of distributed estimation fusion for continuous system with covariances singular and feedback in multisensor system. However, so far, very little study work had been done on optimal distributed estimation fusion researches of continuous dynamic systems for basing on covariances singualarity and feedback, even the study of continuous dynamic systems for basing on covariances nonsingualarity and feedback don't appear. This project focuses on the following several scientific problems: differential equation of estimation fusion and differential equation of estimation fusion error covariance of optimal distributed estimation fusion formula research of continuous dynamic systems with covariances singualarity; differential equation of estimation fusion and differential equation of estimation fusion error covariance of optimal distributed estimation fusion formula research of continuous dynamic systems with covariances singualarity and feedback. Through this project research, we expect to give a theory on continuous synamic systems multisensors estimation fusion for baseding on covariances singualarity and feedback, and furthermore solve some open problems of the discrete systems multi-sensor optimal distributed estimation fusion theory by a finite element discretization the responding continuous dynamic systems estimation fusion result.

为了适应现代高科技、经济、社会、军事等领域的迅速发展，急切需要解决方差奇异以及带反馈的连续动态系统多传感器分布式估计融合问题。但是目前对多传感器系统中估计误差方差和观测噪声方差奇异条件下带反馈的动态系统最优分布式估计融合算法研究少之又少，甚至在方差非奇异条件下带反馈的动态系统融合算法研究还未见到。本项目重点解决以下几个科学问题：当估计误差方差和观测噪声方差奇异时，研究连续动态系统多传感器最优分布式融合公式中估计融合的微分方程以及估计融合误差方差的微分方程；当估计误差方差和观测噪声方差奇异时，研究带反馈的连续动态系统多传感器最优分布式融合公式中估计融合的微分方程以及估计融合误差方差的微分方程。通过本项目的研究，有望给出方差奇异以及带反馈的连续动态系统多传感器最优分布式估计融合理论，并且借助有限元方法离散连续动态系统多传感器分布式估计融合的结果解决离散系统多传感器估计融合理论中未解决的问题。

为了适应现代高科技、经济、社会、军事等领域的迅速发展, 本课题考虑了方差奇异以及带反馈的连续动态系统多传感器分布式估计融合问题。其主要研究包括：针对估计误差方差奇异系统，利用极限理论和伪逆矩阵技术，给出了连续动态系统多传感器最优分布式融合公式中估计融合的微分方程以及估计融合误差方差的微分方程；针对估计误差方差和观测噪声方差奇异系统，通过引入随机伪逆矩阵理论以及新的分析技巧，解决了带反馈的连续动态系统多传感器最优分布式融合公式中估计融合的微分方程以及估计融合误差方差的微分方程问题。课题的实施将为多传感器信息融合理论研究提供新的思路和方法，为解决实际多传感器分布式估计融合问题提供新的途径。