相关随机系数矩阵Kalman滤波及在估计融合中的应用

The Kalman filtering which assumes that the model coefficient matrices are determinate is known as the best linear unbiased state estimator in the mean square error sense. With the development of information technology, the model coefficient matrices are random and correlated in many realistic systems and backgrounds. Therefore, we should study the estimation and fusion algorithms for dynamic system with random coefficient matrices. Many scholars, including the applicant, have made a serious study of random coefficient matrices Kalman filtering and its fusion in recent years, but they all assume that the random coefficient matrices are independent. The correlated random coefficient matrices Kalman filtering which is more realistic and has more academic significance remains to be unresolved. In this project, we will break the recursive form of the traditional Kalman filtering and study the correlated random coefficient matrices Kalman filtering and its fusion by the latest developments in the modern applied mathematics such as robust optimization and statistical recursive method. We will try to propose the optimal estimation and fusion algorithms for the dynamic system with random coefficient matrices in the mean square error sense. Moreover, we will use the new algorithms to deal with the maneuvering target tracking as well as the multi-target data association and strive for a breakthrough in this research.

经典的Kalman滤波假设模型系数矩阵是已知的确定矩阵。然而，随着信息科学技术在军事、通讯、经济金融等领域的广泛应用，人们更多地面对复杂现实背景问题的挑战，这些问题往往要通过随机系数矩阵动态模型才能更好地描述。因此，我们必须研究随机系数矩阵线性动态系统的估计融合问题。国内外学者包括申请人在随机系数矩阵Kalman滤波及融合方面已取得了一些初步的研究成果，但是这些工作都假设模型的随机系数矩阵是相互独立的，更符合实际背景，更有学术意义和应用价值的相关随机系数矩阵线性动态系统的估计融合问题尚待解决。本项目拟在符合工程实践的假设条件下，突破传统Kalman滤波递推形式的限制，利用稳健优化、统计递推等现代应用数学的最新进展，研究相关随机系数矩阵Kalman滤波与融合，力争给出线性均方误差意义下的最优估计融合算法，并利用新算法处理机动目标跟踪和多目标数据关联问题，获得国际领先成果。

经典的Kalman滤波假设模型系数矩阵是已知的确定矩阵。然而，随着信息科学技术在军事、通讯、经济金融等领域的广泛应用，人们更多地面对复杂现实背景问题的挑战，这些问题往往要通过随机系数矩阵动态模型才能更好地描述。因此，本项目研究随机系数矩阵线性动态系统的估计融合问题。我们利用稳健优化、统计递推等现代应用数学的最新进展，研究相关随机系数矩阵Kalman滤波与融合。我们在1）特殊Kalman滤波与融合；2）随机系数矩阵Kalman滤波融合及应用；3）相关数学工具这三方面都取得了一定研究成果。我们在国际国内期刊会议上发表论文4篇，其中SCI检索2篇，EI检索2篇，并受邀在国际专著中作为独立章节系统总结了随机系数矩阵Kalman滤波融合的相关理论及应用成果。项目研究成果可应用于处理观测随机丢失动态系统、多模型系统及多目标跟踪等重要实际问题。