基于特征函数的非线性非高斯系统滤波器设计

Traditional non-linear filters are mainly designed to handle the dynamic systems subjected to Gaussian noises, where the estimation error covariance is employed to be performance index. However, the practical systems are often affected by the noises satisfied non-Gaussian distribution. The full state information of such systems cannot be obtained just by using the second order statistics, and the new filtering method based on probability density function is needed. The based c haracteristic function filters is popular because of its unique advantage. However, the existing technology can only used to estimate the state for the linear system with one dimension measurments. With such backdrop, the following several issues are studied for the non-linear non-Gaussian systems: 1) Designing the filters for the systems with linear state equation and non-linear measurments. 2) Proposing the filtering methods for the systems with both nonlinear state equation and measurement outputs. 3) Based on measurements form multi-sensors, the data fusion method for the dynamic systems are presented. We will solve following key problems: Designing new performance index and presenting the corresponding filtering methods suitable for multi-dimensional systems. Applying the linearization, particle sampling and Neural networks to modeling the dynamic systems of estimation error. Developing the suitable weighting matrix to fuse the data for the non-Gaussian systems. We intend to obtain some innovative results, and lay a solid theoretical foundation for achieving accurate estimation for the dynamic systems.

传统的非线性滤波器设计主要针对受高斯噪声影响的动态系统，且以估计误差协方差为性能指标。然而，实际系统常常受非高斯噪声的影响，对于这类系统，仅以二阶统计量无法全面的捕捉系统的状态信息，亟需从概率密度函数的角度对滤波器重新设计。基于特征函数的滤波器以其独特的优势受到了人们的重视，但现有的成果仅适用于一维观测系统，且要求状态方程是线性的。为此，本项目拟开展多维非线性非高斯系统的状态估计研究：1) 线性状态方程非线性测量输出系统的滤波器设计；2) 状态方程和测量输出均为非线性的动态系统滤波器设计；3)传感器网络环境下的非线性系统数据融合；重点解决研究中遇到的几个关键问题：设计新的性能指标，研究适用于多维系统的滤波方法；应用线性化、粒子采样及神经网络等技术研究非线性误差动态系统的建立方法；适用于非高斯多传感器系统数据融合时的权重选取方法。力争取得一些创新型成果，为实现系统状态的精确估计打下理论基础。

本项目针对传感器网络下的非线性非高斯动态系统，以状态空间分解、随机分析理论及凸优化理论等数学方法为工具，开展基于特征函数的融合滤波方法研究。针对现有的基于特征函数的滤波器仅能处理一维观测结果的情形，采用状态空间分解的方法，分析了目标特征函数与误差特征函数的关系，构建了新的性能指标，利用数值方法寻求合适的滤波器增益，实现了多维测量时的状态估计。针对多传感器系统，在单传感器的基础上，进一步研究了集中式、分布式和序惯式的数据融合方法，根据不同的融合滤波器结构构造相应的代价函数，研究网络诱导现象对融合精度的影响。针对受饱和约束的非线性系统，建立了饱和约束条件和非完全测量输出模型，用预测和更新两个容易实现的步骤得到了递归的滤波器，进而揭示了测量丢失概率对滤波器精度的影响，并研究网络环境下的分布式滤波器设计方法。针对一类受噪声影响的奇异系统，揭示了时变奇异矩阵下不同时刻状态变量间的演化关系，利用状态空间分解技术并行实现降维状态的预测、估计和平滑，并探讨了噪声有界但统计特性未知的一类系统的状态估计问题。