分维自适应稀疏网格积分非线性滤波器

针对含加性高斯噪声的非线性离散系统，提出了可分别根据各维状态及量测方程的非线性函数特性来确定采样点及其权重的积分滤波器.设计了基于嵌入式高斯采样积分和稀疏网格法则的自适应多变量采样积分方法，可在匹配函数高阶泰勒展开项时，利用低阶采样点，提出了高效的数据结构和遍历算法，便于采用该积分方法分别估计系统状态/量测的预测均值和协方差矩阵.该滤波器既能根据各维非线性函数的特性确定采样点，又实现了对采样值和权重的完全复用，保证了算法效率.理论分析和仿真表明，该滤波算法中自适应调整的运算量小于计算非线性函数采样值.该滤波器与无迹卡尔曼滤波相比，提高了滤波精度，与固定形式的稀疏网格滤波器相比，提高了采样效率，且该方法为两者的广义形式.仿真实验也验证了状态估计的精确性和函数采样的高效性.

Dimension-wise Adaptive Spare Grid Quadrature Nonlinear Filter

For nonlinear discrete systems with addictive Gaussian noises, a new quadrature filter is proposed, which can fix sample points according to each dimension0s nonlinear function, respectively. In order to match higher-order terms of the nonlinear function0s Taylor expanding with reusing the sample points matching lower-order ones, an adaptive sampled multi variable quadrature rule is designed based on the embedded Gaussian sampled quadrature and the spare grid quadrature (SGQ) formula. A group of effective data structures and traversal algorithms are proposed for the sampled quadrature rule to be used for calculating the predict expectations of the states and measurements with their covariances. This filter could not only fix sampled points for different dimensions separately, but also reuse these points and their weights completely, thus enhancing the efficiency of the filter. This filter achieves a higher accuracy than the unscented Kalman filter (UKF), more efficiency than the fixed SGQ filter, as well as generalized form of these two filters. The calculating cost of adaptive steps is much less than computing the function sampled values. Simulations also validates the accuracy and efficiency of this filter.