基于多维数值积分的高阶确定采样型滤波方法

基于多维数值积分讨论了确定采样型滤波器,这一类滤波器的不同之处体现在对滤波器中均值和方差的计算,这一问题与数值积分密切相关.针对以往确定采样型滤波器在提高滤波精度的同时会增加计算量,通过分析高斯权值积分,采用完全对称积分公式,计算积分节点、节点个数及权重,相比高斯厄米特滤波减少了计算量,同时滤波精度可达到五阶以上.选取典型算例对新的滤波方法仿真分析,验证了该滤波方法的可行性和有效性.

High Degree Deterministic Sampling Filter Based on Multiple Numerical Integration Method

Deterministic sampling filter was discussed based on numerical integration. The mean and variance were calculated in the filters based on different rules, which were closely associated with the numerical integration. In the past deterministic sampling filters, the filtering accuracy was ensured, however, the amount of calculation was increased. Through analysis of integral formula, completely symmetric integral formula was used to calculate integral node, node number and weights, which reduced the amount of calculation compared with the Gauss-Hermit filter, and the filter precision could reach above five steps. The new filtering method was analyzed in the typical example simulation to test and verify the feasibility and effectiveness of the method.