线性等式约束下两种集合卡尔曼滤波的等价性  

The Equivalence of Two Kinds of Ensemble Kalman Filter with Linear Equality Constraints

作　　者：谢莉清[1] 何腊梅[1] 

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《成都信息工程大学学报》2016年第3期285-290,共6页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(61374027);数学地质四川省重点实验室开放基金资助项目(scsxdz2011006)

摘　　要：针对含线性等式约束的非线性动力系统状态估计问题,考虑将集合卡尔曼滤波算法和估计投影方法相结合,根据不同的处理对象,提出两种不同的含线性等式状态约束的集合卡尔曼滤波算法:(1)运用估计投影方法对每个粒子进行修正之后再加权平均;(2)直接对加权平均后的状态估计向量使用估计投影方法。在约束矩阵退化为常向量,约束向量退化为常数的情况下,给出了上述两种滤波结果的等价性证明。数值模拟实例验证了这一结论。For the problem of state estimation for nonlinear systems with linear state equality constraints,the method that combines ensemble Kalman filter with estimate projection approaches is presented. According to the different objects,there are two different algorithms of the ensemble Kalman filter with linear equality constraints：（ 1） calculating weighted average after using estimate projection method to correct each particle;（ 2） applying estimate projection method to calculating weighted average of the unconstrained state estimation vector. It is theoretically proved that the state estimation results of the two proposed algorithms are equivalent when the constraint matrix reduces to a constant vector,and the constraint vector reduces to a constant. Simulation results verify this conclusion.

关 键 词：概率论与数理统计 信息融合 集合卡尔曼滤波 估计投影 非线性系统 状态估计 状态约束 

分 类 号：TN713[电子电信—电路与系统]