Abstract: A new constrained filtering method based on Unscented Kalman Filter (UKF) and pseudo-observation called SPUKF (Sub-system Parallel Unscented Kalman Filter) was proposed for state estimation of nonlinear system with nonlinear constraints. In the proposed method, the system and constraint equations were fictitiously divided and reconstructed into two sub-systems, and then the state estimation was obtained from two concurrent filtering processes which were established on these two sub-systems alternately. Compared to sequential processing method of pseudo-measurement, SPUKF did not need to determine the processing order between measurement and constraint, but achieved better performances, so as to address the problem of deciding processing order beforehand in sequential processing method. In the simulation of pendulum motion, it is verified that SPUKF gets better estimation performance and less running time than the two forms of sequential processing method, and enhances the estimation error improvement ratio by 22 percentage points than UKF. Furthermore, it obtains comparable estimation results with batch processing way.

Key words: state estimation, Unscented Kalman Filter (UKF), nonlinear equality constraint, batch processing, sequential processing

摘要： 针对带非线性等式约束的非线性系统的状态估计问题，给出了一种新形式的基于无迹卡尔曼滤波及伪观测手段的处理约束的状态估计方法（SPUKF）。在该方法中原动态系统被虚拟地分离成两个并行的子系统，各时刻的状态估计由基于这两个子系统构建的两套滤波链交替得到。相对于伪观测法中的序贯形式估计器，SPUKF无需事先确定观测及约束的处理次序且能获得更好的估计结果，故可以用来解决序贯方法中观测与约束的处理次序问题。由钟摆运动的实例仿真结果看到，SPUKF不仅有好于序贯形式无迹卡尔曼滤波的估计效果，误差改善比达到22%左右，而且算法运行时间与序贯形式估计器相近。此外，其估计效果还与批处理无迹卡尔曼滤波相当。

关键词: 状态估计, 无迹卡尔曼滤波, 非线性等式约束, 批处理, 序贯处理