欠观测条件下的增量容积卡尔曼滤波

Incremental Cubature Kalman Filtering Under Poor Observation Condition

在工程实践中,由于环境影响、量测设备不稳定等因素,非线性滤波系统中的量测方程可能会出现较大的系统误差,而标准的非线性滤波算法不能消除这类系统误差。针对该问题,假定过程噪声和量测噪声服从高斯分布,利用相邻量测时刻的量测值之差建立增量量测方程,采用3阶球面径向规则获得容积点及其权值。使用容积点对贝叶斯滤波过程中的积分进行数值近似,从而提出增量容积卡尔曼滤波算法。仿真实验结果表明,增量容积卡尔曼滤波算法滤波精度优于标准容积卡尔曼滤波算法与增量卡尔曼滤波算法,能够成功消除量测方程中的系统误差。

In some engineering applications, there are some cases like the effect of environment, the instability of measurement devices. Large error comes into being from the measurement equation in the nonlinear filtering system. The standard nonlinear filtering algorithm cannot remove this kind of system error. This paper addresses this problem,assumes that process noises and measurement noises are subject to Gaussian distribution,establishes the incremental measurement equation using the difference between the adjacent measurements,and obtains the cubature points and its weights using the third-degree spherical-radial rule. The cubature points are employed to approximate the integrals in the Bayesian filtering process numerically,and the incremental cubature Kalman filtering is obtained. Simulation results show that the filtering accuracy of the incremental cubature Kalman filtering is not only better than that of the standard cubature Kalman filtering but also better than that of the incremental extended Kalman filtering. The new algorithm can eliminate the system error of the measurement equation successfully.