卡尔曼滤波框架下优化增益异类噪声处理方法及其应用

针对基于卡尔曼滤波框架算法只能处理已知高斯噪声系统的局限性,设计能够同时处理含有异类噪声系统的改进算法。将不确定系统受到的干扰分成高斯噪声和未知有界噪声,对噪声特点进行分析,并将其加入状态方程和观测方程;在吸收集员滤波优点的基础上,对标准卡尔曼滤波进行改进,通过计算包含两种异类噪声系统状态的最小均方误差,得到该条件下滤波增益的调整值;将利用集员滤波得到的状态统计量以及两类噪声信息和调整后的滤波增益代入卡尔曼滤波体系,得到改进后的滤波算法。将提出的改进方法应用于不确定车辆导航系统中进行解算,仿真结果表明:改进滤波方法能够有效克服异类噪声的干扰,性能优于扩展卡尔曼滤波方法,对异类噪声具有较好的抵抗能力。

Optimal gain processing method of heterogeneous noises based on Kalman filtering framework and its application

Aiming at the limitation that methods based on Kalman filtering framework can deal with the known Gaussian white noise only, an improved method was proposed to deal with the system with heterogeneous noises. The disturbance from an unknown system was classified to Gaussian white noise and unknown but bounded noise which are both added into the state equation and observation equation on the basis of the noise characteristics analyzed. The set-membership filter was employed to improve standard Kalman filtering, and the adjusted value of the gain filtering was obtained by calculating the minimum mean square error of system with two noises. The improved filtering was proposed to incorporate the estimator statistics of the set-membership filter, two noises statistics and the adjusted filter gain. The improved algorithm was applied to an uncertain vehicle navigation system, and the simulation results show that the improved filtering algorithm which overcomes the heterogeneous disturbance noise performs better than the extended Kalman filtering.