北斗/惯导的快速混合高斯UKF算法

Gaussian mixture model UKF for BDS/INS navigation system

为进一步改善北斗/惯导中无迹卡尔曼滤波的精度,针对导航系统中噪声随机模型本质上的非高斯分布特性,结合有限高斯概率分布可近似任意概率密度函数的理论,以混合高斯UKF滤波为框架,提出了一种快速混合高斯UKF算法。该算法使用奇异值分解替代无迹变换产生采样点中的协方差平方根计算,和迭代中构造有限分量混合高斯模型二次近似后验二阶矩减少子滤波器数量的思路,改善了传统算法子滤波器数量随迭代次数成指数变化而增加计算成本的状况,一定程度上提高了计算的实时性。通过对北斗/惯导紧耦合系统的数据仿真实验,结果分析表明:相对于传统算法,本文提出的新算法在保证滤波精度的同时,计算量较低、实时性较好,适合于处理非高斯非线性北斗/惯导组合导航定位的滤波计算问题。

To improve the performance of unscented kalman filter（UKF）algorithm in BDS/SINS navigation system, on the background of non-Gaussian distribution in the navigation system model an improved Gaussian mixture model unscented kalman filter（GM-UKF）is discussed in this paper. The new al gorithm is based on Singular Value Decomposition（SVD）to alternative covariance square root calculation in sigma point production. And to end the rapidly increase number of Gaussian distributions, pdf re approximation is conducted in the new algorithm. In principle the efficiency algorithm proposed here can achieve higher computational speed compared with GM UKF. And the simulation experiment results show that, compared with the UKF and GM-UKF algorithm, the new algorithm implemented in BDS and SINS tightly integrated navigation system is suitable for handling non linear non-Gaussian filter calculation problem, for its low computational complexity with high accuracy.