无人驾驶汽车系统感知模块的重要技术——卡尔曼滤波,应用包括:
卡尔曼滤波与行人状态估计
扩展卡尔曼滤波(EKF)与传感器融合
处理模型,无损卡尔曼滤波(UKF)与车辆状态轨迹KF卡尔曼滤波
卡尔曼滤波器是基于贝叶斯法则的,且相关不确定性的概率分布是符合高斯分布,
The main differences are:
the F matrix will be replaced by Fj when calculating P′.
the H matrix in the Kalman filter will be replaced by the Jacobian matrix Hj when calculating S, K, and P.
to calculate x′, the prediction update function, f, is used instead of the F matrix.
to calculate y, the h function is used instead of the H matrix.
For this project, however, we do not need to use the f function or Fj. If we had been using a non-linear model in the prediction step, we would need to replace the F matrix with its Jacobian, Fj. However, we are using a linear model for the prediction step. So, for the prediction step, we can still use the regular Kalman filter equations and the F matrix rather than the extended Kalman filter equations.
One important point to reiterate is that the equation y=z−Hx′ for the Kalman filter does not become y=z−Hjx for the extended Kalman filter.UKF无迹卡尔曼滤波
核心思想:近似非线性函数的概率分布比近似任意一个非线性函数本身要容易;UKF只是将非线性函数映射通过关键点的映射来实现。
涉及知识:UT变换
(个人理解:选取概率分布中具有代表意义的sigma点,对sigma点进行非线性转换,然后将转换后的点用高斯分布近似表达出来)
如果状态量的后验分布近似高斯分布,那么UKF很高效,相比EKF,UKF的优点:精度高;不需要计算雅克比矩阵
缺点:如果状态量的后验分布和高斯分布差很远,UKF的滤波效果就比较差。(即:其不适用于状态量的后验分布和高斯分布差很远的问题)