卡尔曼滤波及其无人驾驶应用

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−Hj​x 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)