自动驾驶基础技术-无迹卡尔曼滤波UKF
Unscented Kalman Filter是解决非线性卡尔曼滤波的另一种思路,它利用Unscented Transform来解决概率分布非线性变换的问题。UnScented Kalman Filter不需要像Extended Kalman Filter一样计算Jacobin矩阵,在计算量大致相当的情况下,能够获得更加精确非线性处理效果。
附赠自动驾驶学习资料和量产经验:链接
1.Unscented Kalman Filter的思想
it is easier to approximate a probability distribution than it is approximate an arbitary nonlinear function.
逼近概率分布要比逼近任意的非线性函数要容易的多,基于这种思想,Unscented Kalman Filter利用概率分布逼近来解决非线性函数逼近的问题。
以一维的高斯分布为例,如下图所示,左侧是一维高斯分布, 是非线性变化,右侧是变换后的高斯分布。
图片来源:State Estimation and Localization for Self-Driving Cars:Lesson 6: An Alternative to the EKF - The Unscented Kalman Filter
2.Unscented Transform
Unscented Transform的流程如下:
2.1 Choose Sigma Points
首先从Input Distribution进行点采样,注意,这里不是随机采样,采样点距离Input Distribution的mean距离是标准差的倍数,因此这些采样点也被称为Sigma Point。Unscented Transform有时也被称为Sigma Point Transform。
图片来源:State Estimation and Localization for Self-Driving Cars:Lesson 6: An Alternative to the EKF - The Unscented Kalman Filter
Sigma Points个数
Sigma Point的个数如何选择呢?通常情况下,N维的高斯分布选择2N+1个Sigma Point(一个Point是Mean,其它Point关于Mean对称分布)。一维高斯分布选择3个Sigma Point,二维高斯分布选择5个Sigma Point。
图片来源:State Estimation and Localization for Self-Driving Cars:Lesson 6: An Alternative to the EKF - The Unscented Kalman Filter
Sigma Points的选取
2.2 Transform Sigma Points
将Sigma Points通过非线性变换 h ( x ) h(x) h(x)映射到Output Distribution。
图片来源:State Estimation and Localization for Self-Driving Cars:Lesson 6: An Alternative to the EKF - The Unscented Kalman Filter
2.3 Compute Weighted Mean And Covariance of Transformed Sigma Points
3.The Unscented Kalman Filter (UKF)
4.UKF在自动驾驶定位中的应用举例
4.1 已知参数
4.2 应用UKF
首先是Prediction过程:
参考链接
1)本文主要来自Coursera自动驾驶课程: State Estimation and Localization for Self-Driving Cars:Lesson 6: An Alternative to the EKF - The Unscented Kalman Filter
2)Research Paper: https://www.seas.harvard.edu/course