The over-extended Kalman filter - don't use it!
The over-extended Kalman filter - don't use it!
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DOI：
10.1109/icif.2003.177424
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发表时间：
2003-07
期刊：
影响因子：
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通讯作者：
D. Bizup;D.E. Brown
中科院分区：
文献类型：
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作者：
D. Bizup;D.E. Brown
由于雷达距离变化率在笛卡尔空间中是高度非线性的，因此在目标跟踪滤波器中并不总是使用它们。在扩展卡尔曼滤波器的测量方程中，有时采用距离变化率对轨道状态向量的偏导数的线性近似。不幸的是，这种天真的线性化可能会降低滤波器的位置估计值。本文研究了这种现象的根源，发现是由于轨道状态矢量的位置元素与距离变化率新息之间的线性化所引起的函数关系。推导了另一种不随位置元素变化的距离变化率线性化方法。结果表明，新的线性化改善了一些弹道的位置估计。通过分析和仿真，将普通卡尔曼滤波器的增益与常用的和替代的扩展卡尔曼滤波器的增益进行了比较。结果表明，替代线性化导致一个过滤器具有相同的位置增益作为一个普通的卡尔曼滤波器，和一个额外的增益上的轨道的径向速度。这种新的扩展卡尔曼滤波器可以提高跟踪系统的速度估计，而不会对其位置估计造成风险。
Radar range rate measurements are not always used in target tracking filters because they are highly nonlinear in Cartesian space. A linear approxi- mation of range rate composed of its partial derivatives with respect to the track state vector is sometimes used in the measurement equation of an Extended Kalman filter. Unfortunately, this naive linearization can de- grade the filter's position estimates. The origins of this phenomenon are investigated and found to lie in the functional relationship induced by the linearization between the position elements of the track state vec- tor and the range rate innovation. An alternative lin- earization of range rate that is not a function of the position elements is derived. It is shown that the new linearization improves position estimate for some tra- jectories. An ordinary Kalman filter's gains are com- pared to those of the usual and alternative extended Kalman filters analytically and via simulation. The results show that the alternative linearization leads to a filter having the same position gains as an ordinary Kalman filter, and an additional gain on the track's radial velocity. This new extended Kalman filter can improve a tracking system's velocity estimates without risk to its position estimates.