Variants of extended Kalman filtering approaches for Bayesian tracking
Variants of extended Kalman filtering approaches for Bayesian tracking
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DOI：
10.1002/rnc.3576
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发表时间：
2017-01-25
影响因子：
3.9
通讯作者：
Hwang, Woonjae
中科院分区：
文献类型：
--
作者：
Lim, Jaechan;Shin, Myoungin;Hwang, Woonjae
我们提供了扩展卡尔曼滤波(EKF)的许多变体的教程。在这些方法中，所谓的Sigma点被用来处理问题的非线性。西格玛点精确地表示动态状态方程中状态分布函数的均值和方差。最初提出的扩展卡尔曼滤波的变体，即无迹卡尔曼滤波(Unscented Kalman Filter，UKF)(也称为Sigma点卡尔曼滤波)，与文献中传统的扩展卡尔曼滤波相比，具有更好的性能。另一种不为人熟知的变体是中心差分卡尔曼滤波(CDKF)，其逼近非线性的方法是基于斯特林多项式插值公式而不是泰勒级数。为了减少计算量，UKF和CDKF的平方根版本都得到了发展，即平方根无迹卡尔曼滤波和平方根中心差分卡尔曼滤波(SR-CDKF)。由于避免了矩阵分解的步骤，保证了状态协方差是正定的，因此这些SR版本应该比它们的原始版本在数值上更稳定。在本文中，我们给出了上述EKF变体的逐步算法，并指出了它们的优缺点。我们将这些滤波方法应用于不同学科中的一些问题，从均方误差(MSE)和处理速度两个方面进行性能评估。此外，我们还展示了如何根据不同的场景根据MSE性能来优化过滤器。仿真结果表明，CDKF和SR-CDKF在大多数场景下表现出最好的MSE性能，特别是SR-CDKF的处理速度要快于CDKF。因此，我们证明SR-CDKF是包括EKF在内的各种非线性问题的卡尔曼变种中最有效和最好的方法。本文的目的是为了促进卡尔曼变种方法的传播使用，特别是SR-CDKF，它利用了它的估计性能和较高的处理速度。版权所有(C)2016 John Wiley&Sons，Ltd.
We provide a tutorial for a number of variants of the extended Kalman filter (EKF). In these methods, so called, sigma points are employed to tackle the nonlinearity of problems. The sigma points exactly represent the mean and the variance of the state distribution function in a dynamic state equation. The initially developed EKF variant, that is, unscented Kalman filter (UKF) (also called sigma point Kalman filter) shows enhanced performance compared with that of conventional EKF in the literature. Another variant, which is not well known, is central difference Kalman filter (CDKF) whose way to approximate the nonlinearity is based on the Sterling's polynomial interpolation formula instead of the Taylor series. Endeavor to reduce the computational load resulted in the development of square root versions of both UKF and CDKF, that is, square root unscented Kalman filter and square root central difference Kalman filter (SR-CDKF). These SR-versions are supposed to be numerically more stable than their original versions because the state covariance is guaranteed to be positive definite by avoiding the step of matrix decomposition. In this paper, we provide the step-by-step algorithms of above-mentioned EKF variants with their pros and cons. We apply these filtering methods to a number of problems in various disciplines for performance assessment in terms of both mean squared error (MSE) and processing speed. Furthermore, we show how to optimize the filters in terms of MSE performance depending on diverse scenarios. According to simulation results, CDKF and SR-CDKF show the best MSE performance in most scenarios; particularly, SR-CDKF shows faster processing speed than that of CDKF. Therefore, we justify that SR-CDKF is the most efficient and the best approach among the Kalman variants including the EKF for various nonlinear problems. The motivation of this paper targets at the contribution to the disseminative usage of the Kalman variants approaches, particularly, SR-CDKF taking advantage of its estimating performance and high processing speed. Copyright (c) 2016 John Wiley & Sons, Ltd.