Variants of extended Kalman filtering approaches for Bayesian tracking

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 © 2016 John Wiley & Sons, Ltd.     

Unscented and square‐root unscented Kalman filters for quaternionic systems

Proper construction of an unscented Kalman filter (UKF) for unit quaternionic systems is not straightforward due to the incompatibility between the algebraic properties of the unit quaternions and the common real vector space operations (additions and scalar multiplications) needed in the steps of a filter algorithm. This work studies, in detail, all UKFs and square‐root UKFs for quaternionic systems proposed in the literature. First, we classify the algorithms according to the preservation of the unity norm of the quaternion variables. Second, we propose two new algorithms: the quaternionic additive unscented Kalman filter (QuAdUKF) and a square‐root variant of it. The QuAdUKF encompasses all known UKFs for quaternionic systems of the literature preserving, in all steps, the norm of the unit quaternion variables. Besides, it can also yield new UKFs with this norm preservation property. The QuAdUKF's square‐root variant has better properties in comparison with all the square‐root UKFs for quaternionic systems of the literature. Numerical experiments for a spacecraft attitude estimation problem illustrate the theoretical results.     

自适应平方根无迹卡尔曼滤波算法

将高斯过程回归融入平方根无迹卡尔曼滤波(SRUKF)算法,本文提出了一种不确定系统模型协方差自适应调节滤波算法.该算法分为学习和估计两部分:学习阶段用高斯过程对训练数据进行学习,得到系统回归模型及噪声协方差;估计阶段由回归模型代替状态方程和观测方程,相应的噪声协方差实时自适应调整.该方法克服了传统方法容易受系统动态模型不确定性和噪声协方差不准确限制的问题,仿真结果验证了算法的有效性.     

一种利用UKF的高速公路实时交通状态估计方法

把无轨迹卡尔曼滤波器（UKF）和宏观随机交通流模型结合在一起,可以实现对高速公路交通状态的实时估计。高速公路被看作是由等距离的路段首尾相接而成的系统,每个路段中交通变量的更新不光与其自身有关,还受到相邻路段的影响。交通传感器通常设置在路段的交界处,而且数量远少于所需估计的交通状态。采用压缩状态空间的形式,将模型参数也作为交通状态而非常量进行估计。仿真结果表明UKF方法能够有效地估计和跟踪交通状态的变化,并且与扩展卡尔曼滤波方法相比具有更高的精确度。     

Unscented Kalman filtering in the additive noise case

The unscented Kalman filter(UKF) has four implementations in the additive noise case,according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted state(which is so-called resampling) for the observation prediction.This paper concerns the differences of performances for those implementations,such as accuracy,adaptability,computational complexity,etc.The conditionally equivalent relationships between the augmented and non-augmented unscente...     

基于加性无迹卡尔曼滤波的雷达目标跟踪方法

提出一种基于加性无迹卡尔曼滤波的雷达目标跟踪方法。雷达跟踪系统为离散非线性系统,传统的解决方法是使用扩展卡尔曼滤波。无迹卡尔曼滤波用少量采样点表示随机变量的分布,通过非线性系统传播,能以三阶精度获得非线性变换的均值和方差的估计。用无迹卡尔曼滤波进行雷达目标跟踪。通过Monte Carlo仿真,验证了该滤波算法比传统的扩展卡尔曼滤波具有更高的滤波精度。     

基于高斯分布的多层无迹卡尔曼滤波算法

在传统无迹卡尔曼滤波(UKF) 中对其估计精度和计算效率起关键作用的是采样算法, 即构造具有权重的样本点. 研究表明, 带权样本点匹配随机变量的阶矩越高滤波的精度越高, 如多项式无迹卡尔曼滤波(PUKF), 但通常此类算法的复杂度过高甚至难以求解. 为此, 基于高斯分布结合高阶矩匹配与无迹卡尔曼滤波线性扩张方 法(LUKF), 提出一种兼顾效率和精度的高斯滤波离线算法. 实验结果表明, 所提出算法拥有比UKF 更高的估计精度和比PUKF 更好的计算效率.

     

加权观测融合非线性无迹卡尔曼滤波算法

针对非线性系统的无迹卡尔曼滤波器(UKF),应用加权最小二乘(WLS)法,提出了加权观测融合UKF滤波算法.证明了加权观测融合UKF滤波算法与集中式观测融合UKF滤波算法在数值上的完全等价性,因而具有全局最优性.一个带两传感器非线性系统的仿真例子说明了两种融合算法的有效性及等价性.     

迭代无味卡尔曼滤波器

通过对无味卡尔曼滤波器(Unscented Kalman filter,UKF)的误差进行分析,提出了迭代UKF(IUKF)算法.该基本思路是用测量更新后的状态估计去重新对状态量和观测量的一步预测,然后再次应用LMMSE估计子估计状态量的均值和协方差阵,如此多次迭代后的滤波估计输出具有更高的精度和更小的方差,故滤波器表现出更好的一致性.Monte Carlo仿真表明,IUKF主要应用于观测噪声较小的场合,其中的迭代只需进行2～3次即可.     

一种基于SR-UKF的FastSLAM算法

标准FastSLAM算法存在着粒子集退化和线性化误差累积的缺陷。针对上述问题,提出了基于平方根无迹卡尔曼滤波(SR-UKF)的FastSLAM算法。SR-UKF选取一组能够代表状态向量统计特性的代表点带入非线性函数处理后重新构建出新的统计特性;使用SR-UFK取代EKF来估计每个粒子的后验位姿提议分布,可以提高粒子采样精度,减缓粒子集的退化;同时SR-UKF可以确保协方差矩阵的非负定,保证了SLAM算法的稳定性。仿真实验结果表明,基于SR-UKF的FastSLAM算法在估计精度和鲁棒性两方面均优于FastSLAM 2.0算法。     

基于无迹卡尔曼滤波估算电池SOC

为了实现在线估计汽车动力电池的荷电状态（SOC）,提出了结合神经网络的无迹卡尔曼滤波算法。以Thevenin电路为等效电路模型,建立了状态空间表达式,采用最小二乘算法对模型参数进行辨识。在此基础上,利用神经网络算法拟合电池的荷电状态与模型各个参数之间的函数关系,经过多次实验,确定了神经网络算法的收敛曲线,此方法比传统的曲线拟合精度高。介绍了扩展卡尔曼滤波和无迹卡尔曼滤波的原理,并设计了等效电路模型验证实验、电池的SOC测试实验和算法的收敛性实验。实验结果表明,在不同的工况环境下,该方法估计SOC具有可在线估算、估算精度高和环境适应度高等优点,最大误差小于4%。最后验证了结合神经网络的无迹卡尔曼滤波的算法具有较好的收敛性和鲁棒性,可以有效解决初值估算不准确和累计误差的问题。     

改进型平方根无迹卡尔曼滤波及其在无轴承永磁同步电机无速度传感器运行中的应用

平方根无迹卡尔曼滤波(SRUKF)解决了标准无迹卡尔曼滤波(UKF)中由于误差协方差阵负定而引起的滤波发散问题, 保证了算法的数值稳定性, 但仍存在对模型参数变化的鲁棒性差、收敛速度慢及对突变状态的跟踪能力低等缺陷. 因此, 本文提出一种改进SRUKF滤波, 通过引入时变渐消因子和弱化因子, 实时修正滤波增益矩阵和误差协方差平方根矩阵, 实现残差序列正交, 确保SRUKF滤波保持对目标实际状态的准确跟踪. 将该算法在无轴承永磁同步电机无速度传感器矢量控制系统中进行仿真研究. 结果表明: 改进SRUKF非线性近似精度、数值稳定性及滤波精度更高, 在系统状态突变或负载扰动时, 鲁棒性更强, 能够有效实现转速及转子角度的准确估计, 确保转子稳定悬浮运行.     

自适应快速弱敏无迹Kalman滤波算法

针对现有弱敏无迹Kalman滤波需要代数求解增益矩阵耗时长和不能实时调节敏感性权重的问题,提出一种自适应快速弱敏无迹Kalman滤波算法.该算法在弱敏控制技术的基础上,重新定义弱敏无迹Kalman滤波的敏感性权重矩阵,将状态估计误差对不确定参数的敏感性加入滤波的代价函数,并通过最小化该代价函数得到滤波增益矩阵的解析解,...     

Reduced-rank unscented Kalman filtering using Cholesky-based decomposition

We consider a reduced-rank square-root unscented Kalman filter based on the Cholesky decomposition of the state-error covariance. The performance of this filter is compared with an analogous filter based on the singular value decomposition. We evaluate the performance of these filters for illustrative linear and non-linear systems.     

基于四元数衍生无迹卡尔曼滤波的二段式多旋翼无人机姿态估计算法

对传统多旋翼无人机姿态估计算法难以兼顾高精度、强实时性以及抗干扰能力差的问题,首先基于一种计算量较小的衍生无迹卡尔曼滤波算法,在量测更新中,将加速度数据和磁力计数据分为两个阶段进行姿态四元数校正处理,然后从旋转四元数的本质出发,推测出四元数各元素分别包含着不同的姿态角信息,最后将校正四元数分别乘上为降低校正过程中的相互干扰所设计的系数,提出一种基于四元数衍生无迹卡尔曼滤波的二段式多旋翼无人机姿态估计算法.通过使用PIXHAWK飞控数据,与传统姿态估计算法进行仿真实验对比,实验表明,本文提出算法与传统使用扩展卡尔曼滤波(EKF)或无迹卡尔曼滤波(UKF)的姿态估计算法相比,在实时性、解算精度和抗干扰能力方面有较大提升.     

Adaptive square-root transformed unscented FastSLAM with KLD-resampling

The FastSLAM relies on particles sampled from the proposal distribution of underlying Rao–Blackwellized particle filter, and its performance is significantly influenced by the quality and quantity of the particles. In this paper, a new improved FastSLAM is proposed based on transformed unscented Kalman filter (TUKF) and Kullback–Leibler distance (KLD) resampling method. In the proposed algorithm, a square-root extension of TUKF is used to calculate the proposal distribution and to generate credible particles. In addition, during the resampling process, the minimum required number of particles is determined adaptively by bounding the KLD error between the sample-based approximation and true posterior distribution of the robot state. Both numerical simulations and real-world dataset experiments are used to evaluate the performance of the proposed algorithm. The results indicate that the proposed algorithm achieves higher estimation accuracy and computational efficiency than conventional approaches.     

A skewed unscented Kalman filter

State estimation of nonlinear systems is a challenging task, especially when the Gaussian approximation fails. The unscented Kalman filter was proposed to deal with state estimation of nonlinear systems. We modify the traditional unscented Kalman filter to capture the third-order moment (skewness) of the state vector. Methods are also proposed to reduce the computation time of the suggested approach, and showing that the proposed algorithm is as fast as the unscented Kalman filter. Simulation results confirm that the method is better than, or at least as good as, the unscented Kalman filter.     

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

Wireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi-square test-based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi-square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real-time attack detection.     

遮挡情况下刚体位姿估计的自适应无迹卡尔曼分布式融合

针对视觉目标位姿估计系统中常出现的因为特征点遮挡而造成系统估计结果不准确的问题,本文提出了一种利用自适应无迹卡尔曼滤波(AUKF)作为局部滤波器的分布式融合估计方法.通过引入改进的Sage-Husa噪声估计器自适应过程噪声.根据特征点识别量将遮挡情况分为部分遮挡和严重遮挡,对部分遮挡子系统根据先验信息修复缺失观测点后进行局部滤波估计,严重遮挡子系统不参与融合,利用当前时刻整体估计结果对其进行初始化.通过仿真获取了区分遮挡情况的阈值,实验结果表明所提方法能够提升系统在遮挡情况下的估计精度与鲁棒性.     

禁忌遗传算法求解最小支配集

如何寻找一个网络图的最小支配集是NP难题。分别设计了逆序启发式算法和禁忌搜索算法,并在此基础上提出了禁忌遗传算法（TSGA）用于求解最小支配集;将禁忌搜索和遗传算法结合起来,弥补了彼此的不足,既有效地避免了算法易陷入局部最优解的缺陷,又加快了算法的收敛速度。经对大量随机网络图的测试和对物流网络选址问题的求解,验证了TSGA算法的优越性。