A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking

Non-intrusive methods for eye tracking are important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robustness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into todays’s interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty in modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and improve the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions. Supported by the National Natural Science Foundation of China (Grant No. 60572027), the Outstanding Young Researchers Foundation of Sichuan Province (Grant No. 03ZQ026-033), the Program for New Century Excellent Talents in University of China (Grant No. NCET-05-0794), and the Young Teacher Foundation of Mechanical School (Grant No. MYF0806)     

含有多普勒频率的无迹卡尔曼滤波

针对扩展卡尔曼滤波不含多普勒频率和非线性的缺陷,提出一种新的含有多普勒频率的无迹卡尔曼滤波算法。新算法通过推导观测向量和状态向量之间的函数关系,结合无迹卡尔曼滤波思想,使滤波结果较扩展卡尔曼滤波算法具有更高的精度。最后对新老算法进行了仿真对比分析,结果表明了新算法的有效性和合理性。     

适用处理非高斯观测噪声的强跟踪卡尔曼滤波器

在高斯噪声条件下,卡尔曼滤波器(KF)能够获得系统状态的一致最小方差线性无偏估计.但当噪声非高斯,KF性能将严重下降.观测噪声非高斯现象在深空探测自主导航中经常遇到,然而现有模型可能存在着精度不高、稳定性不强或者计算复杂度较高的缺点.针对这种现状,本文在传统强跟踪卡尔曼滤波器(STKF)中新息正交原则的基础上,推导了适用处理非高斯观测噪声的强跟踪卡尔曼滤波器(STKFNO),并将其嵌入到无迹卡尔曼滤波(UKF)框架下形成适用处理非线性系统非高斯观测噪声的强跟踪无迹卡尔曼滤波器(STUKFNO).所提出的算法被应用到深空光学自主导航系统中,仿真结果表明所提出的算法能够较好地应对观测噪声的非高斯性.     

一种基于卡尔曼滤波的运动物体跟踪算法

针对实时视频监控领域中传统的Camshift算法不能有效解决遮挡和高速运动等问题,提出一种改进的Camshift算法与卡尔曼滤波相结合的运动物体跟踪算法。首先,通过二次搜索来调整搜索窗口的位置和大小,保证Camshift跟踪的可靠性;然后,在Camshift算法的基础上通过卡尔曼滤波对搜索窗口进行运动预测,保证实时跟踪。实验表明该方法具有较好的实时性,并能够有效地解决遮挡等问题。     

An iterated fuzzy extended Kalman filter for nonlinear systems

The fuzzy extended Kalman filter (FEKF) for state estimation can be used to deal with fuzzy uncertainty effectively. However, the linearisation processing of the FEKF introduces truncation error, which degrades the estimation precision. In order to reduce the error, a new iterated fuzzy extended Kalman filter (IFEKF), based on the FEKF and the maximum a posteriori estimation, is proposed in this article. Compared with the FEKF, the proposed algorithm can be used not only to deal with the fuzzy uncertainty, but also to reduce the truncation error and to estimate the states more accurately. With an algebraic example and a passive location simulation, it is shown that the IFEKF has better estimation precision than that of the FEKF.     

基于序贯无迹卡尔曼滤波的雷达目标跟踪方法

提出一种基于序贯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。为了提高无迹卡尔曼滤波的精度,用序贯无迹卡尔曼滤波方法依次处理方位角、俯仰角和距离,来进行雷达目标跟踪。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和更高的计算效率。     

鲁棒高斯和集合卡尔曼滤波及其在纯角度跟踪中的应用

针对纯角度目标跟踪中量测信息易受异常值和非高斯噪声干扰的问题,提出了一种新的非线性滤波算法–鲁棒高斯和集合卡尔曼滤波(robust Gaussian-sum ensemble Kalman filter,RGSEnKF)算法.首先,采用Huber技术重塑集合卡尔曼滤波的量测更新过程,能够有效地处理量测中的异常值.随后,将改进的集合卡尔曼滤波在高斯和框架下进行扩展,得到RGSEnKF算法,可以进一步解决受非高斯噪声干扰的非线性系统的状态估计问题.此外,新算法中包含距离参数化初始化策略和高斯分量融合策略.前者是为了减小纯角度跟踪中距离信息不可观测的影响,而后者可以避免高斯分量数目随时间不断增长.大量仿真结果验证了新算法的有效性和鲁棒性.     

强跟踪卡尔曼滤波在视频目标跟踪中的应用

针对经典卡尔曼滤波器在滤波数学模型与实际过程的数学规律不匹配、滤波特性较差的情况,提出利用强跟踪卡尔曼滤波器对视频序列图像中的运动目标进行跟踪。该方法是在经典卡尔曼滤波递推公式中的一步验前误差方差阵中引入可在线计算的时变渐消矩阵,从而调节增益K,使之能够不断变化,保证对新息序列的自适应调节,使状态滤波更准确。实验结果表明,较之经典卡尔曼滤波,该方法具有对运动目标更强的跟踪能力,跟踪精度更高,均方误差更小。     

基于多新息理论的 EKF 改进算法

针对标准的扩展卡尔曼滤波算法（EKF）在强非线性系统中估计精度较低的问题,提出了一种改进的扩展卡尔曼滤波算法（MI-EKF）,使得滤波精度得到很大的提高。MI-EKF 是在标准 EKF 基础上,结合多新息理论,不仅考虑了系统当前的测量值,而且也充分考虑了之前时刻的有用信息,从而使得 MI-EKF 的滤波精度和稳定性得到改善。最后,讨论了新息数量对改进算法精度的影响,仿真结果表明包含两个新息的 MI-EKF 算法滤波效果最佳。     

基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法

在机动目标跟踪中,用于模型辨识和状态估计的非线性滤波器的合理选择和优化是提升滤波精度的关键.融合量测迭代更新集合卡尔曼滤波和交互式多模型(interacting multiple models,IMM)方法,本文提出了基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法.通过迭代更新思想的引入构建了一种量测迭代更新下集合卡尔曼滤波的实现结构,并将其作为IMM的模型滤波器实现对于目标运动模式和状态的辨识与估计.针对算法结合过程中滤波精度和计算量的平衡,设计了用于输入交互环节的状态估计样本,同时简化输入交互环节和输出交互环节中滤波误差协方差矩阵的交互过程.理论分析和仿真结果验证了算法的可行性和有效性.     

基于均值漂移与卡尔曼滤波的目标跟踪算法

均值漂移算法在目标跟踪过程中没有利用目标的运动方向和速度信息,在目标受到干扰时容易跟踪失败,而Kalman滤波能够较为准确地预测目标的速度和位置。因此,提出了一种结合均值漂移与Kalman滤波的跟踪算法,使用Kalman滤波对目标运动速度和空间位置进行预测。根据干扰的不同情况,使用不同的比例因子将两算法的跟踪结果线性加权得到目标的最终位置。实验结果表明该算法是可行有效的。     

基于扩展卡尔曼滤波的主动视觉跟踪技术

提出一种基于主动视觉的物体跟踪系统.该系统利用基于扩展卡尔曼滤波的物体锁定(Object Locked Based on Extended Kalman Filter,OLBEKF)技术,根据物体的运动预测摄像头的运动,并通过控制摄像头的两个关节实现主动跟踪.实际运用表明,在复杂的环境下,能够实时地获得高准确率的跟踪结果,并且显著提高摄像头拍摄图像的质量.     

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。     

A Zakai equation derivation of the extended Kalman filter

A discrete time filter is considered where both the observation and signal process have non-linear dynamics with additive Gaussian noise. Using the reference probability framework a convolution type Zakai equation is obtained which updates the unnormalized conditional density. Using first order approximations this equation can be solved recursively and the extended Kalman filter can be derived.     

基于卡尔曼滤波的移动机器人运动目标跟踪

提出了一种基于卡尔曼滤波的运动目标快速跟踪算法。针对复杂背景下彩色运动目标跟踪问题,采用基于颜色特征和形状特征相结合的方法进行目标识别。利用卡尔曼滤波器的预测功能,预测运动目标在下一帧中的位置,将图像全局搜索问题转换为局部搜索,提高了系统的实时性。实验结果表明:该算法满足移动机器人运动控制的实时性要求,实现了对运动目标的快速跟踪。     

基于平方根求积卡尔曼滤波器的弹道目标跟踪

针对再入阶段的弹道目标跟踪问题,提出运用平方根求积卡尔曼滤波器(SRQKF)估计目标的状态.所提出的算法是求积卡尔曼滤波(QKF)算法的平方根实现.该算法传播了目标状态的均值和协方差的平方根,确保了协方差矩阵的对称性和半正定性,改进了数值精度和稳定性,但其计算复杂性稍有增加.仿真实验表明,所提出算法的估计精度优于QKF算法和扩展卡尔曼滤波(EKF)算法,是一种很有效的非线性滤波方法.     

A Gaussian mixture Bernoulli filter for extended target tracking with application to an ultra-wideband localization system

This paper presents a Gaussian mixture (GM) implementation of the Bernoulli filter for extended target tracking, which we call the extended target GM Bernoulli (ET-GM-Ber) filter. Closed form expressions for the ET-GM-Ber filter recursions are obtained. A clustering step is integrated into the measurement update stage in order to have a computationally tractable filter. Performance of the proposed filter is tested both on the simulated data and experimental data collected using an ultra-wideband (UWB) localization system. Simulations and experimental results demonstrate the accurate and effective performance of the proposed filter.     

嵌入卡尔曼预测器的粒子滤波目标跟踪算法*

针对经典的粒子滤波视频目标跟踪算法进行粒子传播采用随机游走的方式,以及传统颜色直方图无法反映目标空间特征的问题,提出了一种改进的基于颜色的粒子滤波目标跟踪算法。该算法在统计目标二阶颜色直方图的基础上,获得粒子的观察概率密度函数,利用卡尔曼滤波确定粒子动态传播模型中的确定性漂移部分,使粒子状态估计值分布更精确地趋向目标的概率分布,大大提高了粒子的利用效率。实验表明,该改进算法的性能优于经典基于单一颜色特征的粒子滤波算法。     

基于Kalman滤波的反辐射导弹跟踪噪声源研究

本文研究了被动单脉冲导引头对噪声源的跟踪特性,应用Kalman滤波实现机动噪声源跟踪,同时建立了反辐射导弹对噪声源的跟踪模型,最后通过计算机仿真,验证了该算法的准确性和有效性。     

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.