UKF与EKF在卫星姿态估计应用中的比较

针对卫星的姿态和角速度估计问题,分别给出基于Unscented卡尔曼滤波(UKF)与推广卡尔曼滤波(EKF)的估计算法,并做了相应比较.为了避免欧拉角带来的奇异问题,UKF选用Rodrigues参数而EKF选用四元数参数法来描述姿态误差.考虑卫星的非线性模型,UKF采用Unscented变换而EKF采用线性化方法对姿态误差进行估计.利用陀螺和磁强计的测量信息,KF和EKF都可得到三轴稳定卫星的姿态估计值,但UKF的收敛速度高于EKF.数值仿真结果表明,当初始姿态存在大偏差时,所给出的UKF的滤波算法性能明显优于EKF.     

多径衰落信道中多OFC-SAW传感器同时读取算法

针对多个正交频率编码声表面波（OFC-SAW）传感器存在同时读取困难的问题,对理想信道中多OFC-SAW传感器反射信号进行了建模分析,通过理论推导实现了对理想信道中多OFC-SAW传感器信息的同时读取。针对实际应用中的多径衰落信道特点,建立了多径衰落信道中阅读器接收到的OFC-SAW传感器反射信号数学模型。对理想信道中阅读器接收到的信号与多传感器反射信号之间的关系模型进行修正,从而得到多径衰落信道中阅读器接收到的信号与多传感器反射信号之间的关系模型。实际应用中通过适时监测信道来估计信道模型参数,从而实现多径衰落信道中多OFC-SAW传感器信息的同时读取。最后经过仿真分析验证了该算法的有效性。     

Unscented卡尔曼滤波在状态估计中的应用

针对非线形系统的滤波问题,无法使用卡尔曼滤波器（KF）,扩展卡尔曼滤波（EKF）方法虽能应用于非线形系统,但给出的是状态的有偏估计,并且对模型误差的鲁棒性较差。为了给出更好的状态估计值,该文介绍了Unscented卡尔曼滤波（UKF）的基本原理。其思想是：基于unscented变换,UKF滤波算法能够给出更精确的均值和协方差的估计,从而带来更高的精度。最后通过Mackey—Glass模型时间序列的状态估计仿真实侧说明：同EKF相比,UKF的滤波精度和稳定性都显著提高了,还可避免计算烦琐的Jacobi矩阵,是一种良好的非线性滤波方法。     

双层无迹卡尔曼滤波

针对无迹卡尔曼滤波（Unscented Kalman fllter,UKF）在强非线性系统中估计效果差的问题,提出了双层无迹卡尔曼滤波（Double layer unscented Kalman filter,DLUKF）算法,该算法用带权值的采样点表征先验分布,而后用内层UKF算法对每个采样点进行更新,最后引入外层UKF算法的更新机制得到估计值和估计协方差.仿真结果表明,相比于传统算法,所提的DLUKF算法可以在较低计算负载下获得较高滤波估计精度.     

利用混合卡尔曼滤波的混沌信号盲估计

针对混沌动力学系统时变参数未知的混沌信号,在含有状态噪声的情况下,利用混合卡尔曼滤波提出一种盲估计算法.对未知参数和混沌状态构成的高维状态进行估计,先利用卡尔曼滤波给出线性高斯部分的最优精确估计,剩余部分利用粒子滤波方法给出次优估计,文中详细研究了高斯噪声以及非高斯噪声下的最优重要性函数选取并推导了重要性权重的计算公式,最终基于有效粒子的最小均方误差准则实现了信号的盲估计.仿真结果表明该算法能有效实现含有状态噪声混沌信号的盲估计,并取得了比基本粒子滤波算法更优的性能.     

基于事件的卡尔曼滤波算法及其在移动小车室外导航中的应用研究

为解决GPS信号中断所导致的定位失准、导航精度降低的问题，减少完成室外导航任务所需时间，提出一种基于事件触发机制的卡尔曼滤波算法(KF)。将小车的状态变化作为KF的触发事件，当状态偏差超过一定阈值时，KF估计器响应并给出新的状态估计；设计能提供模拟GPS信号的估计器，在GPS信号中断时为KF估计器提供连续可用的位置信息使滤波过程不受影响。实验结果表明，相比于传统卡尔曼滤波，基于事件的卡尔曼滤波算法不仅能够应对GPS信号中断的情况，保证室外导航的精度，同时能够降低算法的时间复杂度。     

基于Kalman滤波的MIMO时变信道估计

研究了一种基于Kalman滤波的MIMO时变信道估计与跟踪问题。利用衰落信道功率谱统计特性的先验信息,将信道冲击响应近似为一个低阶自回归滑动平均过程,通过信道传输函数逼近信道功率谱的幅频特性,建立时变衰落单径信道的状态方程,导出MIMO信道状态模型参数,并通过Kalman滤波跟踪信道的时变特性。理论分析和仿真试验表明,该算法在时变信道下具有较好的性能,和传统信道估计方法相比,接收机性能有了较大的改进。     

一种LTE自适应参数MMSE信道估计算法

在工程中,为了达到高速率的数据传输和良好的外场接收性能,LTE系统通常采用最小均方误差(MMSE)信道估计方法。针对传统的MMSE算法对多径时变信道的适应能力较差,提出了一种自适应参数MMSE信道估计系数调整算法。通过对信道均方根时延扩展(RMS Delay Spread)和对信噪比的估计,自适应地调整信道估计参数并生成准最佳的MMSE信道估计系数进行滤波。仿真结果表明,此算法比固定系数的MMSE信道估计算法有更好的信道估计性能。     

频率选择性衰落信道下的同步参数联合盲估计算法

对于多径频率选择性衰落信道以及低信噪比环境下线性调制信号的同步参数盲估计问题,提出基于循环累积量的载波频偏、初始相偏和符号定时误差前向联合盲估计算法。通过理论推导得出多径频率选择性衰落信道下信号的循环累积量与初始相偏和符号定时误差的数学关系。在此基础上先以较大频率间隔进行粗估计确定频偏范围,再以较高精度遍历检测信号特定循环频率,提高载波频偏估计精度,进而由累积量值估计出初始相偏和符号定时误差,不依赖于信道衰落和加性噪声的分布特性,尤其适用于频偏、相偏、定时误差和信道衰落同时存在的复杂情况。仿真结果表明,该算法 能有效实现低信噪比和多径频率选择性衰落信道下对线性调制信号同步参数的联合盲估计。     

利用sigma点卡尔曼滤波的多UUV协同定位

融合无人水下航行器（UUV）内部航位递推估计和外部量测信息的协同定位方法是一种提高只配备低精度自定位装置的UUV定位精度的有效手段。当协同系统结构固定时,滤波器的选择就决定了精度提高的幅度。针对扩展卡尔曼滤波（EKF）在处理非线性系统时具有较大的截断误差和繁琐的计算,提出了使用sigma点卡尔曼滤波（SPKF）的协同定位方法。与EKF相比,无味卡尔曼滤波（UKF）和中心差分卡尔曼滤波（CDKF）具有更好的鲁棒性,在没有增加计算复杂度的基础上进一步提高了UUV的定位精度。仿真比较了采用不同滤波算法的协同定位方法提高定位精度的效果,验证了利用sigma点卡尔曼滤波的多UUV协同定位方法的有效性和一致性。     

基于改进的扩展卡尔曼滤波伺服系统建模技术研究

研究永磁同步电机系统建模技术问题。传统的建模技术在对系统进行建模时,由于算法复杂度较高,不利于实时控制系统,提出一种新的基于卡尔曼滤波技术构建速度观测器替代位置传感器;卡尔曼滤波技术适用于线性控制场合,针对PMSM的非线性特性,改进卡尔曼滤波算法为扩展卡尔曼滤波算法。仿真实验结果表明,利用扩展卡尔曼滤波算法构建的速度观测器准确度高,是一种有效的伺服系统建模方法。     

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)     

具有双重不确定性系统的联合滤波算法

卡尔曼滤波在高斯白噪声的假设下是一种最优滤波, 基于区间数学理论的集员滤波 (Set-membership filter, SMF)能够有效处理有界噪声假设下的滤波问题. 然而, 随机噪声和有界噪声在许多情况下会同时干扰控制系统. 由于两种滤波算法都受到各自适用范围的限制, 使用单一滤波算法难以得到理想的估计结果. 本文通过建立具有双重不确定性系统的模型, 提出了一种基于贝叶斯估计联合滤波算法. 该算法用卡尔曼滤波处理系统的随机不确定性, 用集员滤波处理系统的有界不确定性, 得出一个易于实现的滤波器. 最后通过对雷达跟踪系统的仿真, 结果表明, 较单一滤波算法, 联合滤波具有更强的噪声适应性和有效性.     

A strong tracking nonlinear robust filter for 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 pose the primary obstacle to the integration of eye movements into today’s interfaces. In this paper, we present a strong tracking unscented Kalman filter (ST-UKF) algorithm, aiming to overcome the difficulty in nonlinear eye tracking. In the proposed ST-UKF, the Suboptimal fading factor of strong tracking filtering is introduced to improve robustness and accuracy of eye tracking. Compared with the related Kalman filter for eye tracking, the proposed ST-UKF has potential advantages in robustness and tracking accuracy. The last experimental results show the validity of our method for eye tracking under realistic conditions.     

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.     

基于非线性卡尔曼平滑的GPS定位估计方法

在GPS单机定位中,通常采用卡尔曼滤波作为位置状态解算的方法.文中提出一种将非线性平滑技术用于GPS定位估计的方法,该方法可用于单机GPS接收机的定位解算,在非线性滤波的基础上进一步提高定位精度.提出一种随接收卫星数量而实时改变测量参数的动态测量模型,根据GPS的伪距、多普勒频移和导航信息等原始数据进行定位模型的解析,运用新型的平淡卡尔曼平滑算法求解该动态模型.GPS定位实验结果表明,与通用的最小二乘迭代法和非线性滤波等方法获得的结果相比,所提出的方法能获得更高的定位精度.     

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.     

一种基于遗传算法和卡尔曼滤波的运动目标跟踪方法

提出了一种基于遗传算法和卡尔曼滤波的运动目标跟踪方法。该方法利用卡尔曼滤波预测目标中心在下一帧图像中可能出现的位置,以该位置为中心,建立候选的目标搜索区域。以跟踪目标的灰度统计特征为模板,以Bhattacharyya系数来度量目标模板与候选目标区域的相似性,并以此相似性作为遗传算法适应度函数,以候选目标中心坐标作为参数编码,利用遗传算法进行匹配搜索,最终获得最佳候选区域中心位置,同时以该位置作为观测值,进行下一帧预测。实验结果表明,该方法具有较好的实时性和鲁棒性。     

基于改进UKF的GPS非线性动态滤波研究

为了提高动态定位精度,将一种改进的UKF(Unscented galman Filter)算法应用在GPS非线性动态定位解算中.将UKF算法与IEKF(Iterated Improved Kalman Filter)算法相结合,因此保持了基本UKF算法易于实现和收敛速度快的优点,同时由于滤波值是通过迭代扩展的卡尔曼滤波机制得到,进而更新值能更准确的逼近非线性系统状态概率密度函数,具有更高的精度.应用于GPS非线性动态滤波定位中,仿真结果表明:与UKF算法相比,算法能够明显提高定位精度.