带非线性等式约束无迹卡尔曼滤波方法

针对带非线性等式约束的非线性系统的状态估计问题,给出了一种新形式的基于无迹卡尔曼滤波及伪观测手段的处理约束的状态估计方法（SPUKF）。在该方法中原动态系统被虚拟地分离成两个并行的子系统,各时刻的状态估计由基于这两个子系统构建的两套滤波链交替得到。相对于伪观测法中的序贯形式估计器,SPUKF无需事先确定观测及约束的处理次序且能获得更好的估计结果,故可以用来解决序贯方法中观测与约束的处理次序问题。由钟摆运动的实例仿真结果看到,SPUKF不仅有好于序贯形式无迹卡尔曼滤波的估计效果,误差改善比达到22%左右,而且算法运行时间与序贯形式估计器相近。此外,其估计效果还与批处理无迹卡尔曼滤波相当。     

Sparse-grid quadrature nonlinear filtering

In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss–Hermite Quadrature Filter (GHQF) with the same performance.     

Estimation of nonlinear systems via a Chebyshev approximation approach

This paper proposes to decompose the nonlinear dynamic of a chaotic system with Chebyshev polynomials to improve performances of its estimator. More widely than synchronization of chaotic systems, this algorithm is compared to other nonlinear stochastic estimator such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Chebyshev polynomials orthogonality properties is used to fit a polynomial to a nonlinear function. This polynomial is then used in an Exact Polynomial Kalman Filter (ExPKF) to run real time state estimation. The ExPKF offers mean square error optimality because it can estimate exact statistics of transformed variables through the polynomial function. Analytical expressions of those statistics are derived so as to lower ExPKF algorithm computation complexity and allow real time applications. Simulations under the Additive White Gaussian Noise (AWGN) hypothesis, show relevant performances of this algorithm compared to classical nonlinear estimators.     

基于均方根容积卡尔曼的δ-GLMB多目标跟踪算法

在非线性高杂波密度场景下,高斯混合(Gaussian Mixture,GM)实现的δ-广义标签多伯努利滤波器(δ-Generalized Labeled Multi-Bernoulli Filter,δ-GLMB)难以准确地估计目标数目及运动状态。针对这一问题,提出基于均方根容积卡尔曼滤波(Square-rooted Cubature Kalman Filter,SCKF)的δ-GLMB高斯混合实现算法。基于三阶球面-径向容积准则选取一组等权的容积点集,对GM-δ-GLMB滤波器的伯努利分量传递过程中的高斯参量进行预测及更新,实现非线性模型系统下的目标跟踪。仿真结果表明,与现有的δ-GLMB滤波器的扩展卡尔曼滤波(Extended Kalman Filter,EKF)高斯混合实现及无迹卡尔曼滤波(Unscented Kalman Filter,UKF)高斯混合实现相比,该算法可提高非线性高杂波密度环境下的目标跟踪精度。     

UKF、PF与UPF跟踪性能的比较

无迹卡尔曼滤波器(UKF)是用一系列确定样本来逼近状态的后验概率密度,对任何非线性高斯系统都有较好的跟踪性能。粒子滤波器(PF)是用随机样本来近似状态后验概率密度函数,适用于任何非线性非高斯系统,但当似然函数出现在转移概率密度函数的尾部或者在高精度测量的场合,PF的跟踪性能降低。针对强非线性、非高斯系统、高精度测量的环境,文中提出采用UPF算法进行跟踪,并对PF、UKF和UPF三种跟踪算法进行了仿真,结果表明,UPF的跟踪精度要远高于PF、UKF的精度。     

基于UKF的闪烁噪声机动目标跟踪

闪烁噪声下的机动目标跟踪是一个非线性非高斯系统滤波问题,传统的卡尔曼理论很难保证其跟踪精度.文中提出了一种基于UKF的闪烁噪声机动目标跟踪算法,首先对目标系统的状态方程进行无味变换,然后再进行滤波估计,以减小跟踪误差.UKF不需要求导,它能比EKF更好地迫近目标运动模型的非线性特性,具有更高的估计精度,计算量却与EKF同阶.在仿真实验中采用"协同转弯模型"作为机动目标的运动模型,雷达的量测方程也是非线性的,分别应用UKF和EKF跟踪闪烁噪声下的机动目标,结果表明,UKF能够较好地解决闪烁噪声下跟踪机动目标的难题,其跟踪精度要远远高于EKF.     

基于UKF的CDMA系统信道参数估计

CDMA系统信道时间延迟估计是一个非线性的迭代过程。UKF算法能够避免EKF由于线性化非线性系统而带来的误差过大等问题,比EKF估计的更加精确。利用UKF算法对CDMA系统信道的幅度衰减参数与延时参数进行了估计。在研究中考虑到了多址干扰和远近效应对信道参数的影响,仿真结果表明UKF算法能有效地抑制远近效应及多址干扰,估计出无线信道参数。     

高动态下基于AUKF的载波跟踪算法

当载体处于高动态运动状态时,GPS接收机载波跟踪信号极易受到外部环境不确定因素的影响。若采用标准的无迹卡尔曼滤波 (UKF),在先验的噪声统计特性与实际的噪声统计特性不相符时,状态估计性能将变差甚至发散。针对上述问题,提出采用主从式自适应UKF的算法(AUKF)。AUKF能自适应调整过程噪声方差,从而达到减小模型估计误差、抑制滤波发散的目的。Matlab仿真结果表明,在高动态下噪声统计特性发生变化时,基于AUKF的载波跟踪算法具有较好的稳定性。     

改进的UPF在GPS/INS导航中的应用

针对UPF（Unscented Particle Filter）由于计算量大而难以应用于GPS/INS（Global Positioning System/Inertial Navigation System）组合导航中的问题,提出一种基于全局采样的UPF算法。结合了最新的量测值,对粒子集整体利用一次UKF（Unscented Kalman Filter）算法产生建议分布,免去了UPF中对每个粒子循环套用UKF的环节,省去了重采样步骤,减少了UPF的计算量。仿真实验采用以伪距为观测量的状态变量为10维的非线性模型,结果表明,改进的UPF与PF相比,具有更高的估计精度,与UPF相比,具有更小的计算量,能够解决UPF难以应用于GPS/INS组合导航中的问题。     

Online identification of nonlinear multivariable processes using self‐generating RBF neural networks

This paper addresses the problem of online model identification for multivariable processes with nonlinear and time‐varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self‐organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP‐RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input‐output data pairs in real‐time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF‐based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP‐RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)‐based approaches for the case of non‐Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self‐generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time‐varying multivariable non‐isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP‐RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Unscented Kalman滤波的流量测量研究

将UKF滤波用于超声波流量测量,使用UKF滤波算法来处理超声波回波信号,得到回波信号的包络线,并且将包络模型的参数作为UKF处理的状态向量。根据流量测量的特点改进了UKF滤波运算过程,给出了UKF迭代开始和结束的条件。最后在Matlab上仿真UKF的性能及收敛速度,证明UKF是有效的和容易实现的。     

自适应UKF应用于反辐射导弹抗静止目标雷达关机

抗目标雷达关机是反辐射导弹的技术难题,也是关键问题。针对基于目标状态估计的抗目标雷达关机方案,将自适应UKF算法应用于抗静止雷达关机措施中。利用EKF,UKF和自适应UKF算法对反辐射导弹抗关机性能进行了仿真实验。通过实验得出的结果表明,自适应UKF算法相对于其他2种滤波算法在对抗雷达关机方面具有明显的优越性。     

以改善精度为目标的人手跟踪方法研究

分别从UKF滤波器的内在机理和人手运动模型两个方面入手,以改善跟踪结果的精确度为基本目标,重点对UKF算法中存在的部分理论问题进行了探讨,在此基础上提出了改进后的UKFDUT算法,同时也对IMM进行了改进,把IMM模型变为MM模型,再进一步将UKFDUT算法和MM模型相融合,得到UKFDUT MM算法,研究表明,Sigma点具有一些特性,通过对这些特性进行研究,可以找到改进跟踪精度的新途径;把MM模型和人手模型评价标准相结合,可以取得比单独使用IMM更好的跟踪精度,实验结果也表明了算法的有效性和令人满意的跟踪精度.     

基于Unscented卡尔曼滤波的室内定位

基于RSSI值的测距技术中,通过对天线全向性问题的分析,提出基于Unscented卡尔曼滤波（UKF）的定位算法。利用基于RSSI值的测距模型进行距离测量,并使用Unscented卡尔曼滤波算法估计节点坐标。由于RSSI值的测量和测距模型参数受到环境的影响,采用高斯滤波对RSSI值进行优化,对环境参数使用线性回归算法进行优化并采用自适应机制更新。通过与最大似然估计法（ML）的比较实验表明,该算法能有效地减小定位误差,提高定位精度。     

UKF在INS/GPS直接法卡尔曼滤波中的应用

提出将Unscented卡尔曼滤波(UKF)用于INS/GPS组合导航系统的直接法卡尔曼滤波,避免了对非线性的系统状态方程进行线性化.以INS输出的导航参数及平台误差角等作为系统状态,惯导力学编排方程和姿态误差方程作为系统状态方程,GPS输出的导航参数作为量测,采用UKF方法对系统导航参数直接进行估计.仿真结果表明,UKF方法有效地解决了直接法卡尔曼滤波中系统状态方程的非线性问题,并使INS/GPS组合导航系统具有较高的导航定位精度.     

基于UKF滤波的测向定位算法及性能分析

基于传统的The Unscented Kalman Filter(UKF)滤波算法,提出了一种新的改良后的UKF滤波算法.该算法直接选用动态模型中的状态变量,并增加一个再抽样过程,使得计算量更小,实现更简单.将改良后的UKF滤波算法应用到单站无源定位的测向法中,得到优于The extended Kalman Filter(EKF)滤波的定位效果,大大提高了定位精度.计算机仿真实验表明,应用该改进后的UKF算法比以往EKF类算法在滤波性能上有明显的提高.但是由于测向法自身的局限性,即使应用改良后的UKF滤波,当方位角逐渐增大时,测向法的定位效果仍然会严重恶化.因此,所提出的新UKF算法适合在非线性估计等问题中广泛应用,但对于单站无源定位,则应探究更优越的定位算法来代替测向法.     

An O(N²) Square Root Unscented Kalman Filter for Visual Simultaneous Localization and Mapping

This paper develops a Square Root Unscented Kalman Filter (SRUKF) for performing video-rate visual simultaneous localization and mapping (SLAM) using a single camera. The conventional UKF has been proposed previously for SLAM, improving the handling of nonlinearities compared with the more widely used Extended Kalman Filter (EKF). However, no account was taken of the comparative complexity of the algorithms: In SLAM, the UKF scales as O(N^{3}) in the state length, compared to the EKF's O(N^{2}), making it unsuitable for video-rate applications with other than unrealistically few scene points. Here, it is shown that the SRUKF provides the same results as the UKF to within machine accuracy and that it can be reposed with complexity O(N^{2}) for state estimation in visual SLAM. This paper presents results from video-rate experiments on live imagery. Trials using synthesized data show that the consistency of the SRUKF is routinely better than that of the EKF, but that its overall cost settles at an order of magnitude greater than the EKF for large scenes.     

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Unscented Kalman filter (UKF) has been extensively used for state estimation of nonlinear stochastic systems, which suffers from performance degradation and even divergence when the noise distribution used in the UKF and the truth in a real system are mismatched. For state estimation of nonlinear stochastic systems with non-Gaussian measurement noise, the Masreliez–Martin extended Kalman filter (EKF) gives better state estimates in relation to the standard EKF. However, the process noise and the measurement noise covariance matrices should be known, which is impractical in applications. This paper presents a robust Masreliez–Martin UKF which can provide reliable state estimates in the presence of both unknown process noise and measurement noise covariance matrices. Two numerical examples involving relative navigation of spacecrafts demonstrate that the proposed filter can provide improved state estimation performance over existing robust filtering approaches. Vision-aided robot arm tracking experiments are also provided to show the effectiveness of the proposed approach.     

基于最小均方误差估计的噪声相关UKF设计

传统Unscented卡尔曼滤波器(UKf)要求系统噪声和量测噪声必须是互不相关的.针对此局限性,研究了一类带相关噪声的非线性离散系统UKF设计方法.基于最小均方误差估计和正交变换,给出了噪声相关UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验分布.所设计的UKF有效解决了传统UKF在噪声相关条件下非线性滤波失效的问题,拓展了UKF的应用范围.最后,仿真实例表明了所设计UKF的有效性.     

基于UKF的环境自适应UWB/DR室内定位方法

针对复杂室内环境下超宽带（Ultra WideBand,UWB）信号传播的非视距（Non Line Of Sight,NLOS）误差问题,本文提出了一种基于无迹卡尔曼滤波（Unscented Kalman Filter,UKF）的环境自适应UWB/DR室内定位方法.该方法通过建立自适应UKF滤波模型,将UWB定位信息和航迹推算（Dead Reckoning,DR）定位信息进行融合.依据新息和高斯分布的3σ原则来对UWB定位结果进行非视距检测,再通过新息的实时估计协方差和理论协方差来构建环境适应系数,进而用此系数动态修正UWB定位的观测噪声,使得观测噪声自适应真实环境,降低NLOS误差对融合定位结果的影响.实验结果表明,该方法能有效减小UWB定位的NLOS误差,并且由于环境适应系数的创新引入,比UKF定位和粒子滤波定位（Particle Filtering,PF）有更高的定位精度和更强的抗NLOS误差性能.