基于鲁棒容积卡尔曼滤波的自适应目标跟踪算法

目标跟踪系统的观测野值将大大降低滤波算法对目标状态的估计精度.为了解决这个问题,提出了一种基于鲁棒容积卡尔曼滤波的自适应目标跟踪算法.借鉴Huber等价权函数的思想,构造了基于平方根平滑逼近函数的修正因子以抑制观测野值的影响,并结合容积卡尔曼滤波器求解框架推导出该算法.区别于Huber方法对观测残差的每个维度分别进行处理,提出的算法能够对观测残差进行综合评判.理论分析证明所提算法具有更好的数值稳定性.仿真实验表明,所提算法能够自适应地减少异常值的不利影响,与现有算法相比具有更优的滤波性能.在仿真实验中还对几种滤波算法的计算花费进行了比较,发现所提算法未大幅增加计算成本.     

传感器网络中鲁棒状态信息融合抗差卡尔曼滤波器

研究了无线传感器网络中的分布式鲁棒状态信息融合问题. 在局部状态估计层, 基于鲁棒统计学理论提出了适用于噪声相关情况的抗差(扩展)卡尔曼滤波器. 在融合中心层, 针对局部估计相关未知性和不完整性, 给出了不依赖于互协方差阵的稳健航迹融合方法—–内椭球逼近法. 仿真结果证实了算法的有效性: 所提出的抗差卡尔曼滤波器在野值存在情况下, 性能退化远低于传统卡尔曼滤波器(28.6%比428.6%); 所提出的内椭球逼近法获得比协方并交叉法更好的融合估计性能, 且不需要局部估计相关性的先验知识.     

基于Huber M估计的鲁棒Cubature 卡尔曼滤波算法

Cubature卡尔曼滤波器(CKF)在非高斯噪声或统计特性未知时滤波精度将会下降甚至发散,为此提出了统计回归估计的鲁棒CKF算法.推导出线性化近似回归和直接非线性回归的鲁棒CKF算法,直接非线性回归克服了观测方程线性化近似带来的不足.具有混合高斯噪声的仿真实例比较了3种Cubature卡尔曼滤波器的滤波性能,结果表明这两种鲁棒CKF滤波精度及估计一致性明显优于CKF,直接非线性回归的CKF的鲁棒性更强,滤波性能更好.     

野值存在下的BP网络自适应卡尔曼滤波

野值的存在会严重影响滤波器的稳定性和滤波精度,甚至会引起滤波器发散。定量分析了野值对卡尔曼滤波器的影响,提出了一种抗野值的BP网络自适应卡尔曼滤波算法。通过BP网络对新息序列估计方差的变化率进行实时监测和计算,输出一组加权系数对模型中系统噪声和量测噪声作＂在线＂修正,从而有效地抑制了连续野值对滤波器的影响。经仿真证明算法提高了滤波器的精度和稳定性,同时对单个离散野值也有较好的滤波效果。     

鲁棒核主元分析的数据重构

针对野值点噪声对样本均值和协方差估计带来的不利影响,在线性鲁棒M位置估计方法的基础上,结合了核原理来估计协方差,提出了一种新型的鲁棒KPCA(核主元分析)算法.将所提出的算法应用于数据重构仿真实验,仿真测试结果表明当样本数据中存在野值点噪声时,由所提出的鲁棒KPCA算法实现样奉数据重构时,要比KPCA具有更高的重构精度,抗野值点噪声性能更强.     

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.     

基于M估计的非线性鲁棒检测卡尔曼滤波算法

针对传统鲁棒非线性滤波在观测噪声为非高斯强干扰噪声情况下,滤波性能下降的问题,提出一种利用卡方检测法预判断的非线性鲁棒检测滤波算法。该算法通过卡方检测设置门限,剔除突变野值,利用M估计修正量测更新。仿真实验对比了几种典型非线性滤波方法在不同观测噪声环境下的性能。所提算法在非高斯强干扰噪声情况下,比传统鲁棒滤波算法估计精度平均提高了25.5%;估计方差平均减少了18.3%。实验结果表明:所提算法可以抑制观测量非高斯强干扰噪声的影响,提高滤波精度及稳定性。     

基于递推近似最小一乘的多传感器系统偏差稳健估计算法

对于多传感器多目标跟踪问题,系统偏差对航迹融合精度有较大影响,因此在信息融合系统中,首先要对各传感器的系统偏差进行估计,而在含错误关联和观测野值的复杂环境下,传统系统偏差估计方法的性能会严重退化.对此,提出一种具有递推形式的近似最小一乘稳健估计算法,以减少异常噪声对偏差估计的不利影响.使用平方根平滑逼近函数替代最小一乘法的目标函数,基于牛顿方向及其秩1修正推导出该方法的递推求解框架.基于条件数分析,证明所提出算法的数值稳定性好于Huber方法.通过两个仿真算例,将所提出算法与已有其他算法进行对比验证.仿真结果表明,在含错误关联和观测野值的条件下,所提出算法可以改善偏差估计精度,并且明显好于已有的其他算法.     

鲁棒核主元分析的数据重构

针对野值点噪声对样本均值和协方差估计带来的不利影响,在线性鲁棒M 位置估计方法的基础上,结 合了核原理来估计协方差,提出了一种新型的鲁棒KPCA 算法．将所提出的算法应用于数据重构仿真实验,仿真测 试结果表明当样本数据中存在野值点噪声时, 由所提出的鲁棒KPCA 算法实现样本数据重构时,要比KPCA 具有更 高的重构精度, 抗野值点噪声性能更强．     

基于Huber的鲁棒广义高阶容积卡尔曼滤波算法

为提高随机变量非高斯分布时广义高阶容积卡尔曼滤波(GHCKF)的鲁棒性,提出一种基于Huber的鲁棒GHCKF算法.从近似贝叶斯估计角度,解释Huber方法作用于卡尔曼滤波的本质是对新息进行截断平均.采用Huber方法处理观测量,进行标准的GHCKF量测更新,从而实现算法的鲁棒化.所提出算法充分利用容积变换的优势,无需通过统计线性回归模型对系统的非线性量测模型进行近似.仿真结果表明,所提出算法具有鲁棒性强和估计精度高的特点.     

基于固定点迭代的Huber鲁棒容积卡尔曼滤波算法

对于非线性系统而言,容积卡尔曼滤波（Cubature Kalman Filter,CKF）算法是处理状态估计问题的一种有效方法,并且其在高斯噪声下可以获得良好的估计性能。然而,当噪声被重尾噪声污染时,其性能通常会急剧下降。为解决此问题,将Huber方法应用于CKF框架中,取代了传统的最小均方误差（Minimum Mean Square Error,MMSE）准则,以提高算法的鲁棒性。在所提算法中,通过将量测方程线性化构造了线性回归模型,并采用固定点迭代的方法求解基于Huber方法的最小化问题。因此,推导了基于固定点迭代的Huber鲁棒CKF（FP-IHCKF）算法,在该算法中先验信息和量测信息通过Huber方法进行了重构。通过对再入目标跟踪问题进行仿真,验证了所提算法的有效性和鲁棒性。     

Robust unscented Kalman filter for nanosat attitude estimation

A robust unscented Kalman filter based on a multiplicative quaternion-error approach is proposed for nanosat estimation in the presence of measurement faults. The global attitude parameterization is given by a quaternion, while the local attitude error is defined using a generalized three-dimensional attitude representation. The proposed algorithm uses a statistical function including measurement residuals to detect measurement faults and then uses an adaptation scheme based on multiple measurement scale factor for filter robustness against faulty measurements. The proposed algorithm is demonstrated for the attitude estimation of a nanosat with an on-board three-axis magnetometer and rate-integrating gyros in the presence of measurement faults as well as satellite orbit errors. To compare the estimation performance of the proposed algorithm, the robust unscented Kalman filter with single measurement noise scale factor, the standard extended Kalman filter and the unscented Kalman filter are also implemented under the same simulation conditions.     

基于Huber的鲁棒高阶容积卡尔曼滤波算法

为提高随机变量非高斯分布时高阶容积卡尔曼滤波（High-degree Cubature Kalman Filter,HCKF）算法的鲁棒性,提出了一种基于Huber方法的鲁棒高阶容积卡尔曼滤波算法。从近似贝叶斯估计角度解释了Huber方法作用于卡尔曼滤波算法的本质是对新息进行截断平均,通过在现有滤波框架内利用Huber方法对观测量进行预处理,并将处理后的观测量进行标准的HCKF量测更新,实现了HCKF算法的鲁棒化。所提算法无需通过统计线性回归模型对系统的非线性量测模型进行近似,高阶容积变换的优势得到充分利用,从而在保持鲁棒性的前提下提高了算法的滤波精度。单变量非平稳增长模型和再入飞行器目标跟踪问题验证了该算法在鲁棒性和滤波精度方面的优势。     

分簇传感网络系统两级鲁棒观测融合Kalman滤波器

研究了分簇传感网络分布式融合Kalman滤波器.根据最邻近原则将传感网络分成簇,每簇由传感节点和簇首组成.应用极大极小鲁棒估计原理,基于带噪声方差最大保守上界的最坏保守系统,对带不确定性噪声方差的分簇传感网络系统提出了两级鲁棒观测融合Kalman滤波器.当传感器数量非常多的时候它可以明显减小通信负担.在鲁棒性分析中利用Lyapunov方程方法证明了局部和融合Kalman滤波器的鲁棒性.提出了鲁棒精度的概念,并证明了局部和融合鲁棒Kalman滤波器之间的鲁棒精度关系.证明了两级加权观测融合器的鲁棒精度等价于相应的全局集中式鲁棒融合器的鲁棒精度,并且高于每个局部观测融合器的鲁棒精度.一个仿真例子说明上述结果的准确性.     

分簇传感网络系统两级鲁棒观测融合Kalman滤波器（英文）

This paper investigates the distributed fusion Kalman filtering over clustering sensor networks. The sensor network is partitioned as clusters by the nearest neighbor rule and each cluster consists of sensing nodes and cluster-head. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, twolevel robust measurement fusion Kalman filter is presented for the clustering sensor network systems with uncertain noise variances.It can significantly reduce the communication load and save energy when the number of sensors is very large. A Lyapunov equation approach for the robustness analysis is presented, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented, and the robust accuracy relations among the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the two-level weighted measurement fuser is equal to that of the global centralized robust fuser and is higher than those of each local robust filter and each local weighted measurement fuser. A simulation example shows the correctness and effectiveness of the proposed results.     

带观测滞后和不确定噪声方差的多智能体传感网络鲁棒序贯协方差交叉融合Kalman滤波

针对带观测滞后和不确定噪声方差的分簇多智能体传感网络系统,研究鲁棒序贯协方差交叉融合Kalman滤波器的设计问题.应用最邻近法则,传感网络被分成簇.应用极大极小鲁棒估计原理,基于带噪声方差最差保守上界的最差保守传感网络系统,提出了两级序贯协方差交叉(SCI)融合鲁棒稳态Kalman滤波器,可减小通信和计算负担并节省能量,且保证实际滤波误差方差有一个最小保守上界.一种Lyapunov方程方法被提出用于证明局部和融合滤波器的鲁棒性.提出了鲁棒精度的概念且证明了局部和融合鲁棒Kalman滤波器的鲁棒精度关系.证明全局SCI融合器的鲁棒精度高于每簇SCI融合器的精度且两者的鲁棒精度都高于每个局部鲁棒滤波器的精度.一个跟踪系统的仿真例子证明了鲁棒性和鲁棒精度关系.     

带观测滞后和不确定噪声方差的多智能体传感网络鲁棒序贯协方差交叉融合Kalman滤波（英文）

This paper deals with the problem of designing robust sequential covariance intersection(SCI) fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances. The sensor network is partitioned into clusters by the nearest neighbor rule. Using the minimax robust estimation principle, based on the worst-case conservative sensor network system with conservative upper bounds of noise variances, and applying the unbiased linear minimum variance(ULMV) optimal estimation rule, we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources, and guarantee that the actual filtering error variances have a less-conservative upper-bound. A Lyapunov equation method for robustness analysis is proposed, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented and the robust accuracy relations of the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter. A simulation example for a tracking system verifies the robustness and robust accuracy relations.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.