欠观测条件下的高斯和增量卡尔曼滤波算法

欠观测条件下的增量卡尔曼滤波算法能够消除未知的量测系统误差,提高滤波精度。当系统的过程噪声和量测噪声为非高斯分布时,该算法不能直接使用。针对该问题,结合高斯和滤波算法,提出一种欠观测条件下的高斯和增量卡尔曼滤波算法。该算法将初始状态、过程噪声和量测噪声近似为高斯和的形式,然后按照增量卡尔曼滤波的思想对每个高斯项进行预测和更新,最后以累加和的形式对状态向量进行近似。仿真结果表明,该算法在非高斯噪声分布的情况下,既能成功地消除量测系统误差,又能有效地提高滤波估计的准确度和可靠性。     

自适应高阶无迹增量卡尔曼滤波算法

在工程实际中,由于环境因素的影响、测量设备的不稳定性、模型和参数的选取不当等往往会对量测方程带来未知的系统误差.针对这一问题,提出了一种自适应高阶无迹增量卡尔曼滤波算法.首先,利用增量建模技术建立增量量测方程.其次,将其与高阶无迹卡尔曼滤波器相结合,并引入自适应加权因子对滤波发散进行抑制,发展出一种自适应增量滤波算法.计算机仿真实验表明,新算法能够成功消除这种未知的系统误差,提高估计精度和稳定性,具备良好的应用前景.     

广义容积卡尔曼滤波

传统CKF采用三阶球面径向容积定律来计算非线性积分,该定律将球面数值积分与径向积分相结合,难以构造高阶CKF算法。此外,CKF在许多非线性问题上表现出估计精度低等问题。为了解决以上问题,提出了一种广义CKF族,所提算法彻底抛弃了球面径向积分定律。进一步指出,传统CKF是这种滤波算法的特殊形式。实验结果表明,高阶CKF比传统的非线性滤波器准确性更高。     

基于容积卡尔曼滤波算法估计动力锂电池荷电状态

动力锂电池荷电状态的准确估计是电池管理系统的关键功能之一。该文结合二阶电阻-电容等效电路模型,通过建立状态空间表达式,利用最小二乘法对等效电路模型各参数进行辨识,并通过多项式拟合方法获得了开路电压与剩余电荷的关系曲线,进而基于容积卡尔曼滤波方法对锂电池荷电状态进行建模,建立了基于数字信号处理器的充放电实验平台,实现了锂电池放电时荷电状态的实时估算。实验结果表明,该方法能够实现实时在线估算,且最大误差小于 2%,具有良好的估算精度。     

基于迭代容积卡尔曼滤波的神经网络训练算法

针对现有应用非线性滤波算法对神经网络进行训练时存在精度不足的问题,提出了一种基于迭代容积卡尔曼滤波的神经网络训练算法。首先,将前馈神经网络各个节点的连接权值和偏置作为状态向量,建立前馈神经网络的状态空间模型。其次,利用Spherical-Radial准则生成容积点,并依据Gauss-Newton迭代策略来优化量测更新过程中获取的状态估计值和状态估计误差协方差,通过容积卡尔曼滤波估计精度的改善,提升神经网络节点的连接权值和偏置的训练效果。理论分析和仿真实验结果验证了所提算法的可行性和有效性。     

交互式容积卡尔曼滤波及其应用 交互式容积卡尔曼滤波及其应用

针对非线性系统模型参数未知情况下的状态估计问题, 提出一种融合极大后验估计的交互式容积卡尔曼滤波算法(InCKF). 该算法利用二阶斯特林插值公式和无迹变换对非线性函数的近似思想, 实现对模型未知参数的确定, 从而使滤波算法摆脱对模型参数精确已知的依赖, 并通过容积卡尔曼滤波算法完成状态估计和量测更新. 仿真结果表明, 相比于经典的参数扩维方法, InCKF 算法具有更高的精度和更强的数值稳定性.

     

基于改进容积卡尔曼滤波的认知雷达跟踪算法

在认知雷达目标跟踪过程中,由于存在初始跟踪误差及系统量测方程的非线性等原因,导致卡尔曼滤波算法性能较差.为解决上述问题,将Gauss-Newton迭代方法与容积卡尔曼滤波算法相结合,建立迭代容积卡尔曼滤波算法.算法在迭代过程中利用最新的量测信息并更新迭代过程中产生的新息方差,降低了目标初始状态的估计误差,并且减小了线性化量测方程引入的传递误差.仿真结果表明,迭代容积卡尔曼滤波算法与传统的扩展卡尔曼滤波算法、无迹卡尔曼滤波算法、容积卡尔曼滤波算法相比,在认知雷达中的跟踪精度更高,稳定性更好,对初始误差的容错性更强.结果可为雷达目标跟踪优化提供科学依据.     

多传感器自适应容积卡尔曼滤波融合算法

当容积卡尔曼滤波的系统模型不准确或测量出现异常时容易出现滤波发散。为了解决这一问题,提出了一种自适应容积卡尔曼滤波算法,构造了一组噪声统计估计器对噪声的统计特征进行在线实时估计,并在测量异常时采用修正函数对滤波过程进行修正,有效提高了滤波估计的精度和对滤波发散的抑制能力;在集中式滤波结构和联邦式滤波结构的基础上,设计了一种基于自适应容积卡尔曼滤波算法的多传感器系统混合式组合滤波结构,并给出了融合各传感器的局部滤波信息以得到全局滤波估计的计算方法。以对车辆的定位导航为应用背景进行了仿真实验,仿真结果证明了所提方法的有效性。     

多传感器集中式增量卡尔曼滤波融合算法

在单个传感器的状态估计系统中,标准的增量卡尔曼滤波方法可以有效消除量测系统误差。对于多传感器情况,标准算法失效。针对该问题,提出了多传感器集中式增量卡尔曼滤波融合算法,即:增量卡尔曼滤波的扩维融合算法和增量卡尔曼滤波的序贯融合算法。在标准增量卡尔曼滤波算法的基础上,结合扩维融合和序贯融合的思想来实现多传感器数据的融合。实验结果表明,当存在量测系统误差时,提出的集中式融合算法与传统的集中式融合算法相比,提高了滤波精度,并且能够成功地消除量测系统误差。     

强跟踪平方根容积卡尔曼滤波和 自回归模型融合的故障预测

为了解决非线性系统中不可测量参数的预测问题,提出一种带有次优渐消因子的强跟踪平方根容积卡尔曼滤波(STSCKF)和自回归(AR)模型相结合的故障预测方法.利用AR模型时间序列预测法预测未来时刻的测量值,将预测的测量值作为STSCKF的测量变量,从而将预测问题转化为滤波估计问题.STSCKF通过在预测误差方差阵的均方根中引入渐消因子调节滤波过程中的增益矩阵,克服了故障参数变化函数未知情况下普通SCKF跟踪故障参数缓慢甚至失效的局限性,使得STSCKF能较好地预测故障参数的发展趋势.连续搅拌反应釜(CSTR)仿真结果表明,STSCKF的预测精度高于普通SCKF和强跟踪无迹卡尔曼滤波(STUKF),验证了方法的有效性.     

A New Derivation of the Cubature Kalman Filters

This paper investigates the cubature Kalman filtering (CKF) for nonlinear dynamic systems. This third‐degree rule based filter employs a spherical‐radial cubature rule to numerically compute the integrals encountered in nonlinear filtering problems, thereby removing the requirements of explicitly computing the Jacobians. The cubature rule, however, requires computing the intractable integrals over a high‐dimensional spherical region for multidimensional applications. Moreover, the cubature formula that has been used to construct the spherical cubature formula has some demerits, most notably its inconvenient properties in computation and low estimation accuracy. Aimed at these issues, a general class of CKFs that uses only cubature rules is derived in this paper. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes higher‐degree CKFs, especially two representative types of the fifth‐degree CKFs. Performance of the proposed algorithms is demonstrated via two target tracking problems. The experimental results, presented herein, illustrate the superior performance of higher‐degree CKFs to conventional nonlinear filters.     

基于CKF的GPS定位误差估计及故障检测

针对卡尔曼滤波(KF,Kalman filter)算法无法解决非线性系统估计的问题和扩展卡尔曼滤波(EKF,extended Kalman filter)算法在GPS卫星导航定位误差估计中存在的线性化误差大、需求解繁琐的Jacobian矩阵等问题,将较新型的卡尔曼滤波算法——容积卡尔曼滤波(CKF,cubature Kalman filter)应用于GPS定位计算,在算法精度上与KF和EKF算法进行了比较,并利用定位误差进行GPS故障卫星的检测.利用实测导航电文数据进行实验,结果表明:CKF用于导航定位估计不仅精度高,而且实现简单,无可调参数,性能明显优于KF和EKF,并可进一步用于故障检测.     

Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics (e.g., mean and covariance) conditioned on a system's measurement data. This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering (KF) techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.      

Major Development Under Gaussian Filtering Since Unscented Kalman Filter

Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements. Such problems appear in several branches of science and technology, ranging from target tracking to biomedical monitoring. A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering. The early Gaussian filters used a derivative-based implementation, and suffered from several drawbacks, such as the smoothness requirements of system models and poor stability. A derivative-free numerical approximation-based Gaussian filter, named the unscented Kalman filter (UKF), was introduced in the nineties, which offered several advantages over the derivative-based Gaussian filters. Since the proposition of UKF, derivative-free Gaussian filtering has been a highly active research area. This paper reviews significant developments made under Gaussian filtering since the proposition of UKF. The review is particularly focused on three categories of developments: i) advancing the numerical approximation methods; ii) modifying the conventional Gaussian approach to further improve the filtering performance; and iii) constrained filtering to address the problem of discrete-time formulation of process dynamics. This review highlights the computational aspect of recent developments in all three categories. The performance of various filters are analyzed by simulating them with real-life target tracking problems.      

平方根体积积分卡尔曼滤波

体积积分是一种新的具有较高代数精度的积分方法。为了提高非线性滤波算法的精度和数值稳定性,将体积积分规则和平方根分解引入卡尔曼滤波框架中,提出了平方根体积积分卡尔曼滤波算法（SRCQKF）。新算法采用球半径体积规则和高斯-拉盖尔积分规则计算积分点,利用矩阵的QR分解得到协方差矩阵的平方根并传播平方根。两个典型的非线性系统的实验结果表明,与体积卡尔曼滤波相比,新算法提高了非线性状态的估计精度,具有较高的数值稳定性。     

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。     

基于Kalman滤波的Wiener状态估值器

应用经典稳态Kalman滤波理论提出了设计Wiener状态估值器的新方法,其原理是:基于在Wiener滤波器形式下的稳态Kalman滤波器和预报器及ARMA新息模型,由稳态最优非递推状态估值器的递推变形引出Wiener状态估值器.所提出的Wiener状态估值器可统一处理状态滤波、预报和平滑问题.它们具有ARMA递推形式,且具有渐近稳定性和最优性,仿真例子说明了它们的有效性.