Robust cubature Kalman filter based on variational Bayesian and transformed posterior sigma points error

An improved robust cubature Kalman filter (RCKF) based on variational Bayesian (VB) and transformed posterior sigma points error is proposed in this paper, which not only retains the robustness of RCKF, but also exhibits adaptivity in the presence of time-varying noise. First, a novel sigma-point update framework with uncertainties reduction is developed by employing the transformed posterior sigma points error. Then the VB is used to estimate the time-varying measurement noise, where the state-dependent noise is addressed in the iteratively parameter estimation. The new filter not only reduces the uncertainty on sigma points generation but also accelerates the convergence of VB-based noise estimation. The effectiveness of the proposed filter is verified on integrated navigation, and numerical simulations demonstrate that VB-RCKF outperforms VB-CKF and RCKF.     

基于CKF的SINS大方位失准角初始对准

大方位失准角捷联惯导系统(strapdown inertial narigation system,SINS)误差方程是非线性的,为改善非线性模型下初始对准的精度,提出将一种新的非线性滤波方法(cubature Kalman filter,CKF)应用于捷联惯导系统初始对准中。为此建立了大方位失准角下初始对准非线性模型,分析了基于spherical-radial cubature准则的CKF滤波原理,对非线性模型进行了CKF滤波仿真。仿真结果表明CKF能够很好地处理初始对准中的非线性问题,提高初始对准精度,方位失准角误差能够收敛到-33.13’,接近理论估计精度-32.40’,优于EKF的-84.14’。     

Maximum correntropy square-root cubature Kalman filter with application to SINS/GPS integrated systems

For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter.     

基于CKF的永磁同步电机无传感器控制

永磁同步电机（PMSM）是典型的非线性系统。为提高转速估计精度,提出了将cubatureKalmanfilter（CKF）方法应用在PMSM无速度传感器控制中。和扩展卡尔曼滤波（EKF）算法相比,CKF无需对系统非线性模型进行线性化处理。其根据spherical—radialcubature准则,通过一些相等权值的cubature点经非线性系统方程转换后产生新的点来给出下一时刻系统状态的预测,不需要对系统模型进行线性化处理。文中在对CKF算法分析的基础上,建立了基于CKF的PMSM无速度传感器控制仿真模型,通过和传统的EKF算法的仿真对比实验,验证了CKF算法的有效性和优越性。     

基于高斯混合容积卡尔曼滤波的UUV自主导航定位算法

针对过程噪声为非理想高斯分布时无人水下航行器(UUV)自主导航定位存在噪声模型失配的问题,将高斯混合密度模型与容积卡尔曼滤波(CKF)相结合,设计了基于高斯混合容积卡尔曼滤波(GM-CKF)的UUV导航定位算法。建立了UUV运动模型及观测模型,利用CKF完成各高斯分量的预测更新,并将更新结果进行融合缩减与加权求和,从而实现UUV自主导航定位。通过与EKF、UKF和CKF算法仿真对比实验,验证了GM-CKF可以提高估计精度;通过UUV湖试试验,验证了基于GM-CKF的UUV自主导航定位精度和稳定性优于传统算法,其计算时间满足实时导航定位的要求。     

Performance analysis of improved iterated cubature Kalman filter and its application to GNSS/INS

In order to improve the accuracy and robustness of GNSS/INS navigation system, an improved iterated cubature Kalman filter (IICKF) is proposed by considering the state-dependent noise and system uncertainty. First, a simplified framework of iterated Gaussian filter is derived by using damped Newton–Raphson algorithm and online noise estimator. Then the effect of state-dependent noise coming from iterated update is analyzed theoretically, and an augmented form of CKF algorithm is applied to improve the estimation accuracy. The performance of IICKF is verified by field test and numerical simulation, and results reveal that, compared with non-iterated filter, iterated filter is less sensitive to the system uncertainty, and IICKF improves the accuracy of yaw, roll and pitch by 48.9%, 73.1% and 83.3%, respectively, compared with traditional iterated KF.     

四轮驱动电动汽车质心侧偏角与轮胎侧向力非线性鲁棒融合估计

针对四轮驱动电动汽车质心侧偏角和轮胎侧向力难以直接测量的问题,考虑系统未建模的动态特性、模型参数摄动、系统过程噪声及测量噪声等因素,提出了一种基于遗忘因子递归最小二乘法(FFRLS)与鲁棒容积卡尔曼滤波(RCKF)的联合估计方法。基于FFRLS法对整车质量进行实时估计,并将极大值背景下的估计误差最小化嵌入标准容积卡尔曼滤波(CKF)以实现RCKF,提出了联合估计算法的改进策略,有效提高了复杂工况下滤波对模型参数摄动以及未建模噪声的抗干扰能力,可以实现质心侧偏角与轮胎侧向力的精准估计。在CarSim/Simulink联合仿真环境下,采用不同工况验证了算法的准确性、鲁棒性和抗干扰性。在四轮驱动电动汽车实车平台上分析了算法的有效性。研究结果表明,所提方法比RCKF和CKF精度更高,解决了复合工况下四驱电动汽车质心侧偏角和轮胎侧向力的联合估计问题。     

一种基于椭圆变形模板的唇动跟踪算法

本文给出了一种新的唇动跟踪算法框架，算法结合目标的形状、运动及彩色信息，综合利用可变形模板、光流、Kalman滤波技术，得到一种快速、鲁棒的跟踪结果。该算法使用多条椭圆弧段构成唇模板，基于彩色YCrCb信息进行光流估计，由于利用模型约束的特征光流技术，故不需加入任何附加的平滑性约束；最后借助扩展Kalman（EKF）滤波器将形状与运动信息有机结合起来，给出有效的融合解，而不必直接计算光流；该算法同时利用光流测量方程给出的误差测度及EKF给出的估计方差对虚假边缘点做出判断与舍弃，提高了算法的鲁棒性。文中还给出了相应的实例。     

Analysis of a robust Kalman filter in loosely coupled GPS/INS navigation system

GPS/INS integrated system is very subject to uncertainties due to exogenous disturbances, device damage, and inaccurate sensor noise statistics. Conventional Kalman filer has no robustness to address system uncertainties which may corrupt filter performance and even cause filter divergence. Based on the INS error dynamic equation, a robust Kalman filter is analyzed and applied in loosely coupled GPS/INS integration system. The norm bounded robust Kalman filter, with recursive form by solving two Riccati equations, guarantees a estimation variance bound for all the admissible uncertainties, and can evolve into the conventional Kalman filter if no uncertainties are considered. This paper will analyze the suitable case for the robust Kalman filter in GPS/INS system, the filter characteristics including parameter setting, parameter meaning, and filter convergence condition are discussed simutaneously. The robust filter performance will be compared with conventional Kalman filter through simulation results.     

基于NACKF的分布式驱动电动汽车轮胎侧向力与质心侧偏角估计

针对传统容积卡尔曼滤波算法在进行车辆关键状态估计时要求噪声统计特性已知的问题,提出一种噪声自适应容积卡尔曼滤波（Noise adaptive cubature Kalman filter, NACKF）算法来进行车辆关键状态的估计。基于次优无偏极大后验估计器对量测噪声协方差进行实时更新并将其嵌入到标准容积卡尔曼算法中实现自适应容积卡尔曼滤波。针对车辆不同子系统间耦合特性对滤波精度的影响,构建双重自适应容积卡尔曼滤波器分别进行侧向力与质心侧偏角的估计,两者在估计过程中互为输入构成闭环反馈,利用分布式模块化结构弱化系统耦合特性对估计精度的影响,实现轮胎侧向力与质心侧偏角的实时准确估计。利用Simulink-Carsim联合仿真平台进行仿真验证和实车试验验证。结果表明,基于双重自适应容积卡尔曼滤波的估计算法相对标准容积卡尔曼滤波估计精度更高,较好地改善了传统容积卡尔曼滤波器在噪声先验统计特性未知条件下非线性滤波精度下降的问题。     

Robust SDRE filter design for nonlinear uncertain systems with an H∞ performance criterion

In order to remedy the effects of modeling uncertainty, measurement noise and input disturbance on the performance of the standard state-dependent Riccati equation (SDRE) filter, a new robust H(∞) SDRE filter design is developed in this paper. Based on the infinity-norm minimization criterion, the proposed filter effectively estimates the states of nonlinear uncertain system exposed to unknown disturbance inputs. Moreover, by assuming a mild Lipschitz condition on the chosen state-dependent coefficient form, fulfillment of a modified H(∞) performance index is guaranteed in the proposed filter. The effectiveness of the robust SDRE filter is demonstrated through numerical simulations where it brilliantly outperforms the conventional SDRE filter in presence of model uncertainties, disturbance and measurement noise, in terms of estimation error and region of convergence.     

Estimation of intra-operative brain shift based on constrained Kalman filter

In this study, the problem of estimation of brain shift is addressed by which the accuracy of neuronavigation systems can be improved. To this end, the actual brain shift is considered as a Gaussian random vector with a known mean and an unknown covariance. Then, brain surface imaging is employed together with solutions of linear elastic model and the best estimation is found using constrained Kalman filter (CKF). Moreover, a recursive method (RCKF) is presented, the computational cost of which in the operating room is significantly lower than CKF, because it is not required to compute inverse of any large matrix. Finally, the theory is verified by the simulation results, which show the superiority of the proposed method as compared to one existing method.     

基于鲁棒自适应SCKF的智能汽车目标状态跟踪研究

准确的自车和前车状态估计是智能汽车有效决策和控制的前提,而以往的研究通常不考虑噪声统计特性不确定的问题,导致某些情况下车辆状态估计的误差很大。为此,提出一种鲁棒自适应平方根容积卡尔曼滤波（Robust adaptive square-root cubature Kalman filter,RASCKF）算法,以降低噪声统计不确定性对估计精度的影响。首先,采用最大后验概率准则估计了过程噪声协方差和测量噪声协方差的统计值,以提高噪声稳定时状态估计的精确性。然后,基于标准化测量新息序列设计了故障检测规则,利用实时测量新息对噪声协方差进行校正处理,保证状态估计算法的鲁棒性。最后,在不同的噪声干扰工况下对RASCKF算法进行了仿真验证。结果表明,RASCKF算法在估计精度和稳定性上明显优于标准SCKF算法,有效地解决了智能汽车目标状态跟踪过程中噪声统计特性不确定的问题。     

Concentration distribution estimation of fluid through electrical impedance tomography based on interacting multiple model scheme

In this paper, a dynamic reconstruction algorithm is proposed to monitor the concentration distribution inside the fluid vessel based on electrical impedance tomography (EIT). The interacting multiple model (IMM) scheme is employed to enhance the performance of the extended Kalman filter (EKF) in the presence of abrupt measurement uncertainties by inclusion of covariance compensation extended Kalman filter (CCEKF). Computer simulations are also provided to evaluate the reconstruction performance of the proposed algorithm.     

Moving-window extended Kalman filter for structural damage detection with unknown process and measurement noises

The extended Kalman filter (EKF), as a popular tool for optimally estimating system state from noisy measurement, has been used successfully in various areas over the past several decades. However, classical EKF has several limitations when applied to structural system identification; thus, researchers have proposed a number of variations for this method. The current study focuses on using EKF for real-time system identification and damage detection in civil structures. An improved EKF approach, called moving-window EKF (MWEKF), is proposed in this paper after a discussion on the problems associated with the application of classical EKF in time-variant systems. The proposed approach uses the moving-window technique to estimate several statistical properties. MWEKF is more robust and adaptive in structural damage detection compared with classical EKF because of the following reasons: (1) it is insensitive to the selection of the initial state vector; (2) it exhibits more accurate system parameter identification; and (3) it is immune to the inaccurate assumption of noise levels because measurement and process noise levels are estimated in this approach. The salient features of MWEKF are illustrated through numerical simulations of time-variant structural systems and an experiment on a three-story steel shear building model. Results demonstrate that MWEKF is a robust and effective tool for system identification and damage detection in civil structures.     

基于ASRCKF算法的锂电池SOC估算

针对平方根容积卡尔曼滤波(SRCKF)估算SOC时需要准确获得系统状态及测量噪声协方差这一缺陷,将基于电池模型输出电压残差序列的协方差匹配思想引入平方根容积卡尔曼滤波,提出了自适应平方根容积卡尔曼滤波算法(ASRCKF)。以18650型锂电池为实验对象,建立了戴维南等效电路模型,采用递推最小二乘法辨识电池模型参数,最后,利用UDDS电池实验数据对ASRCFK算法进行了仿真。实验结果表明,传统的SRCKF算法估算SOC产生的均方根误差为3.41%;而提出的ASRCKF算法估算SOC产生的均方根误差仅为0.97%,与传统算法相比具有更高的精度,对噪声的适应能力更强。     

Initial orientation of inertial navigation system realized through nonlinear modeling and filtering

Alignment is the process whereby the orientation of the axes of an inertial navigation system is determined with respect to the reference system. In this paper, the initial alignment error equations of the strapdown inertial navigation system (SINS) with large initial azimuth error have been derived with inclusion of nonlinear characteristics. Simulations have been carried out to validate and corroborate the stationary alignment case employing a strapdown inertial measurement unit (SIMU). A performance comparison between the extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the second-order divided difference filter (DDF2) demonstrate that the accuracy of attitude error estimation using the DDF2 is better than that of using the EKF or the UKF.     

基于模糊卡尔曼滤波器的锂电池荷电状态与健康状态预测

针对当前锂电池荷电状态(State of charge, SOC)与健康状态(State of health, SOH)预测精度较低的问题,提出了一种基于模糊卡尔曼滤波器的预测方法。采用非线性二阶电阻电容模型表示锂电池,并通过最小二乘误差优化算法对模型参数进行估计,从而更准确地确定蓄电池容量作为SOH值的基础。扩展卡尔曼滤波器(Extended Kalman filter, EKF)可在初始SOC值未知的情况下对其进行准确预测,而模糊逻辑有助于消除测量和过程噪声。仿真结果表明,在城市测功机驱动计划期间(Urban dynamometer drving schedule, UDDS)测试中最大的SOC估算误差是0.66%;通过离线更新卡尔曼滤波器,可对电池容量进行估计,结果表明,最大估计误差为1.55%,从而有效提高了SOC值的预测精度。     

An attitude determination algorithm for a spacecraft using nonlinear filter

In this paper, the algorithm for a real time attitude estimation of a spacecraft motion is investigated. The proposed algorithm for attitude estimation is the second order nonlinear filter form not containing truncation error in estimation values. The proposed second order nonlinear filter has improved performance compared with the EKF (extended Kalman filter), because the algorithm does not contain any truncation bias and covariance of the estimator is compensated by the nonlinear terms of the system. Therefore, the proposed second order nonlinear filter is a suboptimal estimator. However, the proposed estimator requires a lot of computation because of an inherent nonlinearity and complexity of the system model. For more efficient computation, this paper introduces a new attitude estimation algorithm using the state divided technique for a real time processing which is developed to provide an accurate attitude determination capability under a highly maneuverable dynamic environment. To compare the performance of the proposed algorithm with the EKF, simulations have been performed with various initial values and measurement covariances. Simulation results show that the proposed second order nonlinear algorithm outperforms the EKF. The proposed algorithm is useful for a real time attitude estimation since it has better accuracy compared with the EKF and requires less computing time compared with any existing nonlinear filters.