Cubature Kalman Filter Based Millimeter Wave Beam Tracking for OTFS Systems

In this paper,a Millimeter wave(mmWave)beam tracking problem is studied in orthogonal time frequency space(OTFS)systems.Considering the nonlinearity of beamforming and the constraints of existing Kalman-filtering based beam tracking schemes,we propose a novel Cubature Kalman Filter(CKF)framework tracking the channel state information(CSI)to manage the challenge of highspeed channel variation in single-user moving scene for OTFS systems.Aiming for low complexity for mobile settings,this paper trains only one beam pair to track a path to maintain the reliable communication link in the analog beamforming architecture.Simulation results show that our proposed method has better tracking performance to improve the accuracy of the estimated beam angle compared with prior work.

基于CKF的四轮驱动电动汽车质心侧偏角估计

针对传统质心侧偏角观测精度不高、实时性能差的问题,提出了一种基于CKF算法的质心侧偏角观测器。首先基于CKF算法结合Dugoff轮胎模型,实时观测路面附着系数,计算实时的轮胎力。再结合七自由度整车模型,基于CKF算法,实时、精确观测车辆的质心侧偏角。最后,利用Simulink/Carsim联合仿真验证平台和硬件在环平台进行仿真验证。试验结果表明,CKF算法相比与传统无迹卡尔曼滤波估计精度更高、实时性能更好,较好的改善了传统质心侧偏角观测器在非线性条件下的观测精度。

基于MACF-CKF多传感器融合的姿态解算算法

针对惯性导航测量单元姿态解算精度低的问题,提出了一种基于多传感器隶属度自适应互补滤波(Membership Adaptive Complementary Filtering,MACF)和容积卡尔曼滤波(Cubature Kalman Filter,CKF)相融合的姿态解算算法。使用指数加权移动平均修正陀螺仪噪声偏差,为了避免出现陀螺仪和加速度计的权重在互补滤波中分配不当而导致俯仰角和横滚角误差较大的现象,通过构造陀螺仪偏差的隶属度函数,判断互补滤波对陀螺仪的信任度,根据信任度动态调整互补滤波自适应因子,同时用磁力计和陀螺仪进行CKF来解决航向角发散的问题。实验表明:所提出的算法无论在静态条件还是动态条件下均能快速、准确实现姿态解算,在动态车载实验中,横滚角和俯仰角精度分别提升了24.5%和63.2%,航向角提升了48.8%,可以保证解算精度。

基于SRCKF算法的多自由度非线性系统动载荷识别方法

为识别铁道车辆车钩等存在非线性刚度阻尼的单一维度、多自由度系统的外部动载荷,提出一种基于平方根容积卡尔曼滤波(SRCKF)算法的载荷识别方法。以一个二自由度的非线性弹簧阻尼系统为例,建立包含外部动载荷和系统部件状态变量的非线性过程函数,以各自由度振动加速度为观测量,基于平方根容积卡尔曼滤波算法识别外部动载荷。仿真结果表明,该方法可以较好地识别作用在多自由度非线性系统上的随机载荷,刚度非线性系统和阻尼非线性系统的识别结果相关系数分别为0.997和0.999。

基于CKF-SLAM改进的无人水下航行器动态目标跟踪算法研究

针对容积卡尔曼滤波(cubature Kalman filter,CKF)同步定位与建图(simultaneous localization and mapping,SLAM)算法在动态目标跟踪(object tracking,OT)的应用中,存在算法实时性不高、计算复杂以及对动态目标物跟踪精度较低的问题,提出基于平方根容积卡尔曼滤波SLAM的无人水下航行器(unmanned underwater Vehicle,UUV)目标跟踪算法(SRCKF-SLAM-OT).该算法将CKF-SLAM-OT中复杂的计算部分,利用3阶容积准则选取一组相同权值的容积点来近似计算,再利用数值积分法计算非线性方程模型的后验状态估计平均值和方差,并对协方差矩阵的平方根因子进行更新.仿真结果表明:SRCKF-SLAM-OT算法简化了计算量和改善了数值精度,提高了UUV在未知水下环境中自身定位的精度和动态目标物跟踪的能力.

Stochastic convergence analysis of cubature Kalman filter with intermittent observations

The stochastic convergence of the cubature Kalmanfilter with intermittent observations （CKFI） for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to describe the phenomenon of intermit-tent observations. According to the cubature sample principle, theestimation error and the error covariance matrix （ECM） of CKFIare derived by Taylor series expansion, respectively. Afterwards, itis theoretically proved that the ECM will be bounded if the obser-vation arrival probability exceeds a critical minimum observationarrival probability. Meanwhile, under proper assumption corre-sponding with real engineering situations, the stochastic stabilityof the estimation error can be guaranteed when the initial estima-tion error and the stochastic noise terms are sufficiently small. Thetheoretical conclusions are verified by numerical simulations fortwo illustrative examples; also by evaluating the tracking perfor-mance of the optical-electric target tracking system implementedby CKFI and unscented Kalman filter with intermittent observa-tions （UKFI） separately, it is demonstrated that the proposed CKFIslightly outperforms the UKFI with respect to tracking accuracy aswell as real time performance.

Robust range-parameterized cubature Kalman filter for bearings-only tracking

In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,the robust extremal rule based on the pollution distribution was introduced to the cubature Kalman filter(CKF)framework.The improved Turkey weight function was subsequently constructed to identify the outliers whose weights were reduced by establishing equivalent innovation covariance matrix in the CKF.Furthermore,the improved range-parameterize(RP)strategy which divides the filter into some weighted robust CKFs each with a different initial estimate was utilized to solve the fuzzy initial estimation problem efficiently.Simulations show that the result of the RRPCKF is more accurate and more robust whether outliers exist or not,whereas that of the conventional algorithms becomes distorted seriously when outliers appear.

Low-cost adaptive square-root cubature Kalman filter forsystems with process model uncertainty

A novel low-cost adaptive square-root cubature Kalmanfilter （LCASCKF） is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman filter cannot handle uncertainties ina process model, such as initial state estimation errors, parametermismatch and abrupt state changes. These uncertainties severelyaffect filter performance and may even provoke divergence. Astrong tracking filter （STF）, which utilizes a suboptimal fading factor,is an adaptive approach that is commonly adopted to solvethis problem. However, if the strong tracking SCKF （STSCKF）uses the same method as the extended Kalman filter （EKF） tointroduce the suboptimal fading factor, it greatly increases thecomputational load. To avoid this problem, a low-cost introductorymethod is proposed and a hypothesis testing theory is applied todetect uncertainties. The computational load analysis is performedby counting the total number of floating-point operations and it isfound that the computational load of LCASCKF is close to that ofSCKF. Experimental results prove that the LCASCKF performs aswell as STSCKF, while the increase in computational load is muchlower than STSCKF.

Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration

Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances.To address this issue,a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points(MEEF-CKF)is proposed.The MEEF-CKF behaves a strong robustness against complex nonGaussian noises by operating several major steps,i.e.,regression model construction,robust state estimation and free parameters optimization.More concretely,a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step.The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points(MEEF)under the framework of the regression model.In the MEEF-CKF,a novel optimization approach is provided for the purpose of determining free parameters adaptively.In addition,the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic.The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex nonGaussian noises.

Robust cubature Kalman filter method for the nonlinear alignment of SINS

Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system(SINS).Cubature Kalman filter(CKF)is a popular tool for nonlinear initial alignment.Standard CKF assumes that the statics of the observation noise are pre-given before the filtering process.Therefore,any unpredicted outliers in observation noise will decrease the stability of the filter.In view of this problem,improved CKF method with robustness is proposed.Multiple fading factors are introduced to rescale the observation noise covariance.Then the update stage of the filter can be autonomously tuned,and if there are outliers exist in the observations,the update should be less weighted.Under the Gaussian assumption of KF,the Mahalanobis distance of the innovation vector is supposed to be Chi-square distributed.Therefore a judging index based on Chi-square test is designed to detect the noise outliers,determining whether the fading tune are required.The proposed method is applied in the nonlinear alignment of SINS,and vehicle experiment proves the effective of the proposed method.

Generalized cubature quadrature Kalman filters:derivations and extensions

A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the QR decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.

基于改进模型与优化自适应CKF的锂离子电池快速变温工况下的SOC估计

为实现锂离子电池在快速变温环境下高精度强鲁棒性的状态监测,本文提出了一种基于改进电池模型与优化自适应容积卡尔曼滤波器的锂离子电池荷电状态估计方法。首先,讨论了伪二维电化学模型与等效电路模型中对于电池荷电状态定义上的差异,并通过中间变量来修正传统等效电路模型中安时积分法计算得到的荷电状态结果,提出了一种新的改进电池模型。其次,基于多组恒温环境下所获得的锂离子电池开路电压测试数据与动态应力测试工况数据获取了所建立模型与环境温度相关的各项参数。同时,基于矩阵对角化原理与协方差矩阵自适应原理改进了传统的容积卡尔曼滤波器,进一步提升了整体算法的稳定性和处理随机采样噪声的能力。最后,在快速变温环境中6组不同的电池工况下验证了所建立改进电池模型的精度以及存在随机采样噪声干扰时所提荷电状态估计方法的有效性。结果显示,所提出的荷电状态估计方法适用于快速变温环境下的各类电池工况,在随机采样噪声干扰下估计结果的均方根误差均在1.3%以内。

Maneuvering target tracking algorithm based on cubature Kalman filter with observation iterated update

Reasonable selection and optimization of a filter used in model estimation for a multiple model structure is the key to improve tracking accuracy of maneuvering target.Combining with the cubature Kalman filter with iterated observation update and the interacting multiple model method,a novel interacting multiple model algorithm based on the cubature Kalman filter with observation iterated update is proposed.Firstly,aiming to the structural features of cubature Kalman filter,the cubature Kalman filter with observation iterated update is constructed by the mechanism of iterated observation update.Secondly,the improved cubature Kalman filter is used as the model filter of interacting multiple model,and the stability and reliability of model identification and state estimation are effectively promoted by the optimization of model filtering step.In the simulations,compared with classic improved interacting multiple model algorithms,the theoretical analysis and experimental results show the feasibility and validity of the proposed algorithm.

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

高超目标强跟踪CKF自适应交互多模型跟踪算法

高超目标运动状态复杂且具有高机动性,传统的交互多模型(IMM)跟踪精度低、收敛速度慢,基于此,提出了一种基于多重渐消因子的强跟踪容积卡尔曼滤波(CKF)自适应交互多模型(AIMM)跟踪算法。以IMM-CKF算法为基础,通过对CKF算法的结构进行分析,在时间更新和量测更新的协方差矩阵中引入强跟踪算法的渐消因子,在线实时调整滤波增益,减小模型不匹配导致的滤波精度下降;在IMM的模型集中选择Singer模型、“当前”统计模型和Jerk模型,并针对模型扩维导致CKF算法中无法Cholesky分解的问题引入奇异值分解(SVD)算法;对IMM算法中马尔可夫矩阵提出自适应算法,通过模型似然函数值对转移概率进行自适应修正,增强匹配模型所占比例。仿真结果表明:所提算法跟踪收敛速度提高了约37.5%,跟踪精度提高了16.51%。

Multi-sensor Hybrid Fusion Algorithm Based on Adaptive Square-root Cubature Kalman Filter

In the normal operation condition, a conventional square-root cubature Kalman filter （SRCKF） gives sufficiently good estimation results. However, if the measurements are not reliable, the SRCKF may give inaccurate results and diverges by time. This study introduces an adaptive SRCKF algorithm with the filter gain correction for the case of measurement malfunctions. By proposing a switching criterion, an optimal filter is selected from the adaptive and conventional SRCKF according to the measurement quality. A subsystem soft fault detection algorithm is built with the filter residual. Utilizing a clear subsystem fault coefficient, the faulty subsystem is isolated as a result of the system reconstruction. In order to improve the performance of the multi-sensor system, a hybrid fusion algorithm is presented based on the adaptive SRCKF. The state and error covariance matrix are also predicted by the priori fusion estimates, and are updated by the predicted and estimated information of subsystems. The proposed algorithms were applied to the vessel dynamic positioning system simulation. They were compared with normal SRCKF and local estimation weighted fusion algorithm. The simulation results show that the presented adaptive SRCKF improves the robustness of subsystem filtering, and the hybrid fusion algorithm has the better performance. The simulation verifies the effectiveness of the proposed algorithms.

基于抗差自适应CKF的水下重力匹配导航SITAN算法

为提高水下重力匹配算法的定位精度和稳健性,将容积卡尔曼滤波应用到水下重力匹配惯性导航中,同时引入抗差估计和自适应因子,提出了基于抗差自适应容积卡尔曼滤波的水下重力匹配导航SITAN算法。利用重力异常模型数据开展仿真实验,结果表明,所提算法能有效修正惯导整体航迹,在观测值未加入粗差的情况下较普通容积卡尔曼滤波算法提高了76%的导航定位精度,在观测值加入30 mGal粗差的情况下,提高了88%的导航定位精度。该研究成果可为后续水下重力匹配导航算法的理论研究及工程实践提供一定的数据支撑。

一种基于IMM-SCKF的组合导航算法

针对在实际应用中组合导航系统存在的噪声干扰多变造成系统滤波精度降低问题,提出了基于交互式多模型(IMM)和平方根容积卡尔曼滤波(SCKF)(IMM-SCKF)算法。IMM-SCKF滤波算法拥有多个模型集,通过调节子模型的概率后进行融合输出,能够尽可能地模拟实际噪声协方差。仿真试验和道路试验结果均表明,IMM-SCKF算法的速度误差和位置误差均方根均优于传统单模型CKF算法,能有效提高组合导航系统的可靠性。在实际道路跑车试验中,与传统CKF算法相比,IMM-SCKF算法的东、北、天速度误差均方根分别降低了52%、55%、30%,位置误差均方根分别降低了47%、60%、32%,IMM-SCKF算法显著提高了系统的定位精度及抗干扰能力。

Fuzzy Adaptive Strong Tracking Cubature Kalman Filter

To solve the problem that the choice of softening factor in conventional adaptive strong tracking filter( STF) greatly relies on the experience and computer simulation,a new concept of softening factor matrix is introduced and a fuzzy adaptive strong tracking cubature Kalman filter( FASTCKF) based on fuzzy logic controller is proposed. This method monitors residual absolute mean and standard deviation of each measurement component with fuzzy logic adaptive controller( FLAC),and adjusts the softening factor matrix dynamically by fuzzy rules,which is capable to modify suboptimal fading factor of STF adaptively and improve the filter's robust adaptive capacity. The simulation results show that the improved filtering performance is superior to the conventional square root cubature Kalman filter( SCKF) and the strong tracking square root cubature Kalman filter( STSCKF).

Adaptive cubature Kalman filter based on variational Bayesian inference under measurement uncertainty

A novel variational Bayesian inference based on adaptive cubature Kalman filter(VBACKF)algorithm is proposed for the problem of state estimation in a target tracking system with time-varying measurement noise and random measurement losses.Firstly,the Inverse-Wishart(IW)distribution is chosen to model the covariance matrix of time-varying measurement noise in the cubature Kalman filter framework.Secondly,the Bernoulli random variable is introduced as the judgement factor of the measurement losses,and the Beta distribution is selected as the conjugate prior distribution of measurement loss probability to ensure that the posterior distribution and prior distribution have the same function form.Finally,the joint posterior probability density function of the estimated variables is approximately decoupled by the variational Bayesian inference,and the fixed-point iteration approach is used to update the estimated variables.The simulation results show that the proposed VBACKF algorithm considers the comprehensive effects of system nonlinearity,time-varying measurement noise and unknown measurement loss probability,moreover,effectively improves the accuracy of target state estimation in complex scene.