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.

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.

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.

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.

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.

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

处于正常操作条件，一个常规方形根的求容积法 Kalman 过滤器(SRCKF ) 给足够地好的评价结果。然而，如果大小不是可靠的， SRCKF 可以给不精密的结果并且到时间分叉。这研究与过滤器获得修正介绍一个适应 SRCKF 算法因为测量的盒子失灵。由建议一个切换的标准，一个最佳的过滤器根据测量质量从适应、常规的 SRCKF 被选择。一个分系统软差错察觉算法与过滤器剩余被造。利用一个清楚的分系统差错系数，有缺点的分系统由于系统重建被孤立。以便改进多传感器系统的性能，一个混合熔化算法基于适应 SRCKF 被介绍。状态和错误协变性矩阵被 priori 熔化估计也预言，并且被分系统的预言并且估计的信息更新。建议算法被用于容器动态放系统模拟。他们与正常 SRCKF 和本地评价相比是加权的熔化算法。模拟结果证明介绍适应 SRCKF 改进分系统过滤的坚韧性，并且混合熔化算法有更好的表演。模拟验证建议算法的有效性。

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.

Marginalized cubature Kalman filtering algorithm based on linear/nonlinear mixed-Gaussian model

Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the marginalized technique is adopted to model the target system dynamics with nonlinear state and linear state separately,and the two parts are estimated by cubature Kalman filter and standard Kalman filter respectively. Therefore,the linear part avoids the generation and propagation process of cubature points. Accordingly,the computational complexity is reduced.Meanwhile,the accuracy of state estimation is improved by taking the difference of nonlinear state estimation as the measurement of linear state. Furthermore,the computational complexity of marginalized cubature Kalman filter is discussed by calculating the number of floating-point operation. Finally,simulation experiments and analysis show that the proposed algorithm can improve the performance of filtering precision and real-time effectively in target tracking system.

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).

Cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion

The GM-PHD framework as recursion realization of PHD filter is extensively applied to multitarget tracking system. A new idea of improving the estimation precision of time-varying multi-target in non-linear system is proposed due to the advantage of computation efficiency in this paper. First,a novel cubature Kalman probability hypothesis density filter is designed for single sensor measurement system under the Gaussian mixture framework. Second,the consistency fusion strategy for multi-sensor measurement is proposed through constructing consistency matrix. Furthermore,to take the advantage of consistency fusion strategy,fused measurement is introduced in the update step of cubature Kalman probability hypothesis density filter to replace the single-sensor measurement. Then a cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion is proposed. Capabilily of the proposed algorithm is illustrated through simulation scenario of multi-sensor multi-target tracking.

Adaptive “Cubature and Sigma Points” Kalman Filtering Applied to MEMS IMU/GNSS Data Fusion during Measurement Outlier

In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific problem generally occurs in intentional and non-intentional interferences caused by other radio navigation sources, or by the GNSS receiver’s deterioration. Non linear approximation techniques such as Extended Kalman filter EKF, Sigma Point Kalman Filters such as UKF and CDKF are computed to estimate the navigation states for UAV flight control. Several comparisons are conduced and analyzed in order to compare the accuracy and the convergence of different approaches usually applied in navigation data fusion purposes. The last non linear filter algorithm developed is the Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application. In this work, CKF is compared with SPKF and EKF in ideal conditions and during GNSS outliers supposed to occur during specific interval of time, innovation based adaptive approach is selected and used to modify the covariance calculation of the non linear filters performed in this paper. Interesting results are observed, discussed with real perspectives in navigation data fusion for real time applications. Three parallel modified algorithms are simulated and compared to non-adaptive forms according to Root Mean Square Error (RMSE) criteria.

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.

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.

Distributed cubature Kalman filter based on observation bootstrap sampling

Aiming at the adverse effect caused by observation noise on system state estimation precision,a novel distributed cubature Kalman filter(CKF) based on observation bootstrap sampling is proposed.Firstly,combining with the extraction and utilization of the latest observation information and the prior statistical information from observation noise modeling,an observation bootstrap sampling strategy is designed.The objective is to deal with the adverse influence of observation uncertainty by increasing observations information.Secondly,the strategy is dynamically introduced into the cubature Kalman filter,and the distributed fusion framework of filtering realization is constructed.Better filtering precision is obtained by promoting observation reliability without increasing the hardware cost of observation system.Theory analysis and simulation results show the proposed algorithm feasibility and effectiveness.

Robust SLAM using square-root cubature Kalman filter and Huber's GM-estimator

Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algorithm is proposed.It is based on the square-root cubature Kalman filter equipped with a Huber' s generalized maximum likelihood estimator(GM-estimator).In particular,the square-root cubature rule is applied to propagate the robot state vector and covariance matrix in the time update,the measurement update and the new landmark initialization stages of the SLAM.Moreover,gain weight matrices with respect to the measurement residuals are calculated by utilizing Huber' s technique in the measurement update step.The measurement outliers are suppressed by lower Kalman gains as merging into the system.The proposed algorithm can achieve better performance under the condition of non-Gaussian measurement noise in comparison with benchmark algorithms.The simulation results demonstrate the advantages of the proposed SLAM algorithm.

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。

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.