Robust cubature Kalman filter for GNSS/INS with missing observations and colored measurement noise

In order to improve the accuracy of GNSS/INS working in GNSS-denied environment, a robust cubature Kalman filter (RCKF) is developed by considering colored measurement noise and missing observations. First, an improved cubature Kalman filter (CKF) is derived by considering colored measurement noise, where the time-differencing approach is applied to yield new observations. Then, after analyzing the disadvantages of existing methods, the measurement augment in processing colored noise is translated into processing the uncertainties of CKF, and new sigma point update framework is utilized to account for the bounded model uncertainties. By reusing the diffused sigma points and approximation residual in the prediction stage of CKF, the RCKF is developed and its error performance is analyzed theoretically. Results of numerical experiment and field test reveal that RCKF is more robust than CKF and extended Kalman filter (EKF), and compared with EKF, the heading error of land vehicle is reduced by about 72.4%.     

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。     

基于置信度传播的变分自适应协同导航方法

协同导航过程中先验信息的准确性是保证协同导航系统精度和可靠性的重要关键因素。针对协同导航系统在复杂环境下会因外界干扰产生未知且时变噪声问题,提出一种基于置信度传播的变分自适应协同导航方法(SWSP)。首先以置信度传播(SPBP)协同导航贝叶斯框架为基础,完成基于置信传播机制的前向滤波;随后通过IW处理过程噪声和量测噪声作为贝叶斯估计的先验信息;进而利用前向滤波值构造滑动窗口对噪声进行平滑估计,从而解决因噪声时变而造成的协同导航系统滤波精度下降问题。仿真结果表明:当噪声时变时,进行平滑操作的SWSP算法与未进行平滑操作的SPBP算法相比,位置误差降低了90%,精度更接近于最优opt SPBP算法。     

Ellipsoid bounding estimation for kinematic geodetic positioning

In kinematic position estimation, a Kalman filter procedure is often used to provide improved solution benefiting from the history information. However, the optimal Kalman filtering solutions are subject to precise function models and statistic knowledge of noises, which may be difficult to obtain in advance. As a result, Kalman filter does not necessarily provide better performance for kinematic positioning solutions. In real world situations, a bound of the noise distribution would be easily and more reasonably determined than noise statistics. This paper studies ellipsoid bounding estimation for kinematic position estimation. In this estimation, neither process nor measurement noise characteristics are necessary, as long as the noises at each sample points can be confined in a bound (ellipsoid). A general trace criteria is adopted to choose the optimal estimator. For a the special case that only scalar measurement is available, e.g., a position measurement, we designed a modified intersection approach to reduce the estimation conservatism. Numerical results are given in each estimation step to illustrate the algorithm. A flight trajectory data is processed and the estimation results are compared under three different measurement noise cases: Gaussian white noise, uniformly noise (non-Gaussian) and the real measurement noise. Kalman filter results are also given for comparison. Results demonstrate the ellipsoid estimation indeed offers improved kinematic position solution in the sense of robustness for non-Gaussian noises, and retains nearly the same estimation error variance.     

Estimation of time-varying power quality indices using a computationally efficient algorithm

In this paper a new recursive adaptive filter based on a fast Gauss–Newton method has been proposed for the estimation of power quality (PQ) indices for time-varying voltage and current signals in an electric power system. The presented algorithm is based on the minimization of a weighted forgetting factor based error cost function by the use of Recursive Gauss–Newton method. Further a Hessian matrix approximation is used to produce a fast recursive algorithm, which is immune to random noise, waveform distortion and increases the speed of convergence and accuracy. The algorithm models the typical time-varying signal and the accompanied distortions due to harmonics and random noise in a manner that will be suitable for real-time PQ indices estimation. Further, the forgetting factor is tuned in accordance with signal error covariance to provide improved performance. Also power system frequency variations are estimated and correction factors are derived. The effects of sub harmonics, and interharmonics in the signal have been considered while estimating the various PQ indices.     

基于EMMAP的MEMS陀螺噪声估计与滤波方法研究

针对MEMS陀螺仪测量精度低、随机噪声具有不确定性和非线性的问题,提出一种基于最大期望算法(Expectation maximum,EM)和极大后验估计(Maximum a posterion,MAP)的无迹卡尔曼滤波(Unscented Kalman filter,UKF)——EMMAP-UKF的陀螺噪声估计与滤波方法。根据极大后验估计原理,构造出一种次优无偏MAP噪声统计估计模型,并在此基础上引入最大期望算法将噪声估计问题转换为数学期望极大化问题,实现对观测噪声方差的动态调整,最终实现陀螺仪随机漂移误差的估计与滤波处理。最后通过Allan方差对陀螺噪声滤波方法的性能进行评估,通过半实物仿真验证了本方法的有效性。     

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。     

径向基粒子滤波状态跟踪测量算法

状态跟踪测量的过程噪声降低了目标信噪比,增加了自适应滤波跟踪的难度。当误差较大时,基本粒子滤波算法的预测累积误差效应将导致系统发散。无迹粒子滤波算法利用无迹卡尔曼滤波提高重要性函数估计精度,减少后验概率密度分布误差,但同时也将大幅增加运算时间。提出一种基于径向基函数网络(RBFN)的改进型粒子滤波算法PF-RBF,利用RBFN通过目标状态观测值和全局预测值拟合状态变化趋势,更新各粒子状态,提高先验概率密度分布估计精度,消除过程噪声引起的估计误差。与无迹粒子滤波(UPF)算法相比,该算法无需构造无迹卡尔曼滤波(UKF)重要性函数,提高了运算速度。机动目标跟踪试验表明,径向基粒子滤波算法在线性和非线性观测方程下的状态跟踪测量精度和算法稳定性均优于UKF、PF和UPF算法,可有效实现对状态变化的实时鲁棒跟踪。当参与运算的粒子数增加时,PF-RBF算法执行时间的增长速率较UPF算法更低,可满足高精度状态跟踪应用。     

Robust preview control for a class of uncertain discrete-time systems with time-varying delay

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.     

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。     

基于迭代中心差分卡尔曼滤波的飞机姿态估计

在飞机姿态估计中,系统模型非线性严重、初始估计误差大和可观测性弱等固有缺陷使得对估计算法的精度要求更高。针对这一问题,给出了一种基于迭代中心差分卡尔曼滤波(ICDKF)的飞机姿态估计方法,并将其应用于由低精度高噪声传感器组成的低成本飞机姿态估计系统。首先建立基于四元数的飞机姿态数学模型,然后用ICDKF方法进行姿态估计,并通过实测数据进行验证。实验结果表明,ICDKF不仅有效地提高了飞机姿态估计的稳定性、收敛速度和滤波精度,而且无需计算雅克比矩阵,实现简单,其性能明显优于标准CDKF和EKF方法。     

基于变分贝叶斯的鲁棒自适应因子图优化组合导航算法

复杂环境下的量测粗差和时变噪声严重影响了状态估计的精度和可靠性,对此提出了一种基于变分贝叶斯的鲁棒自适应因子图优化组合导航算法。首先,基于先验和后验两阶段更新将变分贝叶斯推断引入因子图优化框架中,以估计时变量测噪声协方差;其次,利用相邻帧间的平均新息构造量测协方差预测值,作为粗差判据来实现稳健估计。基于INS/GNSS组合导航的仿真和现场实验评估表明,所提方法能在粗差干扰的情况下有效估计时变量测噪声,相比M估计和滑动窗口自适应因子图优化算法的水平定位误差分别减小了26.7%和39.8%,兼顾了估计精度和抗差性能,具有较好的复杂环境适应性。     

点采样曲面的曲率估计

本文提出一种直接在点采样曲面上计算曲面的高斯曲率、平均曲率及主曲率等局部微分性质的方法。首先，为了去除测量产生的噪声和误差，引入高斯核函数为每个采样点加权；接着计算每个采样点的最近邻域点集；然后用双三次B样条曲面最小二乘拟合邻域点集，构造局部参数曲面来逼近原始曲面，以局部参数曲面的曲率估计点采样曲面的曲率；最后给出曲率估计的应用。实验结果表明，该方法能有效地反映曲面的基本特征。     

Improved adaptive integral line-of-sight guidance law and adaptive fuzzy path following control for underactuated MSV

This paper presents an adaptive fuzzy path following control law based on an improved adaptive integral line-of-sight (IAILOS) guidance law for the underactuated marine surface vessel (MSV) exposed to the time-varying ocean currents and time-varying sideslip angle. Initially, the IAILOS guidance law is proposed which can not only calculate the desired yaw angle but also estimate the time-varying ocean currents and time-varying sideslip angle simultaneously. Furthermore, the adaptive fuzzy path following control law is established by combining with the estimator to cope with the MSV’s attitude tracking control and velocity tracing control problem via backstepping technique. Specifically, the dynamic uncertainties and unknown environment disturbances are compensated by the fuzzy logic system with fuzzy updating law based on estimation error rather than tracking error. Additionally, two high-order tracking differentiators (TDs) are designed to construct derivatives of virtual control vector and reduce computational complexity inherent in backstepping method. It is proved that the proposed adaptive fuzzy path following control law can drive the vessel to track the desired path and tracking error can converge to an arbitrarily small compact set, while guaranteeing all signals in the closed-loop control system are uniformly ultimately bounded. Finally, simulation results and comparisons are carried out to demonstrate the effectiveness of the proposed control approach.     

基于变分贝叶斯的自适应 PF-SLAM 方法研究

针对移动机器人即时定位与地图构建中时变观测噪声及粒子位置分布对SLAM精度的影响,本文提出基于变分贝叶斯的自适应PF-SLAM算法,采用高斯混合模型对时变的观测噪声建模,并通过变分贝叶斯方法,迭代估算出混合模型中的未知参数;同时根据粒子权值将粒子划分为固定粒子和优化粒子,通过粒子间的近邻拓扑位置关系调整粒子分布,处理时变观测噪声与优化粒子的位置分布,使得优化的粒子集可以更好地表示机器人位置概率分布,实现观测噪声及粒子位置分布自适应。仿真实验表明本算法对比传统PF-SLAM算法定位与地图构建误差降低了76.45%。实际实验表明本算法处理下的环境轮廓误差对比传统PF-SLAM算法的环境轮廓误差减小了61.87%。该算法有效提高了移动机器人的状态估计精度,为移动机器人即时定位与地图构建提供了新的参考。     

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.     

A hybrid unscented filtering and particle swarm optimization technique for harmonic analysis of nonstationary signals

This paper presents a modified unscented Kalman filter for accurate estimation of frequency and harmonic components of a time-varying signal embedded in noise with low signal-to-noise ratio. Further, the model and measurement error covariances along with the unscented Kalman filter parameters are selected using a modified particle swarm optimization algorithm. To circumvent the problem of premature convergence and local minima, a dynamically varying inertia weight based on the variance of the population fitness is used. This results in a better local and global searching ability of the particles, which improves the convergence of the velocity and better accuracy of the unscented Kalman filter parameters. Various simulation results for nonstationary sinusoidal signals with time varying amplitude, phase and harmonic content corrupted with noise, reveal significant improvement in noise rejection and speed of convergence and accuracy in comparison to the well known extended Kalman filter.     

基于AEKF的车辆质量与道路坡度实时估计

针对车辆在实际行驶过程中外界噪声的统计特性无法已知的问题,以车辆纵向动力学模型为基础,提出了自适应扩展卡尔曼滤波(adaptive extended Kalman filter,简称AEKF)的车辆质量及道路坡度估计算法。以动态估计车辆系统中的质量与坡度为研究对象,引入了旋转质量换算系数,建立车辆纵向动力学系统的状态空间模型,考虑了不同时刻的档位匹配与行驶特殊工况的处理。对系统状态方程进行离散化处理,得到系统状态方程与系统测量方程,在扩展卡尔曼滤波(extended Kalman filter,简称EKF)的基础上引入带遗忘因子的噪声统计估计器,通过AEKF对状态方程与测量方程实时更新,进行在线估计和校正噪声统计值,从而解决系统的噪声时变问题。本研究算法与EKF算法估计及实测结果的对比分析表明,本研究算法能够很好地对车辆质量和坡度信号进行有效滤波和估计,在短时间内逐渐收敛并逼近实测值,从而能够合理有效地检测车辆在行驶过程中的状态信息。     

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.     

A thinning algorithm for GPS-based unbiased FIR estimation of a clock TIE model

A thinning algorithm is proposed for real-time unbiased finite impulse response (FIR) estimation of the local clock time interval error (TIE) model (time error, fractional frequency offset, linear frequency drift rate, etc.) employing GPS-based sawtooth measurements. We show that the approach allows obtaining practically optimal estimates of the clock states, by large horizons (number of the points in the average). The algorithm is applied to the TIE measurements allowing for different time steps and averaging horizons for each of the clock states and compared to the three state Kalman filter. It is demonstrated that, in the presence of the sawtooth noise induced by the GPS receiver, the unbiased FIR estimates with thinning out fit the clock states better than the Kalman filter, in terms of the Allan deviation and precision time protocol deviation.