EKF和PF算法及其在目标跟踪中的应用

基于贝叶斯滤波的目标跟踪原理,介绍了扩展卡尔曼滤波(Extended Kalman Filter,EKF)和粒子滤波(ParticleFilter,PF)的基本思想和算法实现步骤。在非线性环境下对比分析了EKF算法和PF算法的估计精度,并给出两种方法的适用条件。EKF算法采用Taylor展开的线性变换来近似非线性模型,而PF算法采用一些带有权值的随机样本来表示所需要的后验概率密度。仿真结果表明,在强非线性非高斯环境下,PF算法的跟踪性能远优于EKF算法,当系统非线性强度不大时,EKF算法和PF算法的估计精度相差不大,但PF算法计算复杂,跟踪时间长,实时性差。     

A New Optimized Algorithm with Nonlinear Filter for Ultra-Tightly Coupled Integrated Navigation System of Land Vehicle

The extended particle filter (EPF) assisted by the Takagi-Sugeno (T-S) fuzzy logic adaptive system (FLAS) is used to design the ultra-tightly coupled GPS/INS (inertial navigation system) integrated navigation, which can maneuver the vehicle environment and the GPS outages scenario. The traditional integrated navigation designs adopt a loosely or tightly coupled architecture, for which the GPS receiver may lose the lock due to the interference/jamming scenarios, high dynamic environments, and the periods of partial GPS shading. An ultra-tight GPS/INS architecture involves the integration of I (in-phase) and Q (quadrature) components from the correlator of a GPS receiver with the INS data. The EPF is a particle filter (PF) which uses the extended Kalman filter (EKF) to generate the proposal distribution. The PF depends mostly on the number of particles in order to achieve a better performance during the high dynamic environments and GPS outages. The T-S FLAS is one of these approaches that can prevent the divergence problem of the filter when the precise knowledge on the system models is not available. The results show that the proposed fuzzy adaptive EPF (FAEPF) can effectively improve the navigation estimation accuracy and reduce the computational load as compared with the EPF and the unscented Kalman filter (UKF).     

Modeling and state of charge estimation of lithium-ion battery

Modeling and state of charge(SOC) estimation of lithium-ion(Li-ion) battery are the key techniques of battery pack management system(BMS) and critical to its reliability and safety operation.An auto-regressive with exogenous input(ARX) model is derived from RC equivalent circuit model(ECM) due to the discrete-time characteristics of BMS.For the time-varying environmental factors and the actual battery operating conditions,a variable forgetting factor recursive least square(VFFRLS)algorithm is adopted as an adaptive parameter identification method.Based on the designed model,an SOC estimator using cubature Kalman filter(CKF) algorithm is then employed to improve estimation performance and guarantee numerical stability in the computational procedure.In the battery tests,experimental results show that CKF SOC estimator has a more accuracy estimation than extended Kalman filter(EKF) algorithm,which is widely used for Li-ion battery SOC estimation,and the maximum estimation error is about 2.3%.     

Bayesian state and parameter estimation of uncertain dynamical systems

The focus of this paper is Bayesian state and parameter estimation using nonlinear models. A recently developed method, the particle filter, is studied that is based on stochastic simulation. Unlike the well-known extended Kalman filter, the particle filter is applicable to highly nonlinear models with non-Gaussian uncertainties. Recently developed techniques that improve the convergence of the particle filter simulations are introduced and discussed. Comparisons between the particle filter and the extended Kalman filter are made using several numerical examples of nonlinear systems. The results indicate that the particle filter provides consistent state and parameter estimates for highly nonlinear models, while the extended Kalman filter does not.     

光电跟踪的非线性卡尔曼滤波算法

为得到最小方差意义下的光电跟踪目标的最优状态估计,提出将部分状态卡尔曼滤波和非线性系统的一阶线性化思想相结合,构成一种适用于非线性光电跟踪目标的卡尔曼滤波算法,并总结出详细算法结构.同时将此方法应用到非线性测量光电跟踪系统中,并与扩展卡尔曼滤波和U卡尔曼滤波进行性能对比.仿真实验结果证明,将部分状态卡尔曼滤波和非线性系统的一阶线性化思想相结合是有效可行的,而且其性能明显优于扩展卡尔曼滤波和U卡尔曼滤波.     

基于Sigma点全局迭代参数卡尔曼滤波的折线型本构模型参数识别

折线型本构模型控制参数少,物理意义明确,但其数学表达式复杂因而识别困难。针对折线型本构模型的参数识别,提出基于Sigma点变换的全局迭代参数卡尔曼滤波算法。所提方法以待识别参数作为状态向量,降低状态向量维度,减少计算量;基于Sigma点卡尔曼滤波避免求解雅克比(Jacobian)矩阵,实现非连续型函数本构模型的参数识别;通过设定目标函数进行全局迭代,以获得最优解。由于非线性系统下一时刻响应与历史路径有关,量测更新时由初始时刻计算到当前时刻。最后,在地震荷载下,将隔震支座系统简化为单自由度双线性模型,将桥墩简化为单自由度Takeda模型,根据该文所提出的方法理念,分别基于无迹卡尔曼滤波(unscented Kalman filter,UKF)、容积卡尔曼滤波(cubature Kalman filter,CKF)和球面单纯形径向容积正交卡尔曼滤波(spherical simplex-radial cubature quadrature Kalman filter,SSRCQKF)采样规则识别折线型本构模型参数。结果表明所提方法能够准确识别非线性参数,同时具有较强的鲁棒性,不同滤波器收敛过程及结果也有所差异。     

非线性无序测量无迹滤波在地面跟踪目标指示器的应用

对于多传感器融合系统,在处理中心往往由于通信数据链的失误,出现滞后数据(即无序量测),这对数据不利于融合的正常进行.本文对此提出一种最优和次优的无序量测无迹卡尔曼(UKF)滤波器,基于UT变换,把多步滞后量测转化为等价一步滞后量测,用无序量测直接滤波更新.通过最优、次优UKF滤波器和扩展KF滤波器在不同情况下对地面跟踪目标指示器(GMTI)组合跟踪的无序量测处理作比较,可看出本文所述滤波器提高了非线性条件下的无序量测滤波精度.     

基于RFF及GWO-PF的锂电池SOC估计

为了提高锂电池剩余电量估计的准确性,提出一种在线参数辨识与改进粒子滤波算法相结合的锂电池SOC估计方法。针对粒子滤波中的粒子退化问题,引入灰狼算法,利用灰狼算法较强的全局寻优能力优化粒子分布,保证粒子多样性,有效抑制粒子退化现象,提高滤波精度。采用带遗忘因子的递推最小二乘法实时更新模型参数,并与改进粒子滤波算法交替运行,进一步提高SOC的估计精度。实验结果表明,改进算法的平均估计误差始终保持在±0.15%以内,相比扩展卡尔曼滤波与无迹卡尔曼滤波算法,在电池SOC估计上有更高的估计精度与稳定性。     

Huber-based unscented filtering and its application to vision-based relative navigation

A new algorithm called Huber-based unscented filtering (UF) is derived and applied to estimate the precise relative position, velocity and attitude of two unmanned aerial vehicles in the formation flight. The relative states are estimated using line-of-sight measurements between the vehicles along with acceleration and angular rate measurements of the follower. By making use of the Huber technique to modify the measurement update equations of standard UF, the new filtering could exhibit robustness with respect to deviations from the commonly assumed Gaussian error probability, for which the standard unscented filtering would exhibit severe degradation in estimation accuracy. Furthermore, contrast to standard extended Kalman filtering, more accurate estimation and faster convergence could be achieved from inaccurate initial conditions. During filter design, the global attitude parameterisation is given by a quaternion, whereas a generalised three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is used to guarantee that quaternion normalisation is maintained in the filter. Simulation results are shown to compare the performance of the new filter with standard UF and standard extended Kalman filtering for non-Gaussian case.     

扩展容积卡尔曼滤波定位技术研究

为提高被动定位技术的精度与环境适应性,本文提出运用一种新的非线性滤波方法—扩展容积卡尔曼滤波算法进行多角度传感器目标定位;它首先利用EMD(经验模态分解)算法对目标的量测噪声协方差矩阵进行估计;然后,将过程噪声协方差和量测噪声协方差融入循环过程;同时,为保持算法的稳定性和正定性,利用求平方根的形式对算法改进。通过对扩展容积卡尔曼滤波与UKF(不敏卡尔曼滤波)算法跟踪目标的结果进行比较,在运算复杂度与UKF相当的前提下,扩展容积卡尔曼滤波算法不仅可以对未知量测噪声情况下的目标进行跟踪,而且显著提高了被动定位的精度。     

被动定向浮标阵卡尔曼滤波目标跟踪研究

文章研究利用被动定向浮标阵定位跟踪水下机动目标的方法,基于卡尔曼滤波(Kalman Filter, KF)原理提出一种定位跟踪滤波器的具体实现方法。该方法能够整合多枚浮标现在及过去有误差的测量数据,提高定位精度,同时连续输出水下目标运动参数估计从而锁定目标运动轨迹。该方法实现的关键在于建立水下目标与浮标阵的数学迭代运算模型,包括状态空间的动态与观测过程。由于被动定向浮标阵目标跟踪是一个非线性估计问题,而卡尔曼滤波器是线性的,因此文章设计了近似的线性观测方程以利用卡尔曼滤波来解决这个问题。通过计算机仿真研究该滤波器的跟踪效果并与最小二乘法进行比较,估计精度明显高于最小二乘法。同时通过仿真验证该滤波器可以自适应跟踪目标的非稳态运动过程。该方法在工程实践上具有一定应用前景与指导意义。     

一种新的自适应非线性卡尔曼滤波算法

为避免由于系统噪声统计特性不准确所导致的滤波性能下降问题,改进了一种基于新息的系统噪声方差调整方法,并将其与扩展卡尔曼滤波、Unscented 卡尔曼滤波和差分滤波相结合,形成自适应非线性卡尔曼滤波.将此方法应用到非线性测量光电跟踪系统中,并与采用基本非线性卡尔曼滤波进行性能对比.仿真实验结果证明该方法可以实时调整系统噪声方差,有效地避免由于系统噪声统计特性不准确所带来的滤波性能下降的问题,而且其性能明显优于基本非线性卡尔曼滤波.     

Estimate-Merge-Technique-based algorithms to track an underwater moving target using towed array bearing-only measurements

Bearing-only passive target tracking is a well-known underwater defence issue dealt in the recent past with the conventional nonlinear estimators like extended Kalman filter (EKF) and unscented Kalman filter (UKF). It is being treated now-a-days with the derivatives of EKF, UKF and a highly sophisticated particle filter (PF). In this paper, two novel methods based on the Estimate Merge Technique are proposed. The Estimate Merge Technique involves a process of getting a final estimate by the fusion of a posteriori estimates given by different nonlinear estimates, which are in turn driven by the towed array bearing-only measurements. The fusion of the estimates is done with the weighted least squares estimator (WLSE). The two novel methods, one named as Pre-Merge UKF and the other Post-Merge UKF, differ in the way the feedback to the individual UKFs is applied. These novel methods have an advantage of less root mean square estimation error in position and velocity compared with the EKF and UKF and at the same time require much lesser number of computations than that of the PF, showing that these filters can serve as an optimal estimator. A testimony of the afore-mentioned advantages of the proposed novel methods is shown by carrying out Monte Carlo simulation in MATLAB R2009a for a typical war time scenario.     

基于最大后验概率密度的粒子过滤器跟踪算法

Kalman滤波的弱点是它无法解决非线性、非高斯问题的跟踪。为此提出了一种新型的跟踪算法,粒子过滤器算法。该算法采用加权的粒子集模型表示状态的分布,迭代跟踪状态的变化。其优点是它可以适应复杂环境的重叠和遮挡情况,且能同时跟踪多目标。采用最大后验概率模型确保了状态判断和估计的准确性。对重采样的分析减少了算法对噪声的敏感。并把样本安排在目标可能出现的区域。在眼睛跟踪系统上实现了该算法。仿真结果表明MAP模型在精度上与传统的方法比较提高7%。眼睛跟踪的结果证实了仿真的结果。     

Minimum Error Entropy Based EKF for GPS Code Tracking Loop

This paper investigates the minimum error entropy based extended Kalman filter (MEEKF) for multipath parameter estimation of the Global Positioning System (GPS). The extended Kalman filter (EKF) is designed to give a preliminary estimation of the state. The scheme is designed by introducing an additional term, which is tuned according to the higher order moment of the estimation error. The minimum error entropy criterion is introduced for updating the entropy of the innovation at each time step. According to the stochastic information gradient method, an optimal filer gain matrix is obtained. The mean square error criterion is limited to the assumption of linearity and Gaussianity. However, non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases. Most of the existing multipath estimation algorithms are usually designed for Gaussian noise. The I (in-phase) and Q (quadrature) accumulator outputs from the GPS correlators are used as the observational measurements of the EKF to estimate the multipath parameters such as amplitude, code delay, phase, and carrier Doppler. One reasonable way to obtain an optimal estimation is based on the minimum error entropy criterion. The MEEKF algorithm provides better estimation accuracy since the error entropy involved can characterize all the randomness of the residual. Performance assessment is presented to evaluate the effectivity of the system designs for GPS code tracking loop with multipath parameter estimation using the minimum error entropy based extended Kalman filter.     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

基于WOA-UKF算法的锂电池容量与SOC联合估计

锂电池的荷电状态(SOC)和有效容量是表征电池当前剩余电量和电池寿命的重要参数,提出一种锂离子电池有效容量和SOC的联合估计方法。在电池全寿命周期内,给出一种开路电压与SOC和电池有效容量非线性模型的两变量多项式描述;当电池循环使用次数超过预设值,采用鲸鱼优化算法估计当前电池容量与电池模型参数,根据模型参数与容量值采用无迹卡尔曼滤波器估计电池SOC;在SOC估计过程中,采用鲸鱼优化算法更新无迹卡尔曼滤波器的观测噪声方差和过程噪声方差,实现噪声方差的自适应调节,进而提高估计精度。实验结果验证了该方法的有效性和联合估计方案的可行性。     

基于二阶转换测量Kalman滤波的目标跟踪算法(英文)

为了减小传统跟踪滤波算法线性化误差,提高光电跟踪系统的跟踪速度和跟踪精度,本文在三维空间中,提出了二阶去偏转换测量卡尔曼滤波算法.该算法利用二阶泰勒展开的方法,推导出了光电跟踪系统观测方程的转换测量值误差的均值和协方差矩阵表达式,并对测量误差进行去偏差补偿处理,再经过转换测量卡尔曼滤波,可显著减小传统滤波算法的线性化误差.仿真结果表明,二阶去偏转换测量卡尔曼滤波(SCMKF)算法的跟踪精度优于非去偏转换测量卡尔曼滤波(CMKF)和扩展卡尔曼滤波(EKF),以及unscented卡尔曼滤波(UKF)算法,并且具 有更快的收敛速度,和采用统计方法的去偏转换测量卡尔曼滤波(DCMKF)的跟踪精度相当,但计算简单,提高了跟踪速度.     

Estimation of parameters for plasma glucose regulation in type‐2 diabetics in presence of meal

In this study, the authors propose a methodology for the estimation of glucose masses in stomach (both in solid and liquid forms), intestine, plasma and tissue; insulin masses in portal vein, liver, plasma and interstitial fluid using only plasma glucose measurement. The proposed methodology fuses glucose–insulin homoeostasis model (in the presence of meal intake) and plasma glucose measurement with a Bayesian non‐linear filter. Uncertainty of the model over individual variations has been incorporated by adding process noise to the homoeostasis model. The estimation is carried out over 24 h for the healthy people as well as a type II diabetes mellitus patients. In simulation, the estimator follows the truth accurately for both the cases. Moreover, the performances of two non‐linear filters, namely the unscented Kalman filter (KF) and cubature quadrature KF are compared in terms of root mean square error. The proposed methodology will be helpful in future to: (i) observe a patient''s insulin–glucose profile, (ii) calculate drug dose for any hyperglycaemic patients and (iii) develop a closed‐loop controller for automated insulin delivery system.Inspec keywords: blood, diseases, biochemistry, parameter estimation, biological tissues, liver, Bayes methods, nonlinear filters, Kalman filters, drugs, drug delivery systems, medical signal processingOther keywords: automated insulin delivery system, closed‐loop controller, hyperglycaemic patients, drug dose, root mean square error, cubature quadrature KF, Kalman filter, type II diabetes mellitus, process noise, Bayesian nonlinear filter, glucose‐insulin homoeostasis model, interstitial fluid, liver, portal vein, insulin mass, biological tissues, intestine, stomach, glucose mass, meal intake, type‐2 diabetics, plasma glucose regulation, parameter estimation     

部分加速度测量下结构恢复力与质量非参数化识别方法

传统的基于扩展卡尔曼滤波方法的结构非线性行为识别方法往往要求结构质量以及结构非线性恢复力的参数化模型已知。该研究为解决非线性结构质量,结构参数,非线性恢复力的识别问题,提出了一种两阶段识别方法;为提高计算效率采用遗忘因子扩展卡尔曼滤波算法结合等效线性模型实现结构非线性位置的定位,随后采用无迹卡尔曼滤波算法与恢复力的二重切比雪夫多项式非参数化模型识别结构参数,质量与恢复力。在对一个含形状记忆合金(SMA)阻尼器的多自由度体系的数值模型进行了数值模拟验证的基础上,设计了一个含SMA阻尼器的四自由度框架开展动力试验,验证了所提出方法对结构质量以及恢复力的识别效果。