WSN Mobile Target Tracking Based on Improved Snake-Extended Kalman Filtering Algorithm

A wireless sensor network mobile target tracking algorithm(ISO-EKF)based on improved snake optimization algorithm(ISO)is proposed to address the difficulty of estimating initial values when using extended Kalman filtering to solve the state of nonlinear mobile target tracking.First,the steps of extended Kalman filtering(EKF)are introduced.Second,the ISO is used to adjust the parameters of the EKF in real time to adapt to the current motion state of the mobile target.Finally,the effectiveness of the algorithm is demonstrated through filtering and tracking using the constant velocity circular motion model(CM).Under the specified conditions,the position and velocity mean square error curves are compared among the snake optimizer(SO)-EKF algorithm,EKF algorithm,and the proposed algorithm.The comparison shows that the proposed algorithm reduces the root mean square error of position by 52%and 41%compared to the SOEKF algorithm and EKF algorithm,respectively.

Improved Adaptive Iterated Extended Kalman Filter for GNSS/INS/UWB-Integrated Fixed-Point Positioning

To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satellite system,inertial navigation system,and ultra wide band(UWB)is proposed.In thismethod,the switched global navigation satellite system(GNSS)and UWB measurement are used as the measurement of the proposed filter.For the data fusion filter,the expectation-maximization(EM)based IEKF is used as the forward filter,then,the Rauch-Tung-Striebel smoother for IEKF filter’s result smoothing.Tests illustrate that the proposed AIEKF is able to provide an accurate estimation.

FPGA Implementation of Extended Kalman Filter for Parameters Estimation of Railway Wheelset

It is necessary to know the status of adhesion conditions between wheel and rail for efficient accelerating and decelerating of railroad vehicle.The proper estimation of adhesion conditions and their real-time implementation is considered a challenge for scholars.In this paper,the development of simulation model of extended Kalman filter(EKF)in MATLAB/Simulink is presented to estimate various railway wheelset parameters in different contact conditions of track.Due to concurrent in nature,the Xilinx®System-on-Chip Zynq Field Programmable Gate Array(FPGA)device is chosen to check the onboard estimation ofwheel-rail interaction parameters by using the National Instruments(NI)myRIO®development board.The NImyRIO®development board is flexible to deal with nonlinearities,uncertain changes,and fastchanging dynamics in real-time occurring in wheel-rail contact conditions during vehicle operation.The simulated dataset of the railway nonlinear wheelsetmodel is tested on FPGA-based EKF with different track conditions and with accelerating and decelerating operations of the vehicle.The proposed model-based estimation of railway wheelset parameters is synthesized on FPGA and its simulation is carried out for functional verification on FPGA.The obtained simulation results are aligned with the simulation results obtained through MATLAB.To the best of our knowledge,this is the first time study that presents the implementation of a model-based estimation of railway wheelset parameters on FPGA and its functional verification.The functional behavior of the FPGA-based estimator shows that these results are the addition of current knowledge in the field of the railway.

Notes on Convergence and Modeling for the Extended Kalman Filter

The goal of this work is to provide an understanding of estimation technology for both linear and nonlinear dynamical systems.A critical analysis of both the Kalman filter(KF)and the extended Kalman filter(EKF)will be provided,along with examples to illustrate some important issues related to filtering convergence due to system modeling.A conceptual explanation of the topic with illustrative examples provided in the paper can help the readers capture the essential principles and avoid making mistakes while implementing the algorithms.Adding fictitious process noise to the system model assumed by the filter designers for convergence assurance is being investigated.A comparison of estimation accuracy with linear and nonlinear measurements is made.Parameter identification by the state estimation method through the augmentation of the state vector is also discussed.The intended readers of this article may include researchers,working engineers,or engineering students.This article can serve as a better understanding of the topic as well as a further connection to probability,stochastic process,and system theory.The lesson learned enables the readers to interpret the theory and algorithms appropriately and precisely implement the computer codes that nicely match the estimation algorithms related to the mathematical equations.This is especially helpful for those readers with less experience or background in optimal estimation theory,as it provides a solid foundation for further study on the theory and applications of the topic.

Proactive traffic responsive control based on state-space neural network and extended Kalman filter

The state-space neural network and extended Kalman filter model is used to directly predict the optimal timing plan that corresponds to futuristic traffic conditions in real time with the purposes of avoiding the lagging of the signal timing plans to traffic conditions. Utilizing the traffic conditions in current and former intervals, the network topology of the state-space neural network （SSNN）, which is derived from the geometry of urban arterial routes, is used to predict the optimal timing plan corresponding to the traffic conditions in the next time interval. In order to improve the effectiveness of the SSNN, the extended Kalman filter （EKF） is proposed to train the SSNN instead of conventional approaches. Raw traffic data of the Guangzhou Road, Nanjing and the optimal signal timing plan generated by a multi-objective optimization genetic algorithm are applied to test the performance of the proposed model. The results indicate that compared with the SSNN and the BP neural network, the proposed model can closely match the optimal timing plans in futuristic states with higher efficiency.

Speed Sensorless Vector Control of Induction Motor Based on Reduced Order Extended Kalman Filter

A speed sensorless vector control system of induction motor with estimated rotor speed and rotor flux using a new reduced order extended Kalman filter is proposed. With this method, two rotor flux components are selected as the state variables, and the rotor speed as an estimated parameter is regarded as an augmented state variable. The algorithm with reduced order decreases the computational complexity and makes the proposed estimator feasible to be implemented in real time. The simulation results show high accuracy of the estimation algorithm and good performance of speed control, and verify the usefulness of the proposed algorithm.

基于IQPSO-EKF的多传感器融合姿态测量方法研究

为解决自动化竖井掘进设备的定位调姿精度对竖井、孔桩挖掘效率与质量的影响,提出了一种基于改进量子粒子群(IQPSO)-扩展卡尔曼滤波(EKF)的姿态测量算法,以提高微机电系统(MEMS)传感器测量精度。首先,对MEMS传感器数据进行了预处理(除噪、滤波、校准等);然后,参考现有飞行器的坐标系,建立了姿态解算模型,通过姿态角数学模型及运动学分析,构建了EFK状态方程,针对EKF方法参数估计不准确的问题,以分段混沌映射优化初始种群,引入平均位置最优值来避免陷入局部最优的IQPSO-EFK算法,优化EKF的系统、测量噪声的协方差参数;最后,对改进算法和三组姿态误差估计进行了对比实验。研究结果表明:对比三种典型目标函数,IQPSO-EFK相较于普通粒子群算法(QPSO-EFK)具有更强的寻优能力与收敛精度;对比三组旋转速度姿态测量误差,基于IQPSO-EKF算法的姿态测量方法在测量误差时比真实测量误差减少了约86.3%,比扩展卡尔曼滤波减少了约68.7%,比普通粒子群算法减少了约28.2%,证明该算法有效地提高了MEMS传感器测量精度。

引入PID反馈的SHAEKF算法估算电池SOC

电池荷电状态(SOC)的估算精度是电动汽车电池组的重要指标。为提升SOC估算精度,在融合Sage-Husa扩展卡尔曼滤波(SHEKF)算法与自适应扩展卡尔曼滤波(AEKF)算法的基础上,增加比例积分微分(PID)反馈环节,形成改进算法。采用粒子群优化(PSO)算法对二阶RC等效电路模型进行参数辨识;用开源电池数据集对模型和算法进行实验和分析。改进的SHAEKF算法在电池动态应力测试(DST)、北京动态应力测试(BJDST)和美国联邦城市驾驶(FUDS)等工况下的平均估计误差都在1%以内,与单纯的融合算法SHAEKF算法相比,最大误差可减小5%。

基于EKF和UKF的随钻姿态解算方法研究

目的为解决煤层松软中随钻测量系统测量精度不高的问题。方法提出一种改进的无迹卡尔曼滤波(UKF)和扩展卡尔曼滤波(EKF),分别应用于钻具的姿态滤波算法中并作比较。该方法基于旋转坐标变换的四元数理论和陀螺测量原理,建立钻具姿态传感器数据的非线性观测方程和状态方程,以四元数将测量数据进行转换与更迭,最终消除惯性传感器数据中的误差。与EKF算法相比较,UKF算法利用了UT变换对非线性函数的概率密度分布进行近似,没有忽略高项阶,因此对于非线性分布的统计量有较好的计算精度。结果经仿真验证,UKF的各个滤波误差峰峰值以及标准差小于EKF。结论改进的UKF的滤波算法精度明显高于EKF滤波算法,更加有效地去除惯性传感器中的干扰噪声,有利于提高微机电系统(MEMS)惯性传感器的测量精度,进而提高钻进效率。

基于VB-EKF的GPS/INS松组合导航定位算法

针对应用在无人机(Unmanned Aerial Vehicle,UAV)中的全球定位系统/惯性导航系统(GPS/INS)松组合导航非线性系统受到外界噪声干扰导致量测噪声在滤波时不断变化,从而造成滤波精度下降等问题,提出一种变分贝叶斯扩展卡尔曼滤波(VB-EKF)算法。该算法利用EKF(Extended Kalman Filter)将非线性系统中的状态函数和量测函数展开为线性方程,并将两个不同的导航系统数据进行融合,避免了单系统导航定位发散的问题。考虑到组合系统中量测噪声的时变特性,引入变分贝叶斯算法进行改进,有效解决了系统滤波精度下降问题。仿真结果表明,VB-EKF较EKF算法可有效提高滤波稳定性,进而提高系统导航定位精度。

基于ISTSMC和改进EKFSMO的PMSM无传感器矢量控制

在采用内环矢量控制(Field orientation control,FOC)和外环经典比例积分(Proportional integral,PI)控制的永磁同步电机(Permanent magnet synchronous motor,PMSM)驱动系统中,容易出现外部扰动检测精度低、抖振、速度环超调大等不确定性缺陷。为了解决PI控制的抖振缺点,提高系统抗干扰性,提出了一种积分超螺旋滑模控制(Integral super twisting sliding mode controller,ISTSMC)。为了实现无位置传感器控制以及电机转速与位置的在线估计,采用基于扩展卡尔曼滤波(Extended Kalmanfilter,EKF)的滑模观测器,并且设计了一种分段正弦型函数代替传统的基于sgn函数的滑模观测器降低抖振现象。在Matlab/Simulink仿真下,分析了该系统在各种故障扰动、反转运行和负载扰动下的速度响应和检测精度能力。结果证明了所提系统的可行性以及优越的动态性能。

一种基于Madgwick-EKF融合算法的卫星姿态测量方法

针对低地球轨道卫星姿态测量时,传感器易受噪声干扰、陀螺仪漂移等问题,提出一种基于Madgwick扩展卡尔曼滤波合算法(EKF)的卫星姿态测量方法。该方法采用陀螺仪、加速度计、磁强计等多传感器数据进行融合,并结合Madgwick算法和EKF算法的优点,实现姿态测量。首先,通过Madgwick算法,利用多个传感器测量数据计算初始姿态。然后,基于初始姿态和实际测量数据,应用EKF算法进行数据融合和噪声滤除,以获得最终准确的姿态估计。实验结果表明:相较Madgwick算法,本算法在测量精度上提升了65.8%,且具有较高的鲁棒性,为低地球轨道卫星姿态测量提供了一种有效的方案。

基于EKF-GRU的车辆轨迹预测

为提升行车安全,实现自动驾驶车辆正确的决策规划,提出基于扩展卡尔曼滤波(EKF)-门控循环单元(GRU)的车辆轨迹预测方法,结合学习方法与物理模型,在提升预测精度的同时,提高轨迹预测的合理性。首先,基于GRU构建预测网络,通过提取车辆的历史轨迹特征预测车辆的纵向加速度及横摆角速度;其次,基于车辆非线性运动学构建EKF状态估计器,结合观测值生成车辆未来有限时域的行驶轨迹;最后,在高速公路多车轨迹数据集NGSIM I-80和US-101上进行轨迹预测方法验证。结果表明:采用传统的物理模型生成预测轨迹,其最终距离误差(FDE)、均方根误差(RMSE)、平均距离误差(ADE)值分别为6.48、7.69和3.03 m。相比之下,利用EKF-GRU生成的预测轨迹表现出更高的准确性,对应的数值分别为5.45、6.67和2.56 m,分别提升15.90%、13.26%和15.51%。

Unscented extended Kalman filter for target tracking

A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of non- lineadty is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter （UKF）, however, the computational time of the UEKF is much less than that of the UKF.

LSTM-EKF算法实现储能集装箱电芯SOC的优化估计

储能集装箱是锂电池储能电站的核心设备,每个集装箱由数千只电芯串并联构成。因此,对集装箱电芯锂电池荷电状态(state of charge,SOC)的准确估计成为表征储能电站运行最核心最基础的参数,并且为辅助新能源高效并网,储能系统的工作状态也会相应地呈现随机性、波动性和不确定性,这对电芯状态估计的准确度提出了更高的要求。为此,首先基于基尔霍夫定律建立Thevenin电池模型,根据安时积分法列出系统的状态和观测方程,并且将其状态和观测方程作为扩展卡尔曼滤波(extended Kalman filtering,EKF)算法的研究对象。然后利用EKF算法对估计值电池SOC更新迭代,再将EKF算法中得到的卡尔曼矩阵和状态变量更新误差值以及UDDS工况下的电池数据,作为长短期记忆(long short-term memory,LSTM)神经网络算法的训练数据集,由此完成LSTM-EKF联合算法,实现对储能集装箱电芯SOC的优化估计。该文所提LSTM-EKF算法可将电芯SOC的误差值降低到1%以下。最后对优化算法在储能电站安全运行与监控平台中的应用情况进行介绍。

Dual Extended Kalman Filter for Combined Estimation of Vehicle State and Road Friction

Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute（HSRI） tire model; the dual extended Kalman filter （DEKF） technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions（high-friction, low-friction, and joint-friction）. On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.

Extended Kalman filtering-based channel estimation for space-time coded MIMO-OFDM systems

A space-time coded multiple-input multiple-output orthogonal frequency-division multiplexing （MIMO-OFDM） system is considered as a solution to the future wideband wireless communication system. This paper proposes an extended Kalman filtering-based （EKF-based） channel estimation method for space-time coded MIMO-OFDM systems. The proposed method can exploit pilot symbols and an extended Kalman filter to estimate channel without any prior knowledge of channel statistics. In comparison with the least square （LS） and the least mean square （LMS） methods, the EKF-based approach has a better performance in theory. Computer simulations demonstrate the proposed method outperforms the LS and LMS methods. Therefore it can offer draznatic system performance improvement at a modest cost of computational complexity.

基于IWHO-EKF的高速免耕播种机播种深度监测系统研究

为解决免耕播种机高速(12~16 km/h)作业时因地势起伏造成机械振动与传感器测量误差导致的播种深度监测系统精度降低,以及单一传感器监测可靠性较差的问题,研究了一种基于改进野马算法(Improved wild horse optimizer,IWHO)优化扩展卡尔曼滤波器(Extended Kalman filter,EKF)中关键参数Q_(sigma)、R_(sigma1)、R_(sigma2)、R_(sigma3)的多传感器数据融合算法(IWHO-EKF)的高速免耕播种机播种深度监测系统。首先,建立以激光、超声波与角度传感器为多传感器监测单元的播种深度监测模型;其次,通过卡尔曼滤波算法对3个单一传感器分别滤波;最后,提出一种加入莱维飞行与高斯变异的IWHO-EKF算法,将滤波后的3个单一传感器进行数据融合,从而解决机械振动干扰与传感器测量误差降低的问题,同时充分发挥多传感器融合信息,确保免耕播种机高速作业时实现高精度、高可靠性播种深度实时监测。为验证其优越性,通过IWHO-EKF算法与单一传感器监测、单一传感器滤波和WHO-EKF算法进行仿真对比试验与田间试验。仿真试验表明:基于IWHO-EKF的高速免耕播种机播种深度监测算法平均绝对误差为0.073 cm,均方根误差为0.090 cm,相关系数为0.983,实现了高精度监测,且精度相较于传感器原始监测值、滤波值与WHO-EKF算法均显著提升。田间试验结果表明:基于IWHO-EKF算法的高速免耕播种机播种深度监测系统相较于3个单一传感器监测值,平均绝对误差和平均均方根误差分别降低0.063 cm和0.067 cm,同时平均相关系数提升0.027,该系统能够提高播种深度监测系统的精确性和可靠性。

Extended Kalman Filter-based localization algorithm by edge computing in Wireless Sensor Networks

The Extended Kalman Filter(EKF)has received abundant attention with the growing demands for robotic localization.The EKF algorithm is more realistic in non-linear systems,which has an autonomous white noise in both the system and the estimation model.Also,in the field of engineering,most systems are non-linear.Therefore,the EKF attracts more attention than the Kalman Filter(KF).In this paper,we propose an EKF-based localization algorithm by edge computing,and a mobile robot is used to update its location concerning the landmark.This localization algorithm aims to achieve a high level of accuracy and wider coverage.The proposed algorithm is helpful for the research related to the use of EKF localization algorithms.Simulation results demonstrate that,under the situations presented in the paper,the proposed localization algorithm is more accurate compared with the current state-of-the-art localization algorithms.

Weak harmonic signal detection method in chaotic interference based on extended Kalman filter

The traditional methods of weak harmonic signal detection under strong chaotic interference often suffer from high computational complexity and poor performance. In this paper, an Extended Kalman Filter (EKF) based detection method is proposed for the detection of weak harmonic signal. The EKF method avoids matrix inversion by iterating measurement equation and state equation, which simultaneously improves the robustness and reduces the complexity. Compared with the existing detection methods, the proposed method has the following advantages: 1) it has better performance than the neural network method;2) it has similar performance with the optimal filtering method, but with lower computational complexity;3) it is more robust compared with the optimal filtering method.