A derivative UKF for tightly coupled INS/GPS integrated navigation

The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.     

QUKF算法及其在SINS初始对准中的应用

针对捷联惯导系统初始对准过程中的大失准角情况,建立了乘性四元数姿态误差方程。结合UKF算法,提出了基于四元数的UKF算法(QUKF)。以姿态矩阵为对象,通过构造姿态矩阵代价函数的方法来求取四元数的一步预测均值,保证了均值四元数的规范化;利用乘性误差四元数表示四元数Sigma点与均值四元数的距离,以求取四元数的预测协方差矩阵。四元数状态更新中,采用乘性四元数更新保证了滤波过程中四元数的规范化。基于该算法的SINS在粗对准水平失准角为小角度、方位失准角为大角度条件下的仿真实验结果表明,与常规EKF相比,纵、横摇角对准精度均略有提高,而航向角误差估计精度提高显著。     

基于视线测量的航天器相对导航滤波方法研究

基于视线测量的航天器相对导航精度会受到相对轨迹形状和滤波算法设计等因素的共同影响。以低轨卫星近距离编队飞行为任务背景,设计了环航飞行、共面漂移和共线保持3种不同轨迹的相对运动模式。对3种模式建立了基于星间非线性相对运动模型的系统状态方程,并引入了J2项地球非球形摄动力的影响;建立了基于视线测量的观测方程,观测量包括星间相对距离、相对俯仰角和相对航向角。结合系统模型和观测模型均为高斯分布的非平稳随机过程的特点,分别在上述3种模式下设计了基于扩展卡尔曼滤波(extended Kalman filter,EKF)和无迹卡尔曼滤波(unscented Kalman filter,UKF)的相对导航滤波算法,对各自的相对运动轨迹进行了数值仿真,并在半物理硬件环境下进行了验证,分析了不同模式下EKF和UKF对于高斯非平稳随机过程的估计精度和稳定性,并结合EKF和UKF的运算复杂度,提出了3种相对运动模式下的滤波器优选方案,对工程设计提供了理论参考。     

Improving ultrasonic-based seamless navigation for indoor mobile robots utilizing EKF and LS-SVM

The ultrasonic positioning system is able to provide centimeter-level location information. However, the signal of the system is easy to be disturbed and the outages of the positioning system appear. Inertial measuring units (IMUs) is a self-contained device and can provide long-term navigation information independently, but it has the drawback of error drift. In order to obtain accurate and continuous location information indoors for indoor mobile robots, this work proposed a seamless integrated navigation utilizing extended Kalman filter (EKF) and Least Squares Support Vector Machine (LS-SVM). In this mode, the EKF estimates the position and the velocity of the robot while the signals of ultrasonic positioning system are available. Meanwhile, the compensation model is trained by LS-SVM with corresponding filter states. Once the signals of ultrasonic positioning system are outages, the model is able to correct inertial navigation system (INS) solution as filter does. A prototype of the system has been worked in a real scenario. The results show that the performance of EKF is robust, and the prediction of LS-SVM is able to work as EKF does during the outages.     

UKF在永磁直线同步电动机无位置传感器控制中的应用

Unscented卡尔曼滤波器(UKF)在许多非线性估计问题中是一种估计性能优于扩展卡尔曼滤波器(EKF)的非线性滤波方法。然而在永磁直线同步电动机无位置传感器控制中,UKF是否能提高永磁直线电动机位置与速度的估计性能却尚未见研究。针对永磁直线同步电动机进给系统的特点,建立用于位置与速度估计器的永磁直线同步电动机进给系统模型,提出永磁直线同步电动机无位置传感器控制系统。通过仿真和试验对UKF的估计性能进行评估,并与EKF进行了比较。仿真及试验结果表明,UKF在估计性能与EKF相当, 然而UKF的计算量却比EKF大,使得在高速永磁直线同步电动机无位置传感器控制这一特定问题上,EKF比UKF更有效。     

Outdoor position estimation based on a combination system of GPS-INS by using UPF

This paper proposes a technique that global positioning system(GPS)combines inertial navigation system(INS)by using unscented particle filter(UPF)to estimate the exact outdoor position.This system can make up for the weak point on position estimation by the merits of GPS and INS.In general,extended Kalman filter(EKF)has been widely used in order to combine GPS with INS.However,UPF can get the position more accurately and correctly than EKF when it is applied to real-system included non-linear,irregular distribution errors.In this paper,the accuracy of UPF is proved through the simulation experiment,using the virtual-data needed for the test.     

一种快速GPS/DR组合导航系统状态估计算法研究

无轨迹卡尔曼滤波(UKF)技术在非线性系统(GPS/DR车载组合导航系统)的状态估计中取得了比扩展卡尔曼滤波(EKF)更好的滤波精度和收敛速度.为了进一步减少采样点数目,提高UKF滤波实时性,一组n+2个采样点被构造用于逼近系统状态分布.蒙特卡洛仿真表明RUKF和UKF在滤波精度和收敛速度上是一致的,RUKF的计算效率好于UKF.     

Improving unmanned ground vehicle navigation by exploiting virtual sensors and multisensor fusion

This paper investigates techniques on improving navigation accuracy using multiple sensors mounted on a mobile platform and exploiting the inherent characteristic of a ground vehicle that does not move along the cross-track and off the ground, often termed nonholonomic constraints (NHC) for car-like vehicles that assume no slip or skid. The forward velocity of the vehicle is obtained using a wheel encoder. The 3D velocity vector becomes observable during the normal moving state of the vehicle by using NHC, which produces one virtual sensor. Another virtual sensor is the zero-velocity update (ZVU) condition of the vehicle; when the condition is true, the 3D velocity vector (which is zero) becomes observable. These observables were employed in an extended Kalman filter (EKF) update to limit the growth of inertial navigation system error. We designed an EKF for data fusion of inertial measurement units, global positioning systems (GPS), and motion constraints (i.e., NHC and ZVU). We analyzed the effects of utilizing these constraints on improving navigation accuracy in stationary and dynamic cases. Our proposed navigation suite provides reliable accuracy for unmanned ground vehicle applications in a GPS-denied environment (e.g., forest canopy and urban canyon).     

交互多模型在车辆组合定位系统中的应用（英文）

为解决扩展卡尔曼滤波器(extended Kalman filter,EKF)在车辆组合定位系统中因车辆加减速、转弯(以下简称机动)而存在的精度低、稳定性差等问题,设计了一种将交互多模型(interacting multiple model,IMM)算法与非线性卡尔曼滤波器相融合的自适应滤波算法。该算法使用三种状态空间模型来描述车辆的运动模式,采用多个非线性滤波器对每个模型并行滤波,通过模型匹配似然函数对滤波结果进行加权融合,最终得到系统的定位信息。该方法具备非线性系统滤波器优点,克服了单一模型滤波算法对机动目标定位效果差的缺点。利用该方法和EKF算法分别对GPS/INS/DR车辆组合定位系统中进行了仿真实验,结果表明,该算法的滤波定位精度明显优于目前组合定位系统中所用的EKF滤波器,大幅提高了组合定位系统的稳定性和定位精度。     

利用火星卫星光学测量实现火星探测器自主导航

以火星探测为例,提出了通过对火星卫星进行光学测量实现火星探测器自主导航的方法。该方法在火星探测器上搭载光学相机,在飞向火星过程中对火星天然卫星（Phobos,火卫一;Deimos,火卫二）拍摄带有恒星背景的图像;通过恒星位置确定精确的惯性指向,利用得到的光学观测数据完成对火星探测器的自主导航。分别给出了基于扩展卡尔曼滤波（EKF）和无迹卡尔曼滤波（UKF）进行自主导航的方法和仿真计算结果。数据显示：EKF和UKF得到的结果基本一致,说明EKF在线性化过程中损失精度并不多。在巡航段后半程,与火星距离越近,导航精度越高。距离火星（1~5）×10⁷ km时,取数据间隔为1 min,如果测量精度为0.1",导航精度可达10~100 km量级,速度精度为0.01 m/s量级;如果测量精度为1",导航精度也相应要低一个量级。另外,单独使用火卫二的导航精度要高于单独使用火卫一,联合使用火卫一和火卫二的精度最高。仿真计算结果表明,利用火星卫星光学测量的火星探测器自主导航,可满足火星探测器高精度导航的要求。     

基于CKF的SINS大方位失准角初始对准

大方位失准角捷联惯导系统(strapdown inertial narigation system,SINS)误差方程是非线性的,为改善非线性模型下初始对准的精度,提出将一种新的非线性滤波方法(cubature Kalman filter,CKF)应用于捷联惯导系统初始对准中。为此建立了大方位失准角下初始对准非线性模型,分析了基于spherical-radial cubature准则的CKF滤波原理,对非线性模型进行了CKF滤波仿真。仿真结果表明CKF能够很好地处理初始对准中的非线性问题,提高初始对准精度,方位失准角误差能够收敛到-33.13’,接近理论估计精度-32.40’,优于EKF的-84.14’。     

一种单轴旋转捷联惯导的三位置对准方法

针对单轴旋转式捷联惯性导航系统,提出了一种基于惯性测量单元(inertial measurement unit,IMU)旋转的三位置初始对准方法.在系统可观测性分析的基础上,建立IMU姿态与失准角之间的关系,提出了使失准角估计偏差为零的三位置对准方法.与以往固定位置对准和两位置对准进行了比较,表明该方法可以消除不可观测的水平加速度计零偏和东向陀螺常值漂移对初始对准精度的影响,大大提高了系统初始对准精度.     

Random misalignment and lever arm vector online estimation in shipborne aircraft transfer alignment

Shipborne aircrafts normally do not have regular position on the carrier. This would lead to large misalignment between the master strapdown inertial navigation system (M-SINS) and slave strapdown inertial navigation system (S-SINS) as well as random lever arm vector. It is critical for the accuracy of the transfer alignment. The large attitude error will make the linear alignment algorithm invalid. And the lever arm vector caused by the location difference will lead to the lever arm effect which is sensed by the accelerometers in the S-SINS. Therefore it is necessary for the shipborne aircraft to estimate the lever arm vector and misalignment before the transfer alignment takes place. In this paper, a new misalignment and lever arm vector online estimation method based on gyroscope, accelerometer measurement and filtering is presented. Sensor measurements of M-SINS and S-SINS will be recorded for a few seconds. Misalignment and the lever arm vector will be calculated from these measurements directly. The values will be filtered according to the chosen threshold of the error gain. Then a second stage estimation based on least square estimation will be applied to acquire a better result. Simulation results demonstrate the effectiveness of the estimation algorithm in the situation when both large misalignment and random lever arm vector exist.     

基于UKF算法的汽车状态估计

准确实时获取行驶过程中的状态信息是汽车动态控制系统研究的关键问题。将unscented卡尔曼滤波(UKF)算法应用到汽车的状态估计之中,建立了包含时不变统计特性噪声和非线性轮胎的汽车动力学模型,采用具有对称采样策略和比例修正的UKF算法对汽车估计了多个关键状态量。将UKF估计器与常见的EKF估计器进行了比较分析,基于ADAMS/Car的虚拟试验和实车试验验证了UKF在汽车状态估计中的可行性。     

High accuracy navigation information estimation for inertial system using the multi-model EKF fusing adams explicit formula applied to underwater gliders

The underwater navigation system, mainly consisting of MEMS inertial sensors, is a key technology for the wide application of underwater gliders and plays an important role in achieving high accuracy navigation and positioning for a long time of period. However, the navigation errors will accumulate over time because of the inherent errors of inertial sensors, especially for MEMS grade IMU (Inertial Measurement Unit) generally used in gliders. The dead reckoning module is added to compensate the errors. In the complicated underwater environment, the performance of MEMS sensors is degraded sharply and the errors will become much larger. It is difficult to establish the accurate and fixed error model for the inertial sensor. Therefore, it is very hard to improve the accuracy of navigation information calculated by sensors. In order to solve the problem mentioned, the more suitable filter which integrates the multi-model method with an EKF approach can be designed according to different error models to give the optimal estimation for the state. The key parameters of error models can be used to determine the corresponding filter. The Adams explicit formula which has an advantage of high precision prediction is simultaneously fused into the above filter to achieve the much more improvement in attitudes estimation accuracy. The proposed algorithm has been proved through theory analyses and has been tested by both vehicle experiments and lake trials. Results show that the proposed method has better accuracy and effectiveness in terms of attitudes estimation compared with other methods mentioned in the paper for inertial navigation applied to underwater gliders.     

State of charge estimation of vanadium redox battery based on improved extended Kalman filter

The accurate state of charge (SOC) estimation can protect the battery from overcharging and over-discharging, and it is useful to make an effective dispatching strategy. The extended Kalman filter (EKF) method is used to estimate SOC widely. But it does not consider the SOC constraints. Moreover, the convergence is influenced by the uncertain initial SOC, which may lead to false alarm, unwanted operation of protection, error dispatching and poor robustness of the system. This paper presents an improved extended Kalman filter (IEKF) method to estimate SOC for vanadium redox battery (VRB) by introducing a gain factor. It can be adjusted automatically according to the output error and SOC boundary. To implement IEKF estimator, a VRB state space model is established and its parameters are identified by recursive least square (RLS) method. Then a VRB of 5kW/30kWh experimental platform is built. Finally, the IEKF method is validated and compared with EKF against unknown initial value through the experiments. The results have shown that IEKF method is superior to EKF in terms of accuracy, convergence speed and robustness. And the estimated SOC remains bounded by using IEKF method. It is more suitable for SOC estimation than EKF algorithm in the industrial applications.     

应用RB无迹卡尔曼滤波组合导航提高GPS重获信号后的导航精度

针对微机电-船舶惯性导航/全球定位(MEMS-SINS/GPS)组合导航系统在GPS信号中断时造成的强非线性误差及重获信号后精度变差的问题,设计了基于Rao-Blackwellised无迹卡尔曼滤波(RB-UKF)的组合导航算法。首先,基于捷联平台欧拉失准角定义了姿态误差,建立了捷联惯导系统的非线性误差传播方程。然后,针对组合导航的状态方程为非线性而量测方程呈线性的特点,设计了RB-UKF算法,在保证精度的同时降低了计算量。最后,设计了滤波算法总体结构,分别给出了GPS信号正常时和中断时组合导航滤波计算的流程。将提出的算法用于跑车实验,结果表明:在GPS失锁20s和40s再重获信号之后,使用RB-UKF算法的组合导航系统位置精度分别优于6m和7.5m,比扩展卡尔曼滤波(EKF)算法精度提高了1.5倍以上,误差收敛速度提高了1.88~16.5倍,计算量比UKF量测更新的计算量减小了41.7%。实验显示该方法显著提升了组合导航系统GPS信号中断再恢复后的滤波精度,且易于工程实现。     

基于高斯混合容积卡尔曼滤波的UUV自主导航定位算法

针对过程噪声为非理想高斯分布时无人水下航行器(UUV)自主导航定位存在噪声模型失配的问题,将高斯混合密度模型与容积卡尔曼滤波(CKF)相结合,设计了基于高斯混合容积卡尔曼滤波(GM-CKF)的UUV导航定位算法。建立了UUV运动模型及观测模型,利用CKF完成各高斯分量的预测更新,并将更新结果进行融合缩减与加权求和,从而实现UUV自主导航定位。通过与EKF、UKF和CKF算法仿真对比实验,验证了GM-CKF可以提高估计精度;通过UUV湖试试验,验证了基于GM-CKF的UUV自主导航定位精度和稳定性优于传统算法,其计算时间满足实时导航定位的要求。     

Detection of broken rotor bars in induction motors using nonlinear Kalman filters

This paper presents a model-based fault detection approach for induction motors. A new filtering technique using Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) is utilized as a state estimation tool for on-line detection of broken bars in induction motors based on rotor parameter value estimation from stator current and voltage processing. The hypothesis on which the detection is based is that the failure events are detected by jumps in the estimated parameter values of the model. Both UKF and EKF are used to estimate the value of rotor resistance. Upon breaking a bar the estimated rotor resistance is increased instantly, thus providing two values of resistance after and before bar breakage. In order to compare the estimation performance of the EKF and UKF, both observers are designed for the same motor model and run with the same covariance matrices under the same conditions. Computer simulations are carried out for a squirrel cage induction motor. The results show the superiority of UKF over EKF in nonlinear system (such as induction motors) as it provides better estimates for rotor fault detection.