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.     

Analysis of a robust Kalman filter in loosely coupled GPS/INS navigation system

GPS/INS integrated system is very subject to uncertainties due to exogenous disturbances, device damage, and inaccurate sensor noise statistics. Conventional Kalman filer has no robustness to address system uncertainties which may corrupt filter performance and even cause filter divergence. Based on the INS error dynamic equation, a robust Kalman filter is analyzed and applied in loosely coupled GPS/INS integration system. The norm bounded robust Kalman filter, with recursive form by solving two Riccati equations, guarantees a estimation variance bound for all the admissible uncertainties, and can evolve into the conventional Kalman filter if no uncertainties are considered. This paper will analyze the suitable case for the robust Kalman filter in GPS/INS system, the filter characteristics including parameter setting, parameter meaning, and filter convergence condition are discussed simutaneously. The robust filter performance will be compared with conventional Kalman filter through simulation results.     

引入滑模观测器的GPS/INS组合导航滤波方法

由低成本器件组成的卫星/惯性(GPS/INS)组合导航系统中,存在较大的非线性与不确定性,为改善这一问题,本文提出一种引入滑模观测器(SMO)的滤波方法。首先,该方法建立了组合导航系统模型,介绍了扩展卡尔曼滤波(EKF)计算过程并分析存在的不足。然后,介绍了滑模观测器的基本原理,根据系统构建观测器。最后,说明了引入滑模观测器的EKF组合导航算法实现流程,滑模观测器将模型误差、状态估计以及均值方差融入EKF算法,修正系统输出。通过轨迹仿真实验与车载实验验证了所提方法优于传统EKF算法,具有更高的滤波精度。在车载实验中,卫星信号失锁15 s情况下,与EKF方法相比,所提方法的东向位置误差降低了53%,北向位置误差降低了37%,证明该方法能够有效抑制GPS/INS组合导航误差发散,为以后工程实践提供一定的参考价值。     

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。     

An adaptive navigation method for a small unmanned aerial rotorcraft under complex environment

Focusing on low navigation performance of small unmanned aerial rotorcraft under complex environment, a composite navigation method combined with adaptive Kalman filtering and radial basis function neural network prediction method is proposed to improve navigation performance during GPS outages. When the GPS signal is available, an adaptive Kalman filter based on covariance scaling is introduced to deal with the process noise in real time. Meanwhile, a radial basis function neural network is trained on line to construct the projection among input (output of the inertial measurement unit, attitude and GPS losing time) and output (position error and velocity error). During GPS outages, the radial basis function neural network can provide high performance error estimation for position and velocity to improve state information. Finally, a land vehicle test and a flight test have confirmed that the proposed method can improve the navigation performance largely under complex environment.     

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.     

GPS/INS组合导航系统的研究

讨论了飞机惯性导航系统(INS)与全球卫星导航系统(GPS)的利与弊以及卡尔曼滤波方法在组合定位中的应用情况,进一步提出了基于神经网络数据融合方法的GPS/INS组合导航系统.系统神经网络结构采用单隐层的三层神经网络,输入输出神经元数目是4个,基于256个训练样本由经验公式求得隐层神经元数目为8个,同时还建立了惯导系统的数学模型和数据融合的数学模型.给出了利用MATLAB编制的神经网络训练程序并对这一神经网络进行了训练和仿真.实验表明,组合导航系统经度误差可达9m,纬度误差可达8m,与单独GPS定位和INS定位相比精度得到了提高.     

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.     

GPS/SINS组合导航系统中卡尔曼滤波器的应用

在现代生活中,GPS/SINS组合导航系统得到了越来越多的应用.文中介绍了卡尔曼滤波器在处理多个导航系统传来的数据中的应用,并且能够自动校正系统,以达到更高精度的要求.     

An accuracy-improvement method for GPS/INS kinematic levelling for use in linear engineering surveying projects

This paper proposes a high-efficiency and continuous levelling method for linear objects, such as highways and railways, by applying a vehicle-borne GPS/INS kinematic surveying system which integrates the Global Positioning System (GPS) and the Inertial Navigation System (INS). Generally, the raw ellipsoid height directly outputted by GPS/INS needs to be transformed to the local orthometric height. However, because of various systematic errors and random errors, such as the measuring error and the quasi-geoid model error, the accuracy of the orthometric height would rarely meet engineering requirements. To solve this problem, a novel sliding least-squares collocation (SLSC) model based on ground control points was constructed to improve the accuracy of GPS/INS kinematic levelling. Two data sets collected from the Chang Ying highway located in Jilin province, China, were used to validate the proposed method. The experimental results indicate that the proposed method improves the trajectory points’ orthometric height accuracy by at least 160%.     

Application of unscented R–T–S smoothing on INS/GPS integration system post processing for airborne earth observation

The Kalman Rauch–Tung–Striebel (R–T–S) smoother has been applied to fuse data from the inertial navigation system (INS) and global positioning system (GPS) for post processing, but its optimality heavily depends on linearity. For the case of in-flight startup, the INS/GPS integration is a nonlinear system with large initial attitude errors, the linear estimation approaches become inapplicable. In this paper, the Unscented R–T–S Smoother (URTSS) is utilized to deal with the nonlinear problem in the INS/GPS integration post processing, and the performance of this algorithm is compared with a similar smoother based on Extended Kalman Filter (ERTSS) through the Monto Carlo simulations. Furthermore, an INS/GPS integration system is implemented using URTSS and applied to airborne digital camera imaging. Through numerical simulation and flight test, it is shown that URTSS has obvious accuracy advantage over ERTSS in attitude estimation.     

ENHANCING KALMAN FILTERING–BASED TIGHTLY COUPLED NAVIGATION SOLUTION THROUGH REMEDIAL ESTIMATES FOR PSEUDORANGE MEASUREMENTS USING PARALLEL CASCADE IDENTIFICATION

Integrated global positioning system (GPS) solutions that utilize micro-electro-mechanical systems (MEMS)-based inertial sensors provide a more accurate navigation solution than stand-alone GPS in challenging scenarios. To keep the integrated solution less affected by sensor errors and to decrease the cost, a reduced inertial sensor system (RISS), which consists of only one gyroscope and two accelerometers, together with an odometer and integrated with GPS, is proposed. Tightly coupled integration is a better choice in demanding scenarios, as it can provide GPS aiding even when the number of visible satellites is three or less. However, inaccuracies of pseudoranges measured by the GPS receiver and used as aiding in the RISS/odometer/GPS integration solution will affect the overall positioning accuracy. This article explores the benefits of using parallel cascade identification (PCI), a nonlinear system identification technique that improves the overall navigation solution by modeling residual pseudorange correlated errors to be used by a Kalman filter (KF)–based tightly coupled RISS/odometer/GPS navigational solution. When less than four satellites are visible, the identified parallel cascade model for the still visible satellites is used to predict the residual pseudorange errors for these respective satellites, and the corrected pseudorange value is provided to KF. The performance of PCI for correcting the pseudoranges is examined and verified using road test trajectories and compared to a traditional tightly coupled RISS/odometer/GPS KF solution. The results demonstrate the advantages of this technique in correcting the pseudoranges and enhancing the positional solution.     

微惯性测量组合与GPS组合导航技术

分析了惯性导航系统和全球定位系统的优缺点;介绍了微惯性器件的发展及其用于惯性导航的前景;分析了由微惯性器件组成的捷联惯导与GPS组合导航的可行性;综述了GPS/INS组合导航的工作原理和关键技术.     

基于VxWorks系统的无人车GPS／INS组合导航

为了实现汽车自主导航,针对实时性导航,提出了一种基于VxWorks操作系统的GPS＋INS（inertial navigation system,惯性导航）组合导航。首先分析了无人车模型,布置导航的总体框架,确定CAN网络为整车通讯网络;然后研究了GPS导航,利用高精度GPS设备得到无人车坐标值,进而实现了GPS导航;接着研究了INS导航,利用一定精度INS的两个加速度计来积分推算无人车的航位,实现导航;再通过VxWorks结合两种导航方式,互相弥补信号的丢失与不可用。同时,开发了基于Windows的可视化导航界面,直观地观察导航效果和进行后台操控。实验验证了此导航的可行性和实时性。     

A new method of seamless land navigation for GPS/INS integrated system

For the last few years, integrated navigation systems have been widely used to calculate positions and attitudes of vehicles. The strapdown inertial navigation system (SINS) provides velocity, attitudes and position information, whereas the global positioning system (GPS) provides velocity and position information. A method using neural network (NN) and wavelet-based de-noising technology is introduced into the SINS/GPS/magnetometer integrated navigation system, because system accuracy may decrease during GPS outages. When the GPS is working well, NN is trained using the velocity and position information provided by SINS as input and the corresponding errors as output. Wavelet multi-resolution analysis (WMRA) is also introduced to de-noise the errors, the desired output of NN. Test results showed that velocity accuracies improved using NN, but other accuracies remained poor. By re-training NN with WMRA, the system accuracies improved to the level of using normal GPS signal. In addition, NN trained with WMRA also improved the approximation to the actual model, further enhancing alignment accuracy.     

惯性/地磁组合导航技术研究

针对此前地磁导航系统完全采用图匹配方式的精度问题,改进了惯性/地磁匹配组合方案,提出了一种新的匹配方法.该方法以磁偏角和磁倾角作为匹配参数进行图匹配,获取粗位置信息.以地磁场模型解算地磁场强度的方式来得到精确位置信息.辅以精确计时进而获得速度信息.以地磁系统获取的速度、位置信息与惯导系统输出的速度、位置信息的差值作为量测值,经过卡尔曼滤波,估计导航系统的误差,然后对惯导系统进行校正.在Matlab环境下的仿真证实了该方案可以达到较高精度.     

GPS单点定位精度优化方法研究

针对GPS单点定位精度低的问题,提出了一种基于卡尔曼滤波和模糊C-均值聚类的联合定位优化方法.该方法首先对GPS采集到的经纬度数据进行卡尔曼滤波,消除较大的数据波动,然后采用模糊C-均值聚类算法确定数据中心.最后通过实验证明了这种优化方法的合理性和有效性.     

Vision coupled GPS/INS scheme for helicopter navigation

This paper presents a framework for a GPS/INS/vision-based helicopter navigation system. The conventional GPS/INS algorithm has weak points such as GPS blockage and jamming, while the helicopter is a speedy and highly dynamic vehicle that may easily lose a GPS signal. A vision sensor is not affected by signal jamming, and the navigation error of such a system does not accumulate. Hence, a GPS/INS/vision-aided navigation scheme was implemented to provide the robust localization suitable for helicopter operations in various environments. The core algorithm is the vision-based SLAM (simultaneous localization and mapping) technique. Flight tests were performed to verify the SLAM-aided vision navigation algorithm. During the tests, it was confirmed that the developed system is sufficiently robust under GPS blockage conditions. The system design, software algorithm, and flight test results are described in this paper.     

非同步量测特性的惯性/星光/卫星组合算法研究

多传感器组合是提高导航系统定位精度和增强系统容错性的有效手段.在分析惯性、星光、卫星导航工作特性的基础上,提出了基于集中滤波器结构的捷联惯性/星光/卫星信息融合导航方案.针对多传感器信息融合中非等间隔量测特性,设计了时间更新和量测更新分离的异步集中卡尔曼滤波算法,设计了基于外推法的卫星信息补偿算法,有效解决了多传感器非等间隔信息融合问题;针对垂直机动研究了惯性/星光姿态组合模型.仿真结果表明,算法可以有效实现对捷联惯导、星光、卫星导航信息的融合,组合精度提高1倍,具有重要的实际应用价值.     

A dead reckoning localization system for mobile robots using inertial sensors and wheel revolution encoding

Inertial navigation systems (INS) are composed of inertial sensors, such as accelerometers and gyroscopes. An INS updates its orientation and position automatically; it has an acceptable stability over the short term, however this stability deteriorates over time. Odometry, used to estimate the position of a mobile robot, employs encoders attached to the robot’s wheels. However, errors occur caused by the integrative nature of the rotating speed and the slippage between the wheel and the ground. In this paper, we discuss mobile robot position estimation without using external signals in indoor environments. In order to achieve optimal solutions, a Kalman filter that estimates the orientation and velocity of mobile robots has been designed. The proposed system combines INS and odometry and delivers more accurate position information than standalone odometry.