Online INS/GPS integration with a radial basis function neural network

Most of the present navigation systems rely on Kalman filtering to fuse data from global positioning system (GPS) and the inertial navigation system (INS). In general, INS/GPS integration provides reliable navigation solutions by overcoming each of their shortcomings, including signal blockage for GPS and growth of position errors with time for INS. Present Kalman filtering INS/GPS integration techniques have some inadequacies related to the stochastic error models of inertial sensors, immunity to noise, and observability. This paper aims to introduce a multi-sensor system integration approach for fusing data from INS and GPS utilizing artificial neural networks (ANN). A multi-layer perceptron ANN has been recently suggested to fuse data from INS and differential GPS (DGPS). Although being able to improve the positioning accuracy, the complexity associated with both the architecture of multi-layer perceptron networks and its online training algorithms limit the real-time capabilities of this technique. This article, therefore, suggests the use of an alternative ANN architecture. This architecture is based on radial basis function (RBF) neural networks, which generally have simpler architecture and faster training procedures than multi-layer perceptron networks. The INS and GPS data are first processed using wavelet multi-resolution analysis (WRMA) before being applied to the RBF network. The WMRA is used to compare the INS and GPS position outputs at different resolution levels. The RBF-ANN module is then trained to predict the INS position errors and provide accurate positioning of the moving platform. Field-test results have demonstrated that substantial improvement in INS/GPS positioning accuracy could be obtained by applying the combined WRMA and RBF-ANN modules.     

基于神经网络的航天器GPS/INS组合定姿系统

基于GPS和惯性技术的组合导航系统是近年来导航系统的研究热点和主要发展方向.目前基于卡尔曼滤波方法的算法在稳定性、计算量、算法鲁棒性以及系统可观测性等方面仍然存在问题.基于神经网络技术研究了一种新的GPS/INS组合定姿自适应卡尔曼滤波方法,理论分析表明,该方法不但对姿态信息具有较好的估计性能,而且对系统模型的精确性、噪声特性具备良好的鲁棒性.最后,利用模拟数据对所研究算法进行了分析计算,与传统的卡尔曼滤波方法进行了比较、分析,结果表明所设计组合算法在精度、稳定性以及鲁棒性等方面较传统卡尔曼方法具有良好的特性.     

Design and Development of a Real-Time DSP and FPGA-Based Integrated GPS-INS System for Compact and Low Power Applications

Emphasis of the present work is on an elegant real-time solution for GPS/INS integration. Micro-electro mechanical system (MEMS) based inertial sensors are light but not accurate enough for inertial navigation system (INS) applications. An integrated INS/GPS system provides better accuracy compared with either INS or GPS, used individually. This paper describes an improved design and fabrication of a loosely coupled INS-GPS integrated system. The systems currently available use commercial off-the-shelf (COTS) hardware and are, therefore, not optimized for compact, single supply, and low power requirements. In the proposed system, a digital signal processor (DSP) is used for inertial navigation solution and Kalman filter computations. A field programmable gate array (FPGA) is used for creating an efficient interface of the GPS with the DSP. Direct serial interface of the GPS involve tedious processing overhead on the navigation processor. Therefore, a universal asynchronous receiver transmitter (UART) and dual port random axis memory (DPRAM) are created on the FPGA itself. This also reduces the total chip count, resulting in a compact system. The system is designed to give real time processed navigation solutions with an update rate of 100 Hz. All the details of this work are presented.     

Quadratic extended Kalman filter approach for GPS/INS integration

GPS/INS integration system has been widely applied for navigation due to their complementary characteristics. And the tightly coupled integration approach has the advantage over the loosely coupled approach by using the raw GPS measurements, but hence introduces the nonlinearity into the measurement equation of the Kalman filter. So the typical method for navigation using measurements of range or pseudorange is by linearizing the measurements in an extended Kalman filter (EKF). However, the modeling errors of the EKF will cause the bias and divergence problems especially under the situation that the low quality inertial devices are included. To solve this problem, a quadratic EKF approach by adding the second-order derivative information to retain some nonlinearities is proposed in this paper. Simulation results indicate that the nonlinear terms included in the filtering process have the great influence on the performance of integration, especially in the case that the low quality INS is used in the integrated system. Furthermore, a two-stage cascaded estimation method is used, which circumvents the difficulty of solving nonlinear equations and greatly decreases the computational complexity of the proposed approach, so the quadratic EKF approach proposed in this paper is of great value in practice.     

基于对偶四元数的INS/GPS组合导航算法研究

在基于对偶四元数的捷联惯导解算方法的基础上,推导了以惯性系作为导航系的惯导误差方程,在此基础上设计了卡尔曼滤波组合导航算法。通过激光惯导跑车采集数据,进行了仿真分析,试验结果表明,该组合导航算法能有效的消除惯导累积的速度误差和位置误差,相比于目前广泛应用的INS/GPS组合导航算法,本文描述了INS/GPS组合导航的另一种实现方式,获得了相当的精度,具有一定的工程应用价值。     

一种适用于跑步状态的惯性/零速/GPS室内外无缝组合导航定位方法

目前,行人导航定位技术已经深入社会的众多领域,受到诸多学者的广泛关注。针对行人跑步状态,研究了一种惯性/零速/GPS室内外无缝组合导航定位方法。首先提出了可靠的、适用于行人跑步零速检测的方法,有效提高了在行人跑步状态下的零速检测的准确性。针对GPS信号容易受到高楼、高架等环境的干扰及在室内容易完全丢失的特点,提出了基于BP神经网络的GPS可用信号筛选方法,提高了GPS信息的可靠性与精准性。在此基础上,研究了基于可变量测的Kalman滤波器,实现了惯性/零速/GPS信息的有效融合,显著提高了在行人跑步状态下的导航定位精度。试验结果表明,所提出的这种适用于跑步状态的惯性/零速/GPS室内外无缝组合导航定位方法的平均定位误差可减小到行人跑步总里程的1%以内。     

Analysis of upgraded GPS internal Kalman filter

GPS receivers with provisions for inertial navigation system (INS) aiding are designed with internal Kalman filters that model generic INSs and process the basic GPS pseudorange and deltarange (range-rate) data to produce an output of inertially-smoothed, “GPS-derived” position and velocity. These Kalman filters model only the basic nine INS errors (position, velocity, and tilt) and do not model any INS gyro or accelerometer errors. It was found that a significant performance improvement could be achieved under conditions of degraded GPS satellite availability by augmenting this type of filter with the six INS gyro and accelerometer bias errors. It is, therefore, recommended that serious consideration be given to incorporating these states into the design of the GPS internal Kalman filter     

卡尔曼滤波在某型组合导航系统模拟器中的应用

为提高某型GPS／INS组合导航系统模拟器模拟数据的真实性和飞行软件包、GPS模拟器、组合导航系统模拟器三者交联的有效性,在该模拟器中设计了卡尔曼滤波器。文中在介绍模拟器工作原理的基础上,建立了GPS／INS位置与速度组合方式下的卡尔曼滤波器的状态方程和量测方程,用U-D分解法建立了卡尔曼滤波方程,给出了纯惯导及组合后系统的位置与速度误差仿真曲线,并对仿真结果进行了系统测试,最后与其它模拟器进行了组网导航训练测试。     

Multipath-adaptive GPS/INS receiver

Multipath interference is one of the contributing sources of errors in precise global positioning system (GPS) position determination. This paper identifies key parameters of a multipath signal, focusing on estimating them accurately in order to mitigate multipath effects. Multiple model adaptive estimation (MMAE) techniques are applied to an inertial navigation system (INS)-coupled GPS receiver, based on a federated (distributed) Kalman filter design, to estimate the desired multipath parameters. The system configuration is one in which a GPS receiver and an INS are integrated together at the level of the in-phase and quadrature phase (I and Q) signals, rather than at the level of pseudo-range signals or navigation solutions. The system model of the MMAE is presented and the elemental Kalman filter design is examined. Different parameter search spaces are examined for accurate multipath parameter identification. The resulting GPS/INS receiver designs are validated through computer simulation of a user receiving signals from GPS satellites with multipath signal interference present The designed adaptive receiver provides pseudo-range estimates that are corrected for the effects of multipath interference, resulting in an integrated system that performs well with or without multipath interference present.     

GPS/INS integration on the Standoff Land Attack Missile (SLAM)

The Standoff Land Attack Missile (SLAM) is a worldwide, all-weather, precision-strike weapon system deployed from carrier-based aircraft. In the primary mode of operation, target location and other mission data are generated from intelligence sources available on the aircraft carrier and loaded into the missile prior to aircraft takeoff. After missile launch, the SLAM inertial navigation system (INS) guides the missile along the planned trajectory. Updating the missile INS from the Global Positioning System (GPS) during flight provides precise midcourse navigation and enhances target acquisition by accurate, on-target pointing of the SLAM Maverick seeker. The GPS/INS avionics and software integration used for SLAM are described in detail, along with some of the design tradeoffs that led to the approach. The avionics configuration integrates the Harpoon midcourse guidance unit, which includes a strapdown inertial sensor package and digital processor, with a Rockwell-Collins single-channel, sequential GPS receiver processor unit (RPU), a derivative of the GPS phase-III user equipment. In addition to the GPS receiver elements the RPU contains the navigation processor, which executes the SLAM navigation, Kalman filter algorithms, and other guidance algorithms including seeker pointing. Flight-test results of the SLAM GPS-aided INS are also included     

Integration of GPS and low cost INS for pedestrian navigation aided by building layout

In outdoor environments, GPS is often used for pedestrian navigation by utilizing its signals for position computation, but in indoor or semi-obstructed environments, GPS signals are often unavailable. Therefore, pedestrian navigation for these environments should be realized by the integration of GPS and inertial navigation system （INS）. However, the lowcost INS could induce errors that may result in a large position drift. The problem can be minimized by mounting the sensors on the pedestrian＇s foot, using zero velocity update （ZUPT） method with the standard navigation algorithm to restrict the error growth. However, heading drift still remains despite using ZUPT measurements since the heading error is unobservable. Also, tbot mounted INS suffers from the initialization ambiguity of position and heading from GPS. In this paper, a novel algorithm is developed to mitigate the heading drift problem when using ZUPT. The method uses building lay- out to aid the heading measurement in Kalman filter, and it could also be combined for the initial- ization. The algorithm has been investigated with real field trials using the low cost Microstrain 3DM-GX3-25 inertial sensor, a Leica GS10 GPS receiver and a uBlox EVK-6T GPS receiver. It could be concluded that the proposed method offers a significant improvement in position accuracy for the long period, allowing pedestrian navigation for nearly40 min with mean position error less than 2.8 m. This method also has a considerable effect on the accuracy of the initialization.     

Balloon gravimetry using GPS and INS

Measurement of the horizontal components of gravity at altitude using balloon-borne instrumentation consisting of a Global Positioning System (GPS) receiver and a strapdown inertial navigation system (INS) is discussed. GPS data are to be used primarily to determine the total inertial acceleration of the balloon, while the INS accelerometers sense all nongravitational accelerations. A covariance analysis based on the Kalman filter shows that conventional gravity estimation from GPS-aided INS data is possible only if external attitude updates are also available. An alternative technique is explored that attempts to estimate at least part of the gravitational spectrum without modeling the gravity disturbance as a state variable or relying on external attitude updates, while, at the same time, admitting uncorrected (long-wavelength) attitude errors. Simulations based on a model for typical balloon motion are used to discuss this possibility     

Fuzzy corrections in a GPS/INS hybrid navigation system

A new concept regarding GPS/INS integration, based on artificial intelligence, i.e. adaptive neuro-fuzzy inference system (ANFIS) is presented. The GPS is used as reference during the time it is available. The data from GPS and inertial navigation system (INS) are used to build a structured knowledge base consisting of behavior of the INS in some special scenarios of vehicle motion. With the same data, the proposed fuzzy system is trained to obtain the corrected navigation data. In the absence of the GPS information, the system will perform its task only with the data from INS and with the fuzzy correction algorithm. This paper shows, using Matlab simulations, that as long as the GPS unavailability time is no longer than the previous training time and for the scenarios a priori defined, the accuracy of trained ANFIS, in absence of data from a reference navigation system, is better than the accuracy of stand-alone INS. The flexibility of model is also analyzed.     

基于RTS滤波的GPS+BDS 非差非组合PPP/INS紧组合模型

GPS高精度定位技术在动态复杂环境中,其定位精度、可靠性和连续性因卫星信号频繁失锁而变差。为此,提出了采用基于RTS滤波(Rauch-Tung-Striebel Filter)的GPS+BDS非差非组合PPP(Precise Point Positioning)与INS(Inertial Navigation System)紧组合模型的策略来克服GPS在动态定位中的弱点。其中,采用GPS+BDS双系统观测数据,可提高PPP解算中的可用卫星数,改善星站间定位几何强度和提高PPP收敛速度;采用PPP/INS紧组合,利用INS的自主定位特性和短期高精度特性,可有效改善复杂环境下的定位精度和连续性;采用RTS滤波,可进一步提高PPP/INS紧组合性能。首先推导了GPS+BDS非差非组合函数模型、PPP/INS紧组合函数模型和RTS滤波函数模型,然后利用一组车载动态数据,对动态GPS PPP、GPS+BDS PPP、GPS/INS紧组合、GPS+BDS PPP/INS紧组合和基于RTS的GPS+BDS PPP/IMU紧组合的定位、测速和定姿性能进行分析。实验结果表明,该方案可有效提高定位(58%～72%)、测速(74%～82%)和定姿(4%～23%)精度,特别是对卫星失锁期间的定位性能改善尤为明显。     

Optimal nonlinear filtering in GPS/INS integration

The application of optimal nonlinear/non-Gaussian filtering to the problem of INS/GPS integration in critical situations is described. This approach is made possible by a new technique called particle filtering, and exhibits superior performance when compared with classical suboptimal techniques such as extended Kalman filtering. Particle filtering theory is introduced and GPS/INS integration simulation results are discussed.     

Enhancing filter robustness in cascaded GPS-INS integrations

Filter robustness is defined herein as the ability of the Global Positioning System/Inertial Navigation System (GPS-INS) Kalman filter to cope with adverse environments and input conditions, to successfully identify such conditions and to take evasive action. The formulation of two such techniques for a cascaded GPS-INS Kalman filter integration is discussed This is an integration in which the navigation solution from a GPS receiver is used as a measurement in the filter to estimate inertial errors and instrument biases. The first technique presented discusses the handling of GPS position biases. These are due to errors in the GPS satellite segment, and are known to be unobservable. They change levels when a satellite constellation change occurs, at which point they introduce undesirable filter response transients. A method of suppressing these transients is presented. The second technique presented deals with the proper identification of the filter measurement noise. Successful formulation of the noise statistics is a factor vital to the healthy estimation of the filter gains and operation. Furthermore, confidence in the formulation of these statistics can lead to the proper screening and rejection of bad data in the filter. A method of formulating the filter noise statistics dynamically based on inputs from the GPS and the INS is discussed     

一种基于冗余测量的自适应卡尔曼滤波算法

针对目前自适应滤波算法的不足,在测量系统量测噪声方差未知的情况下,设计了一种基于冗余测量的自适应卡尔曼滤波(RMAKF)算法。通过对系统冗余测量值的一阶、二阶差分序列进行有效的统计分析,可以准确估计系统量测噪声统计特性,进而在滤波过程中自适应调节噪声方差阵R,提高滤波精度。以全球定位系统/惯性导航系统(GPS/INS)松组合导航系统为对象进行了仿真实验,结果表明该算法在测量系统噪声特性未知或发生改变时,可对其进行准确估计,在采用低精度惯性器件情况下,滤波结果较其他主要自适应卡尔曼滤波算法有较明显的改进。     

GPS Aided Inertial Navigation

The Global Positioning System is an extremely accurate satellite-based navigation system which, after its completion in 1989, will provide users worldwide, 24 hour. all weather coverage. A joint research project among Boeing, Rockwell-Collins, and Northrop has been completed in which a GPS receiver was integrated with a low-cost strap-down inertial navigation system and a flight computer. A Kalman filter in the latter allows in-fight alignment and calibration of the INS. In addition, feedback from the INS to the GPS receiver improves the system's ability to reacquire satellite signals after outages. The resulting system combines the accuracy of GPS with the jamming immunity and autonomy of inertial navigation. System tests were conducted in which a Boeing owned T-33 jet aircraft was flown through known test pattern to align and calibrate the INS. Earlier tests, including tests against an airborne jammer, were conducted in a modified passenger bus.     

Mahalanobis distance-based fading cubature Kalman filter with augmented mechanism for hypersonic vehicle INS/CNS autonomous integration

Inertial Navigation System/Celestial Navigation System(INS/CNS) integration, especially for the tightly-coupled mode, provides a promising autonomous tactics for Hypersonic Vehicle(HV) in military demands. However, INS/CNS integration is a challenging research task due to its special characteristics such as strong nonlinearity, non-additive noise and dynamic complexity.This paper presents a novel nonlinear filtering method for INS/CNS integration by adopting the emerging Cubature Kalman Filter(C...