[1] EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159 Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm EGM2008 vertical deflections over USA and Australia are within ±11 to ±13 arc-seconds of independent astrogeodetic values These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models EGM2008 performs equally well with other GRACE-based gravitational models in orbit computations Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, asingle global model may satisfy the requirements of a very wide range of applications

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2011JB008916

The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)

In-car positioning and navigation has been a killer application for Global Positioning System (GPS) receivers, and a variety of electronics for consumers and professionals have been launched on a large scale. Positioning technologies based on stand-alone GPS receivers are vulnerable and, thus, have to be supported by additional information sources to obtain the desired accuracy, integrity, availability, and continuity of service. A survey of the information sources and information fusion technologies used in current in-car navigation systems is presented. The pros and cons of the four commonly used information sources, namely, 1) receivers for radio-based positioning using satellites, 2) vehicle motion sensors, 3) vehicle models, and 4) digital map information, are described. Common filters to combine the information from the various sources are discussed. The expansion of the number of satellites and the number of satellite systems, with their usage of available radio spectrum, is an enabler for further development, in combination with the rapid development of microelectromechanical inertial sensors and refined digital maps.

In-Car Positioning and Navigation Technologies—A Survey

This newly revised and greatly expanded edition of the popular Artech House book Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems offers you a current and comprehensive understanding of satellite navigation, inertial navigation, terrestrial radio navigation, dead reckoning, and environmental feature matching . It provides both an introduction to navigation systems and an in-depth treatment of INS/GNSS and multisensor integration. The second edition offers a wealth of added and updated material, including a brand new chapter on the principles of radio positioning and a chapter devoted to important applications in the field. Other updates include expanded treatments of map matching, image-based navigation, attitude determination, acoustic positioning, pedestrian navigation, advanced GNSS techniques, and several terrestrial and short-range radio positioning technologies. The book shows you how satellite, inertial, and other navigation technologies work, and focuses on processing chains and error sources. In addition, you get a clear introduction to coordinate frames, multi-frame kinematics, Earth models, gravity, Kalman filtering, and nonlinear filtering. Providing solutions to common integration problems, the book describes and compares different integration architectures, and explains how to model different error sources. You get a broad and penetrating overview of current technology and are brought up to speed with the latest developments in the field, including context-dependent and cooperative positioning. DVD Included: Features eleven appendices, interactive worked examples, basic GNSS and INS MATLAB simulation software, and problems and exercises to help you master the material.

Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Second Edition

Adaptive unscented Kalman filtering for state of charge estimation of a lithium-ion battery for electric vehicles

Because of their rapid maneuverability, extended operational range, and improved personnel safety, unmanned aerial vehicles (UAVs) with vision-based systems have great potential for monitoring, detecting, and fighting forest fires. Over the last decade, UAV-based forest fire fighting technology has shown increasing promise. This paper presents a systematic overview of current progress in this field. First, a brief review of the development and system architecture of UAV systems for forest fire monitoring, detection, and fighting is provided. Next, technologies related to UAV forest fire monitoring, detection, and fighting are briefly reviewed, including those associated with fire detection, diagnosis, and prognosis, image vibration elimination, and cooperative control of UAVs. The final section outlines existing challenges and potential solutions in the application of UAVs to forest firefighting.

A survey on technologies for automatic forest fire monitoring, detection, and fighting using unmanned aerial vehicles and remote sensing techniques

After reviewing the two main approaches of adaptive Kalman filtering, namely, innovation-based adaptive estimation (IAE) and multiple-model-based adaptive estimation (MMAE), the detailed development of an innovation-based adaptive Kalman filter for an integrated inertial navigation system/global positioning system (INS/GPS) is given. The developed adaptive Kalman filter is based on the maximum likelihood criterion for the proper choice of the filter weight and hence the filter gain factors. Results from two kinematic field tests in which the INS/GPS was compared to highly precise reference data are presented. Results show that the adaptive Kalman filter outperforms the conventional Kalman filter by tuning either the system noise variance–covariance (V–C) matrix `Q' or the update measurement noise V–C matrix `R' or both of them.

Adaptive Kalman Filtering for INS/GPS

SUMMARY The fast Fourier transform (FFT) technique is a very powerful tool for the efficient evaluation of gravity field convolution integrals It can handle heterogeneous and noisy data, and thus presents a very attractive alternative to the classical, time consuming approaches, provided gridded data are available This paper reviews the mathematics of the FFT methods as well as their practical problems, and presents examples from physical geodesy where the application of these methods is especially advantageous The spectral evaluation of Stokes’, Vening Meinesz’ and Molodensky’s integrals, least-squares collocation in the frequency domain, integrals for terrain reductions and for airborne gravity gradiometry , and the computation of covariance and power spectral density functions are treated in detail Numerical examples illustrate the efficiency and accuracy of the FFT methods Key words: FFT, physical geodesy, spectral methods 1 INTRODUCTION Physical geodesy is the branch of geodesy which uses measured gradients of the anomalou6gravity potential T to determine a unique and coherent representation of the terrestrial gravity field at the Earth’s surface and in outer space The anomalous potential T is the difference between the actual gravity potential of the Earth and the reference potential of an ellipsoid with the same mass, flattening, and angular rotation rate as the Earth An approximation of T is needed to model geodetic measurements, to predict perturbations of satellite orbits, to determine global ocean circulation patterns, to assist global geophysics, and to support oil and mineral exploration In recent years, the amount of data available for the solution of this problem has increased dramatically, both in quantity and in type This has made the data processing problems more severe and has created a demand for efficient numerical solutions Since much of the data is available in gridded form, the use of fast spectral techniques was clearly appropriate Progress in the application of these methods to geodetic problems has been rapid during the last three years and it is almost certain that, because of their efficiency and accuracy, they will become standard procedures for a number of applications However, it has also become clear that geodetic and, more generally, geophysical data often present specific problems not usually encountered in typical electrical engineering applications The problems are with the heterogeneity of the data, the complicated surface on which they are given, the uneven spatial distribution, and the non-uniformity of the data noise This paper will discuss the use of

The use of FFT techniques in physical geodesy

In this paper, the development and testing of an airborne fully digital multi-sensor system for digital mapping data acquisition is presented. The system acquires two streams of data, namely, navigation (georeferencing) data and imaging data. The navigation data are obtained by integrating an accurate strapdown inertial navigation system with a differential GPS system (DGPS). The imaging data are acquired by two low-cost digital cameras, configured in such a way so as to reduce their geometric limitations. The two cameras capture strips of overlapping nadir and oblique images. The GPS/INS-derived trajectory contains the full translational and rotational motion of the carrier aircraft. Thus, image exterior orientation information is extracted from the trajectory, during post-processing. This approach eliminates the need for ground control (GCP) when computing 3D positions of objects that appear in the field of view of the system imaging component. Two approaches for calibrating the system are presented, namely, terrestrial calibration and in-flight calibration. Test flights were conducted over the campus of The University of Calgary. Testing the system showed that best ground point positioning accuracy at 1:12,000 average image scale is 0.2 m (RMS) in easting and northing and 0.3 m (RMS) in height. Preliminary results indicate that major applications of such a system in the future are in the field of digital mapping, at scales of 1:5000 and smaller, and in the generation of digital elevation models for engineering applications.

Digital image georeferencing from a multiple camera system by GPS/INS

The accelerometer and gyro sensor errors of a Strapdown Inertial Navigation System (SINS) consist of two parts: a deterministic part and a random part. The deterministic part includes biases and scale factors, which are determined by calibration and then removed from the raw measurements. The random part is correlated over time and is basically due to the variations in the SINS sensor bias terms. Therefore, these errors are modeled stochastically so that they can be included in the SINS error model. For most of the navigation-grade SINS systems, a first-order Gauss-Markov model with a fairly large correlation time is usually used to describe the random errors associated with inertial sensors. By studying the autocorrelation sequences of the noise components at the outputs of inertial sensors, we have determined that a first-order Gauss-Markov is not adequate to model such noise behavior. This paper offers a new method to model the inertial sensor noise as a higher order autoregressive (AR) process and adaptively estimates the AR model parameters. Three different methods of determining the AR model parameters are investigated, namely: the Yule-Walker (autocorrelation) method, the covariance method and the Burg’s method. The three algorithms were tested with different AR model orders with real SINS static data. The results showed that the Burg’s method gives the minimum prediction mean square estimation error and hence this method was used for generating the applied AR models. In this paper, the current algorithms for modeling inertial sensor errors are introduced. The different algorithms for AR modeling are discussed and their results are presented. The results after applying the Burg’s AR models with different orders are also analyzed.

Modeling Inertial Sensor Errors Using Autoregressive (AR) Models

An algorithm for processing strapdown inertial data in an earth-fixed Cartesian frame is developed in this paper. It is compared with the standard algorithm that uses the local-level frame and the geographic coordinate system for the model formulation. A general formulation of the modeling equations for the two approaches is given, and the linearization of the equations and the formulation of the appropriate Kalman filter are outlined. The derivation of the reference gravity model for both frames is briefly discussed, and numerically efficient formulas for the model's computation are given. In the case of the Cartesian algorithm, this leads to new formulas for all three components of the gravity vector. Real data are used to compare the two algorithms and to show that the accuracy is the same in both cases, but that the Cartesian formulation is about 30 percent more efficient.

K. P. Schwarz

Papers

Adaptive Kalman Filtering for INS/GPS

The use of FFT techniques in physical geodesy

Digital image georeferencing from a multiple camera system by GPS/INS

Modeling Inertial Sensor Errors Using Autoregressive (AR) Models

A Strapdown Inertial Algorithm Using an Earth-Fixed Cartesian Frame