Methods and Technologies for Measuring the Earth’s Gravity Field Parameters

Description

This book offers extensive information on the operation of gravimeters, including airborne, marine and terrestrial ones, and on the associated data processing methods such as optimal and adaptive filtering, smoothing, structural and parametric identification. Further, it describes specific features relating to the study of the gravitational field in remote areas of the Earth, with the necessary modifications of equipment and software for all-latitude applications. Findings from gravity studies in such remote areas are also presented. Advanced methods for studying the gravitational field, including those for simultaneous determination of gravity anomalies and deflection of the vertical are described and analyzed in detail. Gravity gradiometers and cold atom gravimeters are also covered. Last but not least, the book deals with the development of Earth’s gravity field models and their various applications, including map-aided navigation, with a special attention to model accuracy estimation. Gathering research findings and best practice recommendations relating to Earth’s gravity field measurements, collected by a team of researchers and professionals, the book offers a unique guide for engineers, scientists and graduate students dealing with terrestrial, marine and airborne gravimetry.  It will also help other specialists involved in developing and using navigation systems in practice, including designers of gravimetric equipment and navigators. Preface About the Book Contents Abbreviations 1 Instruments for Measuring Gravity 1.1 Absolute Gravimeters 1.1.1 Types and Designs of Absolute Ballistic Gravimeters 1.1.2 Sources of Uncertainties and Corrections in Measurements with Absolute Ballistic Gravimeters 1.1.3 Metrological Assurance of Absolute Gravimeters 1.1.4 International Comparisons of Absolute Gravimeters 1.1.5 Comparisons of Absolute Gravimeters: The Results 1.1.6 Practical Applications of Absolute Free-Fall Acceleration Measurements 1.1.7 Conclusions 1.2 Chekan-Series Relative Gravimeters 1.2.1 Gravimeter Parts 1.2.2 Gravimeter Sensing Element 1.2.3 Biaxial Gyro Platform of the Gravimeter 1.2.4 Mathematical Model of the Gravimeter Sensing Element 1.2.5 Algorithms for Gyro Platform Correction 1.2.6 Calibration and Verification of the Chekan-AM Gravimeter 1.2.7 Conclusions 1.3 GT-2 Relative Gravimeters 1.3.1 Gravimeter Parts 1.3.2 Gravimeter Sensing Element 1.3.3 Circuit for Integrated Correction of the Gyro Platform Position 1.3.4 Mathematical Models of the Channels of Inertial Sensing Elements 1.3.5 Analysis of the Gravimeter Main Errors 1.3.6 Main Tasks of the Gravimeter Central Processing Unit 1.3.7 Conclusions References 2 Data Processing Methods for Onboard Gravity Anomaly Measurements 2.1 Chekan-Series Gravimeter Data Acquisition and Processing Software 2.1.1 Calibration and Diagnostics of the Gravimeter Equipment 2.1.2 Real-Time Algorithms and Software 2.1.3 Marine Gravity Measurement Processing 2.1.4 Airborne Gravity Measurement Processing 2.1.5 Postprocessing of Gravimetric Survey Data 2.1.6 Conclusion 2.2 Data Processing in GT-2 Airborne Gravimeters 2.2.1 Airborne Gravimetry Software 2.2.2 Software for GNSS Solutions 2.2.3 Software for INS/GNSS Integration 2.2.4 Software for the Solution of the Basic Gravimetry Equation 2.2.5 Conclusion 2.3 Optimal and Adaptive Filtering and Smoothing Methods for Onboard Gravity Anomaly Measurements 2.3.1 General Formulation and Solution of Optimal Filtering and Smoothing Problems 2.3.2 Optimal Filtering and Smoothing Algorithms for Onboard Gravity Anomaly Measurements 2.3.3 Stationary Estimation Algorithms and Their Performance Analysis 2.3.4 Model and Parametric Identification of Gravity Anomaly and Measurement Errors Using Onboard Gravity Measurements 2.3.5 The Results of Using Adaptive Filtering and Smoothing Algorithms in Airborne Gravity Anomaly Measurements 2.3.6 Conclusion 2.4 Suboptimal Smoothing in Marine Gravimetric Surveys Using GT-2M Gravimeters 2.4.1 Constant-Delay Optimal and Suboptimal Smoothers for Continuous-Time Systems 2.4.2 Suboptimal Gravimetric Filter 2.4.3 Frequency Properties of the Suboptimal Gravimetric Filter 2.4.4 Results of the Experimental Data Processing 2.4.5 Conclusion 2.5 Using Spherical Wavelet Expansion to Combine Airborne Gravimetry Data and Global Gravity Field Model Data 2.5.1 Spherical Wavelet Expansion and Multiscale Representation of the Anomalous Gravity Field 2.5.2 Technique of Local Gravity Anomaly Determination from Airborne Gravimetry Data and Global Gravity Field Model Data Using Multiscale Representation 2.5.3 Multiscale Representation of Gravity Anomaly Based on Combination of Airborne Gravimetry Data and Global Gravity Field Model Data 2.5.4 Results of the Real Data Processing 2.5.5 Conclusion References 3 Methods for Determination and Calculation of Deflections of the Vertical 3.1 DOV Determination on a Moving Base 3.1.1 Basic Methods for DOV Determination 3.1.2 Features of DOV Determination on a Moving Base 3.1.3 Classification Criteria of DOV Determination Methods 3.1.4 Qualitative Comparative Analysis of the Methods 3.1.5 Conclusion 3.2 DOV Determination with the Use of an Automated Zenith Telescope 3.2.1 General Principles of Determining Astronomical Coordinates in Geodetic Astronomy 3.2.2 Description of the AZT and Its Principle of Operation 3.2.3 Algorithm for Determining DOV Components Using the AZT and Error Analysis 3.2.4 Field Studies of the AZT Prototype 3.2.5 Conclusion 3.3 Inertial Geodetic Method for DOV Determination 3.3.1 Inertial Geodetic Method Using Positional and Velocity Measurements 3.3.2 Using ZUPT Technology 3.3.3 DOV Determination in High Latitudes 3.3.4 Simulation Results 3.4 Conclusion References 4 Studying the Gravity Field in Hard-to-Reach Areas of the Earth 4.1 State of Knowledge of the Gravity Field in the Arctic 4.1.1 Brief Historical Overview of Russian Gravimetric Surveys in the Arctic 4.1.2 Modern Russian Arctic Airborne Gravimetry 4.1.3 Modern International Arctic Airborne Gravimetry 4.1.4 Conclusions 4.2 The Results of the Gravimetric Surveys with Chekan Gravimeters in Hard-to-Reach Areas 4.2.1 Marine Gravimetric Surveys in the Polar Regions 4.2.2 Regional Airborne Gravimetric Surveys 4.2.3 Carriers Used for Gravimetric Measurements 4.2.4 Conclusions 4.3 GT-2A Gravimeter All-Latitude Versions 4.3.1 Using Multi-antenna GNSS Receivers 4.3.2 Quasi-Geodetic Coordinates 4.3.3 All-Latitude Version of the GT-2A Gravimeter 4.3.4 Method for Calibration of Instrumental Errors of the Gimbal Suspension Angle Sensor 4.3.5 Test and Operation Results 4.3.6 Polar Versions of the GT-2A Gravimeter 4.3.7 Conclusions References 5 Advanced Gravity Field Survey Methods 5.1 Airborne Vector Gravimetry Based on Strapdown Inertial Navigation Systems 5.1.1 Airborne Vector Gravimetry Equations 5.1.2 Airborne Vector Gravimetry Error Equations 5.1.3 Models of Aiding Measurements 5.1.4 Selected Approaches to the Solution of the Airborne Vector Gravimetry Problem 5.1.5 Spectral Analysis of the Airborne Vector Gravimetry Accuracy 5.1.6 Algorithm for Gravity Disturbance Vector Estimation Based on a Local Harmonic Model 5.1.7 Conclusions 5.2 Current State and Outlook for the Development of Instruments for Onboard Measurements of Second Derivatives of Geopotential 5.2.1 Principles and Challenges of Measuring the Second Derivatives of Geopotential 5.2.2 Gradiometers for High-Precision Autonomous Navigation 5.2.3 Gradiometers for Mineral Exploration 5.2.4 Gradiometers for Space Missions 5.2.5 Promising Gravity Gradiometers 5.2.6 Expanding the Scope of Gradiometer Applications 5.2.7 Conclusions 5.3 Current State and Outlook for the Development of Cold-Atom Gravimeters 5.3.1 Basic Physical Principles of Cold-Atom Gravimeters 5.3.2 Sensitivity and Accuracy of the Cold-Atom Gravimeter 5.3.3 Laser Cooling of Atoms 5.3.4 Physical Design of the Atomic Interferometer-Gravimeter 5.3.5 Modern Designs of Atomic Interferometers 5.3.6 Gravimeter Based on Cold Atoms Trapped in an Optical Dipole Trap 5.3.7 Outlook for the Development of Cold-Atom Gravimeters 5.3.8 Conclusions References 6 Earth’s Gravity Field Models and Their Application 6.1 Estimation of Accuracy of Modern Earth’s Gravity Field Models 6.1.1 A Priori Accuracy Estimates 6.1.2 A Posteriori Accuracy Estimates 6.1.3 Estimation of Accuracy of Geoid Height Models 6.1.4 Estimation of Accuracy of the Global Models of the Earth’s Gravity Field in the Arctic 6.1.5 Conclusions 6.2 Using the Earth’s Gravity Field Model in Marine Gravity Measurements 6.2.1 Comparison of Satellite Data with Marine Gravity Measurements 6.2.2 Method for Tying Marine Measurements to the Earth’s Gravity Field Model 6.2.3 Conclusions 6.3 Map-Aided Navigation 6.3.1 Statement and General Solution of Map-Aided Navigation Problem Based on the Nonlinear Filtering Theory 6.3.2 Algorithms Based on Gaussian Approximations 6.3.3 Algorithms Based on Gaussian Sum Approximations 6.3.4 Point Mass Method 6.3.5 Sequential Monte Carlo Methods 6.3.6 Analysis of the Accuracy of Filtering Algorithms 6.3.7 Comparison of Filtering Algorithms 6.3.8 Conclusions 6.4 Estimating the Navigation Informativity of the Earth’s Gravity Field 6.4.1 Choosing a Model of the Earth’s Gravity Field 6.4.2 Methods for Estimating the Navigation Informativity of the Earth’s Gravity Field 6.4.3 Results of Experimental Studies 6.4.4 Conclusions References Appendix