This book introduces readers to the fundamentals of estimation and dynamical system theory, and their applications in the field of multi-source information fused autonomous navigation for spacecraft. The content is divided into two parts: theory and application. The theory part (Part I) covers the mathematical background of navigation algorithm design, including parameter and state estimate methods, linear fusion, centralized and distributed fusion, observability analysis, Monte Carlo technology, and linear covariance analysis. In turn, the application part (Part II) focuses on autonomous navigation algorithm design for different phases of deep space missions, which involves multiple sensors, such as inertial measurement units, optical image sensors, and pulsar detectors. By concentrating on the relationships between estimation theory and autonomous navigation systems for spacecraft, the book bridges the gap between theory and practice. A wealth of helpful formulas and various types of estimators are also included to help readers grasp basic estimation concepts and offer them a ready-reference guide.
Author(s): Dayi Wang, Maodeng Li, Xiangyu Huang, Xiaowen Zhang
Series: Space Science and Technologies
Edition: 1
Publisher: Springer
Year: 2020
Language: English
Pages: 352
Tags: spacecraft, autonomous, space exploration
Series Editor’s Preface
Preface
Acknowledgements
Contents
About the Authors
Acronyms
1 Introduction
1.1 Autonomous Navigation Technology
1.1.1 Inertial Navigation
1.1.2 Autonomous Optical Navigation
1.1.3 Autonomous Pulsar-Based Navigation
1.2 Multi-source Information Fusion Technology
1.2.1 Definition of Multi-source Information Fusion
1.2.2 Classification of Multi-source Information Fusion Technologies
1.2.3 Multi-source Information Fusion Methods
1.3 Autonomous Navigation Technology Based on Multi-source Information Fusion
1.3.1 Research and Application Progress
1.3.2 Necessity and Advantages
1.4 Outline
References
2 Point Estimation Theory
2.1 Basic Concepts
2.2 Common Parameter Estimators
2.2.1 MMSE Estimation
2.2.2 ML Estimator
2.2.3 Maximum a Posteriori (MAP) Estimator
2.2.4 Weight Least-Square (WLS) Estimator
2.3 Closed Form Parameter Estimators
2.3.1 Linear Estimator
2.3.2 MMSE Estimator for Jointly Gaussian Distribution
2.3.3 Estimation Algorithms for Linear Measurement Equation
2.4 State Estimation Algorithms in Dynamic Systems
2.4.1 Recursive Bayesian Estimation
2.4.2 Kalman Filtering
2.4.3 Extended Kalman Filtering
2.4.4 Unscented Kalman Filtering
2.4.5 Constrained Kalman Filtering
2.5 Brief Summary
References
3 Estimation Fusion Algorithm
3.1 Linear Fusion Models and Algorithms
3.1.1 Linear Unified Model
3.1.2 Fusion Algorithm from the Linear Unified Model
3.1.3 Covariance Intersection Algorithm in the Distributed Fusion
3.2 Centralized-Fusion Kalman Filtering for a Dynamic System
3.2.1 Parallel Filtering
3.2.2 Sequential Filtering
3.2.3 Data Compression Filtering
3.3 Distributed-Fusion Kalman Filtering for a Dynamic System
3.3.1 Standard Distributed Kalman Filtering
3.3.2 Covariance Intersection Algorithm
3.3.3 Federated Filtering Algorithm
3.4 Brief Summary
References
4 Performance Analysis
4.1 Observability of Linear System
4.1.1 Observability Analysis of LTI Systems
4.1.2 Observability Analysis of LTV Systems
4.2 Observability of Nonlinear Systems
4.2.1 Definition and Criteria of the Observability of Nonlinear Systems
4.2.2 Observability Analysis Based on Singular Value Decomposition
4.3 Degree of Observability for Autonomous Navigation System
4.3.1 Observability Gramian Based Method
4.3.2 Error Covariance-Based Method
4.4 Monte Carlo Method
4.5 Technique of Linear Covariance Analysis
4.6 Brief Summary
References
5 Time and Coordinate Systems
5.1 Time Systems
5.1.1 Definition of Time System
5.1.2 Definition and Conversion of Julian Date
5.2 Coordinate Frames
5.2.1 Definition of Reference Coordinate System
5.2.2 Coordinate Transformation
5.3 Ephemeris of Navigational Celestial Bodies
5.3.1 Calculation of High-Precision Celestial Ephemerides
5.3.2 Calculation of Simple Celestial Ephemerides
5.4 Brief Summary
References
6 Dynamic Models and Environment Models
6.1 Orbit Dynamics Model
6.1.1 Orbital Perturbation Model
6.1.2 Spacecraft Orbit Dynamics Model
6.2 Attitude Kinematics Model
6.2.1 Description of Attitude
6.2.2 Attitude Kinematics Equation
6.3 Mars Environment Model
6.3.1 Mars Ellipsoid Model
6.3.2 Mars Gravitation Field Model
6.4 Asteroid Environment Model
6.4.1 Asteroid 3D Model
6.4.2 Asteroid Gravitation Field Model
6.5 Brief Summary
References
7 Inertial Autonomous Navigation Technology
7.1 Measurement Equation
7.1.1 Gyroscope Measurement Equation
7.1.2 Accelerometer Measurement Equation
7.2 Differential Equation of Strapdown Inertial Navigation
7.3 Strapdown Inertial Navigation Update Equations
7.3.1 Attitude Update Equation
7.3.2 Inertial Velocity Update Equation
7.3.3 Inertial Position Update Equation
7.4 Compensation for Coning and Sculling Effects
7.4.1 Coning Effect Compensation
7.4.2 Sculling Effect Compensation
7.5 Calibration and Error Compensation of Inertial Devices
7.6 Numerical Simulation
7.7 Brief Summary
References
8 Optical Autonomous Navigation Technology
8.1 Principle of Optical Autonomous Navigation
8.1.1 Center-Point Information
8.1.2 Edge-Point Information
8.1.3 Feature-Point Information
8.2 Optical Imaging Sensor
8.2.1 Heliocentric Transfer Phase
8.2.2 Approaching Phase
8.2.3 Orbiting Phase
8.2.4 Soft Landing Phase
8.2.5 Impact Phase
8.3 Selection Criteria of Candidate Navigation Beacons
8.3.1 Natural Celestial Bodies as Navigation Beacons
8.3.2 Surface Feature Points as Navigation Beacons
8.4 Measurement Equations for Optical Autonomous Navigation
8.4.1 Measurement Equations Based on the Apparent Radius Information of Large Celestial Bodies
8.4.2 Measurement Equations Based on LOS Direction Information
8.5 Navigation Beacon Planning Based on Geometric Observability Analysis
8.5.1 Geometric Observability Analysis
8.5.2 Optimal Navigation Beacon Planning
8.6 Navigation Filtering Algorithm
8.6.1 Batch Filtering Algorithm
8.6.2 Kalman Filtering Algorithm
8.7 Numerical Simulation
8.7.1 Optical Navigation of the Transfer Phase
8.7.2 Optical Navigation of the Approaching Phase
8.7.3 Optical Navigation of the Orbiting Phase
8.8 Brief Summary
References
9 Optical/Pulsar Integrated Autonomous Navigation Technology
9.1 Review of Optical Autonomous Navigation
9.2 Pulsar-Based Autonomous Navigation
9.2.1 Basic Principle of Pulsar-Based Autonomous Navigation
9.2.2 Scheme and Process of Pulsar-Based Autonomous Navigation
9.2.3 Time-Scale Transformation of Photon TOA
9.2.4 Space Scale Transformation of Photon TOA
9.2.5 Measurement Equation of Pulsar-Based Autonomous Navigation
9.3 Navigation Beacon Planning Algorithm
9.3.1 Navigation Beacon Planning Algorithm Based on Geometric Observability Analysis
9.3.2 Navigation Beacon Planning Algorithm Based on Dynamic Observability Analysis
9.4 Integrated Autonomous Navigation Filtering
9.5 Numerical Simulations
9.5.1 Autonomous Navigation Based on Fused Asteroid and Pulsar Observations at the Deep-Space Transfer Phase
9.5.2 XNAV/Optical Integrated Navigation During the Approach Phase
9.5.3 XNAV/Optical Integrated Navigation During the Surrounding Phase
9.6 Brief Summary
References
10 Altimeter and Velocimeter-/Optical-Aided Inertial Navigation Technology
10.1 Soft Landing Flight Process
10.2 Autonomous Navigation System for Soft Landing
10.2.1 System Composition and Workflow
10.2.2 Inertial Measurement Unit (IMU)
10.2.3 Integrated Altimeter/Velocimeter Sensor
10.2.4 Optical Imaging Sensor
10.3 Measurement Equation
10.3.1 Ranging Measurement Equation
10.3.2 Velocity Measurement Equation
10.3.3 Image-Based Measurement Equation
10.4 Observability Analysis
10.4.1 Altimeter-/Velocimeter-Aided Inertial Navigation
10.4.2 Optical-Aided Inertial Navigation
10.5 Fusion Navigation Method
10.5.1 IMU + Ranging/Velocity Measurement for 3D Position and Velocity Correction
10.5.2 IMU + Ranging/Velocity Measurement for Altitude and Velocity Correction
10.5.3 IMU + Imaging for 3D Position and Velocity Correction
10.6 Simulation Application Examples
10.6.1 Lunar Soft Landing Navigation
10.6.2 Mars Soft Landing Navigation
10.7 Brief Summary
References
11 Simulation Testing Techniques for Autonomous Navigation Based on Multi-source Information Fusion
11.1 Ground Test of Optical and Pulsar Integrated Autonomous Navigation
11.1.1 Scheme Design
11.1.2 System Composition
11.1.3 Test Cases
11.2 Ground Test of Altimeter and Velocimeter Aided Inertial Navigation
11.2.1 Scheme Design
11.2.2 System Composition
11.2.3 Test Case
11.3 Brief Summary
12 Prospect for Multi-source Information Fusion Navigation
12.1 Development of Multi-source Information Fusion Navigation Scheme
12.1.1 Fusion Navigation Based on Optical Measurement
12.1.2 Fusion Navigation Based on Inertial Measurement
12.1.3 Autonomous Navigation Based on Deep-Space Navigation Constellation
12.2 Development of Information Fusion Technology
12.2.1 Development of Fusion Architecture
12.2.2 Development of Filter and Fusion Algorithms
12.3 Development of Fused Autonomous Navigation Sensors
12.4 Conclusion
References
Appendix A Constants and Unit Conversion
A.1 Constants
A.2 Unit Conversion
A.2.1 Time Conversion
A.2.2 Angle Conversion
Appendix B Matrix-Related Knowledge
B.1 Matrix Trace
B.2 Kronecker Operator
B.3 vec Operator
B.4 Matrix Calculus [4, 6
B.5 Cross-Product Algorithm
B.6 Matrix Equalities
B.7 Matrix Inequalities
Appendix C Probability-Related Knowledge
C.1 Basic Concepts
C.1.1 Probability Axioms
C.1.2 Joint Probability and Conditional Probability
C.1.3 Bayes Rule and Total Probability Formula
C.1.4 Independence and Conditional Independence
C.2 A Single Random Variable
C.2.1 Distribution Function and Density Function
C.2.2 Conditional Distribution
C.2.3 Mean and Variance
C.3 Binary Random Variable
C.3.1 Joint Distribution Function and Density Function
C.3.2 Conditional Distribution
C.3.3 Relationship Between Covariance and Two Random Variables
C.4 Random Vector
C.4.1 Joint Distribution Function and Density Function
C.4.2 Formulas Related to Conditional Probability
C.4.3 Statistical Properties of a Single Random Vector
C.4.4 Statistical Properties of Two Random Vectors
C.5 Gaussian Random Variable
C.5.1 Definition
C.5.2 Joint Gaussian Distribution
Appendix D Constrained Optimization
Appendix E Coordinate Transformation of Optical Imaging Sensor
Appendix F Mathematical Terms
