Precise orbit determination using a single satellite laser ranging system within a single arc for space surveillance and tracking

국문 초록 (Abstract)

본 학위논문은 우주 감시 및 추적을 위해 단일 아크 내 단일 위성 레이저 추적 시스템을 사용하여 정밀궤도결정을 수행하는 소프트웨어와 알고리즘을 개발하고 검증하였다. 위성 레이저 추적 시스템은 레이저를 사용하여 지상국부터 우주 물체까지의 거리를 밀리미터 단위의 정밀도까지 측정하는 지상 관측 도구이다. 일반적으로 위치벡터와 속도벡터로 이루어진 우주 물체의 상태를 추정하는 정밀궤도결정은 우주 감시 및 추적의 핵심이다. 최근 위성 레이저 추적 시스템의 기술 발전으로 우주 감시 및 추적을 위한 활용도가 높아지고, 위성 레이저 추적 시스템을 활용한 정밀궤도결정의 연구 범위가 확대되고 있다. 따라서 본 학위논문의 연구는 우주 감시 및 추적 분야에서 위성 레이저 추적 시스템의 기능을 보다 확장하기 위한 세 가지의 주요 주제로 분류된다.
첫째, 단일 아크 내 단일 위성 레이저 추적 시스템을 통해 관측한 거리 데이터만을 사용하여 정밀궤도결정을 수행하는 새로운 알고리즘을 개발하였다. 단일 아크 내 1차원의 거리 값 만을 사용하는 정밀궤도결정 문제는 간단하지 않다. 이 문제는 가관측성이 제한되어 해가 무한히 존재하기 때문에 일반적인 궤도 결정 알고리즘으로는 합리적인 정확도를 달성하기 어렵다. 이 연구에서 개발된 알고리즘은 이러한 한계를 해결하기 위해 정밀궤도결정 과정에서 생성되는 잔차의 경향성을 기반으로 궤도 결정의 비용 값을 재정의하였다. 실제 데이터를 사용하여 3개의 서로 다른 저궤도 위성에 대한 시뮬레이션을 통해 알고리즘의 유효성을 입증하였다.
둘째, 정확도 문제로 인해 일반적으로 사용되지는 않지만 위성 레이저 추적 시스템은 방위각과 고도각 값을 포인팅 각도로 제공할 수 있다. 이와 같은 각도 정보를 위성 레이저 추적 시스템을 활용한 실시간 정밀궤도결정에서 거리 값과 함께 추가 데이터로 사용하면 제한된 가관측성을 극복하는데 이점이 될 수 있다. 본 연구에서는 위성 레이저 추적 시스템에서 제공하는 거리 및 각도 데이터를 활용한 실시간 정밀궤도결정 알고리즘을 개발하고, 2개의 서로 다른 저궤도 위성에 대해 실제 데이터를 사용하여 호 길이, 샘플링 속도, 데이터 품질이라는 세 가지 기준에 따라 검증하였다.
셋째, 위성 레이저 추적 시스템을 활용한 정밀궤도결정의 보다 고도화되고 다양한 연구를 위해 정밀 동역학 모델, 정밀 관측 모델, 추정 알고리즘을 기반으로 임무에 따른 응용이 가능한 소프트웨어를 개발하였다. 상용 소프트웨어와의 비교 및 실제 데이터를 활용한 검증을 통해 개발 목표가 달성되었음을 확인하고 소프트웨어의 신뢰성을 확보했다.
결과적으로 본 연구는 궤도 결정을 위한 보다 효율적이고 정확한 방법을 제공하며, 우주 관련 임무 운영의 안전성 증대, 비용 절감 및 효율성 향상에 광범위하게 기여할 것이다.

다국어 초록 (Multilingual Abstract)

This dissertation presents the precise orbit determination using a single satellite laser (SLR) ranging system within a single arc for space surveillance and tracking (SST). SLR system is a ground-based observation tool that uses lasers to measure the range from ground stations to space objects with millimeter-level precision. Precise orbit determination (POD), generally estimating the state of a space object, is the core of SST. Recent technological advances in SLR systems have increased their use in POD for SST. Consequently, the scope of POD using SLR systems in SST has expanded through various research.
Therefore, this study is categorized into three primary research to further extend the capabilities of the SLR system on the SST. First, a developed novel algorithm is presented for POD using only SLR range data of single-station and single-arc. The problem addressed, the POD using only 1-dimensional range observations within a single arc, is not straightforward. Because the problem has infinite solutions due to limited observability, general orbit determination algorithms are limited in achieving reasonable accuracy. The algorithm developed in this study redefines the cost value for orbit determination based on the tendency of residuals in the POD process to address these limitations. Simulations of three satellites using real data demonstrate the validity of the algorithm. In all cases, the errors of the two-line element (TLE) data used as the initial values, which have an approximately 3D position error of 1 km and velocity error of 1 m/s, were reduced by tens of meters and cm/s level, respectively.
Second, despite not being commonly used due to accuracy concerns, SLR systems have the potential to provide azimuth and elevation angle values as pointing angles. In real-time POD, the angular data from SLR systems can be an innovative advantage as additional data to overcome the limited observability with only range values. Therefore, a real-time POD algorithm using the range and angle data provided by the SLR system is developed and verified for two satellite cases using real data based on three criteria, which are arc length, sampling rate, and data quality.
Third, for more advanced and diverse research on POD using SLR, it is developed software that can be customized based on precise dynamic model, precise SLR measurement model, and required estimation algorithms. The validation results confirm that the development goals have been met, ensuring the reliability of the software and the research.
Consequently, these studies offer a more efficient and accurate method for orbit determination, with broad implications for improving the safety, cost-efficiency, and effectiveness of space operations.

목차 (Table of Contents)

• Chapter 1 Introduction 1
• 1.1 Research background 1
• 1.2 Objectives of the research 7
• 1.3 Contributions 9
• 1.4 Outlines of the dissertation 11
• Chapter 2 Novel Algorithm for a SS-R Problem 13
• 2.1 R-squared value of the residual (RSR) method 13
• 2.1.1 Bow-tie effect and inadequacies of least squares 15
• 2.1.2 Fourier series fitting and R-squared value 20
• 2.1.3 Cost function of RSR method 22
• 2.2 Proposed RSR POD algorithm 23
• 2.2.1 Grid search method for velocity vector searching 23
• 2.2.2 Least squares method for a SS-R problem 27
• 2.2.3 RSR POD algorithm 28
• 2.3 Numerical simulation 31
• 2.3.1 Initial value data set 34
• 2.3.2 Case 1: Cryosat-2 satellite 37
• 2.3.3 Case 2: Sentinel-3A satellite 44
• 2.3.4 Case 3: Saral satellite 52
• 2.4 Characteristics of the RSR POD algorithm 58
• 2.4.1 Influences of arc length 61
• 2.4.2 Influences of altitude 65
• 2.4.3 Comparison to Kalman filter 66
• Chapter 3 Real-time Precise Orbit Determination 69
• 3.1 Real-time POD strategies with range and angular measurements 69
• 3.1.1 Pointing angle data from SLR system 72
• 3.1.2 Measurement model for angular data 74
• 3.2 Trade-off between robustness and speed 76
• 3.2.1 Extended Kalman filter 77
• 3.2.2 Unscented Kalman filter 78
• 3.2.3 Particle filter 82
• 3.3 Numerical simulation 84
• 3.3.1 Initial value data set 87
• 3.3.2 Measurements data set 88
• 3.3.3 Case 1: Larets satellite 91
• 3.3.4 Case 2: Cryosat-2 satellite 97
• Chapter 4 Development of POD Software using SLR 103
• 4.1 Software configuration 103
• 4.2 Dynamic model 105
• 4.2.1 Gravity field 106
• 4.2.2 Tidal variation in geopotential 108
• 4.2.3 Air drag 111
• 4.2.4 Third body 113
• 4.2.5 Solar radiation pressure 114
• 4.2.6 Earth radiation pressure 116
• 4.2.7 Relativistic effect 118
• 4.2.8 Verification of dynamic model 119
• 4.3 SLR measurement model 124
• 4.3.1 Troposphere 125
• 4.3.2 Tidal displacements 128
• 4.3.3 Relativistic range 132
• 4.3.4 Light time correction 132
• 4.3.5 Center of mass 134
• 4.3.6 Verification of SLR measurement model 138
• 4.4 Estimation algorithm 142
• 4.5 Time and coordinate reference frame 144
• Chapter 5 Conclusions 147
• 5.1 Summary 147
• 5.2 Discussions 152
• References 156

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