Nonlinear solver-aided estimation filter based geostationary satellite navigation with available GNSS signals

Abstract

The advancement of geostationary satellite navigation systems is a cornerstone for numerous modern applications, including telecommunications, weather monitoring, and defense systems. Despite their utility, navigating geostationary satellites presents unique challenges due to the nonlinear dynamics of their orbits, orbital perturbations, and the limited geometric diversity of Global Navigation Satellite System (GNSS) signals. Traditional estimation methods, such as the Extended Kalman Filter (EKF), are often inadequate for addressing these challenges, particularly in scenarios involving limited satellite visibility or high noise conditions. This thesis proposes an innovative approach combining nonlinear solvers with adaptive filtering techniques to overcome these limitations, delivering enhanced accuracy and robustness in satellite navigation. The methodology centers around integrating nonlinear solvers, including the Newton-Raphson Method (NRM), Levenberg-Marquardt Algorithm (LMA), and Least Squares Method (LSM), within an Adaptive Extended Kalman Filter (AEKF) framework. This hybrid approach leverages the strengths of both linear and nonlinear estimation methods, incorporating historical data through a configurable window size to balance responsiveness and noise reduction. The adaptive nature of the filter allows dynamic adjustments to varying environmental conditions and measurement noise, making it particularly suitable for constrained scenarios, such as narrow Field of View (FOV) configurations. To evaluate the proposed methodology, extensive simulation scenarios were designed. These scenarios varied in satellite visibility, FOV, and window size parameters, providing a comprehensive assessment of the filter's performance. Key scenarios included wide FOV configurations, narrow FOV setups, and scenarios with varying filter window sizes (N). Performance metrics focused on position and velocity Root Mean Square (RMS) errors, maximum errors, and statistical adherence to the 3-sigma boundary. The results demonstrated significant improvements in both position and velocity estimation accuracy compared to conventional EKF and standalone AEKF methods. For instance, under narrow FOV conditions, the LSM-Aided AEKF consistently maintained errors within acceptable limits, demonstrating robustness against limited satellite geometry and high noise. Specific findings include the following: Position Estimation: The adaptive framework achieved substantial error reductions, with RMS errors significantly lower than those of traditional methods, even in narrow FOV scenarios. For example, under Scenario M, the position RMS errors were approximately 13 meters (X), 20 meters (Y), and 2 meters (Z), highlighting the effectiveness of the adaptive approach. Velocity Estimation: Velocity RMS errors were consistently low, reflecting the filter's capability to track dynamic changes accurately. The integration of nonlinear solvers improved stability during rapid state transitions. Clock Bias Synchronization: The proposed filter maintained robust temporal synchronization, with minimal mean clock bias errors, even under narrow FOV conditions. Additionally, the study explored the impact of filter window size (N) on performance. Scenarios with smaller window sizes provided better responsiveness but higher sensitivity to noise, while larger windows improved noise resilience at the cost of reduced adaptability. A balance was achieved with window sizes around N = 59, which offered a favorable trade-off between accuracy and stability. The thesis also underscores the importance of adaptive capabilities in navigation systems. The integration of nonlinear solvers allows the filter to handle challenging conditions, such as limited satellite visibility and high orbital perturbations. Moreover, the study highlights the potential of machine learning techniques for further enhancing the filter's adaptability, paving the way for future research in intelligent navigation systems. In conclusion, this research contributes to the advancement of geostationary satellite navigation technologies by presenting a robust, adaptive estimation framework. The LSM-Aided AEKF proves to be an effective solution for overcoming the limitations of traditional methods, offering improved accuracy, reliability, and adaptability across a wide range of operational conditions. The findings of this thesis have significant implications for the design and deployment of next-generation satellite navigation systems, enabling more precise and dependable operations in diverse applications.