Pseudorange Kalman Filter for Satellite Orbit Determination (KALMAN)

Pseudorange Kalman Filter satellite orbit determination is an orbit estimation method based on the Kalman filtering algorithm, primarily used for orbit state prediction and correction in satellite navigation systems (such as GPS, BeiDou, etc.). The core concept involves utilizing pseudorange measurement data (approximate distance measurements between satellites and receivers) combined with dynamic models and observation models to estimate satellite orbital parameters through recursive computation. ### Fundamental Principles The Kalman filter models the system through state equations and observation equations. In satellite orbit determination, the state equation typically describes the satellite's motion model, such as orbital dynamic equations considering Earth's gravitational forces, perturbation forces, and other factors. The observation equation is based on pseudorange measurements, reflecting the geometric relationship between satellites and ground receivers. Implementation in code typically involves defining state variables (position, velocity, clock bias) and system matrices. The state transition matrix would incorporate orbital mechanics, while the measurement matrix handles the pseudorange-to-state relationship. ### Implementation Workflow State Prediction: Based on the previous epoch's orbit state and dynamic model, predict current orbital parameters (position, velocity, etc.). This step involves propagating the state vector using numerical integration methods like Runge-Kutta. Measurement Update: Use pseudorange observation data to correct prediction results. Calculate the Kalman gain to adjust weightings, making estimated values closer to the true state. This requires solving the measurement equation and updating the state estimate. Error Covariance Update: Dynamically adjust prediction uncertainty to ensure filter stability. This involves updating the covariance matrix through both prediction and correction phases. Key functions in implementation include state propagation, measurement residual calculation, and covariance matrix management. ### Application Advantages Pseudorange Kalman filtering effectively suppresses observation noise and dynamic model errors, making it suitable for real-time, high-precision satellite orbit determination. It is widely applied in navigation, spacecraft control, and related fields. The algorithm's recursive nature allows for efficient real-time processing with minimal computational overhead.