Filtering Module on Satellite Tracking

Satellite dynamics and tracking remain important challenges in the context of space exploration and communication systems. Accurate state estimation is essential to maintain reliable orbital motion and system performance. This paper presents a mathematical framework for satellite state estimation based on a linearized model described by radial and angular states. The model incorporates two types of measurement noise corresponding to range and scaled angular deviations, which are assumed to be mutually independent with known covariance structures. The estimation problem is formulated using the Kalman filter, together with the associated Algebraic Riccati Equation (ARE), leading to both time-varying and steady-state solutions. In addition, a micro-Kalman filter ($\mu$KF) formulation is considered and compared with the classical Kalman filter, as well as with the extended Kalman filter (EKF), unscented Kalman filter (UKF), and an adaptive Kalman filter under a unified simulation setup. The results demonstrate that the proposed $\mu$KF achieves estimation performance nearly identical to that of the classical Kalman filter and its variants, with small and bounded estimation errors. The mean square estimation error (MSEE) remains low for all state variables under both noise configurations, confirming the effectiveness of the proposed approach for linear Gaussian systems.