Optimal Finite Difference Angular Velocity Estimation for Spacecraft

This paper presents a practical, computationally efficient approach to spacecraft angular velocity estimation using the finite difference (FD) differentiation of star tracker attitude measurements. Intended for gyro-free applications such as within the star tracker processors themselves, this technique is not reliant on external sensors. Although prior studies have proposed similar finite difference techniques, this study provides a more accurate and rigorous model of angular velocity covariance. Additionally, we derive an analytical model of optimal measurement timing to balance noise and bias in the finite difference estimates. A series of simulations validates the revised covariance models and benchmarks the performance of the finite difference rate estimator against a conventional Multiplicative Extended Kalman Filter (MEKF). Although the FD estimates show significant latency-induced bias, the standard deviation of the measurements are improved by 40% or more compared to the MEKF.