# Optimal Finite Difference Angular Velocity Estimation for Spacecraft

## TL;DR

This paper introduces a new method to estimate spacecraft angular velocity using star tracker data, which is more accurate and efficient than previous approaches.

## Contribution

The paper introduces an analytical model for optimal measurement timing and a more accurate angular velocity covariance model for finite difference estimation.

## Key findings

- The FD estimator reduces measurement standard deviation by 40% or more compared to MEKF.
- Optimal timing analysis balances noise and bias in finite difference estimates.
- Simulations validate improved performance of FD estimation over conventional MEKF.

## Abstract

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.