Optimal Finite Difference Angular Velocity Estimation for Spacecraft.

Area of Science:

• Spacecraft attitude determination
• Angular velocity estimation
• Sensor fusion

Background:

• Star trackers provide attitude measurements crucial for spacecraft navigation.
• Accurate angular velocity estimation is vital for spacecraft control and stability.
• Gyro-free systems require alternative methods for precise motion sensing.

Purpose of the Study:

• To develop a practical and computationally efficient method for spacecraft angular velocity estimation.
• To improve upon existing finite difference techniques with a more rigorous covariance model.
• To derive an optimal measurement timing strategy for finite difference estimators.

Main Methods:

• Utilizing finite difference (FD) differentiation of star tracker attitude data.
• Developing an accurate and rigorous model for angular velocity covariance.
• Deriving an analytical model for optimal measurement timing to minimize noise and bias.
• Benchmarking FD estimator performance against a Multiplicative Extended Kalman Filter (MEKF) via simulations.

Main Results:

• The finite difference (FD) method demonstrates improved standard deviation in measurements by over 40% compared to the MEKF.
• Simulations validated the revised covariance models for FD-based angular velocity estimation.
• Significant latency-induced bias was observed in FD estimates, necessitating careful timing optimization.

Conclusions:

• The proposed FD approach offers a viable, gyro-free solution for spacecraft angular velocity estimation.
• Optimized measurement timing is critical for mitigating bias in FD estimates.
• This technique provides a computationally efficient alternative to traditional Kalman filtering methods for specific applications.