Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation with Online Calibration

This letter presents a new generic formulation for a gyroscope aided attitude estimator using N direction measurements. The approach incorporates navigation, extrinsic calibration for all direction sensors, and gyroscope bias states in a single geometric structure. The proposed filter-based estimator improves the transient response, and the asymptotic bias and extrinsic calibration estimation compared to state-of-the-art approaches. The estimator is verified in simulations and tested in real-world experiments.