Estimation of Spacecraft Inertia Tensor Using Attitude-Only Data from Torque-Free Motion

2026-08-09

AI Summary

This work proposes a method to accurately estimate the normalized inertia tensor of a spacecraft using only attitude observations under torque-free motion, without requiring gyroscope measurements or known control torques. By integrating the Jacobi elliptic function analytical solution of Euler’s equations with a Magnus expansion–based quaternion propagation model, and leveraging Karush–Kuhn–Tucker–based optimization for initialization together with a nonlinear shooting technique, the approach achieves high-precision and computationally efficient estimation. It accommodates both single long arcs and multiple short arcs jointly; on a 500-second arc, it reduces estimation error by nearly an order of magnitude and accelerates computation by almost two orders of magnitude compared to the extended Kalman filter. For a 2000-second arc, median errors fall below 0.1%, enabling attitude prediction over 10 hours with errors under 1°.

Abstract

We present an attitude-only framework for estimating a spacecraft's normalized inertia tensor from torque-free rotational motion. Our method supports both continuous single-arc observations and the joint use of multiple short torque-free arcs, while requiring neither gyroscope measurements nor known control torques. A Karush-Kuhn-Tucker formulation provides a fast linear initialization, which is refined by nonlinear shooting using the exact Jacobi-elliptic solution of Euler's equations and a Magnus-expansion quaternion map. Under controlled attitude noise, tests using a single 500-second arc reduced inertia-tensor error by approximately one order of magnitude relative to an Extended Kalman Filter initialized from the same estimate, while requiring nearly two orders of magnitude less computation. Joint estimation from three 100-second arcs provided a similar improvement in accuracy and remained more than one order of magnitude faster. Photorealistic proximity-operations simulations further evaluated both strategies using monocular image-derived attitudes. The 2000-second single-arc cases achieved sub-thousandth median inertia-tensor error and supported 10-hour attitude predictions with single-digit-degree median error. In three-arc cases using 30-300 seconds per arc, our method consistently outperformed the EKF refinement, with performance governed by rotational excitation and temporal sampling.

Problem

• inertia tensor estimation
• attitude-only data
• torque-free motion
• spacecraft dynamics
• rotational motion

Innovation

• inertia tensor estimation
• attitude-only navigation
• torque-free motion
• Jacobi-elliptic solution
• Magnus expansion