Attitude estimation based on inertial and position measurements

Attitude estimation arises in many applications, and is crucial for the aerospace and aeronautic industry. A classical approach to perform the attitude estimation is via Inertial Measurement Unit (IMU) data and a set of measured observation vectors, both in the object and inertial reference frame. The attitude estimation can be then formulated as a constrained least-squares problem. As a possible alternative, attitude estimation can be performed using IMU data and a set of measured positions, hence removing the need for observation vectors. Attitude estimation based on IMU and position measurements is already undergoing industrial research. However, the underlying estimation problem does not necessarily admit a unique solution, and can therefore degenerate depending on the object trajectories. This paper theoretically investigates this approach to attitude estimation, and provides a simple, explicit relationship between the standard deviation of the attitude estimation and the object trajectories, which is independent of the choice of parametrization of the special orthogonal group SO(3).