Attitude estimation from vector measurements: Necessary and sufficient conditions and convergent observer design

TL;DR

This paper establishes a weaker necessary and sufficient condition for attitude estimation from vector measurements, enabling the design of almost globally convergent observers that effectively handle noisy data.

Contribution

It introduces a new distinguishability condition for attitude estimation that is weaker than previous ones, and provides two explicit observer designs with proven convergence.

Findings

The new condition is necessary and sufficient for distinguishability.

Two observer designs achieve almost global convergence.

Simulation confirms accurate estimation with noisy measurements.

Abstract

The paper addresses the problem of attitude estimation for rigid bodies using (possibly time-varying) vector measurements, for which we provide a necessary and sufficient condition of distinguishability. Such a condition is shown to be strictly weaker than those previously used for attitude observer design. Thereafter, we show that even for the single vector case the resulting condition is sufficient to design almost globally convergent attitude observers, and two explicit designs are obtained. To overcome the weak excitation issue, the first design employs to make full use of historical information, whereas the second scheme dynamically generates a virtual reference vector, which remains non-collinear to the given vector measurement. Simulation results illustrate the accurate estimation despite noisy measurements.