A convex solution to Psiaki's first joint attitude and spin-rate estimation problem

TL;DR

This paper reformulates Psiaki's joint attitude and spin-rate estimation problem for spinning spacecraft as a convex semidefinite optimization problem, enabling global solutions and extensions for more complex scenarios.

Contribution

It introduces a convex reformulation of Psiaki's problem, allowing for efficient and globally optimal solutions using semidefinite programming techniques.

Findings

Exact convex reformulation of Psiaki's problem

Global solutions via semidefinite optimization routines

Framework for extending to more complex estimation scenarios

Abstract

We consider the problem of jointly estimating the attitude and spin-rate of a spinning spacecraft. Psiaki (J. Astronautical Sci., 57(1-2):73--92, 2009) has formulated a family of optimization problems that generalize the classical least-squares attitude estimation problem, known as Wahba's problem, to the case of a spinning spacecraft. If the rotation axis is fixed and known, but the spin-rate is unknown (such as for nutation-damped spin-stabilized spacecraft) we show that Psiaki's problem can be reformulated exactly as a type of tractable convex optimization problem called a semidefinite optimization problem. This reformulation allows us to globally solve the problem using standard numerical routines for semidefinite optimization. It also provides a natural semidefinite relaxation-based approach to more complicated variations on the problem.