Minimum-energy filtering for attitude estimation

Abstract

In this work, we study minimum-energy filtering for attitude kinematics with vectorial measurements using Mortensen's approach. The exact form of a minimum-energy attitude observer is derived and is shown to depend on the Hessian of the value function of an associated optimal control problem. A suitably chosen matrix representation of the Hessian operator leads to a Riccati equation that approximates a minimum-energy attitude filter. An extended version of the proposed approximate filter is included for a situation where there is slowly time-varying bias in the gyro measurements. A unit quaternion version of the proposed filter is derived and shown to outperform the multiplicative extended Kalman filter (MEKF) for situations with large initialization errors or large measurement errors. Show more