Abstract
This paper conveys attitude and rate estimation without rate sensors by performing a critical comparison, validated by extensive simulations. The two dominant approaches to facilitate attitude estimation are based on stochastic and set-membership reasoning. The first one mostly utilizes the commonly known Gaussian-approximate filters, namely the EKF and UKF. Although more conservative, the latter seems to be more promising as it considers the inherent geometric characteristics of the underline compact state space and accounts -- from first principles -- for large model errors. We address the set-theoretic approach from a control point of view, and we show that it can overcome reported deficiencies of the Bayesian architectures related to this problem, leading to coordinate-free optimal filters. Lastly, as an example, we derive a modified predictive filter on the tangent bundle of the special orthogonal group $\mathbb{TSO}(3)$.
Highlights
Attitude and rate estimation is an important aspect of aerial robotics
We demonstrate attitude and rate estimation from vector measurements for unmanned aerial vehicles (UAVs) and Low Earth Orbit (LEO) satellites
To stress the significance of the dual optimal control formulation, we replace the model error with an unknown deterministic disturbance that exerts on the existing system
Summary
Attitude and rate estimation is an important aspect of aerial robotics. Throughout the decades, it has proven very accurate and versatile in applications from the first Low Earth Orbit (LEO) satellites [1] to unmanned aerial vehicles (UAVs) [2] and from the unmanned aerial systems [3] to recent aerial robotic workers [4]. Of them is motivated by the fact that deterministic modelling naturally leads to a coordinate-free problem formulation To this extent, the present paper is motivated by the dual optimal control approach, that accounts directly both for the underlying state-space and the environmental phenomena affecting the existing system without ad-hoc simplification assumptions. The present paper is motivated by the dual optimal control approach, that accounts directly both for the underlying state-space and the environmental phenomena affecting the existing system without ad-hoc simplification assumptions To this direction, we derive the modified predictive filter on TSO(3). Extensive simulations are used to compare the second-order-optimal minimum energy filter (MEF) [34] and predictive filter (PF) performance versus the EKF and UKF Both the analysis and the simulations’ results conclusively indicate that coordinate-free deterministic filtering tackles the vices of the stochastic approach. The estimate of X is denoted by X , while the optimal estimate of X by X ∗
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