Attitude Sensor from Ellipsoid Observations: A Numerical and Experimental Validation

Abstract

The preliminary design and validation of a novel, high accuracy horizon-sensor for small satellites is presented, which is based on the theory of attitude determination from ellipsoid observations. The concept consists of a multi-head infrared sensor capturing images of the Earth limb. By fitting an ellipse to the imaged limb arcs, and exploiting some analytical results available from projective geometry, a closed form solution for computing the attitude matrix is provided. The algorithm is developed in a dimensionless framework, requiring the knowledge of the shape of the imaged target, but not of its size. As a result, the solution is less sensitive to the limb shift caused by the atmospheric own radiance. To evaluate the performance of the proposed method, a numerical simulator is developed, which generates images captured in low Earth orbit, including also the presence of the atmosphere. In addition, experimental validation is provided due to a dedicated testbed, making use of a miniature infrared camera. Results show that our sensor concept returns rms errors of few hundredths of a degree or less in determining the local nadir direction.

A Tutorial on Horizon-Based Optical Navigation and Attitude Determination With Space Imaging Systems

“…Since we know the Earth's attitude (both inertially and within it's own principal axis frame), the spacecraft must be the object with unknown attitude if there is to be an attitude determination problem to solve. This is exactly the problem solved by Earth horizon sensors [14]- [17]. In this case we would know r P but have no knowledge of T P C .…”

“…The associate editor coordinating the review of this manuscript and approving it for publication was Ze Ji . determination using Earth horizon sensors (both scanning and staring) [14]- [17], the relationship between OPNAV and attitude determination is rarely made. Indeed, the mathematics used to solve these two horizon-based navigation problems have been developed separately-often bearing little obvious connection.…”

Planet–Sun Sensor Revisited

“…In [6] it was shown that from a single observation of an ellipsoidal celestial body, a closed form formulation for the attitude matrix can be obtained by solving a quadricto-conic correspondence problem. The theoretical framework was later applied to infrared images of an ellipsoid, to develop a triaxial horizon sensor [7]. Unfortunately, celestial bodies feature typically a very small degree of polar or equatorial (if any) oblateness, so that, in practice, the orientation about camera boresight can be only loosely constrained using such a sensor as a standalone source for the attitude.…”

“…In particular, it formulates and solves the attitude determination problem through joint quadric-conic and conic-conic correspondences. Despite the quadric-conic correspondence problem alone has been already successfully tackled for computing whether the attitude [6,7], position [9][10][11][12][13] or a combination of both [14,15] from ellipsoids limb, to the best of the authors' knowledge a general framework for estimating the direction of the light partially illuminating an ellipsoid has not been tackled yet, neither alone, nor together with the LOS to develop a full attitude sensor.…”

“…Sub-section II.A faces the problem of computing the line-of-sight vector from the limb ellipse. Two alternative solutions are discussed for this problem: one, derived from previously published results [6,7], allows computing the LOS as a byproduct of the entire attitude matrix estimate; the other, instead, directly computes the line-of-sight only. Sub-section II.B deals with the computation of the illumination direction.…”