Numerical Solution of a Generalized Wahba Problem for a Spinning Spacecraft

A numerical solution algorithm has been developed to solve a generalization of Wahba's attitude determination problem in the case of unknown attitude and attitude rate. It provides a robust global solution to nonlinear batch attitude and rate estimation problems for spinning spacecraft. The ori...

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Bibliographic Details
Published in:Journal of guidance, control, and dynamics control, and dynamics, 2012-05, Vol.35 (3), p.764-773
Main Authors: Psiaki, Mark L, Hinks, Joanna C
Format: Article
Language:English
Subjects:
Aerospace engineering
Algorithms
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Convergence
Exact sciences and technology
Exact solutions
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Modelling and identification
Physics
Sensors
Simulation
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Spacecraft
Spinning
Time series
Vectors (mathematics)
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Summary:A numerical solution algorithm has been developed to solve a generalization of Wahba's attitude determination problem in the case of unknown attitude and attitude rate. It provides a robust global solution to nonlinear batch attitude and rate estimation problems for spinning spacecraft. The original Wahba problem seeks the attitude that fits a set of unit-normalized direction vector measurements. The generalized problem seeks an initial attitude and rate that, when combined with a torque-free rigid-body attitude dynamics model, fit a time series of direction vector measurements. The new algorithm combines an inner analytic solution for the unknown initial attitude quaternion with an outer numerical solution for the unknown initial rate. The inner problem can be cast in a standard Wahba form, and it is solved in closed form using an adaptation of the qq method. The outer problem relies on a trust-region implementation of Newton's method to ensure global convergence. The global solution is determined by re-solving starting from a random set of first guesses of the attitude rate that cover the space of nonaliasing rates. Tests on truth-model simulation data for minor-axis and major-axis spinning spacecraft confirm the new algorithm's ability to achieve global convergence and its estimation accuracy's consistency with its computed estimation error covariance matrix. [PUBLISHER ABSTRACT]
ISSN:0731-5090
1533-3884
DOI:10.2514/1.56151