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Optimal multi-rate rigid body attitude estimation based on Lagrange-dAlembert principle

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Document pages: 11 pages

Abstract: The rigid body attitude estimation problem under multi-rate measurements istreated using the discrete-time Lagrange-d Alembert principle. Angular velocitymeasurements are assumed to be sampled at a higher rate compared to thedirection vector measurements for attitude. The attitude determination problemfrom two or more vector measurements in the body-fixed frame is formulated asWahba s problem. At instants when direction vector measurements are absent, adiscrete-time model for attitude kinematics is used to propagate pastmeasurements. A discrete-time Lagrangian is constructed as the differencebetween a kinetic energy-like term that is quadratic in the angular velocityestimation error and an artificial potential energy-like term obtained fromWahba s cost function. An additional dissipation term is introduced and thediscrete-time Lagrange-d Alembert principle is applied to the Lagrangian withthis dissipation to obtain an optimal filtering scheme. A discrete-timeLyapunov analysis is carried out by constructing an appropriate discrete-timeLyapunov function. The analysis shows that the filtering scheme isexponentially stable in the absence of measurement noise and the domain ofconvergence is almost global. For a realistic evaluation of the scheme,numerical experiments are conducted with inputs corrupted by boundedmeasurement noise. These numerical simulations exhibit convergence of theestimated states to a bounded neighborhood of the actual states.

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