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A Semidefinite Relaxation-Based Algorithm for Robust Attitude Estimation

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3 Author(s)
Ahmed, S. ; Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK ; Kerrigan, E.C. ; Jaimoukha, I.M.

This paper presents a tractable method for solving a robust attitude estimation problem, based on a weighted least squares approach with nonlinear constraints. Attitude estimation requires information of a few vector quantities, each obtained from both a sensor and a mathematical model. By considering the modeling errors, measurement noise, sensor biases and offsets as infinity-norm bounded uncertainties, we formulate a robust optimization problem, which is nonconvex with nonlinear cost and constraints. The robust min-max problem is approximated with a nonconvex minimization problem using an upper bound. A new regularization scheme is also proposed to improve the robust performance. We then use semidefinite relaxation to convert the suboptimal problem with quadratic cost and constraints into a tractable semidefinite program with a linear objective function and linear matrix inequality constraints. We also show how to extract the solution of the suboptimal robust estimation problem from the solution of the semidefinite relaxation. Further, a mathematical proof supported by numerical results is presented stating the gap between the suboptimal problem and its relaxation is zero under a given condition, which is mostly true in real life scenarios. The usefulness of the proposed algorithm in the presence of uncertainties is evaluated with the help of examples.

Published in:

Signal Processing, IEEE Transactions on  (Volume:60 ,  Issue: 8 )

Date of Publication:

Aug. 2012

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