A Semidefinite Relaxation-Based Algorithm for Robust Attitude Estimation

作者：Ahmed Shakil^*; Kerrigan Eric C; Jaimoukha Imad M

来源：IEEE Transactions on Signal Processing, 2012, 60(8): 3942-3952.

DOI：10.1109/TSP.2012.2198820

• Estimation
• min-max techniques
• optimization methods
• relaxation methods
• robustness
• uncertainty

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.

• 出版日期2012-8