Title :
A Semidefinite Relaxation-Based Algorithm for Robust Attitude Estimation
Author :
Ahmed, Shakil ; Kerrigan, Eric C. ; Jaimoukha, Imad M.
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
Abstract :
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.
Keywords :
estimation theory; least mean squares methods; linear matrix inequalities; minimax techniques; signal detection; infinity-norm bounded uncertainties; linear matrix inequality constraint; linear objective function; measurement error; measurement noise; min-max problem; nonconvex minimization problem; nonlinear constraint; quadratic constraint; quadratic cost; regularization scheme; robust attitude estimation; robust optimization problem; semidefinite relaxation-based algorithm; suboptimal problem; suboptimal robust estimation problem; tractable method; weighted least squares approach; Eigenvalues and eigenfunctions; Estimation; Least squares approximation; Optimization; Robustness; Uncertainty; Vectors; Estimation; min-max techniques; optimization methods; relaxation methods; robustness; uncertainty;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2012.2198820