Abstract-We develop a nonlinear minimax estimator for the classical linear regression model assuming that the true parameter vector lies in an intersection of ellipsoids. We seek an estimate that minimizes the worst-case estimation error over the given parameter set. Since this problem is intractable, we approximate it using semidefinite relaxation, and refer to the resulting estimate as the relaxed Chebyshev center (RCC). We show that the RCC is unique and feasible, meaning it is consistent with the prior information. We then prove that the constrained least-squares (CLS) estimate for this problem can also be obtained as a relaxation of the Chebyshev center, that is looser than the RCC. Finally, we demonstrate through simulations that the RCC can significantly improve the estimation error over the CLS method. Index Terms-Bounded error estimation, Chebyshev center, constrained least-squares, semidefinite programming, semidefinite relaxation.
Inspired by the work in REF , we design a position estimator that minimizes the worst-case position estimation error for robust localization.
A Minimax Chebyshev Estimator for Bounded Error Estimation
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Computer Science Mathematics