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Robust Solutions To LeastSquares Problems With Uncertain Data
, 1997
"... . We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpret ..."
Abstract

Cited by 149 (13 self)
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. We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution, and a rigorous way to compute the regularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomialtime using semidefinite programming (SDP). We also consider the case when A; b are rational functions of an unknownbutbounded perturbation vector. We show how to minimize (via SDP) upper bounds on the optimal worstcase residual. We provide numerical examples, including one from robust identification and one from robust interpolation. Key Words. Leastsquares, uncertainty, robustness, secondorder cone...
Robustness Analysis at the Technical Level of Situation Assessment
"... In a typical air defence scenario, the probability of threat posed to an asset by an intruder can be calculated using tactical data received from a Tracking and Data Fusion unit [1]. However, the outcomes of the calculation can be considerably influenced by the accuracy of the input data and the sys ..."
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In a typical air defence scenario, the probability of threat posed to an asset by an intruder can be calculated using tactical data received from a Tracking and Data Fusion unit [1]. However, the outcomes of the calculation can be considerably influenced by the accuracy of the input data and the system disturbance. In this paper, the robustness analysis of a situation assessment system built upon a Bayesian network is presented. The problem under consideration has two aspects: 1) Determine the maximum allowable data disturbance; 2) Establish a probabilistic procedure to estimate the input data accuracy online. An example of data accuracy estimation for demonstrating the effectiveness of our approach is presented.