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- Lieven Vandenberghe, Stephen P. Boyd, Katherine Comanor
- SIAM Review
- 2007

A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev's inequality for univariate random variables. Two semidefinite programming formulations are presented, with a constructive proof based on… (More)

We propose to use the Approximate Maximum-Likelihood (AML) method to estimate the direction-of-arrival (DOA) of multiple targets from various spatially distributed sub-arrays, with each sub-array having multiple acoustical/seismic sensors. Localization of the targets can with possibly some ambiguity be obtained from the cross bearings of the sub-arrays.… (More)

Chebyshev inequalities provide bounds on the probability of a set based on known expected values of certain functions, for example, known power moments. In some important cases these bounds can be efficiently computed via convex optimization. We discuss one particular type of generalized Chebyshev bound, a lower bound on the probability of a set defined by… (More)

A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev's inequality for scalar random variables. Two semidefinite programming formulations are presented, with a constructive proof based on… (More)

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