Relaxed Maximum a Posteriori Fault Identification
Stephen Boyd. Stanford University
joint work with argyrios zymnis and dimitri gorinevski
Abstract
We consider the problem of estimating a pattern of faults, represented as a binary vector, from a set of measurements.
The measurements can be noise corrupted real values, or quantized versions of noise corrupted signals,
including even 1-bit (sign) measurements. Maximum a posteriori probability (MAP) estimation of the fault pattern leads to a
difficult combinatorial optimization problem, so we propose a variation
in which an approximate maximum a posteriori probability estimate is
found instead, by solving a convex relaxation of the original problem,
followed by rounding and simple local optimization.
Our method is extremely efficient, and scales to very large problems,
involving thousands (or more) possible faults and measurements. Using synthetic examples, we show that the method performs extremely
well, both in identifying the true fault pattern, and in identifying
an ambiguity group, i.e., a set of alternate fault patterns that explain
the observed measurements almost as well as our estimate.
Slides
