v2010.10.26 - Convex Optimization

316 CHAPTER 4. SEMIDEFINITE PROGRAMMINGFigure 85: Sensor-network localization in R 2 , illustrating connectivity andcircular radio-range per sensor. Smaller dark grey regions each hold ananchor at their center; known fixed sensor positions. Sensor/anchor distanceis measurable with negligible uncertainty for sensor within those grey regions.(Graphic by Geoff Merrett.)called multilateration. 4.27 [228] [266] Indeed, practical contemporarynumerical methods for global positioning (GPS) by satellite do not rely onconvex optimization. [290]Modern distance geometry is inextricably melded with semidefiniteprogramming. The beauty of semidefinite programming, as relates tolocalization, lies in convex expression of classical multilateration: So & Yeshowed [320] that the problem of finding unique solution, to a noiselessnonlinear system describing the common point of intersection of hyperspheresin real Euclidean vector space, can be expressed as a semidefinite program4.27 Multilateration − literally, having many sides; shape of a geometric figure formed bynearly intersecting lines of position. In navigation systems, therefore: Obtaining a fix frommultiple lines of position. Multilateration can be regarded as noisy trilateration.