v2010.10.26 - Convex Optimization

4.4. RANK-CONSTRAINED SEMIDEFINITE PROGRAM 3192314Figure 86: 2-lattice in R 2 , hand-drawn. Nodes 3 and 4 are anchors;remaining nodes are sensors. Radio range of sensor 1 indicated by arc.Our problem formulation is extensible to any spatial dimension.proposed standardized testJin proposes an academic test in two-dimensional real Euclidean space R 2that we adopt. In essence, this test is a localization of sensors andanchors arranged in a regular triangular lattice. Lattice connectivity issolely determined by sensor radio range; a connectivity graph is assumedincomplete. In the interest of test standardization, we propose adoptionof a few small examples: Figure 86 through Figure 89 and their particularconnectivity represented by matrices (746) through (749) respectively.0 • ? •• 0 • •? • 0 ◦• • ◦ 0(746)Matrix entries dot • indicate measurable distance between nodes whileunknown distance is denoted by ? (question mark). Matrix entries hollowdot ◦ represent known distance between anchors (to high accuracy) whilezero distance is denoted 0. Because measured distances are quite unreliablein practice, our solution to the localization problem substitutes a distinct