Cooperative Localization with Velocity-Assisted for Mobile Wireless Sensor Networks

An Intelligent Prediction System for Mobile Source Localization Using Time Delay Measurements

“…When η is chosen to be large enough, the SDP problem depicted by (22) provides a rank-one solution of the positive semidefinite X. However, a concerned issue is that whether the rank-one solution is the original solution of (10) or not.…”

“…It is also observed that the dimension of X in the problem depicted by ( 22) is also M + 2p + 3 when rank(X) = 1. Due to the similar constraints, the problem depicted by (22) has also only 2p independent variables. Therefore, the rank-one solution of the SDP problem depicted by ( 22) is also the original solution of (10) since the convex SDP form of ( 22) is derived from the non-convex problem depicted by (10).…”

“…Too large η increases the proportion of penalty terms to the total cost function of (22), so it will weaken the original objective Tr(CX). To avoid the chosen η to be too large, η starts from a small value and increases gradually, until the rank-one condition is satisfied.…”

“…To avoid the chosen η to be too large, η starts from a small value and increases gradually, until the rank-one condition is satisfied. To clearly observe the effect of the penalty coefficient in the problem depicted by (22), we conducted a random test and the results are plotted in Fig. 1, where X * and Tr(CX * ) represent the optimal solution and objective, respectively.…”

“…When meeting the condition CX < ǫ, we accept the solution that is considered as a final solution X * . If not, we relax the rank-one condition with δ = αδ (α > 1) and resolve the problem depicted by (22) until two conditions hold.…”