  In this paper, we introduce an intelligent prediction system for mobile
source localization in industrial Internet of things. The position and velocity
of mobile source are jointly predicted by using Time Delay (TD) measurements in
the intelligent system. To predict the position and velocity, the Relaxed
Semi-Definite Programming (RSDP) algorithm is firstly designed by dropping the
rank-one constraint. However, dropping the rank-one constraint leads to produce
a suboptimal solution. To improve the performance, we further put forward a
Penalty Function Semi-Definite Programming (PF-SDP) method to obtain the
rank-one solution of the optimization problem by introducing the penalty terms.
Then an Adaptive Penalty Function Semi-Definite Programming (APF-SDP) algorithm
is also proposed to avoid the excessive penalty by adaptively choosing the
penalty coefficient. We conduct experiments in both a simulation environment
and a real system to demonstrate the effectiveness of the proposed method. The
results have demonstrated that the proposed intelligent APF-SDP algorithm
outperforms the PF-SDP in terms of the position and velocity estimation whether
the noise level is large or not.
