Updated: Apr 2
The localization problem that I am trying to solve is to figure out the position of passive RFID tags in a box. Essentially I measure the backscattered signals from the RFID tags and try to figure out their relative position. The problem is formulated as a statistical maximum a-posteriori (MAP) estimator where the unknown parameters are the radial separation between the tags and they will be estimated from the backscattered signal strength measurements.
The objective function for this MAP estimator has lots of local maxima. In addition, the global maxima is not easily differentiable from the surrounding. Deterministic optimization algorithms like Newton-Raphson method has no chance for finding the global maxima unless the starting point is very close to it. To make the matter more complicated, the number of parameters that I have to tweak to search for global maxima increase as the square of the number RFID tags that I am trying to localize. The optimization function plot for single RFID tag in the presence of 57 other RFID tags in the box is shown below.
Fig 1. Objective function using
Fig 2. Objective function using
I tried the constrained simulated annealing to solve this problem and it took 2 days to converge and the solution is only 50% better than an alternate approach called Multi-Dimensional Scaling. So effectively, after you have measured the backscattered signals from the box you will have to come back 2 days later to find out the position of items in that box. Not a very appealing solution isn’t it.. My plan was to submit this work to a journal but I am worried that it might not pass the peer review stage due to the time it takes to converge to an answer. I am hoping that the reviewers would at least notice the innovation in the mathematical formulation of the problem and worry about the practical application later.
One thing to note is that as the measurement noise decreases by increasing the no. o f backscattered samples, the objective function gets more convex.