So this is the first time I got into a “cart before the horse” situation with regarding to writing technical papers. I have collected extensive data regarding wireless signal strength variation in an indoor environment and I have figured out a method to track a transmitter’s position using Bhattacharyya coefficient. You can see a quick demo of this technique in action here. However, I am unable to figure out the math behind it.
Essentially, my method measures signal strength of a transmitter using multiple receivers placed around my lab. After removing the fast fading noise, I compute the bhattacharyya coefficient between two set of signal strength measurements done at time t and t-1. The larger the value of bhattacharyya coefficient greater the distance the transmitter has moved between time t-1 to t. The figure below shows the bhattacharyya coefficient computed for various transmitter position when compared to a point that is located at 1200 units. Consequently, bhattacharyya coefficient is lower closer to the ref point and increase as the transmitter moves away from it.
Just to recap about bhattacharyya coefficient, it is a divergence measure between probability distributions or in other words how much one probability distribution differ from another.
For my problem, the divergence between joint distribution of shadow fading at time t-1 and at time t is computed using bhattacharyya coefficient. My hypothesis is that this divergence is a function of the distance the transmitter has moved from time t-1 to t. I was able to show that is the case from my experiments but I am having trouble proving that analytically. I have everything ready for the paper except the main proof and just 3 weeks to submit….