This project involved recreating much of the work done in our professor's paper on a distributed algorithm for sensor localization (U. A. Khan, S.Kar, and J. M. F. Moura, “Linear theory for self-localization: Convexity, barycentric coordinates, and Cayley-Menger determinants,” IEEE Access, vol. 3, pp. 1326–1339, Aug. 2015). The first part of the project was a report where we went through most of the math to veryify the method. The second part of the project was 4 different MATLAB simulations. The first simulation was an implimentation of the DT algorithm in R2. The second simulation was an implimentation of the DT algorithm in R3. The third simulation was an implimentation of the CT algorithm in R2. The fourth and final simulation was an implimentation of the CT algorithm in R3.
The algorithm works by having a small number of points that know where they are and a large number of points that do not know where they are. The points can talk to other points up to a certain distance away and find their distance. Each point uses the distance between each neighbor and assumes that the neighbors know where they are and updates its posistion. The algorithm iterates this process and given a certain criteria on the points, the algorithm converges to the true location of the points.