MDS Based SLAM Solutions: The localization problem has been studied extensively, and is known to have numerous types of solutions which require various algorithms. Further, simultaneous localization and room mapping (SLAM) has become a popular area of research in recent years. One current lab project in localization and mapping is based on Multi-Dimensional Scaling (MDS), most commonly expressed as an optimization problem, which requires computationally expensive and iterative methods such as particle filtering and gradient descent to obtain a solution. In order to validate the accuracy of such solutions, an exhaustive search method which guarantees the discovery of a global minimum has been developed and used in our SLAM problems. This method is computationally expensive, as it requires the search of all possible solutions in a given set. Since we are simulating the performance of such algorithms, Monte-Carlo analysis is required in order to obtain stable solutions.
Error Propagation in Localization Problems: One of the aspects of localization is determining the effects of noise on the system. This becomes especially important when attempting sequential localization (where newly found targets are used to find more targets). The error introduced when finding a target is propagated through the system as each newly discovered target is used to localize a new target. The simulations to capture error propagation are iterative Monte-Carlo simulations, and is a perfect candidate for parallel computing.