Multiple target tracking using neural networks and set estimation

Estimating the positions of several targets in the same neighborhood from noisy measurements becomes challenging when the knowledge of the correct origin of the measurements is unknown. One of the most popular approach to multiple-target tracking (MTT) is the joint probabilistic data association (JPDA) filter. The JPDA relies upon the calculations of the association probabilities between targets and measurements. Kamen recently developed a different approach based on the construction of new measurements insensitive to any actual measurements' shuffling--this technique has been referred to as the symmetric measurement equation (SME) filter. The SME filter, which does not assess association probabilities, is computationally less cumbersome than the JPDA. However, it transforms an original linear estimation problem into a nonlinear one. In its original version, sums of products of the actual measurements are filtered by an extended Kalman filter (EKF).; This thesis aims to achieve a major improvement over the original SME implementation in the one-dimensional case. We first state and prove an important result about the choice of the new symmetric measurements. We use a recurrent neural network instead of the EKF to obtain better target position estimates. Then, set estimation strategies are designed and implemented--they significantly augment the targets' resolution in the crossing neighborhood. The optimal set estimator is characterized. Finally, a symmetric neural network (SNN) structure is introduced and used to approximate the optimal SME filter. SNN filters are very attractive because a specific recurrent structure (yet to be determined) is likely to become a universal approximator of the optimal symmetric filter. The symmetric structure of SNNs developed in this thesis for one-dimensional MTT simply generalizes to three-dimensional MTT.