Expectation Maximization 1D Tracking Demo

This package demonstrates how to use an expectation maximization algorithm to solve a simplified one-dimensional multiple object tracking problem. Multiple object tracking typically involves making a series of position measurements over time, and then answering two questions: a.) what is the minimum number of objects that would be necessary in order to reasonably account for all the position measurements that were observed, and b.) what trajectory did each of the objects take? Since the true number of objects is unknown, estimating this from the data becomes an exercise in model order selection. In general, the goal of model order selection is to comport with Occam's razor: i.e., the total number of components in the entire model (in this case, the number of parameters per trajectory times the number of objects) should be both parsimonious, and not overfit the data with too many parameters, while still accurately modeling all of the data. The expectation maximization algorithm, which has frequently been used in the past to estimate items such as the parameter values and total number of nodes in Gaussian mixture models, is adapted here to estimate the trajectory parameters and the total number of objects in a one dimensional tracking practice exercise.