Bayesian Estimation and Tracking: A Practical Guide

1.4 Modeling and Simulation with Matlab^®

It is important to the learning process that the reader be given concrete examples of application of estimation methods to a set of complex problems. This will be accomplished in this book through the use of simulations using MATLAB^®. We present a set of four case studies that provide an increase in complexity from the first to the last. Each case study will include an outline of how to set up a simulation that models both the dynamics and observations of the system under study. We then show how to create a set of randomly generated observational data using a Monte Carlo methodology. This simulated observational data can then be used to exercise each tracking filter, producing sets of track data that can be compared across multiple track filters.

The first case study examines the problem of tracking a ship as it moves through a distributed field of DIFAR buoys. A DIFAR buoy uses the broadband noise signal radiated from the ship as in input and produces noisy observations of the bearing to the ship as an output. As we will show in Chapter 4, the probability density of the bearing estimates at the DIFAR buoy output is dependent on the SNR of the input signal. The density will be Gaussian for high SNR but will transition to a uniform distribution as the SNR falls. The purpose of this case study will be to examine what happens to the filter tracking performance for each track estimation method as the observation noise transitions from Gaussian ...