Models and Algorithms - with applications to vehicle tracking and frequency estimation

Doctoral thesis, 2007

This thesis considers two different research problems; one concerned with the issue of tracking vehicles and one related to estimating frequencies in harmonic signals. The vehicle-tracking problem is addressed from the perspective of an automotive-safety application, which seeks to monitor the course of surrounding road users with the objective to make decisions regarding if, how and when to intervene. For these systems to make appropriate decisions, the information provided by the tracking system must be reliable. In this thesis two modelling frameworks and associated tracking algorithms are introduced. The first considers vehicle tracking using low-level data in terms of radar detections. According to recent studies, automotive radar sensors often receive detections from a discrete set of reflection centers on a vehicle. Based on these results, a family of sensor models is proposed and incorporated in a tracking filter. The filter is able to constructively handle situations when multiple radar detections can originate from each vehicle, and thereby extract valuable information such as the orientation of the vehicles. The second framework provides a tool for designing accurate vehicle motion models. These models differ from conventional ones in that the expected effect of the driver is included. By also providing a methodology for a formal treatment of the uncertainties, motion models well suited to e.g. a tracking algorithm are obtained. The research contributions related to frequency estimation is focused on analyzing and extending a recently developed subspace based algorithm referred to as F-ESPRIT. In this algorithm the user can specify a subset of frequency domain data on which the estimation is based. Two different analyses are contained in the thesis. The first derives and proves necessary and sufficient conditions required for F-ESPRIT to produce accurate estimates under noise free conditions. The second is an asymptotical performance analysis, where a closed form for the mean square error of the frequency estimates is derived. Finally, a bias compensation scheme using weighting matrices is developed and evaluated.