Author: Anthony Marshall
Marshall, Anthony, 2022 An information geometric approach to sensor management, Flinders University, College of Science and Engineering
Terms of Use: This electronic version is (or will be) made publicly available by Flinders University in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. You may use this material for uses permitted under the Copyright Act 1968. If you are the owner of any included third party copyright material and/or you believe that any material has been made available without permission of the copyright owner please contact copyright@flinders.edu.au with the details.
This work examines optimal trajectories through the space of target tracking system parameters. In particular, the focus is on pulsed signals with linear frequency modulation. The signal configuration parameters are the pulse width, T, the inter-pulse spacing, Tp, and chirp rate, b. The study is motivated by the observation that optimal values for these parameters, from the point of view of maximising the information gathered regarding the target, depend on time varying target parameters.
The view taken in this study is that the configuration parameters should change in such a way as to maintain optimality from the point of view of information gathering. Thus the trajectory of the curve
γ(t) = (T(t), Tp(t), b(t)) through the parameter space should be a geodesic on a suitable manifold. To this end, mathematical aspects of a pulse-Doppler radar transmitter/receiver system are considered, beginning with the radar ambiguity function. This function measures the disparity between transmitted and returning signals and is obtained by taking the square of a radar auto-correlation function.
The ambiguity function is also referred to as the likelihood, describing the probability of locating
the target given a set of measurements and forming the basis for construction of the Fisher
information matrix which, in turn, allows measurement of the information content of a given
location for a specific target as a function of the configuration parameters.
The auto-correlation function leads to a collection of integrals containing the products of shifted
sinc functions. These integrals did not appear in the literature and so a novel method for solving
such integrals is developed.
Once the calculation of the Fisher information metric for a given sensor configuration is achieved,
a family of such metrics is required in order that the optimal selection of configuration parameters
may be undertaken. This family of metrics is accounted for by construction of the Gil Medrano
metric, which provides a metric for the manifold of all Riemannian metrics corresponding to
sensor configurations.
The calculation of geodesics on this manifold allows an optimal choice of sensor configuration
to be made, facilitating efficient selection of sensor parameters and increasing the information
content of received signals. Such configurations are those that possess an optimal Time-
Bandwidth product, an important feature in signal processing that describes how efficiently the
available bandwidth is being utilised while simultaneously describing the inverse relationship
between the range and frequency resolution of the system.
The main contributions of the thesis are:
1) Computing an ambiguity function for an infinite Gaussian modulated pulse with linear
frequency modulation.
2) Using notions from information geometry to determine optimal trajectories for configuration
parameters.
3) A method for computing a class of definite integrals comprising products of sinc function
shifted by integer multiples of pi and derivatives of such functions.
This thesis explores the mathematics needed, in principle, to determine geodesics for configuration
parameters and the mathematics represent the sole focus of this thesis, ignoring all aspects
of physical implementation via real world sensor systems.
Keywords: Information Geometry, Radar, Ambiguity Function
Subject: Engineering thesis
Thesis type: Doctor of Philosophy
Completed: 2022
School: College of Science and Engineering
Supervisor: Associate Professor Murk Bottema