Statistics Seminar: Barry Quinn -- Estimating the period of a Point Process/ Estimating the parameters in an exponentially damped sinusoid

Barry Quinn Department of Statistics Macquarie University 

Location: Carslaw 273 

Time: 2pm Friday, May 25, 2012 

Title: Estimating the period of a Point Process/ Estimating the parameters in an
exponentially damped sinusoid 

Abstract: The motivation for the first problem is from passive radar.  Pulses are
received from a radar emitter and the times of arrival recorded.  However, some pulses
may not be recorded and some may be recorded more than once.  There is also additive
noise in the recorded times.  The model for the arrival times is a linear regression
with unknown but integer-valued independent variable.  The slope represents the period
of transmission, and is known to lie in an interval for which the upper limit is twice
the lower.  Two estimation methods are suggested, and their asymptotic properties
discussed.  The work has been conducted jointly with Vaughan Clarkson of the University
of Queensland, and Robby McKilliam of the University of South Australia.  I started
working on the second problem when my son James came home from his Sydney University
Physics practical with some data from a damped mass-spring system, for which he had to
estimate the period or frequency and the damping coefficient.  The first solution to the
problem was obtained by Prony (1795).  We have adapted a simple technique I developed
for frequency estimation, based on Fourier coefficients.  I shall discuss the asymptotic
theory and the simple ideas behind the development of the algorithm.