4
Parameter Estimation
Very often we know the waveform of the signal that we are
searching for in the data in terms of a finite number of unknown
parameters. We would like to find optimal procedures of
estimating these parameters. An estimator of a parameter
is a function
that assigns to each data the “best” guess of the true value of
. Note that because
depends on the random data it is a random variable. Ideally we
would like our estimator to be (i)
unbiased, i.e., its expectation value to be equal to the true value of
the parameter, and (ii)
of minimum variance
. Such estimators are rare and in general difficult to find. As
in the signal detection there are several approaches to the
parameter estimation problem. The subject is exposed in detail in
reference
[53]
. See also
[88]
for a concise account.