The continuum band light curve is reconstructed from the data using the technique of PRH92. For completeness, this section summarizes their method. The reader who is primarily interested in the application of this method may skip to Section 3.
Suppose that the true flux of the source at time t is s(t), but we
measure y(t)=s(t)+n(t), where n(t) is the noise in the measurement. In
our case, the noise is Poisson in nature. Our knowledge of s(t) is
further impeded by the fact that the measurement is only made at a finite
number of times
, where i=1,...,N. We denote
as
and
refer to this as the continuum data vector.
We seek an optimal reconstruction of s(t) which is continuous in time,
, such that
is minimized for all t. As usual, angle brackets denote the expectation
value. We impose that
is linear in the data vector in the
sense that
where
are a set of inverse response functions that are also
continuous in time.
Assuming that the noise is uncorrelated with both s(t) and itself, PRH92 showed that eqn (3) can be minimized to yield,
Here,
is the total covariance matrix. To keep the notation concise, PRH92 define the correlation statistics:
These functions define what PRH92 call the `covariance model'. The expected variance of the real signal from the optimal reconstruct in eqn (5) is then given by
Once the covariance model is known, eqns (5) and (10) define the optimal reconstruction of the continuum light curve together with a statistic measuring the expected deviation of the real signal from the reconstruction.