Background#
Given a gravitational-wave HEALPix probability sky map, this Python package finds an optimal sequence of Dorado observations to maximize the probability of observing the (unknown) location of the gravitational-wave event, within one orbit.
The problem is formulated as a mixed integer programming problem with the following arrays of binary decision variables:
schedule
(npix
×nrolls
×ntimes - ntimes_per_exposure + 1
): 1 if an observation of the field that is centered on the given HEALPix pixel, at a given roll angle, is begun on a given time step; or 0 otherwisepix
(npix
): 1 if the given HEALPix pixel is observed, or 0 otherwise
The problem has the following parameters:
nexp
(scalar, integer): the maximum number of exposuresprob
(npix
, float): the probability sky mapregard
(npix
×ntimes
, binary): 1 if the field centered on the given HEALPix pixel is within the field of regard at the given time, 0 otherwise
The objective function is the sum over all of the pixels in the probability sky
map for which the corresponding entry in pix
is 1.
The constraints are:
At most one observation is allowed at a time.
At most
nexp
observations are allowed in total.A given pixel is observed if any field that contains it within its footprint is observed.
A field may be observed only if it is within the field of regard.