Method for all-sky searches of continuous gravitational wave signals using the frequency-Hough transform

In this paper we present a hierarchical data analysis pipeline for all-sky searches of continuous gravitational wave signals, like those emitted by spinning neutron stars asymmetric with respect to the rotation axis, with unknown position, rotational frequency, and spin-down. The core of the pipeline is an incoherent step based on a particularly efficient implementation of the Hough transform, which we call frequency-Hough, that maps the data time-frequency plane to the source frequency and spin-down plane for each fixed direction in the sky. Theoretical ROCs and sensitivity curves are computed and the dependency on various thresholds is discussed. A comparison of the sensitivity loss with respect to an ``optimal'' method is also presented. Several other novelties, with respect to other wide-parameter analysis pipelines, are also outlined. They concern, in particular, the construction of the grid in the parameter space, with over-resolution in frequency and parameter refinement, candidate selection, and various data cleaning steps that are introduced to improve search sensitivity and rejection of false candidates.