We describe a novel, very fast and robust, directed search incoherent method for periodic gravitational waves (GWs) from neutron stars in binary systems. As directed search, we assume the source sky position to be known with enough accuracy, but all other parameters are supposed to be unknown. We exploit the frequency-modulation due to source orbital motion to unveil the signal signature by commencing from a collection of time and frequency peaks. We validate our pipeline adding 131 artificial continuous GW signals from pulsars in binary systems to simulated detector Gaussian noise, characterized by a power spectral density Sh = 4x10^-24 Hz^-1/2 in the frequency interval [70, 200] Hz, which is overall commensurate with the advanced detector design sensitivities. The pipeline detected 128 signals, and the weakest signal injected and detected has a GW strain amplitude of ~10^-24, assuming one month of gapless data collected by a single advanced detector. We also provide sensitivity estimations, which show that, for a single- detector data covering one month of observation time, depending on the source orbital Doppler modulation, we can detect signals with an amplitude of ~7x10^-25. By using three detectors, and one year of data, we would easily gain more than a factor 3 in sensitivity, translating into being able to detect weaker signals. We also discuss the parameter estimate proficiency of our method, as well as computational budget, which is extremely cheap. In fact, sifting one month of single-detector data and 131 Hz-wide frequency range takes roughly 2.4 CPU hours. Due to the high computational speed, the current procedure can be readily applied in ally-sky schemes, sieving in parallel as many sky positions as permitted by the available computational power.
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