  The 5-vector method is one of the main pipeline used by the LIGO-Virgo-KAGRA
Collaboration for the analysis of continuous gravitational waves (CWs). This
method is a matched filter in the frequency domain based on the splitting in
five frequencies of the expected gravitational wave frequency due to the Earth
sidereal motion. The data 5-vector is composed by five components, each defined
as the Fourier transform of the data at one of the five frequencies where the
signal power is split. When dealing with a scenario involving $n$ detectors,
the standard multidetector extension combines the data 5-vector from each
detector, resulting in a total of $5n$ components. In this letter, we introduce
a novel multidetector extension that goes beyond the standard approach. It
takes into consideration the varying noise levels and observation times
associated with each detector, offering a more sophisticated and effective
approach for CWs analysis.
