  We present a method for coherently combining short data segments from
gravitational-wave detectors to improve the sensitivity of semi-coherent
searches for continuous gravitational waves. All-sky searches for continuous
gravitational waves from unknown sources are computationally limited. The
semi-coherent approach reduces the computational cost by dividing the entire
observation timespan into short segments to be analyzed coherently, then
combined together incoherently. Semi-coherent analyses that attempt to improve
sensitivity by coherently combining data from multiple detectors face a
computational challenge in accounting for uncertainties in signal parameters.
In this article, we lay out a technique to meet this challenge using summed
Fourier transform coefficients. Applying this technique to one all-sky search
algorithm called TwoSpect, we confirm that the sensitivity of all-sky,
semi-coherent searches can be improved by coherently combining the short data
segments. For misaligned detectors, however, this improvement requires careful
attention when marginalizing over unknown polarization parameters. In addition,
care must be taken in correcting for differential detector velocity due to the
Earth's rotation for high signal frequencies and widely separated detectors.
