  The accurate determination of the true redshift distributions in tomographic
bins is critical for cosmological constraints from photometric surveys. The
proposed redshift self-calibration method, which utilizes the photometric
galaxy clustering alone, is highly convenient and avoids the challenges from
incomplete or unrepresentative spectroscopic samples in external calibration.
However, the imperfection of the theoretical approximation on broad bins as
well as the flaw of the previous algorithm risk the accuracy and application of
the method. In this paper, we propose the improved self-calibration algorithm
that incorporates novel update rules, which effectively accounts for
heteroskedastic weights and noisy data with negative values. The improved
algorithm greatly expands the application range of self-calibration method and
accurately reconstructs the redshift distributions for various mock data. Using
the luminous red galaxy (LRG) sample of the Dark Energy Spectroscopic
Instrument (DESI) survey, we find that the reconstructed results are comparable
to the state-of-the-art external calibration. This suggests the exciting
prospect of using photometric galaxy clustering to reconstruct redshift
distributions in the cosmological analysis of survey data.
