  The uncertainty in the photometric redshift estimation is one of the major
systematics in weak lensing cosmology. The self-calibration method is able to
reduce this systematics without assuming strong priors. We improve the recently
proposed self-calibration algorithm to enhance the stability and robustness
with the noisy measurement. The improved algorithm is tested on the power
spectra measured from the simulated catalogues constructed according to DECaLS
DR8 photometric catalogue. For the fiducial analysis with 5 equal-width
redshift bins over $0<z<1$ and 6 bands over scales $100 \leq \ell<1000$, we
find that the improved algorithm successfully reconstructs the scatter rates
and the auto power spectrum in true redshift bins at the level of $\sim0.015$
and $\sim4.4$ per cent, respectively. The bias of the mean redshift is reduced
by more than 50 per cent compared to the photo-$z$ without self-calibration,
especially for the cases with catastrophic photo-$z$ errors. The reconstructed
results of DECaLS DR8 galaxy sample are in line with the expectations from the
simulation validation. The self-calibration code is publicly available at
https://github.com/PengHui-hub/FP-NMF.
