  $ $Future surveys could obtain tighter constraints on the cosmological
parameters with the galaxy power spectrum than with the Cosmic Microwave
Background. However, the inclusion of multiple overlapping tracers, redshift
bins, and more non-linear scales means that generating the necessary ensemble
of simulations for model-fitting presents a computational burden. In this work,
we combine full-shape fitting of galaxy power spectra, analytical covariance
matrix estimates, the MOPED (Massively Optimised Parameter Estimation and Data
compression) method, and the Taylor expansion interpolation of the power
spectrum for the first time to constrain the cosmological parameters directly
from a state-of-the-art set of galaxy clustering measurements. We find it takes
less than a day to compute the analytical covariance while it takes several
months to calculate the simulated ones. Combining MOPED with the Taylor
expansion interpolation of the power spectrum, we can constrain the
cosmological parameters in just a few hours instead of a few days. We also find
that even without a priori knowledge of the best-fit cosmological or galaxy
bias parameters, the analytical covariance matrix with the MOPED compression
still gives consistent cosmological constraints to within 0.1$\sigma$ after two
iterations. Therefore, the pipeline we have developed here can significantly
speed up the analysis for future surveys such as DESI and Euclid.
