  Cosmology constraints serve as a crucial criterion in discriminating
cosmological models. The traditional combined method to constrain the
cosmological parameters designates the corresponding theoretical value and
observational data as functions of redshift, however, sometimes the redshift
cannot be measured directly, or the measurement error is large, or the
definition of redshift is controversial. In this paper, we propose a novel
joint method to constrain parameters that eliminates the redshift $z$ and makes
full use of the multiple observables $\left\lbrace
\mathcal{F}_{1,\mathrm{obs}},\mathcal{F}_{2,\mathrm{obs}},\cdots,\mathcal{F}_{M,\mathrm{obs}}\right\rbrace$
spanning in $M$-dimensional joint observables space. Considering the generality
of the mathematical form of the cosmological models and the guidance from low
to high dimensions, we firstly validate our method in a three-dimensional joint
observables space spanned by $H(z)$, $f\sigma_{8}(z)$ and $D_{A}(z)$, where the
three coordinates can be considered redshift-free measurements of the same
celestial body (or shared-redshift data reconstructed model independently). Our
results are consistent with the traditional combined method but with lower
errors, yielding $H_0=68.7\pm0.1\mathrm{~km}
\mathrm{~s}^{-1}\mathrm{~Mpc}^{-1}$, $\Omega_{m0}=0.289\pm0.003$,
$\sigma_{8}=0.82\pm0.01$ and showing alleviated parametric degeneracies to some
extent. In principle, our joint constraint method allows an extended form
keeping the redshift information as an independent coordinate and can also be
readily degraded to the form of a traditional combined method to constrain
parameters.
