$H_0$ Reconstruction with Type Ia Supernovae, Baryon Acoustic
  Oscillation and Gravitational Lensing Time-Delay
  There is a persistent $H_0$-tension, now at more than $\gtrsim 4\sigma$
level, between the local distance ladder value and the \emph{Planck} cosmic
microwave background measurement, in the context of flat $\Lambda$CDM model. We
reconstruct $H(z)$ in a cosmological-model-independent way using three
low-redshift distance probes including the latest data from baryon acoustic
oscillation, Type Ia supernova and four gravitational lensing Time-Delay
observations. We adopt general parametric models of $H(z)$ and assume a
Gaussian prior on the sound horizon at drag epoch, $r_{\mathrm s}$, from
\emph{Planck} measurement. The reconstructed $H_0$ using Pantheon SN Ia and BAO
data are consistent with the \emph{Planck} flat $\Lambda$CDM value. When
including the GLTD data, $H_0$ increases mildly, yet remaining discrepant with
the local measurement at $\sim 2.5\sigma$ level. Our reconstructions being
blind to the dark sectors at low redshift, we reaffirm the earlier claims that
the Hubble tension is not likely to be solved by modifying the energy budget of
the low-redshift universe. We further forecast the constraining ability of
future realistic mock BAO data from DESI and GLTD data from LSST, combining
which, we anticipate that the uncertainty of the inferred $H_0$ would be
improved by $\sim 38\%$, reaching $\sigma_{H_0} \approx 0.56$ uncertainty
level.
