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We have analyzed the atmospheric neutrino data to study the octant of$\theta_{23}$ and the precision of the oscillation parameters for a large IronCALorimeter (ICAL) detector. The ICAL being a tracking detector has the abilityto measure the energy and the direction of the muon with high resolution. Frombending of the track in magnetic field it can also distinguish its charge. Wehave generated events by Nuance and then considered only the muons (directlymeasurable quantities) produced in charge current interactions in our analysis.This encounters the main problem of wide resolutions of energy and baseline.The energy-angle correlated two dimensional resolution functions are used tomigrate the energy and the zenith angle of the neutrino to those of the muon. Anew type of binning has been introduced to get better reflection of theoscillation pattern in chi-square analysis. Then the marginalization of the$\chi^2$ over all parameters has been carried out for neutrinos andanti-neutrinos separately. We find that the measurement of $\theta_{13}$ ispossible at a significant precision with atmospheric neutrinos. The precisionsof $\Delta m_{32}^2$ and $\sin^2\theta_{23}$ are found $\sim$ 8% and 38%,respectively, at 90% CL. The discrimination of the octant as well as thedeviation from maximal mixing of atmospheric neutrinos are also possible forsome combinations of ($\theta_{23}, ~\theta_{13}$). We also discuss the impactof the events at near horizon on the precision studies.

Sensitivity to neutrino mixing parameters with atmospheric neutrinos