The GRAPES-3 (Gamma Ray Astronomy at PeV EnergieS-3) experiment has been
designed to study the composition and energy spectrum of primary cosmic rays
(PCRs) over TeV - PeV range. It is equipped with 400 plastic scintillators
covering an area of 25000 m$^2$ and a muon detector spread in an area of
560 m$^2$. The precise measurement of particle densities from each detector
is very important for any air shower experiment. Photo-multiplier tubes (PMT)
are widely used as a transducer to collect the light produced in detector
medium to electric signals. These signals are then processed to measure the
particle densities. However, these PMTs tend to show non-linearity and
saturation at higher signals due to the large shower core landing near the
detector. The GRAPES-3 detectors record $\sim$ (50 -70) particles in the
linear range. This results in improper shower size estimation near the knee
energy. In order to overcome this situation and to estimate the correct shower
size, a systematic approach has been devised and demonstrated to correct the
particle density beyond the linear range. It is seen from the method allows us
to estimate particle densities $\sim$ (500 - 800) which can improve the
measurements beyond knee.