  Cosmic ray muons have been considered as a non-conventional radiation probe
in various applications. To utilize cosmic ray muons in engineering
applications, two important quantities, trajectory and momentum, must be known.
The muon trajectories are easily reconstructed using two-fold detector arrays
with a high spatial resolution. However, precise measurement of muon momentum
is difficult to be achieved without deploying large and expensive spectrometers
such as solenoid magnets. Here, we propose a new method to estimate muon
momentum using multi-layer pressurized gas Cherenkov radiators. This is
accurate, portable, compact (< 1m3), and easily coupled with existing muon
detectors without the need of neither bulky magnetic nor time-of-flight
spectrometers. The results show that not only our new muon spectrometer can
measure muon momentum with a resolution of +-0.5 GeV/c in a momentum range of
0.1 to 10.0 GeV/c, but also we can reconstruct cosmic muon spectrum with high
accuracy (~90%).
