  The coolest dwarf stars are intrinsically faint at visible wavelengths and
exhibit rotationally modulated stellar activity from spots and plages. It is
advantageous to observe these stars at near infrared (NIR) wavelengths (1-2.5
microns) where they emit the bulk of their bolometric luminosity and are most
quiescent. In this work we describe our methodology and results in obtaining
precise radial velocity (RV) measurements of low mass stars using K-band
spectra taken with the R~80,000 iSHELL spectrograph and the NASA Infrared
Telescope Facility (IRTF) using a methane isotopologue gas cell in the
calibration unit. Our novel analysis pipeline extracts RVs by minimizing the
RMS of the residuals between the observed spectrum and a forward model. The
model accounts for the gas cell, tellurics, blaze function, multiple sources of
quasi-sinusoidal fringing, and line spread function of the spectrograph (LSF).
The stellar template is derived iteratively using the target observations
themselves through averaging barycenter-shifted residuals. We have demonstrated
5 ms^-1 precision over one year timescales for the M4 dwarf Barnard's Star and
K dwarf 61 Cygni A, and 3 ms^-1 over a month for the M2 dwarf GJ 15 A. This
work demonstrates the potential for iSHELL to determine dynamical masses for
candidate exoplanets discovered with the NASA TESS mission, and to search for
exoplanets orbiting moderately active and/or young K and M dwarfs.
