  We present an updated analysis of radial velocity data of the HD 82943
planetary system based on 10 years of measurements obtained with the Keck
telescope. Previous studies have shown that the HD 82943 system has two planets
that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods
about 220 and 440 days (Lee et al. 2006). However, alternative fits that are
qualitatively different have also been suggested, with two planets in a 1:1
resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1
resonance (Beauge et al. 2008). Here we use \c{hi}2 minimization combined with
parameter grid search to investigate the orbital parameters and dynamical
states of the qualitatively different types of fits, and we compare the results
to those obtained with the differential evolution Markov chain Monte Carlo
method. Our results support the coplanar 2:1 MMR configuration for the HD 82943
system, and show no evidence for either the 1:1 or 3-planet Laplace resonance
fits. The inclination of the system with respect to the sky plane is well
constrained at about 20(+4.9 -5.5) degree, and the system contains two planets
with masses of about 4.78 MJ and 4.80 MJ (where MJ is the mass of Jupiter) and
orbital periods of about 219 and 442 days for the inner and outer planet,
respectively. The best fit is dynamically stable with both eccentricity-type
resonant angles {\theta}1 and {\theta}2 librating around 0 degree.
