  The use of a high precision pulsar timing array is a promising approach to
detecting gravitational waves in the very low frequency regime ($10^{-6}
-10^{-9}$ Hz) that is complementary to the ground-based efforts (e.g., LIGO,
Virgo) at high frequencies ($\sim 10 -10^3$ Hz) and space-based ones (e.g.,
LISA) at low frequencies ($10^{-4} -10^{-1}$ Hz). One of the target sources for
pulsar timing arrays are individual supermassive black hole binaries that are
expected to form in galactic mergers. In this paper, a likelihood based method
for detection and estimation is presented for a monochromatic continuous
gravitational wave signal emitted by such a source. The so-called pulsar terms
in the signal that arise due to the breakdown of the long-wavelength
approximation are explicitly taken into account in this method. In addition,
the method accounts for equality and inequality constraints involved in the
semi-analytical maximization of the likelihood over a subset of the parameters.
The remaining parameters are maximized over numerically using Particle Swarm
Optimization. Thus, the method presented here solves the monochromatic
continuous wave detection and estimation problem without invoking some of the
approximations that have been used in earlier studies.
