  Cosmic strings are predicted to form kinks and cusps that travel along the
string at close to the speed of light. These disturbances are radiated away as
highly beamed gravitational waves that produce a burst like pulse as the cone
of emission sweeps past an observer. Gravitational wave detectors such as the
Laser Interferometer Space Antenna (LISA) and the Laser Interferometer
Gravitational wave Observatory (LIGO) will be capable of detecting these bursts
for a wide class of string models. Such a detection would illuminate the fields
of string theory, cosmology, and relativity. Here we develop template based
Markov Chain Monte Carlo (MCMC) techniques that can efficiently detect and
characterize the signals from cosmic string cusps. We estimate how well the
signal parameters can be recovered by the advanced LIGO-Virgo network and the
LISA detector using a combination of MCMC and Fisher matrix techniques. We also
consider joint detections by the ground and space based instruments. We show
that a parallel tempered MCMC approach can detect and characterize the signals
from cosmic string cusps, and we demonstrate the utility of this approach on
simulated data from the third round of Mock LISA Data Challenges (MLDCs).
