  We formulate a model of a quantum particle continuously monitored by
detectors measuring simultaneously its position and momentum. We implement the
postulate of wavefunction collapse by assuming that upon detection the particle
is found in one of the meters' states chosen as a discrete subset of coherent
states. The dynamics, as observed by the meters, is thus a random sequence of
jumps between coherent states. We generate such trajectories using the Monte
Carlo Wavefunction method. For sparsely distributed detectors, we use methods
from renewal theory of stochastic processes to obtain some semi-analytic
results. In particular, the different regimes of dynamics of the free particle
are identified and quantitatively discussed: from stroboscopic motion in the
case of low interrogation frequency, to delayed dynamics reminiscent of the
Zeno effect if monitoring is frequent. For a semi-continuous spatial
distribution of meters the emergence of classical trajectories is shown. Their
statistical properties are discussed and compared to other detection schemes in
which the effect of measurement corresponds to "spatial filtering" of the
wavefunction.
