Trajectory reconstruction is the process of inferring the path of a moving
object between successive observations. In this paper, we propose a smoothing
spline -- which we name the V-spline -- that incorporates position and velocity
information and a penalty term that controls acceleration. We introduce a
particular adaptive V-spline designed to control the impact of irregularly
sampled observations and noisy velocity measurements. A cross-validation scheme
for estimating the V-spline parameters is given and we detail the performance
of the V-spline on four particularly challenging test datasets. Finally, an
application of the V-spline to vehicle trajectory reconstruction in two
dimensions is given, in which the penalty term is allowed to further depend on
known operational characteristics of the vehicle.Comment: 25 pages, submitte