This paper proposes a sequential Monte Carlo filter (particle filter) for state and parameter estimation of dynamic systems. It is applied to the problem of extended object tracking in the presence of dense clutter. The unknown length of a stick-shape object is estimated in addition to the kinematic parameters. The kernel density estimation technique is utilised to approximate the joint posterior density of target state and static size parameters. The convolution particle filtering approach is validated on a Poisson model for the measurements, originating from the target and clutter. Examples illustrating the filter performance are presented. Simulation results show that the convolution particle filter provides accurate on-line tracking, with very good estimates both for the target kinematic states and for the parameters of the target extent.