Extended object tracking and classification based on piecewise functions

This paper introduces a framework based on piecewise functions for bidimensional extended object tracking and classification. Piecewise functions are used to represent extended objects with arbitrarily complex shape. An exact likelihood is derived for the case in which noisy measurements can be scattered from any point on the contour of the extended object, while an approximate Monte Carlo likelihood is provided for the case in which scattering points can be anywhere, i.e. inside or on the contour, in the object surface. Using such a likelihood to measure how well the observed data fit a given shape, a suitable estimator is developed. The proposed estimator models the extended object in terms of a kinematic state, providing object position and orientation, along with a shape vector, characterizing object contour and surface. The kinematic state is estimated via a nonlinear Kalman filter, while the shape is recognized in a finite set of possible shapes by means of a Bayesian classifier. Numerical experiments are provided to assess, compared to state-of-the-art extended object estimators, the effectiveness of the proposed one.