A Gaussian process approach for extended object tracking with random shapes and for dealing with intractable likelihoods

Abstract

Abstract-Tracking of arbitrarily shaped extended objects is a complex task due to the intractable analytical expression of measurement to object associations. The presence of sensor noise and clutter worsens the situation. Although a significant work has been done on the extended object tracking (EOT) problems, most of the developed methods are restricted by assumptions on the shape of the object such as stick, circle, or other axis-symmetric properties etc. This paper proposes a novel Gaussian process approach for tracking an extended object using a convolution particle filter (CPF). The new approach is shown to track irregularly shaped objects efficiently in presence of measurement noise and clutter. The mean recall and precision values for the shape, calculated by the proposed method on simulated data are around 0.9, respectively, by using 1000 particles.

Spatio-Temporal Gaussian Process Models for Extended and Group Object Tracking With Irregular Shapes

“…where k E (•) represents the spatio-temporal covariance kernel, k E θ (•) represents the spatial and k E t (•) represents the temporal covariance kernel. A periodic [20] or Von-Mises [41] covariance kernel can be used to model k E θ (•). k E t (•) can be modeled in a number of ways, e.g.…”

“…The measurement likelihood is derived in this subsection assuming contour measurements. For the surface measurements case, the model derived in this section and a GP convolution particle filter [41] can be used. Alternatively, Kalman filter based approach, given in this paper, can be adopted using a modified spatial covariance kernel as proposed in [1].…”

A Gaussian Process Convolution Particle Filter for Multiple Extended Objects Tracking with Non-Regular Shapes

“…The contributions of this work are as follows; (i) A new Gaussian process convolution particle filter (GPCPF) based approach for tracking multiple extended objects having non-regular shapes is proposed. A GPCPF for tracking a single extended object is proposed in [1]. (ii) A new convolutional kernel is proposed to track different complex shaped objects using surface measurements without any prior knowledge of the measurement statistics.…”

“…Some advanced shape estimation methods have also been proposed for tracking the object as an irregularly shaped (starconvex) object. These include the random hypersurface model (RHM) [12], Gaussian Process (GP) based models [13], [1] and mixture of sub-objects [14].…”

“…The analytical expression of the measurement likelihood is also not available due to the non-linearity of the problem. The Gaussian Process Convolution Particle Filter (GPCPF) [1] does not require any prior knowledge of measurement statistics and an analytical expression of the likelihood function. Moreover, unlike the method proposed in [13], this method can track a single object moving in clutter.…”