Tracking of Rectangular Object Using Key Points with Regionally Concentrated Measurements

Extended object tracking (EOT) has attracted much attention in recent years. EOT approaches always assume that scattering centers are distributed on the boundary of or uniformly over the object extension. However, a practical distribution is complex and scattering centers can be concentrated on regions of the extension. To describe this phenomenon, a key-point-based model is proposed. It partitions a rectangular object extension into four regions that intersect at a key point. Over different regions scattering centers are assumed uniformly distributed with different densities related to the area of the regions. Thus, the overall complex distribution of regionally concentrated measurements can be described by combining the four local simple ones. The variation of the key point's position on the object can affect the four regions in size and shape, and thus can characterize different overall distributions. Estimation of the extension amounts to that of the key point's kinematic state, the object orientation, and the length and width of each region. Based on the proposed model, measurements are projected into two directions along with and perpendicular to the object orientation approximated by its prediction, respectively. Variances of the projected measurements in the two directions are derived to be Gamma distributed. Using the conjugate property of a Gamma and an inverse Gamma distributions, an analytical recursive estimator of the kinematic state and the length and width variables is obtained. The effectiveness of the proposed approach is illustrated using both simulated and real data.