Extended Object Tracking Using Random Matrix with Extension-Dependent Measurement Numbers

For extended object tracking (EOT), a fluctuating number of measurements are generated by a sensor at a time instant. In practice, the measurement number depends on the object extension, sensor resolution, and sensor-to-object geometry. Given the sensor resolution, the number, thus, contains information on the object state and extension. This article proposes a random-matrix approach to EOT utilizing this information to improve the performance of state and extension estimation. First, a Gamma-alike distribution of the measurement number is proposed to model the dependence of the number on sensor resolution and the object state and extension. This model also fits the random-matrix framework. Second, a Bayesian approach to jointly estimating the state and extension based on an extension-dependent number of measurements is derived. Facilitated by the form of the distribution, the derived approach has an analytical form and it can naturally reduce to an EOT approach without directly using measurement numbers. The proposed number model can also be incorporated with different random-matrix approaches. The effectiveness of the proposed approach is demonstrated by evaluation results using one simulation and two real-data experimental scenarios compared with existing random-matrix algorithms.