Partial likelihood for unbiased extended object tracking

An extended object gives rise to several measurements that originate from unknown measurement sources on the object. In this paper, we consider the tracking and parameter estimation of extended objects that are modeled as a curve in 2D such as a circle or an ellipse. A standard model for such extended objects is to assume that the unknown measurement sources are uniformly distributed on the curve. We argue that the uniform distribution may not be the best choice in scenarios where the true distribution of the measurements significantly differs from a uniform distribution. Based on results from curve fitting and errors-in-variables models, we develop a partial likelihood that ignores the distribution of measurement sources and can be shown to outperform the likelihood for a uniform distribution in these scenarios. If the true measurement sources are in fact uniformly distributed, our new likelihood results in a slightly slower convergence but has the same asymptotic behavior.