Bayesian estimation of line segments

A popular approach when tracking extended objects with elongated shapes, such as ships or airplanes, is to approximate them as a line segment. Despite its simple shape, the distribution of measurement sources on a line segment can be characterized in many radically different ways. The spectrum ranges from Spatial Distribution Models that assume a distinct probability for each individual source, to Greedy Association Models as used in curve fitting, which do not assume any distribution at all. In between these border cases, Random Hypersurface Models assume a distribution over subsets of all sources. In this paper, we compare Bayesian estimators based on these different models. We point out their advantages and disadvantages and evaluate their performance by means of illustrative examples with synthetic and real data using a Linear Regression Kalman Filter.