On Data Association with Possibly Unresolved Measurements

Tracking targets based on measurements provided by radar, sonar, or lidar sensors is essential to obtain situational awareness in important applications, including autonomous navigation and applied ocean sciences. A key challenge in multitarget tracking is the unknown association between the available measurements and the targets to be tracked. In particular, robust data association for closely spaced targets requires advanced methods that explicitly model unresolved measurements. Due to limited sensor resolution, the sensor produces a single measurement for two or more actual targets. If not explicitly modeled in the multitarget tracking method, unresolved measurements lead to track losses and thus, to significant tracking errors. In this paper, we propose a scalable data association method for the tracking of multiple potentially unresolved targets. A loopy belief propagation method is presented that efficiently approximates the marginal association probabilities given a set of potentially unresolved measurements. This method scales quadratically in the number of targets and linearly in the number of measurements. Our numerical results demonstrate that the computed approximate marginal association probabilities are close in $L_{1}$ distance to the true marginal association probabilities, which can only be calculated for very small tracking scenarios.