A Batch Update Using Multiplicative Noise Modelling for Extended Object Tracking

While the tracking of multiple extended targets demands for sophisticated algorithms to handle the high complexity inherent to the task, it also requires low runtime for online execution in real-world scenarios. In this work, we derive a batch update for the recently introduced elliptical-target tracker called MEM-EKF*. The MEM-EKF* is based on the same likelihood as the well-established random matrix approach but is derived from the multiplicative error model (MEM) and uses an extended Kalman filter (EKF) to update the target state sequentially, i.e., measurement-by-measurement. Our batch variant updates the target state in a single step based on straightforward sums over all measurements and the MEM-specific pseudo-measurements. This drastically reduces the scaling constant for typical implementations and indeed we find a speedup of roughly 100x in our numerical experiments. At the same time, the estimation error which we measure using the Gaussian Wasserstein distance stays significantly below that of the random matrix approach in coordinated turn scenarios while being comparable otherwise.