Maximum Physically Consistent Trajectories

Trajectories are usually collected with physical sensors, which prone to errors and cause outliers in the data. We aim identify such via properties of tracked entity, that is, we consider its possibility visit combinations measurements. describe optimal algorithms compute maximum subsequences measurements consistent (simplified) physics models. Our results output-sensitive respect number k a trajectory n Specifically, an O ( log 2 )-time algorithm for 2D trajectories using model unbounded acceleration but bounded velocity, O(nk) -time any where consistency is “concatenable”: subsequence ends another begins together form sequence. also acceleration-bounded models not concatenable. show how ) time, under appropriate realism conditions. Finally, experimentally explore performance our on several large real-world sets trajectories. experiments generally able retain larger fractions noisy than previous work simpler greedy approaches. observe speed-bounded may practice approximate quite well, though observed some variation between datasets.