Maximum Physically Consistent Trajectories

Abstract

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

Measuring Trajectory Similarity Based on the Spatio-Temporal Properties of Moving Objects in Road Networks

“…In this study, the result of matching for each point of a Noise is typically present in the raw movement data collected by tracking devices. In this study, the raw trajectories including noises (outliers) are identified based on the average speed of moving objects and eliminated from the dataset [22,23]. The moving object travels a certain distance based on an average speed recorded by GPS receivers based on a constant sampling rate (e.g., 15 s).…”

A Benchmark of Existing Tools for Outlier Detection and Cleaning in Trajectories

“…In Custers et al (2021), a new method category based on physical movement properties is introduced, such as speed (Optimal Speed-bounded) and acceleration (Optimal Acceleration-bounded). This method defines limits on the minimum and maximum allowed values for these properties and uses them to determine whether a point in the trajectory is consistent with the model.…”

Uma análise comparativa de técnicas de detecção de pontos de parada em ambientes urbanos

“…No trabalho [Duarte and Sakr 2023], é apresentado um método para gerar ground-truth, ou seja, um método para gerar um conjunto de targets ou labels que posteriormente podem ser usados para treinar e testar um ou mais modelos, utilizando validac ¸ão cruzada. Especificamente, esse método serve para gerar labels de 'outliers' ou 'ruído' em quatro conjuntos de dados distintos, que serão utilizados para avaliar os métodos de detecc ¸ão de outliers, e limpeza de trajetória, implementados em sete bibliotecas: (i)Movetk [Custers et al 2021]; (ii) Moving Pandas [Graser and Dragaschnig 2020]; (iii) Scikit-mobility [Pappalardo et al 2022]; (iv) Ptrail [Haidri et al 2021]; (v) Pymove [Sanches 2019, Bráz 2020]; (vi) Argosfilter [Freitas and Freitas 2022]; (vii) Stmove [Seidel et al 2019].…”

“…Outra forma de identificar pontos de parada é através da verificac ¸ão da consistência da trajetória sobre um modelo físico [Custers et al 2021]. Neste trabalho uma versão deste algoritmo foi implementada usando como modelo físico um limite mínimo de velocidade.…”

“…Embora a literatura apresente inúmeros métodos propostos para solucionar essa tarefa [Li et al 2008, Nogueira et al 2018, Aslak and Alessandretti 2020, Custers et al 2021, Duarte and Sakr 2023, poucos trabalhos concentram-se na comparac ¸ão abrangente dessas abordagens.…”