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A Data Model and Predicate Logic for Trajectory Data (Extended Version)

Johann Bornholdt, Theodoros Chondrogiannis, Michael Grossniklaus

TL;DR

This paper presents a data model that treats trajectories as first-class citizens, thus fully capturing their spatio-temporal properties, and introduces a predicate logic that enable query processing under different uncertainty assumptions.

Abstract

With recent sensor and tracking technology advances, the volume of available trajectory data is steadily increasing. Consequently, managing and analyzing trajectory data has seen significant interest from the research community. The challenges presented by trajectory data arise from their spatio-temporal nature as well as the uncertainty regarding locations between sampled points. In this paper, we present a data model that treats trajectories as first-class citizens, thus fully capturing their spatio-temporal properties. We also introduce a predicate logic that enable query processing under different uncertainty assumptions. Finally, we show that our predicate logic is expressive enough to capture all spatial and temporal relations put forward by previous work.

A Data Model and Predicate Logic for Trajectory Data (Extended Version)

TL;DR

This paper presents a data model that treats trajectories as first-class citizens, thus fully capturing their spatio-temporal properties, and introduces a predicate logic that enable query processing under different uncertainty assumptions.

Abstract

With recent sensor and tracking technology advances, the volume of available trajectory data is steadily increasing. Consequently, managing and analyzing trajectory data has seen significant interest from the research community. The challenges presented by trajectory data arise from their spatio-temporal nature as well as the uncertainty regarding locations between sampled points. In this paper, we present a data model that treats trajectories as first-class citizens, thus fully capturing their spatio-temporal properties. We also introduce a predicate logic that enable query processing under different uncertainty assumptions. Finally, we show that our predicate logic is expressive enough to capture all spatial and temporal relations put forward by previous work.
Paper Structure (13 sections, 13 equations, 9 figures)

This paper contains 13 sections, 13 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. A Data Model for Trajectories
  4. Trajectory Representation in NF2
  5. Data Point and Trajectory Properties
  6. Segment Property Uncertainty
  7. Spatio-Temporal Predicate Logic
  8. Spatial Predicates
  9. Temporal Predicates
  10. Combining Spatial and Temporal Predicates
  11. Selection Uncertainty
  12. Proof of Concept
  13. Spatial Trajectory Selection in NF2

Figures (9)

  • Figure 1: Example of a trajectory $T$ and a query region $R$.
  • Figure 2: The relational representation of trajectory $T$.
  • Figure 3: Relational representation $\mathfrak{T}$ of a nested trajectory relation $T_0$.
  • Figure 4: Property relation for trajectories (species) and points (movement type).
  • Figure 5: Query result when interpreting consecutive point properties continuously.
  • ...and 4 more figures

Theorems & Definitions (3)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition: Spatio-temporal Range Query