Space-time Prisms Research Articles

Physics-Based Abnormal Trajectory Gap Detection

Given trajectories with gaps (i.e., missing data), we investigate algorithms to identify abnormal gaps in trajectories which occur when a given moving object did not report its location, but other moving objects in the same geographic region periodically did. The problem is important due to its societal applications, such as improving maritime safety and regulatory enforcement for global security concerns, such as illegal fishing, illegal oil transfers, and trans-shipments. The problem is challenging due to the difficulty of bounding the possible locations of the moving object during a trajectory gap, and the very high computational cost of detecting gaps in such a large volume of location data. The current literature on anomalous trajectory detection assumes linear interpolation within gaps, which may not be able to detect abnormal gaps since objects within a given region may have traveled away from their shortest path. In preliminary work, we introduced an abnormal gap measure that uses a classical space-time prism model to bound an object's possible movement during the trajectory gap and provided a scalable memoized gap detection algorithm (Memo-AGD). In this article, we propose a space time-aware gap detection (STAGD) approach to leverage space-time indexing and merging of trajectory gaps. We also incorporate a dynamic region merge-based (DRM) approach to efficiently compute gap abnormality scores. We provide theoretical proofs that both algorithms are correct and complete and also provide analysis of asymptotic time complexity. Experimental results on synthetic and real-world maritime trajectory data show that the proposed approach substantially improves computation time over the baseline technique.

A novel data-driven approach for customizing destination choice set: A case study in the Netherlands

Modeling the destination choice has been of great interest for travel behavior community as well as policymakers in understanding the demand for land use and transportation infrastructures at aggregate and disaggregate levels and possibly devising policies to balance the demand and supplies. One of the challenges underlying predictions of location choice is the large choice set. While traditionally many methods had been devised to limit the choice set size either on a rather ad hoc basis or based on space–time prism by removing the locations out of reach of the subjects, the current study takes a substantially different approach and proposes a data-driven method to customize the generation of the choice set. The proposition is that observing the mobility patterns of citizens for multiple weeks would enable us to limit the choice set, depending on how far the subjects travel (beyond or within the distance they travel for their most frequent activities) to conduct their various activities. More precisely, using longitudinal trajectory data, we first classify people into two subgroups: returners and explorers, based on the size of the area (around their k most visited locations: k-radius of gyration) they move during the observation period. The destination choice set for four types of activities is then customized for returners (and explorers) and is used in a sequence of decisions represented by decision trees for the prediction of their destinations. The models for the whole sample and each subgroup separately are compared. The results suggest that the accuracy of destination prediction improves substantially for all four selected activity types, especially for the returners whose choice sets are formed based on their radius of gyration.

Visit probability and accessibility within space–time prism of activity program

Space–time prism (STP) is widely applied to measure individuals’ ability to reach opportunities given the resource limitations. The majority of STP models treat prism-based accessibility as binary measures, wherein all locations within a prism are assumed equally accessible while others are deemed inaccessible. Although a few STP models examined heterogeneous interiors by modeling visit probabilities within the STPs, they primarily focused on trip-level analysis and did not explore the application for accessibility measurement. This study proposes a model framework based on multi-state supernetworks for constructing and estimating the probabilistic STPs of daily activity programs. The estimation is implemented with latent class models to account for individual heterogeneities in travel and activity participation. Based on the probabilistic STPs, we suggest a space–time accessibility measurement incorporating visit probabilities. We validate the model framework using mobility trajectory data collected in the Netherlands and demonstrate that the visit probability model can effectively capture the probabilistic STP interiors and the proposed accessibility measurement can provide a comprehensive evaluation of accessibility in the presence of activity chains.

Measuring Reliable Accessibility to High-Speed Railway Stations by Integrating the Utility-Based Model and Multimodal Space–Time Prism under Travel Time Uncertainty

Measuring Reliable Accessibility to High-Speed Railway Stations by Integrating the Utility-Based Model and Multimodal Space–Time Prism under Travel Time Uncertainty

A probabilistic time geographic approach to quantifying seabird‐vessel interactions

AbstractAccounting for uncertainty is essential for precautionary approaches to managing seabird bycatch in commercial fisheries. However, there is no existing mechanism to explicitly quantify the uncertainty of seabird‐vessel interactions (i.e. co‐occurrence in space and time). Here we develop a time geographic method to measure the probability of individual birds encountering (co‐occurring within 30 km) and attending (within 5 km) individual fishing vessels. The approach involves creating voxel‐based probabilistic space–time prisms (PSTPs) to model the movements of individual birds and vessels, with trajectory data from bird‐borne GPS devices and vessel Automatic Identification Systems (AIS). We intersected these PSTPs to quantify the probability of interaction between bird‐vessel pairs over time and space. We demonstrate the approach with a case study of interactions of Endangered Toroa (Antipodean Albatross; Diomedea antipodensis antipodensis) with pelagic longline vessels in part of the South Pacific high seas. We found 15 vessels within 150 km and 3 h of two birds, yet interaction occurred with only two of those vessels. We visualised the probability of encounter and attendance over time and space and determined that interactions lasted several hours each (up to 6.2–14.1 h attendance, 20.8–26.1 h encounter for one bird‐vessel pair). Our time geographic approach adds to existing tools to quantify seabird bycatch risk by providing an explicit measure of uncertainty of seabird‐vessel interactions. We provide a flexible methodological pathway and R scripts, the application of which would allow managers to estimate interaction probability for multiple marine species and fisheries, including those with lower‐resolution positional datasets.

A general characterisation of space-time prisms with spatial anchor uncertainty

We investigate the geometry of space-time prisms and their associated potential path areas (for movement that takes place in the plane) in the setting where the prism anchors have a spatial uncertainty area attached to them. Our main result is a characterisation of such space-time prisms and their potential path areas in terms of a generalised distance function between closed subsets of the ambient space. Since the case where this spatial anchor uncertainty takes the form of a closed disk has already been addressed by Kuijpers and Othman (2017), we focus on the more realistic case where the uncertainty areas are ellipses and we apply our general characterisation to this example to obtain explicit descriptions of the uncertain prisms and their potential path areas.

Space–time prism and accessibility incorporating monetary budget and mobility-as-a-service

Recent years in time geography have witnessed a flourishment of space–time prism (STP) modeling extensions for enhancing realism. However, there is little research on the incorporation of monetary budget in STP models to capture personal potential mobility space more realistically. This study considers both time and monetary budget constraints in STP modeling in a multimodal supernetwork integrating mobility-as-a-service and trip chains. We develop an efficient two-stage bi-criterion bidirectional search method to identify Pareto path sets to construct the resulting STP for conducting a flexible activity between two anchor nodes. To demonstrate the effectiveness of the proposed model and solution method, a case study with varying scenarios is conducted to evaluate the impacts of monetary budget on space–time accessibility and equality. The findings show that the ignorance of monetary budget overestimates accessibility and that MaaS, if not well designed, may not improve equality in accessibility as intended.

Using a Cost-Distance Time-Geographic Approach to Identify Red Deer Habitat Use in Banff National Park, Alberta, Canada

Animal movements are realizations of complex spatiotemporal processes. Central to these processes are the varied environmental contexts in which animals move, which fundamentally impact the movement trajectories of individuals at fine spatial and temporal scales. An emerging perspective in time geography is the direct examination of the influence that varying contexts may have on observed movements. An approach that considers environmental context can yield actionable information for wildlife management, planning, and conservation; for instance, identifying areas of probable occupancy by an animal may improve the efficiency of fieldwork. This research develops the first known practical application of a new cost-distance-based, probabilistic voxel space–time prism (CDBPSTP) in efforts to more realistically characterize the unobserved habitat occupancies of animals occurring between known positions provided by location-aware technologies. The CDBPSTP method is applied to trajectory data collected for a group of red deer (Cervus elaphus) tracked near Banff National Park, Alberta, Canada. As a demonstration of the added value from examining how context influences movement, CDBPSTP habitat occupancy results are compared to the earlier PSTP method in context with empirical and theoretical understandings of red deer habitat preference and space-use behaviors. This comparison reveals that with CDBPSTP, variation present in the mover’s environment is explicitly considered as an influence on the mover’s probable path and occupancies between observations of its location. With the increasing availability of high-resolution geolocational and associated environmental data, this study highlights the potential for CDBPSTP to be leveraged as a broadly applicable tool in animal movement analysis.

Mobility constraints and accessibility to work: Application to Stockholm

This paper investigates workplace accessibility in Stockholm through a workplace choice model within a space–time prism concept. We develop a workplace accessibility measure that incorporates individuals’ constraints in time, space, and resources. The accessibility measure is derived from an activity-based demand model formulated as a Markov decision process in a dynamic discrete choice framework, where space–time constraints affect the possibilities of individuals to engage in activities during spare time. Indeed, the results show that spare time accessibility is significantly linked to workplace accessibility. Applications of the results show how space–time constraints, such as access to a car or having children, affect benefits in terms of consumer surplus for relocating a large workplace (a hospital in our case), car dependency, and segregation.

Inclusive Accessibility: Integrating Heterogeneous User Mobility Perceptions into Space-Time Prisms

Travelers’ day-to-day mobility depends on their perceptions, experiences, and personal characteristics. Many accessibility measures overlook perceptual factors and mainly consider space–time limitations of mobility, overestimating travelers’ potential mobility. We introduce a novel inclusive accessibility concept that advances time-geographic accessibility measures in light of travel behavior theories. We conceptualize inclusive accessibility as a subset of the classic space–time prism (STP) that incorporates hard constraints (e.g., limited infrastructure and services and time) and soft constraints (e.g., perceptions of safety and comfort toward the built environment and infrastructure and travel time preferences). We collected survey data on individual-level mobility perceptions and applied machine learning algorithms to predict personalized soft constraints for walking. Considering public transit and walking, we model and compare three network-based STPs: classic STP with hard constraints, inclusive STP with soft spatial constraints, and inclusive STP with soft spatial and temporal constraints. Our method demonstrates heterogeneities in individuals’ mobility perceptions. We illustrate that the individual’s level of accessibility shrinks substantially as we approach more conservative measures that include travel perceptions. Our method highlights the differences between travelers’ physically and psychologically accessible space depending on their travel choices and exposure.

What can analysis of Space-Time of Action tell us about medium-term changes in adults’ and children’s access to place of activity? The example of Bogotá

This article draws on the space-time prism as formalized in time-geography (Hägerstrand 1970) and on spatial analysis methods to examine medium-term changes to household members’ access to place of activity, against the backdrop of urban change. The analytical framework thus uses the concept of Space-Time of Action (Demoraes et al. 2020a), referring to the combination of all the places of work or study that individuals go to, and the time taken to reach them from home. The analysis is based on two surveys conducted in Bogotá (Colombia) in 1993 and 2009 to apprehend individuals’ spatial mobilities. Two groups at different stages in their life course and co-residing in the same households are studied: schoolchildren and working adults. First, Space-Times of Action are calculated and mapped using kernel outer rings delineating the concentration of destinations for the two groups and the nine survey zones at each date. Second, the statistical significance of the discrepancies between Space-Times of Action is assessed using a bivariate colocation test. The test indicates overall stability in children’s access to place of schooling, but a more contrasting situation for adults.

Spatio-temporal constraints of carer-workers in the Greater Toronto and Hamilton Area: An exploratory analysis using potential path areas

Carer-workers are individuals providing regular unpaid care to an adult dependent while simultaneously employed in the paid labour market, and the group represents a significant portion of the Canadian adult population. Despite the prevalence of unpaid care in Canada, very limited research has explored the spatio-temporal tensions that carer-workers experience. The objective of this study is to explore the space–time constraints experienced by carer-workers. One way of measuring both space and time constraints on an individual is the foundational time geography concept of the Space-Time Prism, and its two-dimensional counterpart, the Potential Path Area (PPA). We collected three to seven day-long trip diaries of 25 carer-workers in the Greater Toronto and Hamilton Area in 2017–18, including all trips made over the diary period and whether the trip involved care work. We developed a customized Python tool and used Open Street Maps to derive PPAs for 12 of the sample carer-workers, which were aggregated to form daily PPAs. Descriptive analyses of the PPAs are presented, and comparisons of PPA size, and therefore, daily accessibility, across carer-workers’ sociodemographic and economic indicators, days of the week, and level of caregiving intensity are examined. Through its ability to represent, quantitatively and visually, the accessibility differences across various population groups, and to fill a gap in our understanding of carer-workers, the PPA represents an important methodological avenue for continuing research into carer-workers in Canada and around the world.

Personalizing the dichotomy of fixed and flexible activities in everyday life: deriving prism anchors from GPS-enabled survey data.

Space-time prism is a fundamental concept in time geography that can model an individual's accessibility to resources under space-time constraints. A prism anchor is often defined by work, school, or home activity with a fixed location and schedule. Trips and other activities are relatively flexible and scheduled between prism anchors. This fixity-flexibility dichotomy may not capture the increasing complexity of human mobility behaviors or variations among individuals. Recent developments in location-aware technologies allow us to collect person-level mobility data with detailed space-time paths and contextual information. This article develops methods to extract prism anchors from these GPS-based survey data and examines whether home, work, and school activities can always be used to define prism anchors for everyone. To illustrate our methods, we use data collected in Minnesota and Beijing as two study cases. Results in both study cases suggest that not everyone has home, work, or school anchors, and people with the same socio-demographic background tend to have similar anchor types. By deriving home, work, and school anchors, we can better understand how a person's everyday schedules are governed by home, work, and school and refine person-based accessibility measures.

Realizable accessibility: evaluating the reliability of public transit accessibility using high-resolution real-time data.

The widespread availability of high spatial and temporal resolution public transit data is improving the measurement and analysis of public transit-based accessibility to crucial community resources such as jobs and health care. A common approach is leveraging transit route and schedule data published by transit agencies. However, this often results in accessibility overestimations due to endemic delays due to traffic and incidents in bus systems. Retrospective real-time accessibility measures calculated using real-time bus location data attempt to reduce overestimation by capturing the actual performance of the transit system. These measures also overestimate accessibility since they assume that riders had perfect information on systems operations as they occurred. In this paper, we introduce realizable real-time accessibility based on space–time prisms as a more conservative and realistic measure. We, moreover, define accessibility unreliability to measure overestimation of schedule-based and retrospective accessibility measures. Using high-resolution General Transit Feed Specification real-time data, we conduct a case study in the Central Ohio Transit Authority bus system in Columbus, Ohio, USA. Our results prove that realizable accessibility is the most conservative of the three accessibility measures. We also explore the spatial and temporal patterns in the unreliability of both traditional measures. These patterns are consistent with prior findings of the spatial and temporal patterns of bus delays and risk of missing transfers. Realizable accessibility is a more practical, conservative, and robust measure to guide transit planning.

Autonomous planning of optimal four-dimensional trajectory for real-time en-route airspace operation with solution space visualisation

One of the challenges in applying autonomous operation-based conflict detection and resolution (CD&R) techniques to practice is their functional completeness, such as the ability to simultaneously consider three-dimensional (3D) scenarios, controlled time of arrival, restricted areas, trajectory recovery, and multi-stakeholder performance preferences. Besides, the effective interaction between controllers, pilots and autonomous operating system can better support the CD&R to work in practice, where humans are able to intuitively understand the rationale for solutions given by automatic decision-making tools. To bridge the gap, a novel operational framework for four-dimensional (4D) trajectory conflict management in the context of free route airspace is proposed. Airspace discretisation based on a 3D grid is used to facilitate the consideration of restricted areas and to balance calculation speed and optimal effect. The core of this framework is a two-stage real-time autonomous 4D trajectory planning method in a restricted en-route sector with multiple flight levels enhanced by solution space visualisation. Stage one is a trajectory pre-planning model based on a visibility graph and the Dijkstra algorithm considering the conflict between aircraft and emerging restricted areas. Stage two is a real-time conflict-free and fuel-optimal 4D trajectory re-planning model. The space–time prism is employed to enable the planned trajectory to meet the controlled time of arrival and trajectory recovery requirements, where the performance preferences of both the air traffic management and airspace users are taken into account. The reachable solution space representation is applied to realise the solution space visualisation that has the potential to support the human–machine interaction and air–ground coordination. A simulation scenario is established to validate the effectiveness, efficiency, stability, and timeliness of the proposed method. Results show that in an artificial en-route sector, the average extra flight distance, average flight delay, average extra fuel consumption, and average computing time for conflict resolution were less than 0.41 km, 2.1 s, 1.5 kg, and 0.08 s in the saturated scenario, respectively, and the domino effect of the flight conflict did not show a significant rise with the increase of traffic density, which verified that the proposed autonomous trajectory operation methodology is a promising approach to facilitate autonomous air traffic management in the future.

Space–time prisms in multimodal supernetwork - Part 2: Application for analyses of accessibility and equality

Space–time prism (STP) is a fundamental concept in time geography and has been predominately constructed in unimodal transportation networks. Due to the vast trip chaining options by private vehicles and public transportation, it was challenging to construct STP over multimodal transportation networks. We previously put forward an efficient method to narrow down the action space for trip chaining and construct STPs effectively in a multimodal supernetwork. This study applies multimodal STP modeling to measure space–time accessibility and equality of daily activity opportunities. Two equality measures (Gini coefficient and 20:20 ratio) are derived from two space–time accessibility measures based on delineated STPs. We examine the equality of access to shopping and leisure opportunities in the Rotterdam–The Hague metropolitan area, the Netherlands. The results show the effects of various factors on accessibility and equality. It is found that although the study area has relatively low inequality using single modes, multimodal trip chaining further reduces inequality to access the distributed space–time opportunities.

Space–time prism in multimodal supernetwork - Part 1: Methodology

Space–time prism (STP) modeling offers a theoretical base for various person-based space–time accessibility measures. It has been challenging to construct STPs in multimodal transportation networks because of the vast multimodal trip chaining options between private vehicles and public transportation. This study suggests an effective method for narrowing down the trip chaining space. The method involves three incremental strategies to eliminate parking locations that contribute little to enlarging the STP. First, an upper bound potential path area (PPA) is constructed to remove all inferior parking locations. Second, the study area is partitioned and only complementary parking locations attractive to trip chaining are selected. Third, triangular inequalities are applied for pruning. The selected parking locations are used to construct a compact multimodal supernetwork encompassing one episode of activity participation. Consequently, the STP and PPA can be found by an existing two-stage bidirectional search method. Experimental tests are conducted to demonstrate the effectiveness of the method. It is found that 1–2 orders of speedups can be achieved with little compromising the accuracy of measuring space–time accessibility. The suggested method is applicable for measuring space–time accessibility in large-scale multimodal transportation networks.

Exact space–time prism of an activity program: bidirectional searches in multi-state supernetwork

ABSTRACT Space–time prism (STP) modeling for activity programs with various realizations of activity chains has been a challenging research topic. This study claims that a bidirectional search scheme in a multi-state supernetwork is capable of pinpointing the exact STP of an activity program. The correctness and search space are first analyzed for the existing two-stage bidirectional search methods originally suggested for constructing trip-based STPs. Two simultaneous bidirectional search methods are further suggested. Travel time lower bounds based on A*, landmarks, and triangular inequalities are applied in goal-directed searches to reduce the search space. The small twists in formalism over the existing methods ensure accuracy and computational efficiency. The performances of the different search methods are compared for conducting activity programs in large networks.

Applying frequent-pattern mining and time geography to impute gaps in smartphone-based human-movement data

ABSTRACT Though GPS-based human trajectory data have been commonly used in travel surveys and human mobility studies, missing data or data gaps that are intrinsically relevant to research reliability remain a critical and challenging issue. This study proposes a novel framework for imputing data gaps based on frequent-pattern mining and time geography, which allows for considering spatio-temporal travel restrictions during imputation by evaluating the spatio-temporal topology relations between the space-time prisms of gaps and corresponding frequent activities or trips. For the validation, the proposed framework is applied to raw GPS trajectories that were collected from 139 participants in Switzerland. In the case study, the temporal and spatio-temporal gaps are artificially generated by randomly choosing activities and trips from the trajectory data. Through comparing the mobility indicators (i.e. duration and distance) calculated from raw data, imputed data, and data with gaps, we quantitatively evaluate the performance of the proposed method in terms of Pearson correlation coefficients and deviation. We further compare the framework with the shortest path interpolation method based on the generated spatio-temporal gaps. The comparison results demonstrate the performance and advantage of the proposed method in imputing gaps from GPS-based human movement data.

Vehicle Trajectory Reconstruction on Urban Traffic Network Using Automatic License Plate Recognition Data

Vehicle trajectory data are critical to urban active traffic management and simulation applications. Automatic license plate recognition (ALPR) data can provide partial vehicle trajectory information by matching the detected vehicle license plates through time series. However, the trajectory extracted from ALPR data tend to be sparse and incomplete due to technical and financial constraints. This paper deals with the problem of sparse trajectory reconstruction based on ALPR data. Firstly, the multiple travel activities of the vehicle are divided based on the reasonable travel time threshold, and the incomplete vehicle trajectory is identified. Then, candidate trajectories are generated by an improved K-shortest-path (KSP) algorithm based on space-time prism theory. Finally, the auto-encoder model is utilized to select the candidate trajectory with optimal decision indicators, which realizes the vehicle trajectory reconstruction. The proposed method was implemented on a realistic urban traffic network in Ningbo, China. The verification results show that the proposed method has a comprehensive accuracy of 85% and good robustness. From the comparison with the baseline algorithm, it can be seen that the proposed method still has high accuracy in low ALPR coverage rate, and there exists a minimum required ALPR coverage rate (50% in the test network) for reconstructing trajectories accurately.