Anchor uncertainty and space-time prisms on road networks

Space-time prisms capture all possible locations of a moving person or object between two known locations and times given the maximum travel velocities in the environment. These known locations or ‘anchor points’ can represent observed locations or mandatory locations because of scheduling constraints. The classic space-time prism as well as more recent analytical and computational versions in planar space and networks assume that these anchor points are perfectly known or fixed. In reality, observations of anchor points can have error, or the scheduling constraints may have some degree of pliability. This article generalizes the concept of anchor points to anchor regions: these are bounded, possibly disconnected, subsets of space-time containing all possible locations for the anchor points, with each location labelled with an anchor probability. We develop two algorithms for calculating network-based space-time prisms based on these probabilistic anchor regions. The first algorithm calculates the envelope of all space-time prisms having an anchor point within a particular anchor region. The second algorithm calculates, for any space-time point, the probability that a space-time prism with given anchor regions contains that particular point. Both algorithms are implemented in Mathematica to visualize travel possibilities in case the anchor points of a space-time prism are uncertain. We also discuss the complexity of the procedures, their use in analysing uncertainty or flexibility in network-based prisms and future research directions.     

The geometry of space-time prisms with uncertain anchors

Space-time prisms envelop all spatio-temporal locations that moving objects may have visited between two of their known spatio-temporal locations, given a bound on their travel speed. In this context, the known locations are often the result of observations or measurements, and they are called ‘anchor points’. The classic space-time prism, in isotropic two-dimensional space, as well as in transportation networks, assumes that the measurements of these anchor points are exact. Whereas, in many applications, we can assume that time can be measured fairly precisely, this assumption is unrealistic for the spatial components of measured locations (we think of Global Positioning System (GPS) errors, for instance). In this paper, we extend the classical prism from anchor points to circular ‘anchor regions’ that capture the uncertainty or error on their measurement. We define the notion of a space-time prism with uncertain anchor points, called uncertain prism, for short. We study the geometry of uncertain prisms in an arbitrary metric space to make this concept as widely applicable as possible. We also focus on the rims of uncertain space-time prisms, which demarcate the area that a moving object can have visited between two anchor regions (given some local speed limitations).     

Modelling accessibility using space-time prism concepts within geographical information systems

Abstract

The space-time Of time geographical framework is a powerful perspective from which to analyse human behaviour. One of the central concepts in this framework is the space-time prism, which models individual accessibility to an environment. In this paper, the derivation and manipulation of space-time prism concepts within a geographical information system (GIS) are discussed. The required system inputs and desired outputs are identified and a generic GIS based procedure is presented Given these basic requirements, issues are discussed which can determine the feasibility of current GIS technology to handle the derivation of space-time prism concepts.     

Gender and Individual Access to Urban Opportunities: A Study Using Space–Time Measures

Conventional accessibility measures based on the notion of locational proximity ignore the role of complex travel behavior and space–time constraints in determining individual accessibility. As these factors are especially significant in women's everyday lives, all conventional accessibility measures suffer from an inherent “gender bias.” This study conceptualizes individual accessibility as space–time feasibility and provides formulations of accessibility measures based on the space–time prism construct. Using a subsample of European Americans from a travel diary data set collected in Franklin County, Ohio, space–time accessibility measures are implemented with a network-based GIS method. Results of the study indicate that women have lower levels of individual access to urban opportunities when compared to men, although there is no difference in the types of opportunities and areas they can reach given their space–time constraints. Further, individual accessibility has no relationship with the length of the commute trip, suggesting that the journey to work may not be an appropriate measure of job access.     

Incorporating behavior into animal movement modeling: a constrained agent-based model for estimating visit probabilities in space-time prisms

ABSTRACT

Animal movement is a dynamic spatio-temporal process. While trajectory data reflect the instantaneous animal position in space and time, other factors influence movement decisions between these observed positions. While some methods incorporate environmental (habitat) context into their understanding of the animal movement process, it is often captured in terms of simple parameters or weights influencing model results; primary behavioral data are not used directly to inform these models. Here, a new space-time constrained agent-based model is introduced, capable of producing ordered, behaviorally informed animal potential paths between observed space-time anchors. Potential paths generated by this approach incorporate both observed animal behavior and classical space-time constraints, and are used to construct associated visit probability distributions. Additionally, the notion of a behavioral space-time path is introduced, a variant of the space-time path based on the results of behaviorally aware animal movement simulation. The results of this approach demonstrate a means to better understand the varied movement opportunities within space-time prisms from an animal behavior perspective. From a spatial ecology perspective, not only is the environmental context considered, but the animal’s choice of transition and movement magnitude between contexts is modeled. This approach provides insight into the complex sequence of behaviorally informed actions driving animal movement decision-making.     

Measuring place-based accessibility under travel time uncertainty

Travel time uncertainty has significant impacts on individual activity-travel scheduling, but at present these impacts have not been considered in most accessibility studies. In this paper, an accessibility evaluation framework is proposed for urban areas with uncertain travel times. A reliable space-time service region (RSTR) model is introduced to represent the space-time service region of a facility under travel time uncertainty. Based on the RSTR model, four reliable place-based accessibility measures are proposed to evaluate accessibility to urban services by incorporating the effects of travel time reliability. To demonstrate the applicability of the proposed framework, a case study using large-scale taxi tracking data is carried out. The results of the case study indicate that the proposed accessibility measures can evaluate large-scale place-based accessibility well in urban areas with uncertain travel times. Conventional place-based accessibility indicators ignoring travel time reliability can significantly overestimate the accessibility to urban services.     

Combining spatial transition probabilities for stochastic simulation of categorical fields

Categorical spatial data, such as land use classes and socioeconomic statistics data, are important data sources in geographical information science (GIS). The investigation of spatial patterns implied in these data can benefit many aspects of GIS research, such as classification of spatial data, spatial data mining, and spatial uncertainty modeling. However, the discrete nature of categorical data limits the application of traditional kriging methods widely used in Gaussian random fields. In this article, we present a new probabilistic method for modeling the posterior probability of class occurrence at any target location in space-given known class labels at source data locations within a neighborhood around that prediction location. In the proposed method, transition probabilities rather than indicator covariances or variograms are used as measures of spatial structure and the conditional or posterior (multi-point) probability is approximated by a weighted combination of preposterior (two-point) transition probabilities, while accounting for spatial interdependencies often ignored by existing approaches. In addition, the connections of the proposed method with probabilistic graphical models (Bayesian networks) and weights of evidence method are also discussed. The advantages of this new proposed approach are analyzed and highlighted through a case study involving the generation of spatial patterns via sequential indicator simulation.     

Uncertainty analysis of space–time prisms based on the moment-design method

Space–time prism (STP) is an important concept for the modeling of object movements in space and time. An STP can be conceptualized as the result of the potential path of a moving object revolving around in the three-dimensional space. Though the concept has found applications in time geography, research on the analysis and propagation of uncertainty in STPs, particularly under high degree of nonlinearity, is scanty. Based on the efficiency and effectiveness of the moment-design (M-D) method, this paper proposes an approach to deal with nonlinear error propagation problems in the potential path areas (PPAs) of STPs and their intersections. Propagation of errors to the PPA and its boundary, and to the intersection of two PPAs is investigated. Performance of the proposed method is evaluated via a series of experimental studies. In comparison with the Monte Carlo method and the implicit function method, simulation results show the advantages of the M-D method in the analysis of error propagation in STPs.     

Random encounters in probabilistic time geography

Probabilistic time geography considers the encounter of moving agents to be random; therefore, a quantitative time geography analysis must consider the actual encounter probability. The existing algorithm of encounter probability is oriented over a discrete space and is sensitive to the unit definition of a virtual grid; thus, it is not suitable for continuous space. For this reason, a new method is presented in this paper for the encounter of two moving agents in continuous space. When the encounters are less than a specified distance threshold apart, an encounter event occurs based on the probability of the product, which is calculated by their respective probability density functions over their respective potential location areas. This probability provides a quantitative basis for predicting the likelihood of two agents meeting, as well as the location of this meeting point. Finally, the validity of the proposed model is verified by an experiment, which uses tracking data to calculate the encounter probabilities of three zebras and analyse the distribution characteristics of these probabilities over time and space.     

Estimating the effect of turn penalties and traffic congestion on measuring spatial accessibility to primary health care

Geographic variations in spatial accessibility to public resources, such as health care services, raise important questions about the efficiencies and inequities of the processes that determine where these services are located. Spatial accessibility can be measured many different ways, but many of methods in use today involve some measure of travel cost (in time or distance). In this study we explore a simple methodological question: how much are models of spatial accessibility influenced by the precise metric of travel cost? We address this question by comparing spatial accessibility to primary care physicians for two different methods of calculating travel cost (in time) on a street network: free-flow travel time and congested with turn penalties travel time—which augments free-flow travel times with the burden of traffic congestion and traffic intersection controls. We consider the effect of these two metrics of travel cost on a gravity-based measure of spatial accessibility to primary health care services in Edmonton, Alberta, Canada. Our results suggest that while travel times between locations of demand and locations of primary care providers greatly differ based on how travel cost is calculated, the gravity-based measure of spatial accessibility provides similar information for both travel cost metrics. Using congested with turn penalties travel time can be an onerous addition to the analysis of spatial accessibility, and is more useful for measuring absolute travel time rather than modeling relative spatial accessibility.     

Bayesian Journey-to-Crime Estimation: An Improvement in Geographic Profiling Methodology

A Bayesian approach to geographic profiling methodology involves updating journey-to-crime probability estimates with probabilities based on the distribution of residences of other offenders who committed crimes in the same locations. Tests were conducted on serial offenders from Baltimore County and Chicago and six different methods using five different criteria were compared. The Bayesian method was more accurate than the existing journey-to-crime methods and was as accurate as the center of minimum distance, the current best method. Suggestions for improving the methodology further are provided.     

Modeling uncertainty of moving objects on road networks via space–time prisms

Moving objects produce trajectories, which are typically observed in a finite sample of time‐stamped locations. Between sample points, we are uncertain about the moving objects's location. When we assume extra information about an object, for instance, a (possibly location‐dependent) speed limit, we can use space–time prisms to model the uncertainty of an object's location.

Until now, space–time prisms have been studied for unconstrained movement in the 2D plane. In this paper, we study space–time prisms for objects that are constrained to travel on a road network. Movement on a road network can be viewed as essentially one‐dimensional. We describe the geometry of a space–time prism on a road network and give an algorithm to compute and visualize space–time prisms. For experiments and illustration, we have implemented this algorithm in MATHEMATICA.

Furthermore, we study the alibi query, which asks whether two moving objects could have possibly met or not. This comes down to deciding if the chains of space–time prisms produced by these moving objects intersect. We give an efficient algorithm to answer the alibi query for moving objects on a road network. This algorithm also determines where and when two moving objects may have met.     

Quantifying multi-modal public transit accessibility for large metropolitan areas: a time-dependent reliability modeling approach

The temporal dimensions of public transit accessibility have recently garnered an increasing amount of interest. However, the existing literature on transit accessibility is heavily based on oversimplified assumptions that transit services operate at deterministic speeds using predetermined timetables. These measurements may overestimate transit accessibility, especially for large metropolitan areas where inter- and intra-modal transfers are frequent. To handle travel time uncertainty, a multi-modal transit accessibility modeling approach is proposed to account for realistic variations in travel time and service reliability. The proposed approach is applied to the mapping of transit accessibility in Shenzhen (China), where transit services exhibit significant travel time variations over space and time. Compared to traditional transit accessibility measures, our method has been demonstrated to better capture intrinsic spatial and temporal accessibility variations with complex multi-modal transit networks. Normal distribution of inter-stop travel times and constant travel speed between GPS sampling points are assumed to simply the computation, which we consider to adjust in future studies to better quantify the dynamics of transit accessibility across space and time.     

人类移动性与健康研究中的时间问题

随着地理信息科学的发展,地理学围绕着社会热点问题不断向其他学科交叉渗透,同时学科的交叉也为地理学研究本身注入了热量。空间一直是地理学研究中的基本问题,而时间与空间密不可分,从时间维度研究人类移动性及其丰富内涵具有重要意义。本文在总结人类移动性热点问题的基础上,重点从时间维度探讨了可达性、出行体验与幸福感、人类健康与疾病等问题的研究内容和方法,并从低收入者社区医疗保健可达性研究和阿帕拉契亚乡村地区吸烟者影响因素研究等案例进行详细阐释,最后对人类移动性与健康研究的发展方向进行了展望。     

Exploring potential human activities in physical and virtual spaces: a spatio‐temporal GIS approach

Today, the opportunity for potential human activity has gone beyond physical space to virtual space. Based on a proposed conceptual framework that models the relationships between physical and virtual spaces, this paper presents an attempt to adjust the space–time prism concept of Hägerstrand's time geography to identify potential activity opportunities in virtual space, focusing on the virtual space access channels available in physical space. A three‐dimensional (3D) spatio‐temporal Geographic Information System (GIS) design has been developed in this research to accommodate the adjusted space–time prism concept to support the representation, visualization, and analysis of potential human activities and interactions in physical and virtual spaces using the prism representation. Following the design, a prototype system has been successfully implemented in a 3D GIS environment. Such a system can provide powerful analytical tools for studies related to potential human activities and applications such as location‐based services (LBS) and accessibility analysis in the information age.     

高斯两步移动搜索法的模型研究——以上海市绿地可达性为例

合理的配置公共服务设施对城市的现代化建设至关重要。空间可达性是度量公共服务设施配置是否合理的方法之一。在诸多的研究方法中,高斯两步移动搜索法由于直观且运算简便,因而得到广泛应用。但该方法也有不足之处,本文运用格网GIS方法,以上海市的绿地空间可达性为例,对两步移动搜索法进行模型方法的改进研究,并对高斯两步移动搜索法和格网化的高斯两步移动搜索法进行对比分析,结果表明：后者可降低空间可达性的误差,提高可达性精度,对上海市绿地空间可达性反映更加真实、客观。如果选择合理的数据将其格网化,该方法也可以用于其他公共服务设施的空间可达性研究。     

Toward space-time buffering for spatiotemporal proximity analysis of movement data

Spatiotemporal proximity analysis to determine spatiotemporal proximal paths is a critical step for many movement analysis methods. However, few effective methods have been developed in the literature for spatiotemporal proximity analysis of movement data. Therefore, this study proposes a space-time-integrated approach for spatiotemporal proximal analysis considering space and time dimensions simultaneously. The proposed approach is based on space-time buffering, which is a natural extension of conventional spatial buffering operation to space and time dimensions. Given a space-time path and spatial tolerance, space-time buffering constructs a space-time region by continuously generating spatial buffers for any location along the space-time path. The constructed space-time region can delimit all space-time locations whose spatial distances to the target trajectory are less than a given tolerance. Five space-time overlapping operations based on this space-time buffering are proposed to retrieve all spatiotemporal proximal trajectories to the target space-time path, in terms of different spatiotemporal proximity metrics of space-time paths, such as Fréchet distance and longest common subsequence. The proposed approach is extended to analyze space-time paths constrained in road networks. The compressed linear reference technique is adopted to implement the proposed approach for spatiotemporal proximity analysis in large movement datasets. A case study using real-world movement data verifies that the proposed approach can efficiently retrieve spatiotemporal proximal paths constrained in road networks from a large movement database, and has significant computational advantage over conventional space-time separated approaches.     

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.     

Directed movements in probabilistic time geography

This article studies probabilistic time geography for space–time prisms, that is, for situations where observers know the location of an agent at one time and then again at another time. In the intervening period, the agent would have moved freely, according to its time budget. The article demonstrates that the probability of finding the agent somewhere in the space–time prism is not equally distributed, so any attempt of a quantitative time geographic analysis must consider the actual probability distribution. This article develops, implements, and demonstrates this distribution. A preceding article introduced probabilistic time geography for space–time cones. With cones and prisms, the elementary space–time volumes of time geography are provided.     

时间地理支持下的核密度估计研究进展

时间地理核密度估计是经典核密度估计(KDE)基于时间地理的一种扩展,主要是将标准核函数的定义域扩展至时间地理的时空可达域,以通过增强定义域在时空方面的物理意义来避免非零密度被分配到可达域之外的问题。时空可达域包括时空碟和由时空碟复合而成的潜在路径区域(PPA)。这2类可达域用作核函数的定义域能解决上述问题,但也带来了新的问题。基于时空碟构建的核函数能叠加成PPA上的概率密度,但敏感于时空碟的时间点。而基于PPA构建的核函数相较于理想布朗桥模型缺乏双峰特性,且也不能生成时空碟上的概率密度函数。因此,时间地理与KDE相结合的研究还处于应用前的理论探索阶段,论文的目标就是对这一进程进行梳理并引出未来的发展趋势。论文围绕时空轨迹不确定性量化这一目标,首先回顾了时间地理与核密度估计的不同功用,然后对两者相融合的意义、框架和模式进行了阐述。最后,认为时间地理的可达域代替核密度估计的定义域是改进时空轨迹不确定性测度的重要手段,但距离目标的落地还有一定的距离。