Kinematic interpolation of movement data

Mobile tracking technologies are facilitating the collection of increasingly large and detailed data sets on object movement. Movement data are collected by recording an object’s location at discrete time intervals. Often, of interest is to estimate the unknown position of the object at unrecorded time points to increase the temporal resolution of the data, to correct erroneous or missing data points, or to match the recorded times between multiple data sets. Estimating an object’s unknown location between known locations is termed path interpolation. This paper introduces a new method for path interpolation termed kinematic interpolation. Kinematic interpolation incorporates object kinematics (i.e. velocity and acceleration) into the interpolation process. Six empirical data sets (two types of correlated random walks, caribou, cyclist, hurricane and athlete tracking data) are used to compare kinematic interpolation to other interpolation algorithms. Results showed kinematic interpolation to be a suitable interpolation method with fast-moving objects (e.g. the cyclist, hurricane and athlete tracking data), while other algorithms performed best with the correlated random walk and caribou data. Several issues associated with path interpolation tasks are discussed along with potential applications where kinematic interpolation can be useful. Finally, code for performing path interpolation is provided (for each method compared within) using the statistical software R.PostprintPeer reviewe

Mathematize urbes by humanizing them : cities as Isobenefit Landscapes

The city reading proposed is a modern-postmodern urbanism approach which quantifies but by passing through subjectivism. The isobenefit lines shown translate cities into benefit landscapes, subjective and continually changeable according to personal moods/needs/preferences and urban transformations. They read attractiveness and how they flow throughout the city. Doing it for each urban point and for each urban attraction, we obtain the isobenefit orography of the city, namely a map of its urban attractions and of their flows. This is a liquid surface rather than solid, as it varies across time and people. It is in this liquidness where resides the complexity of cities, their bottom-up spirit and the dynamicity of equilibriums and networks. People do not necessarily go in the most accessible points, but where they need and want to, and, they flow through paths they need or choose to pass through. It is also introduced the likeability of places and paths: in addition to the usual parameters currently used – which weight distances in terms of physical distance, cost, time or mental easiness representations – psycho- economical distances used in the isobenefit lines proposed here, also consider how a place and a path pleases us. According to the Underground Hedonic Theory, this pleasure to pass through or to stay in agreeable areas has an underground and an inertia effect too which contributes to delight our lives. The final purpose of the science of cities and urban design is to understand cities and make them efficient and attractive to please our lives in them

Mathematize urbes by humanizing them. Cities as Isobenefit Landscapes: Psycho-Economical distances and Personal Isobenefit Lines

The city reading proposed is a modern postmodern urbanism approach which quantifies but by passing through subjectivism. The isobenefit lines shown translate cities into benefit landscapes, subjective and continually changeable according to personal moods needs preferences and urban transformations. They read attractiveness and how they flow throughout the city. Doing it for each urban point and for each urban attraction, we obtain the isobenefit orography of the city, namely a map of its urban attractions and of their flows. This is a liquid surface rather than solid, as it varies across time and people. It is in this liquidness where resides the complexity of cities, their bottom up spirit and the dynamicity of equilibriums and networks. People do not necessarily go in the most accessible points, but where they need and want to, and, they flow through paths they need or choose to pass through. It is also introduced the likeability of places and paths: in addition to the usual parameters currently used, which weight distances in terms of physical distance, cost, time or mental easiness representations, psycho-economical distances used in the isobenefit lines proposed here, also consider how a place and a path pleases us. According to the Underground Hedonic Theory, this pleasure to pass through or to stay in agreeable areas has an underground and an inertia effect too which contributes to delight our lives. The final purpose of the science of cities and urban design is to understand cities and make them efficient and attractive to please our lives in them.Comment: 32 pages, 20 figure

Modeling movement probabilities within heterogeneous spatial fields

Recent efforts have focused on modeling the internal structure of space-time prisms to estimate the unequal movement opportunities within. This paper further develops this area of research by formulating a model for field-based time geography that can be used to probabilistically model movement opportunities conditioned on underlying heterogeneous spatial fields. The development of field-based time geography draws heavily on well-established methods for cost-distance analysis, common to most GIS software packages. The field-based time geographic model is compared with two alternative approaches that are commonly employed to estimate probabilistic space-time prisms - (truncated) Brownian bridges and time geographic kernel density estimation. Using simulated scenarios it is demonstrated that only field-based time geography captures underlying heterogeneity in output movement probabilities. Field-based time geography has significant potential in the field of wildlife tracking (an example is provided), where Brownian bridge models are preferred, but fail to adequately capture underlying barriers to movement.Publisher PDFPeer reviewe

Pedestrian Mobility Mining with Movement Patterns

In street-based mobility mining, pedestrian volume estimation receives increasing attention, as it provides important applications such as billboard evaluation, attraction ranking and emergency support systems. In practice, empirical measurements are sparse due to budget limitations and constrained mounting options. Therefore, estimation of pedestrian quantity is required to perform pedestrian mobility analysis at unobserved locations. Accurate pedestrian mobility analysis is difficult to achieve due to the non-random path selection of individual pedestrians (resulting from motivated movement behaviour), causing the pedestrian volumes to distribute non-uniformly among the traffic network. Existing approaches (pedestrian simulations and data mining methods) are hard to adjust to sensor measurements or require more expensive input data (e.g. high fidelity floor plans or total number of pedestrians in the site) and are thus unfeasible. In order to achieve a mobility model that encodes pedestrian volumes accurately, we propose two methods under the regression framework which overcome the limitations of existing methods. Namely, these two methods incorporate not just topological information and episodic sensor readings, but also prior knowledge on movement preferences and movement patterns. The first one is based on Least Squares Regression (LSR). The advantage of this method is the easy inclusion of route choice heuristics and robustness towards contradicting measurements. The second method is Gaussian Process Regression (GPR). The advantages of this method are the possibilities to include expert knowledge on pedestrian movement and to estimate the uncertainty in predicting the unknown frequencies. Furthermore the kernel matrix of the pedestrian frequencies returned by the method supports sensor placement decisions. Major benefits of the regression approach are (1) seamless integration of expert data and (2) simple reproduction of sensor measurements. Further advantages are (3) invariance of the results against traffic network homeomorphism and (4) the computational complexity depends not on the number of modeled pedestrians but on the traffic network complexity. We compare our novel approaches to state-of-the-art pedestrian simulation (Generalized Centrifugal Force Model) as well as existing Data Mining methods for traffic volume estimation (Spatial k-Nearest Neighbour) and commonly used graph kernels for the Gaussian Process Regression (Squared Exponential, Regularized Laplacian and Diffusion Kernel) in terms of prediction performance (measured with mean absolute error). Our methods showed significantly lower error rates. Since pattern knowledge is not easy to obtain, we present algorithms for pattern acquisition and analysis from Episodic Movement Data. The proposed analysis of Episodic Movement Data involve spatio-temporal aggregation of visits and flows, cluster analyses and dependency models. For pedestrian mobility data collection we further developed and successfully applied the recently evolved Bluetooth tracking technology. The introduced methods are combined to a system for pedestrian mobility analysis which comprises three layers. The Sensor Layer (1) monitors geo-coded sensor recordings on people’s presence and hands this episodic movement data in as input to the next layer. By use of standardized Open Geographic Consortium (OGC) compliant interfaces for data collection, we support seamless integration of various sensor technologies depending on the application requirements. The Query Layer (2) interacts with the user, who could ask for analyses within a given region and a certain time interval. Results are returned to the user in OGC conform Geography Markup Language (GML) format. The user query triggers the (3) Analysis Layer which utilizes the mobility model for pedestrian volume estimation. The proposed approach is promising for location performance evaluation and attractor identification. Thus, it was successfully applied to numerous industrial applications: Zurich central train station, the zoo of Duisburg (Germany) and a football stadium (Stade des Costières Nîmes, France)