Why GPS makes distances bigger than they are

Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), are among the most important sensors for movement analysis. GPS is widely used to record the trajectories of vehicles, animals and human beings. However, all GPS movement data are affected by both measurement and interpolation error. In this article we show that measurement error causes a systematic bias in distances recorded with a GPS: the distance between two points recorded with a GPS is -- on average -- bigger than the true distance between these points. This systematic `overestimation of distance' becomes relevant if the influence of interpolation error can be neglected, which is the case for movement sampled at high frequencies. We provide a mathematical explanation of this phenomenon and we illustrate that it functionally depends on the autocorrelation of GPS measurement error ($C$). We argue that $C$ can be interpreted as a quality measure for movement data recorded with a GPS. If there is strong autocorrelation any two consecutive position estimates have very similar error. This error cancels out when average speed, distance or direction are calculated along the trajectory. Based on our theoretical findings we introduce a novel approach to determine $C$ in real-world GPS movement data sampled at high frequencies. We apply our approach to a set of pedestrian and a set of car trajectories. We find that the measurement error in the data is strongly spatially and temporally autocorrelated and give a quality estimate of the data. Finally, we want to emphasize that all our findings are not limited to GPS alone. The systematic bias and all its implications are bound to occur in any movement data collected with absolute positioning if interpolation error can be neglected.Comment: 17 pages, 8 figures, submitted to IJGI

Capability of movementfeatures extracted fromGPS trajectoriesforthe classification of fine‐grained behaviors

Ponencias, comunicaciones y pósters presentados en el 17th AGILE Conference on Geographic Information Science "Connecting a Digital Europe through Location and Place", celebrado en la Universitat Jaume I del 3 al 6 de junio de 2014.Recent advances in tracking technologies provide an unprecedented opportunity for a better understanding of animal movement. Data from multiple sensors can be used to capture crucial factors deriving the behaviors of the animal. Typically, accelerometer data is used to describe and classify fine-grained behaviors, while GPS data are rather used to identify more large-scale mobility patterns. In this study, however, the main research question was to what extent fine-grained foraging behaviors of wading birds can be classified from GPS tracking data alone. The species used in this study was the Eurasian Oystercatcher, Haematopus ostralegus. First, a supervised classification approach is employed based on parameters extracted from accelerometer data to identify and label different behavioral categories. Then, we seek to establish how movement parameters, computed from GPS trajectories, can identify the previously labeled behaviors. A decision tree was developed to see which movement features specifically contribute to predicting foraging. The methods used in this study suggest that it is possible to extract, with high accuracy, fine-grained behaviors based on high-resolution GPS data, providing an opportunity to build a prediction model in cases where no additional sensor or observational data on behavior is available. The key to success, however, is a careful selection of the movement features used in the classification process, including cross-scale analysis

Uncertainty analysis of step-selection functions: The effect of model parameters on inferences about the relationship between animal movement and the environment

As spatio-temporal movement data is becoming more widely available for analysis in GIS and related areas, new methods to analyze them have been developed. A step-selection function (SSF) is a recently developed method used to quantify the effect of environmental factors on animal movement. This method is gaining traction as an important conservation tool; however there have been no studies that have investigated the uncertainty associated with subjective model decisions. In this research we used two types of animals – oilbirds and hyenas – to examine how systematically altering user decisions of model parameters influences the main outcome of an SSF, the coefficients that quantify the movement-environment relationship. We found that user decisions strongly influence the results of step-selection functions and any subsequent inferences about animal movement and environmental interactions. Differences were found between categories for every variable used in the analysis and the results presented here can help to clarify the sources of uncertainty in SSF model decisions

Exploiting spatial abstraction in predictive analytics of vehicle traffic

By applying visual analytics techniques to vehicle traffic data, we found a way to visualize and study the relationships between the traffic intensity and movement speed on links of a spatially abstracted transportation network. We observed that the traffic intensities and speeds in an abstracted network are interrelated in the same way as they are in a detailed street network at the level of street segments. We developed interactive visual interfaces that support representing these interdependencies by mathematical models. To test the possibility of utilizing them for performing traffic simulations on the basis of abstracted transportation networks, we devised a prototypical simulation algorithm employing these dependency models. The algorithm is embedded in an interactive visual environment for defining traffic scenarios, running simulations, and exploring their results. Our research demonstrates a principal possibility of performing traffic simulations on the basis of spatially abstracted transportation networks using dependency models derived from real traffic data. This possibility needs to be comprehensively investigated and tested in collaboration with transportation domain specialists

Home range and habitat analysis using dynamic time geography

Wildlife home ranges continue to be a common spatial unit for modeling animal habitat selection. Telemetry data are increasing in spatial and temporal detail and new methods are being developed to incorporate fine resolution data into home range delineation. We extended a previously developed home range estimation technique that incorporates theory from time geography, the potential path area (PPA) home range, to allow the home range to be defined at multiple spatial scales depending on the observed rate of movement within the data. The benefits of this approach are demonstrated with a simulation study, which uses multi-state correlated random walks to represent dynamic movement phases to compare the modified PPA home range technique with a suite of other home range estimation methods (PPA home range, kernel density estimation, Brownian bridges, and dynamic Brownian bridges). We used a case study on caribou (Rangifer tarandus) movement from northern Canada to highlight the value of this approach for characterizing habitat conditions associated with wildlife habitat analysis. We used a simple habitat covariate, percent forest cover, to explore the potential for misleading habitat estimates when home ranges do not include potentially visited locations (omission area) or include areas not possibly visited (commission area). We highlight the advantages of the dynamic PPA home range in the context of quantifying omission and commission areas in other home range techniques. Finally, we provide our R code for calculating dynamic PPA home range estimates.PostprintPeer reviewe

The effect of sampling rate on observed statistics in a correlated random walk

Tracking the movement of individual cells or animals can provide important information about their motile behaviour, with key examples including migrating birds, foraging mammals and bacterial chemotaxis. In many experimental protocols, observations are recorded with a fixed sampling interval and the continuous underlying motion is approximated as a series of discrete steps. The size of the sampling interval significantly affects the tracking measurements, the statistics computed from observed trajectories, and the inferences drawn. Despite the widespread use of tracking data to investigate motile behaviour, many open questions remain about these effects. We use a correlated random walk model to study the variation with sampling interval of two key quantities of interest: apparent speed and angle change. Two variants of the model are considered, in which reorientations occur instantaneously and with a stationary pause, respectively. We employ stochastic simulations to study the effect of sampling on the distributions of apparent speeds and angle changes, and present novel mathematical analysis in the case of rapid sampling. Our investigation elucidates the complex nature of sampling effects for sampling intervals ranging over many orders of magnitude. Results show that inclusion of a stationary phase significantly alters the observed distributions of both quantities

Decision rules for determining terrestrial movement and the consequences for filtering high-resolution global positioning system tracks: a case study using the African lion ( Panthera leo )

The combined use of global positioning system (GPS) technology and motion sensors within the discipline of movement ecology has increased over recent years. This is particularly the case for instrumented wildlife, with many studies now opting to record parameters at high (infra-second) sampling frequencies. However, the detail with which GPS loggers can elucidate fine-scale movement depends on the precision and accuracy of fixes, with accuracy being affected by signal reception. We hypothesized that animal behaviour was the main factor affecting fix inaccuracy, with inherent GPS positional noise (jitter) being most apparent during GPS fixes for non-moving locations, thereby producing disproportionate error during rest periods. A movement-verified filtering (MVF) protocol was constructed to compare GPS-derived speed data with dynamic body acceleration, to provide a computationally quick method for identifying genuine travelling movement. This method was tested on 11 free-ranging lions (Panthera leo) fitted with collar-mounted GPS units and tri-axial motion sensors recording at 1 and 40 Hz, respectively. The findings support the hypothesis and show that distance moved estimates were, on average, overestimated by greater than 80% prior to GPS screening. We present the conceptual and mathematical protocols for screening fix inaccuracy within high-resolution GPS datasets and demonstrate the importance that MVF has for avoiding inaccurate and biased estimates of movement

SMoT+NCS: Algorithm for Detecting Non-Continuous Stops

Several algorithms have been proposed in the last years for discovering stops in trajectories of moving objects. Some methods consider as stops the subtrajectories that i) have speed lower than the average trajectory speed, ii) present significant direction changes, iii) have gaps, or iv) intersect a given spatial region. In these approaches a time constraint should be met for the subtrajectory to be considered as a stop, and this constraint is absolute (it is met or not). Indeed, these approaches consider stops as a continuous subtrajectory. In this paper, we show that for several application domains the stops do not need to be continuous, and the time constraint should be relaxed. In summary, we present the definitions of non-continuous stops and present an algorithm to discover a new kind of stops. We evaluate the proposed algorithm with a running example and real trajectory data, comparing it to the most similar approach in the literature, the SMoT algorithm

Similarity of trajectories taking into account geographic context

The movements of animals, people, and vehicles are embedded in a geographic context. This context influences the movement and may cause the formation of certain behavioral responses. Thus, it is essential to include context parameters in the study of movement and the development of movement pattern analytics. Advances in sensor technologies and positioning devices provide valuable data not only of moving agents but also of the circumstances embedding the movement in space and time. Developing knowledge discovery methods to investigate the relation between movement and its surrounding context is a major challenge in movement analysis today. In this paper we show how to integrate geographic context into the similarity analysis of movement data. For this, we discuss models for geographic context of movement data. Based on this we develop simple but efficient context-aware similarity measures for movement trajectories, which combine a spatial and a contextual distance. These are based on well-known similarity measures for trajectories, such as the Hausdorff, Fréchet, or equal time distance. We validate our approach by applying these measures to movement data of hurricanes and albatross