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 ( @math ). We argue that @math 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 @math 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.
The above-mentioned research has mainly focused on describing and understanding GPS measurement error. In addition to this, filtering and smoothing approaches have been proposed for recording movement data, in order to reduce the influence of errors on movement trajectories. A concise summary of these approaches can be found in @cite_2 . @cite_7 tested smoothing methods that best preserve travelled distance, speed, and acceleration. The authors found that Kalman filtering resulted in the least difference between the true movement and its representation.
@cite_7 @cite_2
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In this paper, we focus on the problem of motion tracking in unknown environments using visual and inertial sensors. We term this estimation task visual-inertial odometry (VIO), in analogy to the well-known visual-odometry problem. We present a detailed study of extended Kalman filter (EKF)-based VIO algorithms, by comparing both their theoretical properties and empirical performance. We show that an EKF formulation where the state vector comprises a sliding window of poses (the multi-state-constraint Kalman filter (MSCKF)) attains better accuracy, consistency, and computational efficiency than the simultaneous localization and mapping (SLAM) formulation of the EKF, in which the state vector contains the current pose and the features seen by the camera. Moreover, we prove that both types of EKF approaches are inconsistent, due to the way in which Jacobians are computed. Specifically, we show that the observability properties of the EKF's linearized system models do not match those of the underlying system, which causes the filters to underestimate the uncertainty in the state estimates. Based on our analysis, we propose a novel, real-time EKF-based VIO algorithm, which achieves consistent estimation by (i) ensuring the correct observability properties of its linearized system model, and (ii) performing online estimation of the camera-to-inertial measurement unit (IMU) calibration parameters. This algorithm, which we term MSCKF 2.0, is shown to achieve accuracy and consistency higher than even an iterative, sliding-window fixed-lag smoother, in both Monte Carlo simulations and real-world testing. The Georgia Institute of Technology is evaluating the feasibility and effectiveness of mileage-based pricing programs as transportation control measures. Incentives were provided to study participants who change driving behavior in response to cent per mile pricing (fixed pricing and pricing as a function of congestion level). In-vehicle Global Positioning System (GPS) devices were used to estimate distance traveled and driver behavior (e.g., speed and acceleration profiles). The accuracy of estimated mileage accrual speeds by road classification, and acceleration rates used in pricing algorithms, is paramount. Various data-smoothing techniques were applied to the instrumented vehicle GPS speed data, and performance of the algorithms was evaluated in minimizing the impact of GPS random error on speed, acceleration, and distance estimates. The conventional discrete Kalman filter algorithm was modified to enhance its ability to control GPS random errors. Each smoothing method produces different second-by-se... The use of head movements in control applications leaves the hands free for other tasks and utilizes the mobility of the head to acquire and track targets over a wide field of view. We present the results of applying a Kalman filter to generate prediction estimates for tracking head positions. A simple kinematics approach based on the assumption of a piecewise constant acceleration process is suggested and is shown to track head positions with an rms error under 2 spl deg for head movements with accelerations smaller than 3000 spl deg s. To account for the wide range of head dynamic characteristics, an adaptive approach with input estimation is developed. The performance of the Kalman filter is compared to that based on a simple polynomial predictor. The collection of huge amount of tracking data made possible by the widespread use of GPS devices, enabled the analysis of such data for several applications domains, ranging from traffic management to advertisement and social studies. However, the raw positioning data, as it is detected by GPS devices, lacks of semantic information since this data does not natively provide any additional contextual information like the places that people visited or the activities performed. Traditionally, this information is collected by hand filled questionnaire where a limited number of users are asked to annotate their tracks with the activities they have done. With the purpose of getting large amount of semantically rich trajectories, we propose an algorithm for automatically annotating raw trajectories with the activities performed by the users. To do this, we analyse the stops points trying to infer the Point Of Interest (POI) the user has visited. Based on the category of the POI and a probability measure based on the gravity law, we infer the activity performed. We experimented and evaluated the method in a real case study of car trajectories, manually annotated by users with their activities. Experimental results are encouraging and will drive our future works.