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

Improved Mathematical Modeling for GPS Based Navigation

This thesis is concerned with the development of new closed form GPS position determination algorithms that work in the presence of pseudorange measurement noise. The mathematical derivation of two closed form algorithms, based on stochastic modeling and estimation techniques, is presented. The algorithms provide an estimate of the GPS solution parameters (viz., the user position and the user clock bias) as well as the estimation error covariance. The experimental results are analyzed by comparison to the baseline results from the conventional Iterative Least Squares (ILS) algorithm. In typical GPS scenarios, the closed form algorithms are extremely sensitive to noise, making them unsuitable for stand-alone use; however, they perform very well at estimating horizontal position parameters in ground-based pseudolite planar array scenarios where the ILS algorithm breaks down due to poor geometry. For typical scenarios, the use of a supplementary algorithm is required to refine the solution. Thus, the derivation of two supplementary algorithms is presented; the first based on a maximum likelihood approach and the second uses a Kalman like update approach. Both supplementary algorithms produce results comparable to the ILS results, but the Kalman update approach is preferred. The advantages introduced by the closed form, supplemented by the Kalman update, algorithm are: (1) The capability to estimate its estimation error covariance, and (2) The potential for computational efficiency due to the closed form nature of the solution

Accuracy Study of a Single Frequency Receiver Using a Combined GPS/GALILEO Constellation

As the date of availability of GALILEO approaches, more and more interest appears to pre-evaluate the accuracy of GALILEO and combined GPS+ GALILEO receivers. The majority of simulations made are based on the general use of UERE (often presented as a function of the elevation angle of the satellite) multiplied by the GDOP (Geometric Dilution Of Precision) matrix. This is a too approximate approach to state for the real position error distributions. Therefore, the concept of an Instantaneous Pseudo Range Error (IPRE) is defined and is implemented into NAVSIM the DLR’s end to end GNSS simulator. This new module coupled with the other modules of the simulator permit to lead complete End-to-End simulations. This new functionality has the advantage to augment the field of applications and to couple the generation of errors already implemented in NAVSIM with error distributions coming from real measurements. This study is a good first approach to compare constellations between each other regarding the accuracy issue. The IPRE concept multiplies the functionalities thanks to its ability to generate real distributions of errors. The application to a combined existing constellation (GPS) for which real measurements can be used with a not yet existing constellation (GALILEO) for which only simulated data can be used is an interesting approach. These results can directly be used to test the impact of correction models, of filtering techniques, of antenna types to a combined GPS/GALILEO system thanks to the time series of IPRE and the instantaneous individual errors output from NAVSIM. The best strategy of error mitigation technique can be tested and the result can be used for receiver design before the launch of GALILEO system