Novel closed-loop approaches for precise relative navigation of widely separated GPS receivers in LEO

This paper deals with the relative navigation of a formation of two spacecrafts separated by hundreds of kilometers based on processing dual-frequency differential carrier-phase GPS measurements. Specific requirements of the considered application are high relative positioning accuracy and real-time on board implementation. These can be conflicting requirements. Indeed, if on one hand high accuracy can be achieved by exploiting the integer nature of double-difference carrier-phase ambiguities, on the other hand the presence of large ephemeris errors and differential ionospheric delays makes the integer ambiguities determination challenging. Closed-loop schemes, which update the relative position estimates of a dynamic filter with feedback from integer ambiguities fixing algorithms, are customarily employed in these cases. This paper further elaborates such approaches, proposing novel closed loop techniques aimed at overcoming some of the limitations of traditional algorithms. They extend techniques developed for spaceborne long baseline relative positioning by making use of an on-the-fly ambiguity resolution technique especially developed for the applications of interest. Such techniques blend together ionospheric delay compensation techniques, nonlinear models of relative spacecraft dynamics, and partial integer validation techniques. The approaches are validated using flight data from the Gravity Recovery and Climate Experiment (GRACE) mission. Performance is compared to that of the traditional closed-loop scheme analyzing the capability of each scheme to maximize the percentage of correctly fixed integer ambiguities as well as the relative positioning accuracy. Results show that the proposed approach substantially improves performance of the traditional approaches. More specifically, centimeter-level root-mean square relative positioning is feasible for spacecraft separations of more than 260 km, and an integer ambiguity fixing performance as high as 98% is achieved in a 1-day long dataset. Results also show that approaches exploiting ionospheric delay models are more robust and precise of approaches relying on ionospheric-delay removal techniques. © 2013 IAA

Atmospheric effects and spurious signals in GPS analyses

Improvements in the analyses of Global Positioning System (GPS) observations yield resolvable millimeter to submillimeter differences in coordinate estimates, thus providing sufficient resolution to distinguish subtle differences in analysis methodologies. Here we investigate the effects on site coordinates of using different approaches to modeling atmospheric loading deformation (ATML) and handling of tropospheric delays. The rigorous approach of using the time-varying Vienna Mapping Function 1 yields solutions with lower noise at a range of frequencies compared with solutions generated using empirical mapping functions. This is particularly evident when ATML is accounted for. Some improvement also arises from using improved a priori zenith hydrostatic delays (ZHD), with the combined effect being site-specific. Importantly, inadequacies in both mapping functions and a priori ZHDs not only introduce time-correlated noise but significant periodic terms at solar annual and semiannual periods. We find no significant difference between solutions where nontidal ATML is applied at the observation level rather than as a daily averaged value, but failing to model diurnal and semidiurnal tidal ATML at the observation level can introduce anomalous propagated signals with periods that closely match the GPS draconitic annual (∼351.4 days) and semiannual period (∼175.7 days). Exacerbated by not fixing ambiguities, these signals are evident in both stacked and single-site power spectra, with each tide contributing roughly equally to the dominant semiannual peak. The amplitude of the propagated signal reaches a maximum of 0.8 mm with a clear latitudinal dependence that is not correlated directly with locations of maximum tidal amplitude.Australian Research Council’s Discovery Project

Validation on flight data of a closed-loop approach for GPS-based relative navigation of LEO satellites

This paper describes a carrier-phase differential GPS approach for real-time relative navigation of LEO satellites flying in formation with large separations. These applications are characterized indeed by a highly varying number of GPS satellites in common view and large ionospheric differential errors, which significantly impact relative navigation performance and robustness. To achieve high relative positioning accuracy a navigation algorithm is proposed which processes double-difference code and carrier measurements on two frequencies, to fully exploit the integer nature of the related ambiguities. Specifically, a closed-loop scheme is proposed in which fixed estimates of the baseline and integer ambiguities produced by means of a partial integer fixing step are fed back to an Extended Kalman Filter for improving the float estimate at successive time instants. The approach also benefits from the inclusion in the filter state of the differential ionospheric delay in terms of the Vertical Total Electron Content of each satellite. The navigation algorithm performance is tested on actual flight data from GRACE mission. Results demonstrate the effectiveness of the proposed approach in managing integer unknowns in conjunction with Extended Kalman Filtering, and that centimeter-level accuracy can be achieved in real-time also with large separations. (c) 2013 IAA. Published by Elsevier Ltd. All rights reserved

Ionospheric Delays Compensation for On-The-Fly Integer Ambiguity Resolution in Long Baseline LEO Formations

This paper deals with the real-time onboard accurate relative positioning by Carrier-phase Differential GPS (CDGPS) of LEO formations with baselines of hundreds of kilometers. On long baselines, high accuracy can be achieved only using dual-frequency measurements and exploiting the integer nature of Double Difference (DD) carrier-phase ambiguities. However, large differential ionospheric delays and broadcast ephemeris errors complicate the integer resolution task. The present paper is concerned with analyzing possible approaches to DD ionospheric delays compensation in such applications. Two different strategies are implemented to deal with DD ionospheric delays. The first formulation models differential ionospheric delays as a function of the vertical total electron content above the receivers, whereas the second one is based on combining the DD measurements for removing ionospheric delays from the observation model. The effectiveness of the developed solutions is assessed by comparing the relative positioning accuracy that can be obtained on actual flight data from the Gravity Recovery and Climate Experiment mission. This is done using a recently developed, common relative positioning approach. Results show that ionospheric activity plays a major role in determining the relative positioning performance. Modeling the delays is advantageous for relative positioning in mild ionospheric conditions, but the solution without ionospheric delays becomes preferable as the ionosphere�s electron content increases

Improving Reliability and Assessing Performance of Global Navigation Satellite System Precise Point Positioning Ambiguity Resolution

Conventional Precise Point Positioning (PPP) has always required a relatively long initialization period (few tens of minutes at least) for the carrier-phase ambiguities to converge to constant values and for the solution to reach its optimal precision. The classical PPP convergence period is primarily caused by the estimation of the carrier-phase ambiguity from the relatively noisy pseudoranges and the estimation of atmospheric delay. If the underlying integer nature of the ambiguity is known, it can be resolved, thereby reducing the convergence time of conventional PPP. To recover the underlying integer nature of the carrier-phase ambiguities, different strategies for mitigating the satellite and receiver dependent equipment delays have been developed, and products made publicly available to enable ambiguity resolution without any baseline restrictions. There has been limited research within the scope of interoperability of the products, combining the products to improve reliability and assessment of ambiguity resolution within the scope of being an integrity indicator. This study seeks to develop strategies to enable each of these and examine their feasibility. The advantage of interoperability of the different PPP ambiguity resolution (PPP-AR) products would be to permit the PPP user to transform independently generated PPP-AR products to obtain multiple fixed solutions of comparable precision and accuracy. The ability to provide multiple solutions would increase the reliability of the solution for, e.g., real-time processing: if there were an outage in the generation of the PPP-AR products, the user could instantly switch streams to a different provider. The satellite clock combinations routinely produced within the International GNSS Service (IGS) currently disregard that analysis centers (ACs) provide products which enable ambiguity resolution. Users have been expected to choose either an IGS product which is a combined product from multiple ACs or select an individual AC solution which provides products that enable PPP-AR. The goal of the novel research presented was to develop and test a robust satellite clock combination preserving the integer nature of the carrier-phase ambiguities at the user end. mm-level differences were noted, which was expected as the strength lies mainly in its reliability and stable median performance and the combined product is better than or equivalent to any single ACs product in the combination process. As have been shown in relative positioning and PPP-AR, ambiguity resolution is critical for enabling cm-level positioning. However, what if specifications where at the few dm-level, such as 10 cm and 20 cm horizontal what role does ambiguity resolution play? The role of ambiguity resolution relies primarily on what are the user specifications. If the user specifications are at the few cm-level, ambiguity resolution is an asset as it improves convergence and solution stability. Whereas, if the users specification is at the few dm-level, ambiguity resolution offers limited improvement over the float solution. If the user has the resources to perform ambiguity resolution, even when the specifications are at the few dm-level, it should be utilized

Localization Precise in Urban Area

Nowadays, stand-alone Global Navigation Satellite System (GNSS) positioning accuracy is not sufficient for a growing number of land users. Sub-meter or even centimeter accuracy is becoming more and more crucial in many applications. Especially for navigating rovers in the urban environment, final positioning accuracy can be worse as the dramatically lack and contaminations of GNSS measurements. To achieve a more accurate positioning, the GNSS carrier phase measurements appear mandatory. These measurements have a tracking error more precise by a factor of a hundred than the usual code pseudorange measurements. However, they are also less robust and include a so-called integer ambiguity that prevents them to be used directly for positioning. While carrier phase measurements are widely used in applications located in open environments, this thesis focuses on trying to use them in a much more challenging urban environment. To do so, Real Time-Kinematic (RTK) methodology is used, which is taking advantage on the spatially correlated property of most code and carrier phase measurements errors. Besides, the thesis also tries to take advantage of a dual GNSS constellation, GPS and GLONASS, to strengthen the position solution and the reliable use of carrier phase measurements. Finally, to make up the disadvantages of GNSS in urban areas, a low-cost MEMS is also integrated to the final solution. Regarding the use of carrier phase measurements, a modified version of Partial Integer Ambiguity Resolution (Partial-IAR) is proposed to convert as reliably as possible carrier phase measurements into absolute pseudoranges. Moreover, carrier phase Cycle Slip (CS) being quite frequent in urban areas, thus creating discontinuities of the measured carrier phases, a new detection and repair mechanism of CSs is proposed to continuously benefit from the high precision of carrier phases. Finally, tests based on real data collected around Toulouse are used to test the performance of the whole methodology

Multi-frequency and multi-GNSS PPP phase bias estimation and ambiguity resolution

Multi-frequency and multi-GNSS measurements from modernized satellites are properly integrated for PPP with ambiguity resolution to achieve the state-of-the-art fast and accurate positioning, which provides an important contribution to GNSS precise positioning and applications. The multi-frequency and multi-GNSS PPP phase bias estimation and ambiguity resolution, which is accomplished by a unified model based on the uncombined PPP, are thoroughly evaluated with special focus on Galileo and BDS

Predicting the Success Rate of Long-baseline GPS+Galileo (Partial) Ambiguity Resolution

This contribution covers precise (cm-level) relative Global Navigation Satellite System(GNSS) positioning for which the baseline length can reach up to a few hundred km. Carrier-phase ambiguity resolution is required to obtain this high positioning accuracy within manageable observation time spans. However, for such long baselines, the differential ionospheric delays hamper fast ambiguity resolution as based on current dual-frequency Global Positioning System (GPS). It is expected that the modernization of GPS towards a triple-frequency system, as well as the development of Galileo towards a full constellation will be beneficial in speeding up long-baseline ambiguity resolution. In this article we will predict ambiguity resolution success rates for GPS+Galileo for a 250 km baseline based on the ambiguity variance matrix, where the Galileo constellation is simulated by means of Yuma almanac data. From our studies it can be concluded that ambiguity resolution will likely become faster (less than ten minutes) in the case of GPS+Galileo when based on triple frequency data of both systems, however much shorter times to fix the ambiguities (one-two minutes) can be expected when only a subset of ambiguities is fixed instead of the complete vector (partial ambiguity resolution)