Real-time relative positioning of spacecraft over long baselines

This paper deals with the problem of real-time onboard relative positioning of low Earth orbit spacecraft over long baselines using the Global Positioning System. Large inter-satellite separations, up to hundreds of kilometers, are of interest to multistatic and bistatic Synthetic Aperture Radar applications, in which highly accurate relative positioning may be required in spite of the long baseline. To compute the baseline with high accuracy the integer nature of dual-frequency, double-difference carrier-phase ambiguities can be exploited. However, the large inter-satellite separation complicates the integer ambiguities determination task due to the presence of significant differential ionospheric delays and broadcast ephemeris errors. To overcome this problem, an original approach is proposed, combining an extended Kalman filter with an integer least square estimator in a closed-loop scheme, capable of fast on-the-fly integer ambiguities resolution. These integer solutions are then used to compute the relative positions with a single-epoch kinematic least square algorithm that processes ionospheric-free combinations of de-biased carrier-phase measurements. Approach performance and robustness are assessed by using the flight data of the Gravity Recovery and Climate Experiment mission. Results show that the baseline can be computed in real-time with decimeter-level accuracy in different operating conditions

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

PRECISE KINEMATIC APPLICATIONS OF GPS: PROSPECTS AND CHALLENGES

GPS kinematic positioning in the post-processed or in the real-time mode is now increasingly used for many surveying and navigation applications on land, at sea and in the air. Techniques range from the robust pseudo-range-based differential GPS (DGPS) techniques capable of delivering accuracies at the few metre level, to sophisticated carrier phase-based centimetre accuracy techniques. The distance from the mobile receiver to the nearest reference receiver may range from a few kilometres to hundreds of kilometres. As the receiver separation increases, the problems of accounting for distance-dependent biases grows. For carrier phasebased techniques reliable ambiguity resolution becomes an even greater challenge. In the case of DGPS, more appropriate implementations such as Wide Area DGPS become necessary. In this paper, the challenges, progress and outlook for high precision GPS kinematic positioning for the short-range, medium-range and long-range cases, in both the post-processing and real-time modes will be discussed. Although the focus will be on carrier phase-based systems, some comments will also be made with regards to DGPS systems. Several applications of kinematic GPS positioning will be considered, so as to demonstrate the engineering challenges in addition to GPS, that have to be addressed

The application of signal detection theory to optics Quarterly progress report

Estimation of object parameters by quantum-limited optical syste

Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines

GPS relative navigation filters could benefit notably from an accurate modeling of the ionospheric delays, especially over large baselines (>100 km) where double difference delays can be higher than several carrier wavelengths. This paper analyzes the capability of ionospheric path delay models proposed for spaceborne GPS receivers in predicting both zero-difference and double difference ionospheric delays. We specifically refer to relatively simple ionospheric models, which are suitable for real-time filtering schemes. Specifically, two ionospheric delay models are evaluated, one assuming an isotropic electron density and the other considering the effect on the electron density of the Sun aspect angle. The prediction capability of these models is investigated by comparing predicted ionospheric delays with measured ones on real flight data from the Gravity Recovery and Climate Experiment mission, in which two satellites fly separated of more than 200 km. Results demonstrate that both models exhibit a correlation in the excess of 80% between predicted and measured double-difference ionospheric delays. Despite its higher simplicity, the isotropic model performs better than the model including the Sun effect, being able to predict double differenced delays with accuracy smaller than the carrier wavelength in most cases. The model is thus fit for supporting integer ambiguity fixing in real-time filters for relative navigation over large baselines. Concerning zero-difference ionospheric delays, results demonstrate that delays predicted by the isotropic model are highly correlated (around 90%) with those estimated using GPS measurements. However, the difference between predicted and measured delays has a root mean square error in the excess of 30 cm. Thus, the zero-difference ionospheric delays model is not likely to be an alternative to methods exploiting carrier-phase observables for cancelling out the ionosphere contribution in single-frequency absolute navigation filters

Evaluation of a Method for Kinematic GPS Carrier-Phase Ambiguity Resolution Using a Network of Reference Receivers

New applications for GPS have driven a demand for increased positioning accuracy. The emerging GPS technology particularly affects the test community. The testing equipment and method must provide a solution that is an order of magnitude more precise than the tested equipment to achieve the desired accuracy. Carrier-phase differential GPS methods using a network of reference receivers can provide the centimeter-level accuracy required over a large geographical area. This thesis evaluates the performance of a 5-receiver network over a 50 km x 120 km area of New Mexico, using a GPS network algorithm called NetAdjust. The percentage of time a fixed integer solution was available for a kinematic baseline was investigated for three types of measurements. Results showed that the virtual reference receiver method using NetAdjust-corrected measurements outperformed the raw and NetAdjust-corrected file results. However, these results were only obtained for the shortest baseline receivers. The receivers with longer baselines did not experience the same degree of success, but did lead to several important insights gained from the research. Most importantly, the accuracy of the reference receiver coordinates is critical to the performance of a reference receiver network. Further testing must be accomplished before a full implementation is recommended

GPS-aerotriangulation : in observation space

PhD ThesisThe research completed on UPS-aerial triangulation has been focused on combining of UPS and photogrammetric data in the way using GPS derived antenna coordinates, so called as "combination in position space". Thus, these antenna coordinates are used, or replaced with the normal control points on the ground, as control points which have been moved into the air. It was noticed that it is necessary to use crossing strips and introduce drift parameters into the analytical aerial triangulation estimation to compensate the shifts which are seen in these coordinates, probably caused by cycle slips in the UPS data. UPS offered a good opportunity to supplement, or completely replace, the ground control required by aerial triangulation procedures by determining the positions of an antenna onboard the aircraft, at each moment of exposure, quickly, cheaply and accurately but with crossing strips, drift parameters and stand-by GPS data, postprocessed GPS data as UPS derived antenna coordinates. This thesis offers a new method which is based on a combination of GPS dual frequency phase observations and photogrammetric measurements in a bundle estimation process, so called as "combination in observation space". Thus the new method leads to the solution of the redundancy problem facing the GPS users if the ambiguities and the point coordinates (or coordinate differences) together with the other parameters are to be solved for simultaneously. It also removes the need for cioss strips to compensate for shifts in the antenna coordinates and provides a good basis for the determination of integer ambiguities and cycle slips thereby saving a lot of effort and time. To explain this concept, the thesis reviews the UPS double differencing processes based upon phase observations and analytical aerial triangulation estimation method with emphasis being laid upon estimation using bundles. Alongside these, error sources that are likely to affect the UPS and bundle measurements are discussed and the new combination method is explained. The ability of the combined system to solve for the perspective center coordinates and the attitude of the camera onboard the aircraft, the coordinates of object points and integer ambiguities and to determine cycle slips in the way it propagates several random errors were the focus of the simulated tests carried out. The tests revealed the high potential of the combined system in relation to this. Although the system may be regarded as a reasonably sensitive method to solve for these parameters simultaneously as there are some cases where some of these parameters, especially integer ambiguities, cannot be solved for correctly or cycle slips cannot be detected. This is thought not to be a disadvantage of the method itself, but is rather due to weak geornetly or insufficient observations with the small sample used. The main conclusion from this work is that a combination of GPS and photogramrnetiy is indeed possible in observation space. The advantage in that cycle slips and integer ambiguities can be solved for (i.e. photogrammetry is contributing to GPS - not just the other way around as in the usual case) and additional photogrammetric data (in the form of cross strips) is not needed. The method has been to be successful even in the presence of severe multipath (up to 5 cm).Turkish governmen

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

Enhancement of the accuracy of single epoch positioning for long baselines with application to structure deformation monitoring

Phd ThesisUsing single-epoch GPS positioning has many advantages, especially when monitoring dynamic targets (e.g. structural movements). In this technique, errors occurring in previous epochs cannot affect the current epoch’s accuracy. However, careful processing is required. This research uses the GPS Ambiguity Search Program (GASP) single-epoch software. Resolving the phase ambiguities is essential in this technique. Some statistical ambiguity resolution functions have been introduced to estimate the best values of these ambiguities. The function inputs are the base station position, the approximate roving receiver position, and the shared GPS phase measurements at both receivers. This work investigates different GPS pseudorange solutions to find the optimal ambiguity function inputs. The noise level in an undifferenced pseudorange coordinate solution is less than in the double-differenced case; thus, using it in the ambiguity function improves the results. Regional correlation between the pseudorange-computed positioning errors exists; therefore, applying a regional filter reduces their effects. Multipath errors approximately repeat themselves every sidereal day in the case of static or quasi-static receivers and applying a sidereal filter mitigates their effects. The IGS ionospheric model reduces the effect of the ionosphere on the GPS phase measurements. Also, a local code-based ionospheric correction model can be generated. Applying these models improves the quality of the phase measurements, which leads to improvement of the ambiguity function outputs. A Kalman filter applied to the code-based ionospheric model further improves the corrected phase measurements. There is a correlation between the ambiguity function outputs’ quality and the phase measurement residuals’ . Applying a threshold filter reduces the probability of obtaining inaccurate results. Data for various baseline lengths, with synthetic displacements added, indicate that the improved GASP results are reliable for monitoring movements exceeding 10 cm for baselines up to 60 km.Aleppo University, Syria, Postgraduate Research Studentship

An approach to ground based space surveillance of geostationary on-orbit servicing operations

AbstractOn Orbit Servicing (OOS) is a class of dual-use robotic space missions that could potentially extend the life of orbiting satellites by fuel replenishment, repair, inspection, orbital maintenance or satellite repurposing, and possibly reduce the rate of space debris generation. OOS performed in geostationary orbit poses a unique challenge for the optical space surveillance community. Both satellites would be performing proximity operations in tight formation flight with separations less than 500m making atmospheric seeing (turbulence) a challenge to resolving a geostationary satellite pair when viewed from the ground. The two objects would appear merged in an image as the resolving power of the telescope and detector, coupled with atmospheric seeing, limits the ability to resolve the two objects. This poses an issue for obtaining orbital data for conjunction flight safety or, in matters pertaining to space security, inferring the intent and trajectory of an unexpected object perched very close to one׳s satellite asset on orbit. In order to overcome this problem speckle interferometry using a cross spectrum approach is examined as a means to optically resolve the client and servicer׳s relative positions to enable a means to perform relative orbit determination of the two spacecraft. This paper explores cases where client and servicing satellites are in unforced relative motion flight and examines the observability of the objects. Tools are described that exploit cross-spectrum speckle interferometry to (1) determine the presence of a secondary in the vicinity of the client satellite and (2) estimate the servicing satellite׳s motion relative to the client. Experimental observations performed with the Mont Mégantic 1.6m telescope on co-located geostationary satellites (acting as OOS proxy objects) are described. Apparent angular separations between Anik G1 and Anik F1R from 5 to 1 arcsec were observed as the two satellites appeared to graze one another. Data reduction using differential angular measurements derived from speckle images collected by the 1.6m telescope produced relative orbit estimates with better than 90m accuracy in the cross-track and in-track directions but exhibited highly variable behavior in the radial component from 50 to 1800m. Simulations of synthetic tracking data indicated that the radial component requires approximately six hours of tracking data for an Extended Kalman Filter to converge on an relative orbit estimate with less than 100m overall uncertainty. The cross-spectrum approach takes advantage of the Fast Fourier Transform (FFT) permitting near real-time estimation of the relative orbit of the two satellites. This also enables the use of relatively larger detector arrays (>106 pixels) helping to ease acquisition process to acquire optical angular data