GPS-based Relative Navigation of LEO formations with Varying Baselines

Abstract

This paper deals with the GPS-based relative navigation of LEO formations. Specifically, we consider applications characterized by two co-flying satellites with a large and highly variable separation, which are relevant to next generation monostatic/bistatic Synthetic Aperture Radar missions. In these applications, both scientific goals and control needs require the determination of the relative state with high accuracy. To this end, an Extended Kalman Filter is developed that processes double-difference pseudorange and carrier phase measurements on L1 and L2 frequencies. To preserve accuracy and robustness of the integer solution problem against large variations of the baseline, an original approach is developed in which, for each receiver, the Vertical Total Electron Content is included in the filter state. In addition, the double-difference ambiguities are re-estimated by the filter at each time step. A major technical problem of a filter processing double-differences is re-organizing the filter state when the pivot satellite changes. This is solved by an original and effective procedure that speeds up the filter convergence. Once the floating point estimates of the double-difference ambiguities have been produced by the dynamic filter, their integer values are extracted with the Least-Square Ambiguity Decorrelation Adjustment method and processed within a kinematic filter to estimate the relative position with high accuracy. Filter robustness and performance are evaluated by means of Monte Carlo simulations performed on the reference orbital scenario identified within the Italian SABRINA mission study. Results show that the integer ambiguities are always resolved, allowing to achieve a centimeter-level accuracy in all the simulated conditions.

Ionospheric delays compensation for on-the-fly integer ambiguity resolution in long baseline LEO formations

“…The above model, being concerned with relative dynamics, allows modeling differential perturbations (e.g. differential drag) as process noise while keeping low the computational effort [12]. The same model, i.e.…”

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

“…where Ip is the p-dimensional identity matrix, λ1 and λ2 are L1 and L2 signal wavelength and 1 2 γ λ λ = and j AB I can be derived from Lear mapping function [12]. The observation model relating the state vector to the observables is nonlinear due to the geometric term dependency on the baseline vector.…”

“…The final baseline accuracy is then also limited by the accuracy of VTEC-based ionospheric model (and Lear mapping function too). As shown in [12], the VTEC-based model is accurate enough to aid integer ambiguity resolution, but it can be unsatisfactory to correct the baseline estimate (especially over polar areas) once integer ambiguities have been fixed and validated. For this reason, the fixed ambiguities are used for performing a refinement of the EKF solution.…”

“…Approach effectiveness strongly depends on the accuracy of the float ambiguity estimate performed with the EKF, which in turns is affected by the large inter-satellite separation. Thus, to improve the float ambiguity estimate accuracy, double difference ionospheric delay terms are specifically modeled in terms of the VTEC, which is assumed variable over the baseline and introduced in the filter state [12][13]. Finally, the performance of the developed filtering approach is assessed by using real flight data from the Gravity Recovery and Climate Experiment (GRACE) mission, launched in 2002.…”

Inter-satellite Ranging Augmented GPS Relative Navigation for Satellite Formation Flying

“…over 100 km, even though most common GPS errors can be eliminated by using the doubledifferenced observables, ionospheric delay residuals may still be significant. Moreover, the common-in-view GPS satellites change rapidly, which will degrade the success rates of integer ambiguity resolution and lead to solution gaps when there are insufficient double-differenced observables (Mohiuddin and Psiaki, 2005;Tancredi et al, 2010;Montenbruck and D'Amico, 2013). As a consequence, the navigation performance will deteriorate significantly.…”