Approximate Trajectories for Thermal Protection System Flight Tests Mission Design

A mission profile for advanced thermal protection system suborbital flight testing is identified. Its main goal is to achieve a constant heat flux at a specific area of the vehicle for a limited amount of time. A tool capable of exploring broad regions of the design space for these missions is developed, aiming at reducing possible design options to an extent manageable by conventional, more accurate, numeric-simulation-based methods. Based on a simplified model of the point mass dynamics, trajectories optimal for thermal protection system testing and compliant with prefixed path constraints are identified. The approximate method is validated comparing the obtained optimal trajectories with numeric-optimized standard solutions on three test cases. Then, to demonstrate the method effectiveness and flexibility, the mission design space is investigated for reasonable ranges of relevant parameters. Results show that increasing the vehicle's ballistic coefficient allows reducing the specific mechanical energy at reentry, and that the maximum admissible dynamic pressure plays a principal role in affecting the attainable testing performances. An illustrative mission design for novel ceramic thermal protection system testing is presented that minimizes in the analyzed design space the specific mechanical energy at the trajectory apoge

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

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

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

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

Ionospheric Delay Handling for Relative Navigation by Carrier-Phase Differential GPS

The paper investigates different solutions for ionospheric delay handling in high accuracy long baseline relative positioning by Carrier-Phase Differential GPS (CDGPS). Standard literature approaches are reviewed and the relevant limitations are discussed. Hence, a completely ionosphere-free approach is proposed, in which the differential ionospheric delays are cancelled out by combination of dual frequency GPS measurements. The performance of this approach is quantified over real-world spaceborne GPS data made available by the Gravity Recovery and Climate Experiment (GRACE) mission and compared to the standard solution

Robustness Analysis for Terminal Phases of Re-entry Flight

Advancements in the current practices used in robustness analysis for FCS design refinement by introducing a method that takes into account nonlinear effects of multiple uncertainties over the whole trajectory, to be used before robustness is finally assessed with MC analysis has been reported. Current practice in FCS robustness analysis for this kind of application mainly relies on the theory of linear time-invariant (LTI) systems. The method delivers feedback on the causes of requirement violation and adopts robustness criteria directly linked to the original mission or system requirements, such as those employed in MC analyses. The nonlinear robustness criterion proposed in the present work is based on the practical stability and/or finite time stability concepts. The practical stability property improves the accuracy in robustness evaluation with respect to frozen-time approaches, thus reducing the risk of discovering additional effects during robustness verification with Monte Carlo techniques

A hybrid approach to robustness analyses of flight control laws in re-entry applications

The present paper aims at improving the efficiency of the robustness analyses of flight control laws with respect to conventional techniques, especially when applied to vehicles following time-varying reference trajectories, such as in an atmospheric re-entry. A nonlinear robustness criterion is proposed, stemming from the practical stability framework, which allows dealing effectively with such cases. A novel approach is presented, which exploits the convexity of linear time varying systems, coupled to an approximate description of the original nonlinear system by a certain number of its time-varying linearizations. The suitability of the approximating systems is evaluated in a probabilistic fashion making use of the unscented transformation technique. The effectiveness and potentials of the method are ascertained by application to the robustness analysis of the longitudinal flight control laws of the Italian Aerospace Research Center (CIRA) experimental vehicle USV

A linear time-varying approach for robustness analyses of a re-entry flight technology demonstrator

A novel robustness analysis technique is proposed for atmospheric re-entry applications. The problem is stated as a finite time stability (FTS) analysis of linear time-varying (LTV) systems on a compact time domain, subject to bounded variations in initial state and unknown parameters. The FTS property is formulated as the inclusion of all the possible system trajectories into a pre-specified time-varying subset of the state space. Based on assuming the involved sets are polytopes, the proposed approach allows deducing the system FTS from the property verification on a limited number of numerically computed system trajectories. An additional result is presented which allows determination of a conservative estimate of the maximum norm-bound of time-varying perturbations under which the LTV system remains finite time stable. Results of the application of the proposed technique to a re-entry technology demonstrator are presented which demonstrate its effectiveness in complementing conventional linear time invariant-based analyses. Results also show that it is computationally viable and allows linking the system robustness to a quantitative analysis of the system trajectory dispersion around the nominal one due to concurrent initial state dispersion and uncertain parameters effects, which aids in evaluating mission objectives fulfillment

Navigation Facility for High Accuracy Offline Trajectory and Attitude Estimation in Airborne Applications

The paper focuses on a navigation facility, relying on commercial-off-the-shelf (COTS) technology, developed to generate high-accuracy attitude and trajectory measurements in postprocessing. Target performance is cm-level positioning with tenth of degree attitude accuracy. The facility is based on the concept of GPS-aided inertial navigation but comprises carrier-phase differential GPS (CDGPS) processing and attitude estimation based on multiantenna GPS configurations. Expected applications of the system include: (a) performance assessment of integrated navigation systems, developed for general aviation aircraft and medium size unmanned aircraft systems (UAS); (b) generation of reference measurements to evaluate the flight performance of airborne sensors (e.g., radar or laser); and (c) generation of reference trajectory and attitude for improving imaging quality of airborne remote sensing data. The paper describes system architecture, selected algorithms for data processing and integration, and theoretical performance evaluation. Experimental results are also presented confirming the effectiveness of the implemented approach