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DOE OSTI2014

WE-A-17A-10: Fast, Automatic and Accurate Catheter Reconstruction in HDR Brachytherapy Using An Electromagnetic 3D Tracking System

Purpose: In high dose rate brachytherapy (HDR-B), actual catheter reconstruction protocols are slow and errors prompt. The purpose of this study was to evaluate the accuracy and robustness of an electromagnetic (EM) tracking system for improved catheter reconstruction in HDR-B protocols. Methods: For this proof-of-principle, a total of 10 catheters were inserted in gelatin phantoms with different trajectories. Catheters were reconstructed using a Philips-design 18G biopsy needle (used as an EM stylet) and the second generation Aurora Planar Field Generator from Northern Digital Inc. The Aurora EM system exploits alternating current technology and generates 3D points at 40 Hz. Phantoms were also scanned using a μCT (GE Healthcare) and Philips Big Bore clinical CT system with a resolution of 0.089 mm and 2 mm, respectively. Reconstructions using the EM stylet were compared to μCT and CT. To assess the robustness of the EM reconstruction, 5 catheters were reconstructed twice and compared. Results: Reconstruction time for one catheter was 10 seconds or less. This would imply that for a typical clinical implant of 17 catheters, the total reconstruction time would be less than 3 minutes. When compared to the μCT, the mean EM tip identification error was 0.69 ± 0.29 mm while the CT error was 1.08 ± 0.67 mm. The mean 3D distance error was found to be 0.92 ± 0.37 mm and 1.74 ± 1.39 mm for the EM and CT, respectively. EM 3D catheter trajectories were found to be significantly more accurate (unpaired t-test, p < 0.05). A mean difference of less than 0.5 mm was found between successive EM reconstructions. Conclusion: The EM reconstruction was found to be faster, more accurate and more robust than the conventional methods used for catheter reconstruction in HDR-B. This approach can be applied to any type of catheters and applicators. We would like to disclose that the equipments, used in this study, is coming from a collaboration with Philips Medical.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS1973

Data-aided carrier tracking loops

Power in composite signal sidebands is used to enhance signal-to-noise ratio in carrier tracking loop, thereby reducing radio loss and decreasing probability of receiver error. By adding quadrature channel to phase-lock-loop detector circuit of receiver, dc component can be fed back into carrier tracking loop.

Lindsey, W. C.↗
NASA NTRS2004

Improvement of the TOPEX and Jason Orbit Time Series: Precision Orbit Determination, Calibration, Validation and Improvement Through the Combined Reduction and Analysis of GPS, SLR, DORIS and Altimeter Data

Orbit error is a major component in the overall error budget of all altimeter satellite missions. Jason-I is no exception and a 1 cm radial orbit accuracy goal has been set, which represents a factor of two improvement over what is currently being achieved for TOPEX/Poseidon (TP). Our current analysis suggests this goal has been met and even improved upon, but the challenge is to be able to continually achieve this high accuracy, verify the performance and characterize and quantify the remaining errors over the lifetime of the mission. The computation, verification and error characterization of such high accuracy orbits requires the reduction and analysis of all available tracking data (GPS, SLR, DORIS and altimeter). Current analysis also indicates the history of TP orbits can be further improved employing new solution strategies developed and tested on Jason-I. Our research focuses on the calibration, validation and improvement of orbit accuracies using all available tracking data including altimetry. We will compute and distribute well centered Jason orbits with an accuracy of better than 1-cm in the radial component. In addition to the orbits themselves, a characterization of the orbit error will be distributed and accumulated as a time series of orbit performance metrics to track anomalies and trends. The long time series of orbit error characterization will enable a better understanding of the remaining orbit errors and its impact on the altimeter data analysis. As part of this research effort we are also significantly improving the current level of TP orbit accuracy, re-computing new high-accuracy TP orbits from the beginning of the TP mission and continuing into the future (as long as TP is healthy). Our funded research effort will result in a complete and consistent time series of improved orbits for both TP and Jason, significantly benefiting the long time series of altimeter data analysis and the TP/Jason dual mission. The resultant high accuracy orbits and the characterization of their error will allow further improvements to the accuracy and overall quality of the altimeter measurement time series making possible further strides in radar altimeter remote sensing.

Luthcke, Scott B.↗
NASA NTRS2009

Navigating the Return Trip from the Moon Using Earth-Based Ground Tracking and GPS

NASA s Constellation Program is planning a human return to the Moon late in the next decade. From a navigation perspective, one of the most critical phases of a lunar mission is the series of burns performed to leave lunar orbit, insert onto a trans-Earth trajectory, and target a precise re-entry corridor in the Earth s atmosphere. A study was conducted to examine sensitivity of the navigation performance during this phase of the mission to the type and availability of tracking data from Earth-based ground stations, and the sensitivity to key error sources. This study also investigated whether GPS measurements could be used to augment Earth-based tracking data, and how far from the Earth GPS measurements would be useful. The ability to track and utilize weak GPS signals transmitted across the limb of the Earth is highly dependent on the configuration and sensitivity of the GPS receiver being used. For this study three GPS configurations were considered: a "standard" GPS receiver with zero dB antenna gain, a "weak signal" GPS receiver with zero dB antenna gain, and a "weak signal" GPS receiver with an Earth-pointing direction antenna (providing 10 dB additional gain). The analysis indicates that with proper selection and configuration of the GPS receiver on the Orion spacecraft, GPS can potentially improve navigation performance during the critical final phases of flight prior to Earth atmospheric entry interface, and may reduce reliance on two-way range tracking from Earth-based ground stations.

Berry, Kevin↗
DOE OSTI2020

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf’s ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

4D tumor centroid tracking using orthogonal 2D dynamic MRI: Implications for radiotherapy planning

Purpose: Current pretreatment, 4D imaging techniques are suboptimal in that they sample breathing motion over a very limited “snapshot” in time. Heretofore, long-duration, 4D motion characterization for radiotherapy planning, margin optimization, and validation have been impractical for safety reasons, requiring invasive markers imaged under x-ray fluoroscopy. To characterize 3D tumor motion and associated variability over durations more consistent with treatments, the authors have developed a practical dynamic MRI (dMRI) technique employing two orthogonal planes acquired in a continuous, interleaved fashion.Methods: 2D balanced steady-state free precession MRI was acquired continuously over 9–14 min at approximately 4 Hz in three healthy volunteers using a commercial 1.5 T system; alternating orthogonal imaging planes (sagittal, coronal, sagittal, etc.) were employed. The 2D in-plane pixel resolution was 2 × 2 mm{sup 2} with a 5 mm slice profile. Simultaneous with image acquisition, the authors monitored a 1D surrogate respiratory signal using a device available with the MRI system. 2D template matching-based anatomic feature registration, or tracking, was performed independently in each orientation. 4D feature tracking at the raw frame rate was derived using spline interpolation.Results: Tracking vascular features in the lung for two volunteers and pancreatic features in one volunteer, the authors have successfully demonstrated this method. Registration error, defined here as the difference between the sagittal and coronal tracking result in the SI direction, ranged from 0.7 to 1.6 mm (1σ) which was less than the acquired image resolution. Although the healthy volunteers were instructed to relax and breathe normally, significantly variable respiration was observed. To demonstrate potential applications of this technique, the authors subsequently explored the intrafraction stability of hypothetical tumoral internal target volumes and 3D spatial probability distribution functions. The surrogate respiratory information allowed the authors to show how this technique can be used to study correlations between internal and external (surrogate) information over these prolonged durations. However, compared against the gold standard of the time stamps in the dMRI frames, the temporal synchronization of the surrogate 1D respiratory information was shown to be likely unreliable.Conclusions: The authors have established viability of a novel and practical pretreatment, 4D tumor centroid tracking method employing a commercially available dynamic MRI sequence. Further developments from the vendor are likely needed to provide a reliably synchronized surrogate 1D respiratory signal, which will likely broaden the utility of this method in the pretreatment radiotherapy planning context.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1984

Altimetry, Orbits and Tides

The nature of the orbit error and its effect on the sea surface heights calculated with satellite altimetry are explained. The elementary concepts of celestial mechanics required to follow a general discussion of the problem are included. Consideration of errors in the orbits of satellites with precisely repeating ground tracks (SEASAT, TOPEX, ERS-1, POSEIDON, amongst past and future altimeter satellites) are detailed. The theoretical conclusions are illustrated with the numerical results of computer simulations. The nature of the errors in this type of orbits is such that this error can be filtered out by using height differences along repeating (overlapping) passes. This makes them particularly valuable for the study and monitoring of changes in the sea surface, such as tides. Elements of tidal theory, showing how these principles can be combined with those pertinent to the orbit error to make direct maps of the tides using altimetry are presented.

Colombo, O. L.↗
NASA NTRS1999

Elevation Change of the Southern Greenland Ice Sheet from Satellite Radar Altimeter Data

Long-term changes in the thickness of the polar ice sheets are important indicators of climate change. Understanding the contributions to the global water mass balance from the accumulation or ablation of grounded ice in Greenland and Antarctica is considered crucial for determining the source of the about 2 mm/yr sea-level rise in the last century. Though the Antarctic ice sheet is much larger than its northern counterpart, the Greenland ice sheet is more likely to undergo dramatic changes in response to a warming trend. This can be attributed to the warmer Greenland climate, as well as a potential for amplification of a global warming trend in the polar regions of the Northern Hemisphere. In collaboration with Drs. Curt Davis and Craig Kluever of the University of Missouri, we are using data from satellite radar altimeters to measure changes in the elevation of the Southern Greenland ice sheet from 1978 to the present. Difficulties with systematic altimeter measurement errors, particularly in intersatellite comparisons, beset earlier studies of the Greenland ice sheet thickness. We use altimeter data collected contemporaneously over the global ocean to establish a reference for correcting ice-sheet data. In addition, the waveform data from the ice-sheet radar returns are reprocessed to better determine the range from the satellite to the ice surface. At JPL, we are focusing our efforts principally on the reduction of orbit errors and range biases in the measurement systems on the various altimeter missions. Our approach emphasizes global characterization and reduction of the long-period orbit errors and range biases using altimeter data from NASA's Ocean Pathfinder program. Along-track sea-height residuals are sequentially filtered and backwards smoothed, and the radial orbit errors are modeled as sinusoids with a wavelength equal to one revolution of the satellite. The amplitudes of the sinusoids are treated as exponentially-correlated noise processes with a time-constant of six days. Measurement errors (e.g., altimeter range bias) are simultaneously recovered as constant parameters. The corrections derived from the global ocean analysis are then applied over the Greenland ice sheet. The orbit error and measurement bias corrections for different missions are developed in a single framework to enable robust linkage of ice-sheet measurements from 1978 to the present. In 1998, we completed our re-evaluation of the 1978 Seasat and 1985-1989 Geosat Exact Repeat Mission data. The estimates of ice thickness over Southern Greenland (south of 72N and above 2000 m) from 1978 to 1988 show large regional variations (+/-18 cm/yr), but yield an overall rate of +1.5 +/- 0.5 cm/yr (one standard error). Accounting for systematic errors, the estimate may not be significantly different from the null growth rate. The average elevation change from 1978 to 1988 is too small to assess whether the Greenland ice sheet is undergoing a long-term change.

Haines, Bruce J.↗
NASA NTRS1975

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

Koch, D. W.↗
NASA NTRS1977

Ionospheric range-rate effects in satellite-to-satellite tracking

Investigation of ionospheric range and range-rate corrections in satellite-to-satellite tracking were investigated. Major problems were cited and the magnitude of errors that have to be considered for communications between satellites and related experiments was defined. The results point to the need of using a sophisticated modeling approach incorporating daily solar data, and where possible actual ionospheric measurements as update information, as a simple median model cannot possibly account for the complex interaction of the many variables. The findings provide a basis from which the residual errors can be estimated after ionospheric modeling is incorporated in the reduction. Simulations were performed for satellites at various heights: Apollo, Geos, and Nimbus tracked by ATS-6; and in two different geometric configurations: coplanar and perpendicular orbits.

Lipofsky, J. R.↗
NASA NTRS2013

Flight Deck Surface Trajectory-based Operations (STBO): Results of Piloted Simulations and Implications for Concepts of Operation (ConOps)

The results offour piloted medium-fidelity simulations investigating flight deck surface trajectory-based operations (STBO) will be reviewed. In these flight deck STBO simulations, commercial transport pilots were given taxi clearances with time and/or speed components and required to taxi to the departing runway or an intermediate traffic intersection. Under a variety of concept of operations (ConOps) and flight deck information conditions, pilots' ability to taxi in compliance with the required time of arrival (RTA) at the designated airport location was measured. ConOps and flight deck information conditions explored included: Availability of taxi clearance speed and elapsed time information; Intermediate RTAs at intermediate time constraint points (e.g., intersection traffic flow points); STBO taxi clearances via ATC voice speed commands or datal ink; and, Availability of flight deck display algorithms to reduce STBO RTA error. Flight Deck Implications. Pilot RTA conformance for STBO clearances, in the form of ATC taxi clearances with associated speed requirements, was found to be relatively poor, unless the pilot is required to follow a precise speed and acceleration/deceleration profile. However, following such a precise speed profile results in inordinate head-down tracking of current ground speed, leading to potentially unsafe operations. Mitigating these results, and providing good taxi RTA performance without the associated safety issues, is a flight deck avionics or electronic flight bag (EFB) solution. Such a solution enables pilots to meet the taxi route RTA without moment-by-moment tracking of ground speed. An avionics or EFB "error-nulling" algorithm allows the pilot to view the STBO information when the pilot determines it is necessary and when workload alloys, thus enabling the pilot to spread his/her attention appropriately and strategically on aircraft separation airport navigation, and the many other flight deck tasks concurrently required. Surface Traffic Management (STM) System Implications. The data indicate a number of implications regarding specific parameters for ATC/STM algorithm development. Pilots have a tendency to arrive at RTA points early with slow required speeds, on time for moderate speeds, and late with faster required speeds. This implies that ATC/STM algorithms should operate with middle-range speeds, similar to that of non-STBO taxi performance. Route length has a related effect: Long taxi routes increase the earliness with slow speeds and the lateness with faster speeds. This is likely due to the" open-loop" nature of the task in which the speed error compounds over a longer time with longer routes. Results showed that this may be mitigated by imposing a small number oftime constraint points each with their own RTAs effectively tuming a long route into a series of shorter routes - and thus improving RTA performance. STBO ConOps Implications. Most important is the impact that these data have for NextGen STM system ConOps development. The results of these experiments imply that it is not reasonable to expect pilots to taxi under a "Full STBO" ConOps in which pilots are expected to be at a predictable (x,y) airport location for every time (t). An STBO ConOps with a small number of intermediate time constraint points and the departing runway, however, is feasible, but only with flight deck equipage enabling the use of a display similar to the "error-nulling algorithm/display" tested.

Foyle, David C.↗
DOE OSTI2015

SU-D-BRD-06: Creating a Safety Net for a Fully Automated, Script Driven Electronic Medical Record

Purpose: Demonstrate the effectiveness of in-house software in ensuring EMR workflow efficiency and safety. Methods: A web-based dashboard system (WBDS) was developed to monitor clinical workflow in real time using web technology (WAMP) through ODBC (Open Database Connectivity). Within Mosaiq (Elekta Inc), operational workflow is driven and indicated by Quality Check Lists (QCLs), which is triggered by automation software IQ Scripts (Elekta Inc); QCLs rely on user completion to propagate. The WBDS retrieves data directly from the Mosaig SQL database and tracks clinical events in real time. For example, the necessity of a physics initial chart check can be determined by screening all patients on treatment who have received their first fraction and who have not yet had their first chart check. Monitoring similar “real” events with our in-house software creates a safety net as its propagation does not rely on individual users input. Results: The WBDS monitors the following: patient care workflow (initial consult to end of treatment), daily treatment consistency (scheduling, technique, charges), physics chart checks (initial, EOT, weekly), new starts, missing treatments (>3 warning/>5 fractions, action required), and machine overrides. The WBDS can be launched from any web browser which allows the end user complete transparency and timely information. Since the creation of the dashboards, workflow interruptions due to accidental deletion or completion of QCLs were eliminated. Additionally, all physics chart checks were completed timely. Prompt notifications of treatment record inconsistency and machine overrides have decreased the amount of time between occurrence and execution of corrective action. Conclusion: Our clinical workflow relies primarily on QCLs and IQ Scripts; however, this functionality is not the panacea of safety and efficiency. The WBDS creates a more thorough system of checks to provide a safer and near error-less working environment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1962

Analysis of the ''Range and Range Rate'' Tracking System

The "Range and Range Rate" (r(sub j) + r ̇(sub j)) System in its very simplest form is described. In particular, the errors in position and velocity are treated usingpessimistic values of the measured quantities r(sub j) and r ̇(sub j). Thus, a realistic evaluation of tracking qualities can be made for different orbits over certain tracking stations. The Range and Range Rate System briefly described in this report is a high precision tracking system. Knowledge of the uncertainty in position δ (sub x(sub i) is important, but knowledge of the uncertainty of the velocity vector δ (sub x(sub i) is of the utmost importance. Thus the use of coherent Doppler measurements to determine the velocity has a great advantage over any pulsed system and, in addition, permits extremely narrow frequency bands (in the order of 10 to 100 cps) to be employed, reducing the power requirements considerably. The basis for using range r(sub j) and range rate r ̇(sub j) only is the fact that r(sub j) and r ̇(sub j) can be measured to very high precision, thus furnishing r and r with low errors. The nature of these errors is discussed.

Tracking system↗
NASA NTRS1997

Autonomous Navigation with Ground-to-Space Doppler Measurements Referenced to a Temperature-Compensated Crystal Oscillator

The National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) has spent several years developing operational Onboard Navigation Systems (ONS's) to provide real-time autonomous, high-accuracy navigation products for spacecraft using NASA's space and ground communication systems. The highly successful Tracking and Data Relay Satellite System (TDRSS) ONS (TONS) experiment on the Explorer Platform/Extreme Ultraviolet Explorer (EP/EUVE) spacecraft, launched June 7, 1992, flight-demonstrated the ONS for high-accuracy navigation using TDRSS forward- link communications services, In late 1994, the ground station ONS (GONS) experiment, using the same EP/EUVE flight hardware, flight-demonstrated the feasibility of high-accuracy autonomous navigation using ground station forward-link communication services, with an ultrastable oscillator (USO) as the frequency reference (1 part in 10(exp 10) over 24 hours). This paper provides a follow-on analysis of GONS performance to assess the navigation accuracy achievable if GONS uses the significantly less stable (5 parts in 10(exp 8) over 24 hours, compared with a specification of 1 part in 10(exp 6)) Temperature-Compensated Crystal Oscillator (TCXO), which is integral to the transponder, as a frequency reference rather than an external USO. The GONS TCXO experiment results from a 20-day period are used to project the expected performance of an operational system. The GONS processes Doppler data derived from nominally scheduled ground station forward-link communication services using a sequential estimation algorithm enhanced by a sophisticated process noise model to provide onboard orbit and frequency determination. To evaluate the navigation accuracies achievable if a TCXO were used, actual experiment data (which used the USO as the frequency reference) were corrupted with errors from real TDRSS one-way return tracking measurements taken from EP/EUVE's TCXO. Analysis of the GONS TCXO experiment performance indicates that real-time onboard position accuracies of better than 300 meters (1 sigma) are achievable with as few as two tracking contacts per day for the EP/EUVE 525-kilometer altitude, 28.5-degree inclination orbit, provided the TCXO is as stable as that in EP/EUVE's TDRSS transponder. GONS using a TCXO frequency reference provides a viable option for many upcoming spacecraft missions with moderate position accuracy requirements and an interest in reducing their operational costs with autonomous navigation.

Radomski, M. S.↗
NASA NTRS1977

Study to investigate and evaluate means of optimizing the Ku-band combined radar/communication functions for the space shuttle

The performance of the space shuttle orbiter's Ku-Band integrated radar and communications equipment is analyzed for the radar mode of operation. The block diagram of the rendezvous radar subsystem is described. Power budgets for passive target detection are calculated, based on the estimated values of system losses. Requirements for processing of radar signals in the search and track modes are examined. Time multiplexed, single-channel, angle tracking of passive scintillating targets is analyzed. Radar performance in the presence of main lobe ground clutter is considered and candidate techniques for clutter suppression are discussed. Principal system parameter drivers are examined for the case of stationkeeping at ranges comparable to target dimension. Candidate ranging waveforms for short range operation are analyzed and compared. The logarithmic error discriminant utilized for range, range rate and angle tracking is formulated and applied to the quantitative analysis of radar subsystem tracking loops.

Weber, C. L.↗
NASA NTRS1993

Spectral characteristics of time-dependent orbit errors in altimeter height measurements

A mean reference surface and time-dependent orbit errors are estimated simultaneously for each exact-repeat ground track from the first two years of Geosat sea level estimates based on the Goddard Earth model (GEM)-T2 orbits. Motivated by orbit theory and empirical analysis of Geosat data, the time-dependent orbit errors are modeled as 1 cycle per revolution (cpr) sinusoids with slowly varying amplitude and phase. The method recovers the known 'bow tie effect' introduced by the existence of force model errors within the precision orbit determination (POD) procedure used to generate the GEM-T2 orbits. The bow tie pattern of 1-cpr orbit errors is characterized by small amplitudes near the middle and larger amplitudes (up to 160 cm in the 2 yr of data considered here) near the ends of each 5- to 6-day orbit arc over which the POD force model is integrated. A detailed examination of these bow tie patterns reveals the existence of daily modulations of the amplitudes of the 1-cpr sinusoid orbit errors with typical and maximum peak-to-peak ranges of about 14 cm and 30 cm, respectively. The method also identifies a daily variation in the mean orbit error with typical and maximum peak-to-peak ranges of about 6 and 30 cm, respectively, that is unrelated to the predominant 1-cpr orbit error. Application of the simultaneous solution method to the much less accurate Geosat height estimates based on the Naval Astronautics Group orbits concludes that the accuracy of POD is not important for collinear altimetric studies of time-dependent mesoscale variability (wavelengths shorter than 1000 km), as long as the time-dependent orbit errors are dominated by 1-cpr variability and a long-arc (several orbital periods) orbit error estimation scheme such as that presented here is used.

Chelton, Dudley B.↗
NASA NTRS2003

Navigation Guidelines for Orbital Formation Flying Missions

Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member's semi-major axis are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or vice versa. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

Carpenter, J. Russell↗
NASA NTRS2003

Navigation Accuracy Guidelines for Orbital Formation Flying Missions

Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver we, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

Carpenter, J. Russell↗