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GOES-R Series GEO Side-Lobe Capable GPSR Post-Launch Refinements and Operational Capabilities

This paper addresses three topics: 1) EOPP (EOP (Earth Orientation Prediction) Parameters) file modification, 2) Kalman filter parameter tuning regarding maneuvers and 3) off-pointing GPS (Global Positioning System) tracking capability. GOES-R (Geostationary Operational Environmental Satellite-R Series) is the first in a 4-part series of new weather satellites set to replace and upgrade the older GOES constellation. Two GOES-R series have been launched to date, GOES-S and GOES-R. GOES-R is operational over the Eastern United States and GOES-S over the West. The Global Positioning System Receiver (GPSR) on board this geostationary weather satellite is a mission critical enabling technology which has been both tested on the ground and evaluated on-orbit to verify its effectivity. Since becoming operational in November 2016, the GPSR onboard has performed extremely well under nominal circumstances. Further refinements regarding a variety of facets have taken place since the launch of GOES-R. One such refinement was the implementation of a modified EOP (Earth Orientation Prediction) parameter set to improve ECEF (Earth Centered Earth Fixed) to ECI (Earth Centered Inertial) transformation by restoring zonal tides removed from the EOP parameter fit per tech note 36. Another relevant refinement combined thermal consideration with Kalman filter tuning to improve orbit determination performance during maneuvers. Now with two years of data and two vehicles in orbit many capabilities of the GPSR have been identified and defined to a higher degree. For example, metrics on side-lobe tracking and off-Nadir tracking capabilities have been quantified to a high degree. This paper will seek to supplement the ESA (European Space Agency) GNC 2017 GOES-R GPSR performance paper as a deeper dive on specific tracking capabilities and performance improvements now implemented on the GOES-R and GOES-S vehicles.

GPS Receiver↗

Carrier phase delay altimetry from low eleveation GPSR measurements

GPS-Reflections (GPSR) observations at very low elevation angles take advantage of the apparent smoothness of the surface to enable phase-delay altimetry, of centimetric nominal precision, higher than the GPSR code-delay estimates.

GPS GNSS-reflections altimetry remote sensing bist↗

Post-Flight Analysis of GPSR Performance During Orion Exploration Flight Test 1

On 5 December 2014, the first test flight of the Orion Multi-Purpose Crew Vehicle executed a unique and challenging flight profile including an elevated re-entry velocity and steeper flight path angle to envelope lunar re-entry conditions. A new navigation system including a single frequency (L1) GPS receiver was evaluated for use as part of the redundant navigation system required for human space flight. The single frequency receiver was challenged by a highly dynamic flight environment including flight above low Earth orbit, as well as single frequency operation with ionospheric delay present. This paper presents a brief description of the GPS navigation system, an independent analysis of flight telemetry data, and evaluation of the GPSR performance, including evaluation of the ionospheric model employed to supplement the single frequency receiver. Lessons learned and potential improvements will be discussed.

Barker, Lee↗

Preliminary Results from the GPS-Reflections Mediterranean Balloon Experiment (GPSR MEBEX)

An experiment to collect bistatically scattered GPS signals from a balloon at 37 km altitude has been conducted. This experiment represented the highest altitude to date that such signals were successfully recorded. The flight took place in August 1999 over the Mediterranean sea, between a launch in Sicily and recovery near Nerpio, a town in the Sierra de Segura, Albacete province of Huelva, Spain. Results from this experiment are presented, showing the waveform shape as compared to theoretical calculations. These results will be used to validate analytical models which form the basis of wind vector retrieval algorithms. These algorithms are already being validated from aircraft altitudes, but may be applied to data from future spaceborne GPS receivers. Surface wind data from radiosondes were used for comparison. This experiment was a cooperative project between NASA, the IEEC in Barcelona, and the University of Colorado at Boulder.

Garrison, James L.↗

Preliminary Results from the GPS-Reflections Mediterranean Balloon Experiment (GPSR-MEBEX)

An experiment to collect bistatically scattered GPS signals from a balloon at 37 km altitude has been conducted. This experiment represented the highest altitude to date that such signals were successfully recorded. The flight took place in August 1999 over the Mediterranean sea, between a launch in Sicily and recovery near Nerpio, a town in the Sierra de Segura, Albacete province of Huelva, Spain. Results from this experiment are presented, showing the waveform shape as compared to theoretical calculations. These results will be used to validate analytical models which form the basis of wind vector retrieval algorithms. These algorithms are already being validated from aircraft altitudes, but may be applied to data from future spacebourne GPS receivers. Surface wind data from radiosondes were used for comparison. This experiment was a cooperative project between NASA, the IEEC in Barcelona, and the University of Colorado at Boulder.

Garrison, James L.↗

Complementing a continuum thermodynamic approach to constitutive modeling with symbolic regression

Here, an interpretable machine learning method, physics-informed genetic programming-based symbolic regression (P-GPSR), is integrated into a continuum thermodynamic approach to developing constitutive models. The proposed strategy for combining a thermodynamic analysis with P-GPSR is demonstrated by generating a yield function for an idealized material with voids, i.e., the Gurson yield function. First, a thermodynamic-based analysis is used to derive model requirements that are exploited in a custom P-GPSR implementation as fitness criteria or are strongly enforced in the solution. The P-GPSR implementation improved accuracy, generalizability, and training time compared to the same GPSR code without physics-informed fitness criteria. The yield function generated through the P-GPSR framework is in the form of a composite function that describes a class of materials and is characteristically more interpretable than GPSR-derived equations. The physical significance of the input functions learned by P-GPSR within the composite function is acquired from the thermodynamic analysis. Fundamental explanations of why the implemented P-GPSR capabilities improve results over a conventional GPSR algorithm are provided.

42 ENGINEERING↗

GPS Receiver On-Orbit Performance for the GOES-R Spacecraft

This paper evaluates the on-orbit performance of the first civilian operational use of a Global Positioning System Receiver (GPSR) at a geostationary orbit (GEO). The GPSR is on-board the newly launched Geostationary Operational Environmental Satellite (GOES-R). GOES-R is the first of four next generation GEO weather satellites for NOAA, now in orbit GOES-R is formally identified as GOES-16. Among the pioneering technologies required to support its improved spatial, spectral and temporal resolution is a GPSR. The GOES-16 GPSR system is a new design that was mission critical and therefore received appropriate scrutiny. As ground testing of a GPSR for GEO can only be done by simulations with numerous assumptions and approximations regarding the current GPS constellation, this paper reveals what performance can be achieved in using on orbit data. Extremely accurate orbital position is achieved using GPS navigation at GEO. Performance results are shown demonstrating compliance with the1007575 meter and 6 cms radial/in-track/cross-track orbital position and velocity accuracy requirements of GOES-16. The aforementioned compliance includes station-keeping and momentum management maneuvers, contributing to no observational outages. This performance is achieved by a completely new system design consisting of a unique L1 GEOantenna, low-noise amplifier (LNA) assembly and a 12 channel GPSR capable of tracking the edge of the main beam and the side lobes of the GPS L1 signals. This paper presents the definitive answer that the GOES-16 GPSR solution exceeds all performance requirements tracking up to 12 satellites and achieving excellent carrier-to-noise density (C/N0). Additionally, these performance results show the practicality of this approach. This paper makes it clear that all future GEO Satellites should consider the addition of a GPSR in their spacecraft design, otherwise they may be sacrificing spacecraft capabilities and accuracy along with incurring increased and continual demand on ground support.

GEO GPS↗

Global Positioning System Constellation Modernization Impact on Sidelobe Capable GPS Receivers in Geostationary Orbit

This paper provides on-orbit insight into Global Positioning System Receiver (GPSR) performance at a geostationary orbit (GEO) and contrasts that performance regarding the modernized and heritage GPS constellation currently operational. The subject matter of this paper falls under the following topics a) heritage and modern GPS transmit pattern comparison, b) GOES-R GPSR acquisition and tracking characterization regarding the first four operational GPS III vehicles, and c)relevant signal requirements as it pertains to GEO GPSR facilitation. The GPSR described herein is onboard the GOES-R series satellites. GOES-R (Geostationary Operational Environmental Satellite-R Series) is the first in a 4-part series of new weather satellites set to replace and upgrade the older GOES constellation. Two GOES-R have been launched to date, GOES-16 and GOES-17, the data presented in this paper are from both vehicles over common time spans. The GPSR on board this geostationary weather satellite is a mission critical, enabling technology which has been both tested on the ground and evaluated on-orbit to verify its effectivity[1]. This is a completely new system design consisting of a unique L1 GEO antenna, low-noise amplifier (LNA) assembly and a 12-channel GPSR capable of tracking the edge of the main beam and the sidelobes of the GPS L1 signal. Any satellite intending to maximize GPS navigation performance at GEO will need to implement a GPSR system that tracks sidelobes. GOES-R is the first civilian operational satellite to utilize GPS sidelobes for navigation at GEO, which is the key factor in the systems highly accurate, robust and continuous navigation solution. However, this also renders a distinct sensitivity to changes in the GPS transmit signal pattern in the sidelobe regime as a result of the new GPS III constellation modernization. This paper presents results showing that the GOES-RGPSR solution, given GPS constellation modernization to GPS III, although impacted slightly in received C/N0 at certain geometries, will continue to meet all performance requirements tracking up to 12 satellites and achieving excellent carrier-to-noise spectral density (C/N0).

GPS↗

Generalizing the Gurson model using symbolic regression and transfer learning to relax inherent assumptions

Abstract To generate material models with fewer limiting assumptions while maintaining closed-form, interpretable solutions, we propose using genetic programming based symbolic regression (GPSR), a machine learning (ML) approach that describes data using free-form symbolic expressions. To maximize interpretability, we start from an analytical, derived material model, the Gurson model for porous ductile metals, and systematically relax inherent assumptions made in its derivation to understand each assumption’s contribution to the GPSR model forms. We incorporate transfer learning methods into the GPSR training process to increase GPSR efficiency and generate models that abide by known mechanics of the system. The results show that regularizing the GPSR fitness function is critical for generating physically valid models and illustrate how GPSR allows a high level of interpretability compared with other ML approaches. The method of systematic assumption relaxation allows the generation of models that address limiting assumptions found in the Gurson model, and the symbolic forms allow conjecture of decreased material strength due to void interaction and non-symmetric void shapes.

36 MATERIALS SCIENCE↗

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. Here, in this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

42 ENGINEERING↗

Genetic programming for interpretable, data-driven continuum damage models.

The damage mechanisms that lead to failure in engineering alloys have been studied extensively, but converting this knowledge into constitutive models that are suitable for engineering-scale analysis remains a challenge. Evolution laws for continuum damage have been developed in the past and have proven effective but suffer from many non-physical assumptions that inhibit the overall accuracy of the model. Further, the assumptions inherent in these existing models prevent them from being applicable to a broad class of materials. At the same time, computational models of fine-scale damage mechanisms continue to advance making it tractable to generate large training data sets through computer simulation. Data-driven machine learning approaches can leverage these data sets to avoid making limiting assumptions, and instead produce models directly from the results of microstructural simulations and/or experiments. Many of these machine learning approaches are rapid and accurate, but they offer little to no insight into the underlying relationships among state variables being discovered. Conversely, genetic programming symbolic regression (GPSR) is a machine learning method that produces analytic expressions relating the state variables, allowing maximal insight and interpretability. To that end, we propose using GPSR as a data-driven method of obtaining microstructurally informed continuum damage models. Data is generated using microstructural simulations of damage evolution, parameterized over microstructural statistics (i.e., pore shape) and nominally applied deformations. Analytic expressions for damage evolution are obtained from the data using GPSR, and these expressions are then utilized within a continuum constitutive model. Overall, this approach is a promising method of automatically obtaining analytic relations describing constitutive phenomena in a material.

Buche, Michael Robert↗

Application of a Bayesian Framework for Plasticity Model Selection

Interpretable Machine Learning (IML) has performed well when tasked with deriving constitutive material models. However, IML has been shown to prefer models that overfit noise in data, which tends to lead to bloat and a decrease in interpretability. Due to these issues, the ability of IML to reliably derive models that fit the data and are both interpretable and generalizable is limited. A method developed recently has shown promise to improve upon traditional IML by using a Bayesian fitness definition for the evolution of free-form models with non-deterministic parameters. This framework was developed for genetic-programming-based symbolic regression(GPSR) and involves model parameter estimation using Sequential Monte Carlo sampling (SMC).The method has demonstrated a reduction in bloat when dealing with noisy data in comparison to conventional GPSR. The results of this framework applied to stress-strain data for copper show models that more effectively predict the experimental data better than was previously shown with GPSR.

plasticity↗

Developing a robust strength model using physically-informed genetic programming

The strength of materials is influenced by a range of external conditions, such as temperature and deformation rate. Consequently, materials that demonstrate substantial variations in their mechanical behavior due to fluctuations in temperature and strain rate require complex strength models to accurately predict material performance in real-world applications. To predict such complex behavior, a robust and flexible strength model is necessary. In this work, we utilize genetic programming-based symbolic regression (GPSR) to develop data-driven strength models that accurately represent the measured stress–strain responses of tin across a wide range of strain, strain rate and temperature regimes. The GPSR models are constrained by physically-informed conditions, which leads to significant improvement in extrapolation. The best model is integrated into a multi-physics code to perform Taylor impact simulations, validating the model’s accuracy and robustness. In conclusion, the model predictions showed excellent agreement with experimental results, particularly when compared to predictions using traditional strength models.

Genetic programming↗

Deployment and validation of predictive 6-dimensional beam diagnostics through generative reconstruction with standard accelerator elements

Understanding the 6-dimensional phase space distribution of particle beams is essential for optimizing accelerator performance. Conventional diagnostics such as use of transverse deflecting cavities offer detailed characterization but require dedicated hardware and space. Generative phase space reconstruction (GPSR) methods have shown promise in beam diagnostics, yet prior implementations still rely on such components. Here we present the first experimental implementation and validation of the GPSR methodology, realized by the use of standard accelerator elements including accelerating cavities and dipole magnets, to achieve complete 6-dimensional phase space reconstruction. Through simulations and experiments at the Pohang Accelerator Laboratory X-ray Free Electron Laser facility, we successfully reconstruct complex, nonlinear beam structures. Furthermore, we validate the methodology by predicting independent downstream measurements excluded from training, revealing the reconstruction closely resembling ground truth. This advancement establishes a pathway for predictive diagnostics across beamline segments while reducing hardware requirements and expanding applicability to various accelerator facilities.

Kim, Seongyeol [Pohang Univ. of Science and Techno↗

Digital Beamforming Scatterometer

This paper discusses scatterometer measurements collected with multi-mode Digital Beamforming Synthetic Aperture Radar (DBSAR) during the SMAP-VEX 2008 campaign. The 2008 SMAP Validation Experiment was conducted to address a number of specific questions related to the soil moisture retrieval algorithms. SMAP-VEX 2008 consisted on a series of aircraft-based.flights conducted on the Eastern Shore of Maryland and Delaware in the fall of 2008. Several other instruments participated in the campaign including the Passive Active L-Band System (PALS), the Marshall Airborne Polarimetric Imaging Radiometer (MAPIR), and the Global Positioning System Reflectometer (GPSR). This campaign was the first SMAP Validation Experiment. DBSAR is a multimode radar system developed at NASA/Goddard Space Flight Center that combines state-of-the-art radar technologies, on-board processing, and advances in signal processing techniques in order to enable new remote sensing capabilities applicable to Earth science and planetary applications [l]. The instrument can be configured to operate in scatterometer, Synthetic Aperture Radar (SAR), or altimeter mode. The system builds upon the L-band Imaging Scatterometer (LIS) developed as part of the RadSTAR program. The radar is a phased array system designed to fly on the NASA P3 aircraft. The instrument consists of a programmable waveform generator, eight transmit/receive (T/R) channels, a microstrip antenna, and a reconfigurable data acquisition and processor system. Each transmit channel incorporates a digital attenuator, and digital phase shifter that enables amplitude and phase modulation on transmit. The attenuators, phase shifters, and calibration switches are digitally controlled by the radar control card (RCC) on a pulse by pulse basis. The antenna is a corporate fed microstrip patch-array centered at 1.26 GHz with a 20 MHz bandwidth. Although only one feed is used with the present configuration, a provision was made for separate corporate feeds for vertical and horizontal polarization. System upgrades to dual polarization are currently under way. The DBSAR processor is a reconfigurable data acquisition and processor system capable of real-time, high-speed data processing. DBSAR uses an FPGA-based architecture to implement digitally down-conversion, in-phase and quadrature (I/Q) demodulation, and subsequent radar specific algorithms. The core of the processor board consists of an analog-to-digital (AID) section, three Altera Stratix field programmable gate arrays (FPGAs), an ARM microcontroller, several memory devices, and an Ethernet interface. The processor also interfaces with a navigation board consisting of a GPS and a MEMS gyro. The processor has been configured to operate in scatterometer, Synthetic Aperture Radar (SAR), and altimeter modes. All the modes are based on digital beamforming which is a digital process that generates the far-field beam patterns at various scan angles from voltages sampled in the antenna array. This technique allows steering the received beam and controlling its beam-width and side-lobe. Several beamforming techniques can be implemented each characterized by unique strengths and weaknesses, and each applicable to different measurement scenarios. In Scatterometer mode, the radar is capable to.generate a wide beam or scan a narrow beam on transmit, and to steer the received beam on processing while controlling its beamwidth and side-lobe level. Table I lists some important radar characteristics

Rincon, Rafael F.↗

Bingo: A Customizable Framework for Symbolic Regression with Genetic Programming

In this paper, we introduce Bingo, a flexible and customizable yet performant Python framework for symbolic regression with genetic programming. Bingo maintains a modular code structure for simple abstraction and easily swappable components. Fitness functions, selection methods, and constant optimization methods allow for easy problem-specific customization. Bingo also maintains several features for increased efficiency such as parallelism, equation simplification, and a C++ backend. We compare Bingo’s performance to other genetic programming for symbolic regression (GPSR) methods to show that it is both competitive and flexible.

machine learning↗

Bingo: A Customizable Framework for Symbolic Regression with Genetic Programming

In this paper, we introduce Bingo, a flexible and customizable yet performant Python framework for symbolic regression with genetic programming. Bingo maintains a modular code structure for simple abstraction and easily swappable components. Fitness functions, selection methods, and constant optimization methods allow for easy problem-specific customization. Bingo also maintains several features for increased efficiency such as parallelism, equation simplification, and a C++ backend. We compare Bingo’s performance to other genetic programming for symbolic regression (GPSR) methods to show that it is both competitive and flexible.

David Randall↗