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NASA NTRS1972

Earth-based navigation capabilities for outer planet missions.

The role of new Earth-based radio metric data types and of advanced estimation algorithms in navigating an outer planet spacecraft in the vicinity of Saturn has been analyzed. The data types included in the study consist of conventional range and range-rate measurements taken from a single station and simultaneous and nearly simultaneous measurements obtained from pairs of stations during overlapping viewing periods. The utility of a third data set that is produced by explicitly differencing the simultaneous points has also been investigated. The data was processed with a conventional least squares batch filter and with a sequential filter that estimated parameters describing small stochastic accelerations (process noise) acting on the spacecraft. It was found that process noise can produce large errors in the estimates obtained from batch filtering conventional and simultaneous data, and that the only batch filtered estimates that were reliable were those obtained from differenced data. The performance of the simultaneous data in the presence of process noise is greatly improved by sequential filtering.

Hildebrand, C. E.↗
NASA NTRS2017

Validation of Minimum Display Requirements for a UAS Detect and Avoid System

The full integration of Unmanned Aircraft Systems (UAS) into the National Airspace System (NAS), a prerequisite for enabling a broad range of public and commercial UAS operations, presents several technical challenges to UAS developers, operators and regulators. A primary barrier is the inability for UAS pilots (situated at a ground control station, or GCS) to comply with Title 14 Code of Federal Regulations sections 91.111 and 91.113, which require pilots to “see and avoid” other aircraft in order to maintain well clear. UAS pilots’ removal from the flight deck of the aircraft necessitates the development of a UAS-specific system for detecting nearby traffic and displaying traffic information to the pilot to support their ability to maintain an objectively defined “DAA well clear” threshold from other aircraft. This new UAS-specific function of remaining DAA well clear is called traffic avoidance. The resulting Detect and Avoid (DAA) system, however, will be subject to a collection of requirements that manufacturers will be obligated to meet in order to certify their equipment. RTCA Special Committee 228 (SC-228), a consortium of representatives from government, industry and academia, is responsible for developing and documenting the Minimum Operational Performance Standards (MOPS) for UAS DAA systems. The present study is the final in a series of human-in-the-loop (HITL) experiments designed to explore and test the various display and alerting requirements being incorporated into the DAA MOPS. Whereas the prior DAA HITLs examined a wide variety of DAA display features and concepts, the current experiment aims to validate the latest minimum display requirements for Phase 1 of the DAA MOPS. Rather than test different display concepts, this study tests two configurations of a MOPS-compatible DAA display: a version that is integrated into the primary navigation and control display of the GCS and a version that is physically separated from the primary display. This manipulation tests the draft minimum requirement that allows the DAA traffic display to be a separate, or standalone, configuration. This type of configuration is a more achievable near-term technology solution since it does not stipulate additional certification or integration requirements on UAS manufacturers. However, a standalone display configuration has the potential to result in pilot performance issues resulting from the cognitive costs of switching between the primary DAA display and the primary navigation and control display. This configuration is also particularly susceptible to errors if the displays are in different orientations (e.g., north-up versus track-up). Both the integrated and standalone display configurations were presented to 16 active UAS pilots in a medium-fidelity simulation, which included confederate air traffic controllers and pseudo pilots operating simulated manned traffic. Pilots were tasked with navigating two different mission routes while maintaining DAA well clear with scripted conflicts. Pilot response times (i.e., measured response) and ability to remain DAA well clear are reported. Primary results indicate that both display configurations resulted in favorable response times and well clear rates. While there were clear trends of pilots objectively performing better in the integrated display condition, with several measured response metrics reaching statistical significance, the differences between the two displays were typically moderate. While the primary variable of DAA display location did not have an especially large impact on pilot performance on its own, when examined alongside the type of DAA threat the pilot was facing (a caution-level versus a warning-level alert), the response time benefits associated with the integrated display were amplified. The implications of these American Institute of Aeronautics and Astronautics 2 results on the Phase 1 DAA MOPS and the connection of this data to previous studies is also discussed.

detect and avoid↗
NASA NTRS2024

A High-Performance Computing Predictive GNSS Performance Monitor for Autonomous Air Vehicles in Urban Environments

This report offers analysis and design insights for leveraging High-Performance Computing (HPC) to predict line-of-sight (LOS) Global Navigation Satellite System (GNSS) availability in a city. This work is motivated by the emerging fields of Advanced and Urban Air Mobility (AAM/UAM), where regulatory authorities are seeking city-scale, meter-resolution risk forecasting in order to safely integrate new flight missions with existing urban life and infrastructure. This work addresses the technical challenge of efficiently computing urban GNSS satellite visibility to predict GNSS performance metrics under these requirements. We present a new HPC-optimized shadow casting algorithm variant as a ray-based approach to forecasting satellite visibility. We apply this algorithm variant in a software-defined prognostic service which generates a GNSS navigation risk-correlated map as a path planning-style potential field. We detail dominant computational burdens, viable simplifying assumptions, and different algorithmic implementations, intending to demonstrate a baseline of computation time needed by each stage in such a service. We conclude by analyzing the prototype service’s prediction accuracy compared to receiver data from Corpus Christi, Texas. This informs design trade-offs along the dimensions of hardware, computation time, and tolerable forecasting error (including proportions of false positives and false negatives).

GNSS↗
NASA NTRS2014

Overview and Summary of Advanced UVOIR Mirror Technology Development (AMTD) Project

ASTRO2010 Decadal Survey stated that an advanced large-aperture ultraviolet, optical, near-infrared (UVOIR) telescope is required to enable the next generation of compelling astrophysics and exoplanet science; and, that present technology is not mature enough to affordably build and launch any potential UVOIR mission concept. AMTD is a multiyear effort to develop, demonstrate and mature critical technologies to TRL-6 by 2018 so that a viable flight mission can be proposed to the 2020 Decadal Review. AMTD builds on the state of art (SOA) defined by over 30 years of monolithic & segmented ground & space-telescope mirror technology to mature six key technologies: center dotLarge-Aperture, Low Areal Density, High Stiffness Mirror Substrates: Both (4 to 8 m) monolithic and (8 to 16 m) segmented telescopes require larger and stiffer mirrors. center dotSupport System: Large-aperture mirrors require large support systems to ensure that they survive launch, deploy on orbit, and maintain a stable, undistorted shape. center dotMid/High Spatial Frequency Figure Error: Very smooth mirror is critical for producing high-quality point spread function (PSF) for high contrast imaging. center dotSegment Edges: The quality of segment edges impacts PSF for high-contrast imaging applications, contributes to stray light noise, and affects total collecting aperture. center dotSegment to Segment Gap Phasing: Segment phasing is critical for producing high-quality temporally-stable PSF. center dotIntegrated Model Validation: On-orbit performance is driven by mechanical & thermal stability. Compliance cannot be 100% tested, but relies on modeling. Because we cannot predict the future, AMTD is pursuing multiple design paths to provide the science community with options to enable either large aperture monolithic or segmented mirrors with clear engineering metrics traceable to science requirements

Stahl, H. Philip↗
NASA NTRS2019

Uncertainty in Soil Moisture Retrievals: an Ensemble Approach Using SMOS L-Band Microwave Data

The uncertainty of soil moisture (SM) retrievals from satellite brightness temperature (TB) observations depends primarily on the choice of radiative transfer model (RTM) parameters, prior SM information and TB inputs. This paper studies the sensitivity of several (quasi-)operational and experimental SM retrieval products from the Soil Moisture Ocean Salinity (SMOS) mission to these choices at 11 reference sites, located in 7 watersheds across the United States (US). Different literature-based RTM parameter sets cause large biases between retrievals. Whereas typical RTM parameter sets are calibrated for SM retrievals, it is shown that a parameter set carefully optimized for TB forward modeling can also be used for retrieving SM. It is also shown that the inclusion of dynamic prior SM estimates in a Bayesian retrieval scheme can strongly improve SM retrievals, regardless of the choice of RTM parameters, and that the use of multi-angular and multi-polarization TB does not necessarily lead to superior retrievals compared to retrievals based on TB data at a single incidence angle and polarization. The second part of this paper evaluates ensemble uncertainty metrics for SM retrievals obtained by propagating a wide range of RTM parameters through the RTM. As expected for bounded variables, the spread in the ensemble SM retrievals is smallest for wet and dry SM values and highest for intermediate SM values. After removal of the strong long-term mean bias associated with the RTM parameter values for individual ensemble members, the remaining anomaly ensemble SM spread of 0.037 cu m/cu m approximates the actual time series unbiased root-mean-square-difference of 0.042 cu m/cu m between ensemble mean retrievals and in situ reference data across the reference sites. However, the temporal variability in the anomaly ensemble spread reveals higher-order biases in the retrieval error, which should be accounted for when characterizing retrieval error.

Jan Quets↗
NASA NTRS2010

Shifting the Intertial Navigation Paradigm with the MEMS Technology

"Why don't you use MEMS?" is of the most common questions posed to navigation systems engineers designing inertial navigation solutions in the modern era. The question stems from a general understanding that great strides have been made in terrestrial MEMS accelerometers and attitude rate sensors in terms of accuracy, mass, and power. Yet, when compared on a unit-to-unit basis, MEMS devices do not provide comparable performance (accuracy) to navigation grade sensors in several key metrics. This paper will propose a paradigm shift where the comparison in performance is between multiple MEMS devices and a single navigation grade sensor. The concept is that systematically, a sufficient number of MEMS sensors may mathematically provide comparable performance to a single navigation grade device and be competitive in terms power and mass allocations when viewed on a systems level. The implication is that both inertial navigation system design and fault detection, identification, and recovery could benefit from a system of MEMS devices in the same way that swarm sensing has benefited Earth observation and astronomy. A survey of the state of the art in inertial sensor accuracy scaled by mass and power will be provided to show the scaled error in MEMS and navigation graded devices, a mathematical comparison of multi-unit to single-unit sensor errors will be developed, and preliminary application to an Orion lunar skip atmospheric entry trajectory will be explored.

Crain, Timothy P., II↗
NASA NTRSDate not supplied

US-EUSST SSA Data Exchange for Improved Orbital Safety

Data sharing and exchange among different Space Situational Awareness (SSA) data collectors/providers is frequently discussed as a mechanism to improve the accuracy and precision of orbital safety products. Indeed, at the conceptual level this claim is quite sensible: objects with more tracking, and thus presumably better distribution of that tracking about their orbit, should produce updates with smaller epoch errors and more realistic covariances at epoch, which should then translate into better performance in prediction and thus improved close approach calculations. However, this thesis has not been verified with any large study involving two different data providers, through which the amount of realized improvement can be quantified and, perhaps more importantly, the logistics of effecting observation data sharing in a regularized way can be established and circulated to assist others. To create rubrics for helpful data sharing for conjunction assessment applications, and to collect empirical data on the improvements achieved through sharing of measurement data, the US Office of Space Commerce and the European Union Space Surveillance and Tracking (EUSST) Support Framework have embarked on a joint experiment to collect and exchange satellite metric observations on selected satellites of interest over an experimental period. Each entity will perform orbit determination with their own observations, the other entity’s observations, and with both observation data sets combined. The product results will be compared with each other, showing differences attributable both to the three different data groups and to the two entities’ different approaches to orbit determination. The exemplar satellites include both objects that have external precision reference ephemerides and those that do not, allowing the experiment to exercise both precision-comparison and assimilative-comparison techniques. The present reporting will give preliminary results and a set of lessons learned for data sharing; a second presentation later in 2023 will provide a full accounting of the experiment’s results. The hope is that, through this work, a pathway can be established for the expeditious and fruitful sharing among collection entities, both commercial and governmental.

space situational awareness↗
NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗
NASA NTRS1993

In-situ radio-metric tracking to support navigation for interplanetary missions with multiple spacecraft

Doppler and ranging measurements between spacecraft can be obtained only when the ratio of the total received signal power to noise power density (P(sub t/N(sub 0)) at the receiving spacecraft is sufficiently large that reliable signal detection can be achieved within a reasonable time period. In this paper, the requirements on P(sub t)/N(sub 0) for reliable carrier signal detection is calculated as a function of various system parameters, including characteristics of the spacecraft computing hardware and a priori uncertainty in spacecraft-spacecraft relative velocity and acceleration. Also calculated is the P(sub t)/N(sub 0) requirement for relaible detection of a ranging signal, consistting of a carrier with pseudo-noise phase modulation. Once the P(sub t)/N(sub 0) requirement is determined, then for a given set of assumed spacecraft telecommunication characteristics (transmitted signal power, antenna gains, receiver noise temperatures) it is possible to calculate the maximum range at which a carrier signal or ranging signal may be acquired. A brief error covariance analysis has been conducted to illustrate the utility of in situ Doppler and ranging measurements for Mars approach navigation. The results indicate that navigation accuracies of a few kilometers can be achieved with either data type. The analysis also illustrates dependency of the achievable accuracy on the approach trajectory velocity.

Kahn, Robert D.↗
NASA NTRS2010

A Singular Perturbation Approach for Time-Domain Assessment of Phase Margin

This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter Epsilon. First, a bijective relationship between the Singular Perturbation Margin (SPM) max and the PM of the nominal (slow) system is established with an approximation error on the order of Epsilon(exp 2). In proving this result, relationships between the singular perturbation parameter Epsilon, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.

Zhu, J. Jim↗
NASA NTRSDate not supplied

Quantum-Assisted Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

The quantum computing community has been searching for suitable applications to demonstrate the potential of near-term quantum devices. Quantum machine learning is a potential candidate, particularly using models that cannot be efficiently simulated with classical computers [1, 2]. This work focuses on a transition phase of quantum computers where the quantum machine learning model is still simulable classically but projected not to be simulable as the size of the model grows. Ultimately quantum computers may have advantages for high-dimensional real-world problems. Due to the limited number of qubits in current noisy intermediate-scale quantum (NISQ) devices, the direct application of quantum computers in high dimensional data is not feasible. To remedy this problem, an encoder-decoder architecture can be utilized. The encoder model would transform the high-dimensional data into a compact representation, to a level that small quantum computers can be used today (or in the near future), and the decoder would take the quantum processed outputs back to the high-dimensional space. Addressing the two challenges of quantum machine learning, this work investigates a hybrid supervised generative model with a quantum Ising Born machine embedded as the latent distribution. The model contains four main parts (Figure 1.a.): (1) a U-NET architecture responsible for learning segmentation flow, (2) a Prior network responsible for learning an encoded latent distribution of the input data, (3) a Born machine which represents the latent distribution, and (4) a Posterior network in charge of learning the joint encoded latent distribution of inputs and target data. The initial model, proposed by [3], is optimized by (1) maximizing the overlap of the prior and posterior latent distributions, and (2) minimizing the segmentation loss. The proposed model is designed to be investigated in a simulation environment applied to the real-world application of wildfire segmentation. Specifically, the model is designed to solve the patchy wildfire segmentations of Moderate Resolution Imaging Spectroradiometer (MODIS) by taking the MODIS observations and using Visible Infrared Imaging Radiometer Suite’s (VIIRS) consistent wildfire product as the target. The model solves patchy wildfire segmentations and provides insight into the epistemic errors sourced from model variation. The model utilizes the Born machine as a QUBO solver to represent the latent space as a Bernoulli distribution. The proposed configuration allows the variational segmentation model to leverage the true quantum probabilistic nature and derive a more expressive latent configuration, increasing the model performance in describing wildfire segmentations. The quantum probabilistic information of the Born machine is directly incorporated in the Kullback-Leibler divergence loss in the prior and posterior distributions, forcing the Bernoulli latent distribution to maximize the overlap of input and joint input-target distributions. The proposed model is then trained and compared with a baseline only consisting of direct Bernoulli latent distribution with no Born machine representing the latent space. The models are evaluated based on the segmentation metrics, such as precision, recall, intersect of union, with uncertainty boundaries accounting for the stochastic nature of the model. Our findings show that even in low latent-dimensional space (due to the limit in computational power of the classical quantum simulator), we are able to effectively capture the latent representation and hence the model performs better than the baseline. The findings are a projection for scaling the model into higher dimensional latent space with the Born machine surpassing the baseline performance. Figure 1. Sub-figure (a) demonstrates the architecture for the training phase. The model consists of a Prior and Posterior network that encode inputs and joint input-target data into compact representations, respectively. The Born machine represents the latent distribution, and the U-NET branch learns the segmentation patterns of the data. The stochasticity is introduced to the U-NET through its last layer to create meaningful but stochastic segmentations. Sub-figure (b) represents the inference phase where the model takes the stochastic behavior from the prior network and injects that into the U-NET. Each attempt of inference will generate different but similar segmentations from the same distribution of the wildfire event. REFERENCES [1] Coyle, B., Mills, D., Danos, V., & Kashefi, E. (2020). The Born supremacy: quantum advantage and training of an Ising Born machine. npj Quantum Information, 6(1), 1-11. [2] Liu, J. G., & Wang, L. (2018). Differentiable learning of quantum circuit born machines. Physical Review A, 98(6), 062324. [3] Kohl, S., Romera-Paredes, B., Meyer, C., De Fauw, J., Ledsam, J. R., Maier-Hein, K., ... & Ronneberger, O. (2018). A probabilistic u-net for segmentation of ambiguous images. Advances in neural information processing systems, 31.

quantum machine learning↗
NASA NTRS2018

Polarization Decomposition and Temperature Bias Resolution for SMAP Passive Soil Moisture Retrieval Using Time Series Brightness Temperature Observations

In passive microwave remote sensing of soil moisture, the tau-omega (τ-ω) model has often been used to provide soil moisture estimates at a spatial scale representative of the satellite footprint dimensions. For modeling simplicity, model parameters such as the single scattering albedo (ω) and vegetation opacity (τ) that go into the geophysical inversion process are often assumed to be independent of polarizations. Although this absence of polarization dependence can often be justified in special cases as in low-frequency remote sensing or under dense vegetation conditions, it is not a robust assumption in general. Additional model parameterization errors arising from this assumption are possible, leading to degradation in soil moisture estimation accuracy. In this paper, we propose a time series approach to try to resolve the polarization dependence of several τ-ω model parameters as well as the temperature bias arising from the ancillary temperature data. The Version 4 of the Soil Moisture Active Passive (SMAP) Level 1B brightness temperature time series observations were used to illustrate the mechanics of this approach, with an emphasis on a comparison between resulting satellite soil moisture retrievals and in situ data collected at several core validation sites. It was found that this time series approach resulted in significant reduction of the dry bias exhibited in the current SMAP passive soil moisture data products, while retaining the same performance in other metrics of the current baseline passive soil moisture retrieval algorithm.

time series↗
NASA NTRS2014

Assessment of Satellite Ocean Colour Radiometry and Derived Geophysical Products

Standardization of methods to assess and assign quality metrics to satellite ocean color radiometry and derived geophysical products has become paramount with the inclusion of the marine reflectance and chlorophyll-a concentration (Chla) as essential climate variables (ECV; [1]) and the recognition that optical remote sensing of the oceans can only contribute to climate research if and when a continuous succession of satellite missions can be shown to collectively provide a consistent, long-term record with known uncertainties. In 20 years, the community has made significant advancements toward that objective, but providing a complete uncertainty budget for all products and for all conditions remains a daunting task. In the retrieval of marine water-leaving radiance from observed top-of-atmosphere radiance, the sources of uncertainties include those associated with propagation of sensor noise and radiometric calibration and characterization errors, as well as a multitude of uncertainties associated with the modeling and removal of effects from the atmosphere and sea surface. This chapter describes some common approaches used to assess quality and consistency of ocean color satellite products and reviews the current status of uncertainty quantification in the field. Its focus is on the primary ocean color product, the spectrum of marine reflectance Rrs, but uncertainties in some derived products such as the Chla or inherent optical properties (IOPs) will also be considered.

Ocean↗
NASA NTRS2018

An Assessment of the Differences Between Spatial Resolution and Grid Size for the SMAP Enhanced Soil Moisture Product over Homogeneous Sites

Satellite-based passive microwave remote sensing typically involves a scanning antenna that makes measurements at irregularly spaced locations. These locations can change on a day to day basis. Soil moisture products derived from satellite-based passive microwave remote sensing are usually resampled to a fixed Earth grid that facilitates their use in applications. In many cases the grid size is finer than the actual spatial resolution of the observation, and often this difference is not well understood by the user. Here, this issue was examined for the Soil Moisture Active Passive (SMAP) enhanced version of the passive-based soil moisture product, which has a grid size of 9-km and a nominal spatial resolution of 33-km. In situ observations from core validation sites were used to compute comparison metrics. For sites that satisfied the established reliability and scaling criteria, the impact of validating the 9-km grid product with in situ data collected over a 9-km versus a 33-km domain was very small for the sites studied (0.039 cu. m/cu. m unbiased root mean square difference for the 9-km case versus 0.037 cu. m/cu. m for the 33-km case). This result does not mean that the resolution of the product is 9-km but that for the conditions studied here the soil moisture estimated from in situ observations over 9-km is a close approximation of the soil moisture estimated from in situ observations over the 33-km resolution. The implication is that using the enhanced SMAP product at its grid resolution of 9-km should not introduce large errors in most applications.

Soil moisture↗
NASA NTRSDate not supplied

Evaluating Retrieval Algorithm Climate Stability: Estimating 3D Optical Thickness Bias Distributions by Cloud Type

Detecting climate trends on large spatiotemporal scales requires accurate, stable measurements and stable retrieval algorithms. We strive to estimate how time-variant retrieval algorithm biases may impact trend detection. Here we focus on the 3D cloud optical thickness (τc) bias, which is among the largest in passive cloud retrieval algorithms. If this bias is time dependent, a possibility with potential decadal changes in cloud morphology, it may obscure genuine trends in τc. Although previous studies have evaluated the cloud- and sun-view geometry-dependent 3D τc bias on small spatial scales, before our current study none have evaluated the stability of this well-known bias on climate-relevant large spatiotemporal scales. These studies must estimate large scale distributions of the 3D τc bias by cloud type and estimate how cloud type amount may change between two climate states. We employ a novel approach to estimate large scale distributions of 3D τc using a proxy of the bias that quantifies the departure of clouds from satisfying the 1D radiative transfer assumption used in passive τc retrievals. This existing globally-distributed proxy is an angular consistency metric that was developed using fused Moderate-Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR) measurements. Calculating the 3D τc bias and the proxy, for known cloud fields enables us to establish statistical relationships between these two quantities, which can be used to calculate large-scale distributions of the 3D τc bias. This approach limits the number of 3D radiative transfer simulations required to only those needed to estimate a statistical relationship between the 3D τc bias for known cloud fields and a proxy of the bias. It is likely that future studies will be needed to evaluate retrieval algorithm bias stability for other geophysical variables as the community develops climate data records from satellite observations and their retrievals. This must be done in addition to monitoring and correcting measurement errors and uncertainties and understanding their impact on retrieved essential climate variables.

Yolanda Shea↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗
NASA NTRS2017

The Challenge Posed by Geomagnetic Activity to Electric Power Reliability: Evidence from England and Wales

This paper addresses whether geomagnetic activity challenged the reliability of the electric power system during part of the declining phase of solar cycle 23. Operations by National Grid in England and Wales are examined over the period of 11 March 2003 through 31 March 2005. This paper examines the relationship between measures of geomagnetic activity and a metric of challenged electric power reliability known as the net imbalance volume (NIV). Measured in megawatt hours, NIV represents the sum of all energy deployments initiated by the system operator to balance the electric power system. The relationship between geomagnetic activity and NIV is assessed using a multivariate econometric model. The model was estimated using half-hour settlement data over the period of 11 March 2003 through 31 December 2004. The results indicate that geomagnetic activity had a demonstrable effect on NIV over the sample period. Based on the parameter estimates, out-of-sample predictions of NIV were generated for each half hour over the period of 1 January to 31 March 2005. Consistent with the existence of a causal relationship between geomagnetic activity and the electricity market imbalance, the root-mean-square error of the out-of-sample predictions of NIV is smaller; that is, the predictions are more accurate, when the statistically significant estimated effects of geomagnetic activity are included as drivers in the predictions.

Forbes, Kevin F.↗
NASA NTRS2020

A Demonstration that Correcting for Completeness and Reliability Is Critical for Robust Occurrence Rates

A measurement of planetary occurrence rates based on a planet catalog should be robust against details of how initial detections were classified as planets or false positives. This is accomplished by supplying the catalog’s rate of missed planets (completeness) and rate of non-planets incorrectly called planets (reliability). The final Kepler data release (DR25) includes products that can be used with the DR25 planet candidate catalog to correct for completeness and reliability in occurrence rate estimates. This is made possible by the Kepler Robovetter, which algorithmically and uniformly selects planets based on a variety of metrics and thresholds. Completeness, reliability, and occurrence rates potentially depend on these Robovetter thresholds. We study the impact of varying these vetting thresholds using the techniques of Bryson et al. 2019 (arXiv:1906.03575). We explore sets of thresholds that result in more or fewer planets (trading off completeness for reliability), as well as thresholds tuned to pass DR25 false positives identified as possible planets by the Kepler False Positive Working Group. We find that when correcting only for completeness, and not reliability, the resulting occurrence rates have a strong dependence on these threshold sets. For example, the value of SAG13 eta-Earth varies by over a factor of 4 when not corrected for reliability. However, when correcting for both completeness and reliability, occurrence rates using our threshold sets are statistically indistinguishable, with differences being well inside 1-sigma error bars. We present occurrence rates integrated over several period-radius ranges. For example, SAG13 eta-Earth is consistent with 0.127 (+0.094)(-0.054) (from Bryson et al. 2019) for all the Robovetter threshold sets. This result emphasizes the importance of correcting occurrence rates for both completeness and reliability. This suggests that inconsistent completeness and reliability correction may be a significant contributor to the large variation of occurrence rates in recent literature. We plan to make the Robovetter results for our threshold sets available, and encourage the community to use them to examine whether other occurrence rate methods yield similarly robust results.

Bryson, S.↗