STATISTICAL FILTERING OF SPACE NAVIGATION MEASUREMENTS
Redundant measurements for space navigation - random variables, state vector, bayes estimator
BAYESIAN STATISTICS↗
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Gaussian Process Regression Method for Costing SmallSat Bus Capabilities
NASA is responding to the growing interest in, andcapabilities of, small satellites for science applications with an increasingnumber and frequency of Announcements of Opportunityfor small satellite space missions. Estimating the probabilitythat these mission concepts will fit within the small cost capsof these opportunities is largely driven by the probability thatone of the burgeoning number of small satellite providers will beable to meet the payload’s accommodation requirements withinthe budget for the spacecraft. JPL has collected a databasecontaining technical specifications and cost of commerciallyavailable Smallsat buses across various vendors. The primarypurpose of the database is for use in JPL’s Team X architecturestudies to inform cost estimates of a spacecraft bus which fitsthe customer’s technical requirements for their payload andmission. Customer needs are often unique and don’t alignperfectly with an off-the-shelf commercial spacecraft bus, whichmotivates the need to develop a cost model across the continuoustechnical parameter space.Al’s Bus Cost Distribution Estimator (ABCDE) uses Gaussianprocess regression (GPR) to predict commercial Smallsat spacecraftbus cost based on a subset of a customer’s technicalrequirements (payload mass, payload power, delta V, pointingcontrol, and downlink rate). GPR is implemented in ABCDE asa Bayesian method which fits an implied multivariate regressionon the technical parameters and uses kriging to intentionally“overfit” the residuals. Overfitting the residuals allows costestimates to collapse in uncertainty closer to the data pointswhile maintaining larger uncertainty intervals in regions of parameterspace with fewer data records. The data used to fit thismodel is sensitive and represents cost estimates for off-the-shelfcommercial buses. GPR simultaneously protects the sensitivityof the database and uses the sparse nature of the database toaccount for uncertainty in cost in a useful way. For a givenset of customer technical requirements, the tool provides a costestimate distribution, the percentiles of which can be interpretedas a confidence level of finding a commercial bus under a specifiedcost cap. ABCDE dramatically pushes the boundaries ofspacecraft cost estimation models due to its Bayesian methodology(accounting for the maximum uncertainty in the underlyingregression), the mathematically advanced kriging methodology,and the novelty of its application in Team X architecture tradestudies.
Austin, Alex↗
Bayesian Revision of Residual Detection Power
This paper addresses some issues with quality assessment and quality assurance in response surface modeling experiments executed in wind tunnels. The role of data volume on quality assurance for response surface models is reviewed. Specific wind tunnel response surface modeling experiments are considered for which apparent discrepancies exist between fit quality expectations based on implemented quality assurance tactics, and the actual fit quality achieved in those experiments. These discrepancies are resolved by using Bayesian inference to account for certain imperfections in the assessment methodology. Estimates of the fraction of out-of-tolerance model predictions based on traditional frequentist methods are revised to account for uncertainty in the residual assessment process. The number of sites in the design space for which residuals are out of tolerance is seen to exceed the number of sites where the model actually fails to fit the data. A method is presented to estimate how much of the design space in inadequately modeled by low-order polynomial approximations to the true but unknown underlying response function.
DeLoach, Richard↗
A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis
This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.
Warner, James E.↗
A Sensitive Search for Supernova Emission Associated with the Extremely Energetic and Nearby GRB 221009A
We report observations of the optical counterpart of the long gamma-ray burst GRB 221009A. Due to the extreme rarity of being both nearby (z = 0.151) and highly energetic (E ϒ,iso ≥ 10 54 erg), GRB 221009A offers a unique opportunity to probe the connection between massive star core collapse and relativistic jet formation across a very broad range of γ-ray properties. Adopting a phenomenological power-law model for the afterglow and host galaxy estimates from high-resolution Hubble Space Telescope imaging, we use Bayesian model comparison techniques to determine the likelihood of an associated supernova (SN) contributing excess flux to the optical light curve. Though not conclusive, we find moderate evidence (K Bayes =10 1.2 for the presence of an additional component arising from an associated SN, SN 2022xiw, and find that it must be substantially fainter (<67% as bright at the 99% confidence interval) than SN 1998bw. Given the large and uncertain line-of-sight extinction, we attempt to constrain the SN parameters (M Ni , M ej and E KE ) under several different assumptions with respect to the host galaxy's extinction. We find properties that are broadly consistent with previous GRB-associated SNe: M Ni = 0.05–0.25 M ⊙ , M ej = 3.5–11.1 M ⊙ , and E KE = (1.6–5.2) × 10 52 erg. We note that these properties are weakly constrained due to the faintness of the SN with respect to the afterglow and host emission, but we do find a robust upper limit on M Ni of M Ni < 0.36 M ⊙ . Given the tremendous range in isotropic gamma-ray energy release exhibited by GRBs (seven orders of magnitude), the SN emission appears to be decoupled from the central engine in these systems.
Core-collapse supernovae↗
The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications
The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.
Koshak, William↗
Bounds and Rates of Convergence for the Extended Compound Estimation Problem in the Sequence Case Technical Report No. 81
Convergence bounds and rates for extended compound estimation problem in sequence case
BAYESIAN STATISTICS↗
Sequential estimation of observation error variances in a trajectory estimation problem.
Sequential trajectory estimation improved by implementing simple running estimates of observation error variances
BAYESIAN STATISTICS↗
Filtering in Hybrid Dynamic Bayesian Networks
We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).
Andersen, Morten Nonboe↗
OGLE-2015-BLG-1649Lb: A Gas Giant Planet around a Low-mass Dwarf
We report the discovery of an exoplanet from the analysis of the gravitational microlensing event OGLE-2015-BLG-1649 that challenges the core accretion model of planet formation and appears to support the disk instability model. The planet/host-star mass ratio is q = 7.2 × 10^(−3) and the projected separation normalized to the angular Einstein radius is s = 0.9. We conducted high-resolution follow-up observations using the Infrared Camera and Spectrograph (IRCS) camera on the Subaru telescope and are able to place an upper limit on the lens flux. From these measurements we are able to exclude all host stars greater than or equal in mass to a G-type dwarf. We conducted a Bayesian analysis with these new flux constraints included as priors resulting in estimates of the masses of the host star and planet. These are ML = 0.34 ± 0.19 M⊙ and M(p)=2.5 (+1.5,-1.4) M(Jup), respectively. The distance to the system is D(L)=4.23 (+1.51, -1.64) kpc. The projected star–planet separation is a(┴)=2.07 (+0.65,-0.77) au. The estimated relative lens-source proper motion, ~7.1 mas/yr, is fairly high and thus the lens can be better constrained if additional follow-up observations are conducted several years after the event.
M. Nagakane↗
Quantifying radiation quality for space relevant radiation types: Fitting excess risk models to three combined HZE-irradiated mouse datasets
Radiation health risks are predominantly derived from low linear energy transfer (LET) terrestrial exposures; however, space radiation includes exposure to high-LET and high-charge, high-energy (HZE) particles. Accurately quantifying the differences in radiation quality between the space and terrestrial radiation environments is important for assessing and predicting health risks for astronauts. Weil et al. 2009 and 2014 used two different inbred mouse strains to study differences in hepatocellular carcinoma (HCC) tumorigenesis after exposures to low- and high- LET radiation[1-2]. More recently, Edmondson et al. 2020 provided valuable new tumor data in outbred mice that were exposed to low- and high-LET radiation[3]. The present study aims to rigorously investigate a relative biological effectiveness (RBE) factor by leveraging the HCC tumor data from the three datasets[1-3]. The three experiments were similarly designed, allowing the raw data to be combined into a pooled dataset to estimate excess relative risk (ERR) and excess absolute risk (EAR) models using Bayesian Poisson regression.
Lori J. Chappell↗
Continuity of A Global, Satellite-Based Terrestrial Primary Productivity Dataset in the VIIRS Era Achieved With Model-Data Fusion
The NASA Terra and Aqua satellites have been successfully operating for over two decades and have far exceeded their original 5‐year design life. However, the era of NASA’s Earth Observing System (EOS) may be coming to a close as early as 2023. We conducted a comprehensive calibration and validation of the MODIS MOD17 product [1,2] and the potential for continuity of multi‐decadal ecosystem gross primary productivity (GPP) and annual net primary productivity (NPP), using data from the Visible Infrared Imaging Radiometer Suite (VIIRS) sensors aboard Suomi NPP and NOAA‐20. We combined an 18‐year record of eddy covariance flux tower measurements with hundreds of field measurements of NPP from the Oak Ridge National Laboratories Multi‐Biome collection to benchmark MODIS MOD17 Collection 6.1 (C61) and to develop the first terrestrial productivity estimates from VIIRS. Plant traits from the literature and the global TRY database [3,4] provide strong priors for identifying model parameters in a Bayesian model‐data fusion. As MODIS‐like observations are still needed for global environmental applications, the new VIIRS VNP17 product has the potential to extend these continuous estimates of global, terrestrial primary productivity beyond 2030.
K. Arthur Endsley↗
PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter
Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state (EoS) of this dense matter is to measure both a star’s equatorial circumferential radius Re and its gravitational mass M. Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSRJ0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Explorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are Re = 13.02+1.24-1.06 km andM = 1.44+0.15-0.14 Mmoon (68%). The independent analysis reported in the companion paper by Riley et al. explores different emitting spot models, but finds spot shapes and locations and estimates of Re and M that are consistent with those found in this work. We show that our measurements of Re and M for PSRJ0030+0451 improve the astrophysical constraints on the EoS of cold, catalyzed matter above nuclear saturation density.
M C Miller↗
Statistical distribution of time to crack initiation and initial crack size using service data
Crack growth inspection data gathered during the service life of the C-130 Hercules airplane were used in conjunction with a crack propagation rule to estimate the distribution of crack initiation times and of initial crack sizes. A Bayesian statistical approach was used to calculate the fraction of undetected initiation times as a function of the inspection time and the reliability of the inspection procedure used.
Heller, R. A.↗
Classification results using spacially correlated Landsat data
Tubbs and Coberly (1978) demonstrated that Landsat multispectral scanner data are not independent random observations, but, are in fact highly correlated. They also demonstrated that the correlation structure for the data is similar to that of a stationary autoregressive process of order one. This paper investigates the effect that serially correlated training data have upon both the estimation of parameters and the classification problem. Results are included for both the Bayesian and maximum likelihood classification procedures.
Tubbs, J. D.↗
Low-Earth Orbit Trajectory Optimization in the Presence of Atmospheric Uncertainty
The previous 20 to 25 years have seen a tremendous increase in space exploration, and with that an increase in the level of logistics planning needed to ensure mission success. For spacecraft that are designed to be periodically re-supplied, a key logistics consumable is propellant, as it constitutes the greatest up-mass on re-supply vehicles. A trajectory design strategy is therefore desired that minimizes propellant usage in order to ease the demand for propellant re-supply missions. This thesis develops such a strategy in three stages, and uses the International Space Station (ISS) as its testbed, as no other LEO spacecraft is more challenging from a space logistics standpoint. First, the ISS trajectory planning problem is formulated as a constrained burn optimization problem assuming a deterministic atmosphere. The cost function is total ∆v, with constraints imposed on longitude of ascending viii node (LAN) and semi-major axis (SMA) altitude. Analytic derivatives are constructed for both the cost and constraints, which are necessary given the 6-week to 2-year time frames being considered. A gradient-based optimizer is then utilized to find locally-optimal solutions to real-world ISS trajectory planning problems. Second, atmospheric uncertainty is addressed by constructing a probabilistic model of space weather data using Gaussian Processes (GPs). Bayesian inference is performed using the GP model to generate mean and covariance estimates for space weather predictions, whose pedigree is assessed against test data. The predictions are then mapped into atmospheric density via the analytic Jacchia-Roberts density model, and the effect of space weather uncertainty on orbital lifetime is examined. Third, an ISS burn execution uncertainty model is developed. This model, along with the space weather uncertainty model, are deployed in a linear covariance analysis to ascertain their combined effect on LAN and SMA altitude dispersions. The deterministic constraints from the original problem are re-formulated as stochastic constraints, where now the constraint uncertainty interval is required to fall within specified bounds. An updated optimization framework is constructed using the original ∆v cost function along with the stochastic constraints to solve the trajectory optimization problem under atmospheric uncertainty. Finally, the complete architecture is summarized for deployment in an operational setting.
Trajectory Optimization↗
Mind the Gap: Addressing Data Gaps and Assessing Noise Mismodeling in LISA
Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.
LISA↗
Estimability and simple dynamical analyses of range (range-rate range-difference) observations to artificial satellites
Non-Bayesian statistics were used in simulation studies centered around laser range observations to LAGEOS. The capabilities of satellite laser ranging especially in connection with relative station positioning are evaluated. The satellite measurement system under investigation may fall short in precise determinations of the earth's orientation (precession and nutation) and earth's rotation as opposed to systems as very long baseline interferometry (VLBI) and lunar laser ranging (LLR). Relative station positioning, determination of (differential) polar motion, positioning of stations with respect to the earth's center of mass and determination of the earth's gravity field should be easily realized by satellite laser ranging (SLR). The last two features should be considered as best (or solely) determinable by SLR in contrast to VLBI and LLR.
Vangelder, B. H. W.↗