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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2021

Anomaly detection in the Zwicky Transient Facility DR3

We present results from applying the SNAD anomaly detection pipeline to the third public data release of the Zwicky Transient Facility (ZTF DR3). The pipeline is composed of three stages: feature extraction, search of outliers with machine learning algorithms, and anomaly identification with followup by human experts. Our analysis concentrates in three ZTF fields, comprising more than 2.25 million objects. A set of four automatic learning algorithms was used to identify 277 outliers, which were subsequently scrutinized by an expert. From these, 188 (68 per cent) were found to be bogus light curves – including effects from the image subtraction pipeline as well as overlapping between a star and a known asteroid, 66 (24 per cent) were previously reported sources whereas 23 (8 per cent) correspond to non-catalogued objects, with the two latter cases of potential scientific interest (e.g. one spectroscopically confirmed RS Canum Venaticorum star, four supernovae candidates, one red dwarf flare). Moreover, using results from the expert analysis, we were able to identify a simple bi-dimensional relation that can be used to aid filtering potentially bogus light curves in future studies. We provide a complete list of objects with potential scientific application so they can be further scrutinised by the community. These results confirm the importance of combining automatic machine learning algorithms with domain knowledge in the construction of recommendation systems for astronomy. Our code is publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The PAU Survey: narrow-band photometric redshifts using Gaussian processes

Here, we study the performance of the hybrid template machine learning photometric redshift (photo- z ) algorithm delight , which uses Gaussian processes, on a subset of the early data release of the Physics of the Accelerating Universe Survey (PAUS). We calibrate the fluxes of the 40 PAUS narrow bands with six broad-band fluxes ( uBVriz ) in the Cosmic Evolution Survey (COSMOS) field using three different methods, including a new method that utilizes the correlation between the apparent size and overall flux of the galaxy. We use a rich set of empirically derived galaxy spectral templates as guides to train the Gaussian process, and we show that our results are competitive with other standard photometric redshift algorithms. delight achieves a photo- z 68th percentile error of σ 68 = 0.0081(1 + z ) without any quality cut for galaxies with i auto < 22.5 as compared to 0.0089(1 + z ) and 0.0202(1 + z ) for the bpz and annz 2 codes, respectively. delight is also shown to produce more accurate probability distribution functions for individual redshift estimates than bpz and annz 2. Common photo- z outliers of delight and bcnz 2 (previously applied to PAUS) are found to be primarily caused by outliers in the narrow-band fluxes, with a small number of cases potentially indicating spectroscopic redshift failures in the reference sample. In the process, we introduce performance metrics derived from the results of bcnz 2 and delight , allowing us to achieve a photo- z quality of σ 68 < 0.0035(1 + z ) at a magnitude of i auto < 22.5 while keeping 50 per cent objects of the galaxy sample.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Optimizing the shape of photometric redshift distributions with clustering cross-correlations

We present an optimization method for the assignment of photometric galaxies to a chosen set of redshift bins. This is achieved by combining simulated annealing, an optimization algorithm inspired by solid-state physics, with an unsupervised machine learning method, a self-organizing map (SOM) of the observed colours of galaxies. Starting with a sample of galaxies that is divided into redshift bins based on a photometric redshift point estimate, the simulated annealing algorithm repeatedly reassigns SOM-selected subsamples of galaxies, which are close in colour, to alternative redshift bins. We optimize the clustering cross-correlation signal between photometric galaxies and a reference sample of galaxies with well-calibrated redshifts. Depending on the effect on the clustering signal, the reassignment is either accepted or rejected. By dynamically increasing the resolution of the SOM, the algorithm eventually converges to a solution that minimizes the number of mismatched galaxies in each tomographic redshift bin and thus improves the compactness of their corresponding redshift distribution. This method is demonstrated on the synthetic Legacy Survey of Space and Time cosmoDC2 catalogue. We find a significant decrease in the fraction of catastrophic outliers in the redshift distribution in all tomographic bins, most notably in the highest redshift bin with a decrease in the outlier fraction from 57 percent to 16 percent.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Identifying Anomalous DESI Galaxy Spectra with a Variational Autoencoder

The tens of millions of spectra being captured by the Dark Energy Spectroscopic Instrument (DESI) provide tremendous discovery potential. In this work we show how Machine Learning, in particular Variational Autoencoders (VAE), can detect anomalies in a sample of approximately 200,000 DESI spectra comprising galaxies, quasars and stars. We demonstrate that the VAE can compress the dimensionality of a spectrum by a factor of 100, while still retaining enough information to accurately reconstruct spectral features. We then detect anomalous spectra as those with high reconstruction error and those which are isolated in the VAE latent representation. The anomalies identified fall into two categories: spectra with artefacts and spectra with unique physical features. Awareness of the former can help to improve the DESI spectroscopic pipeline; whilst the latter can lead to the identification of new and unusual objects. To further curate the list of outliers, we use the Astronomaly package which employs Active Learning to provide personalised outlier recommendations for visual inspection. In this work we also explore the VAE latent space, finding that different object classes and subclasses are separated despite being unlabelled. We demonstrate the interpretability of this latent space by identifying tracks within it that correspond to various spectral characteristics. For example, we find tracks that correspond to increasing star formation and increase in broad emission lines along the Balmer series. In upcoming work we hope to apply the methods presented here to search for both systematics and astrophysically interesting objects in much larger datasets of DESI spectra.

Nicolaou, C. [University Coll. London] (ORCID:0000↗
DOE OSTI2026

pop-cosmos : redshifts and physical properties of KiDS-1000 galaxies

ABSTRACT Principled Bayesian inference of galaxy properties has not previously been performed for wide-area weak-lensing surveys with millions of sources. We address this gap by applying the pop-cosmos generative model to perform spectral energy distribution (SED) fitting for 4 million KiDS (Kilo-Degree Survey)-1000 galaxies. Calibrated on deep COSMOS2020 photometric data, pop-cosmos specifies a physically motivated prior over the galaxy population up to $z \simeq 6$ in stellar population synthesis (SPS) parameter space. Using the Speculator SPS emulator with GPU (graphics processing unit)-accelerated Markov Chain Monte Carlo sampling, we perform full posterior inference at 8.2 GPU seconds per galaxy, obtaining joint constraints on galaxy redshifts and physical properties. We validate photometric redshifts against $\sim \!185\,\!000$ KiDS galaxies cross-matched to Dark Energy Spectroscopic Instrument Data Release 1 spectroscopic samples, achieving low bias ($2\times 10^{-3}$), scatter ($\sigma _{\mathrm{MAD}}=0.03$), and outlier fraction (3.2 per cent) for the Bright Galaxy Survey, with comparable performance (bias $3\times 10^{-2}$, $\sigma _{\mathrm{MAD}}=0.05$, 1.0 per cent outliers) for luminous red galaxies (LRGs). Within the LRG sample, we identify massive, dusty, star-forming contaminants at $z \simeq 0.4$ satisfying standard colour selections for quenched populations. We infer trends in stellar mass, star formation, metallicity, and dust across five tomographic redshift bins consistent with established scaling relations. Using specific star formation rate constraints, we identify $\sim$7 per cent of KiDS-1000 galaxies as quenched, versus 37 per cent implied by conservative colour cuts. This enables the construction of weak-lensing samples defined by physical properties while mitigating intrinsic alignment systematics and preserving statistical power. Our analysis validates pop-cosmos out of sample, establishing it as a scalable approach for galaxy evolution and cosmological analyses with photometric surveys.

Halder, Anik [Institute of Astronomy and Kavli Ins↗
DOE OSTI2025

Gravothermal collapse and the diversity of galactic rotation curves

The rotation curves of spiral galaxies exhibit a great diversity that challenges our understanding of galaxy formation and the nature of dark matter. Previous studies showed that in self-interacting dark matter (SIDM) models with a cross section per unit mass of σ/m ≈ $\mathscr{O}$(1) cm 2 /g, the predicted dark matter central densities are a good match to the observed densities in galaxies. Here, in this work, we explore a regime with a larger cross section of σ/m ≈ 20−40 cm 2 /g in dwarf galactic halos. We will show that such strong dark matter self-interactions can further amplify the diversity of halo densities inherited from their assembly history. High concentration halos can enter the gravothermal collapse phase within 10 Gyr, resulting in a high density, while low concentration ones remain in the expansion phase and have a low density. We fit the rotation curves of 14 representative low surface brightness galaxies and demonstrate how the large range of observed central densities is naturally accommodated in the strong SIDM regime of σ/m ≈ 20 – 40 cm 2 /g. Galaxies that are outliers in the previous studies, due to their high halo central densities, are no longer outliers in this SIDM regime as their halos would be in the collapse phase. For galaxies with a low density, the SIDM fits are robust to the variation of the cross section. Our findings open up a new window for testing gravothermal collapse, the unique signature of strong dark matter self-interactions, and exploring a broader SIDM model space. As an example, we illustrate how the larger cross sections favored by our fits, together with upper limits from strong lensing observations in clusters, pick out the preferred SIDM model space for a dark matter particle coupled to a light gauge boson in the Born regime.

dark matter↗
DOE OSTI2020

Robust Online Sequential RVFLNs for Data Modeling of Dynamic Time-Varying Systems with Application of an Ironmaking Blast Furnace

In a world where the increasing complexity of modern industrial processes brings difficulties for accurate mathematical modeling, taking advantage of data has become an efficient solution to complex dynamic process modeling issue. In this paper, we develop a novel robust online sequential version of random vector functional-link networks (RVFLNs) for data-driven modeling of dynamic time-varying system and applied it in a blast furnace (BF) ironmaking process. First, to overcome the time-varying dynamics of process and to enable the RVFLNs to learn online with avoiding data saturation, an improved online sequential version of RVFLNs (OS-RFVLNs) is first presented by online sequential learning with forgetting factor. This improved OS-RVFLNs algorithm is not only suitable for the real-time and large data transfer situation, but also can adjust the sensitivity of the algorithm to different samples with the help of the introduced forgetting factor. Second, since the output weights of the improved OS-RVFLNs as well as other RVFLNs algorithms are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with various outliers. To solve this problem, a Cauchy distribution weighted M-estimator is introduced to improve the robustness of the improved OS- RVFLNs. For this proposed robust OS-RVFLNs (R-OS- RVFLNs), since the weights of different outlier data are properly determined by the Cauchy distribution function, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Experiments using actual industrial data of BF ironmaking process and comparative studies have demonstrated that the proposed method produces a better estimation accuracy and stronger robustness than other methods.

Blast furnace (BF), Modelling, Dynamic systems↗
DOE OSTI2024

Accelerated Depth Computation for Surface Boxplots with Deep Learning

Functional depth is a well-known technique used to derive descriptive statistics (e.g., median, quartiles, and outliers) for 1D data. Surface boxplots extend this concept to ensembles of images, helping scientists and users identify representative and outlier images. However, the computational time for surface boxplots increases cubically with the number of ensemble members, making it impractical for integration into visualization tools. In this paper, we propose a deep-learning solution for efficient depth prediction and computation of surface boxplots for time-varying ensemble data. Our deep learning framework accurately predicts member depths in a surface boxplot, achieving average speedups of 6X on a CPU and 15X on a GPU for the 2D Red Sea dataset with 50 ensemble members compared to the traditional depth computation algorithm. Our approach achieves at least a 99% level of rank preservation, with order flipping occurring only at pairs with extremely similar depth values that pose no statistical differences. This local flipping does not significantly impact the overall depth order of the ensemble members.

Han, Mengjiao↗
DOE OSTI2025

Signatures of Selection for Resistance/Tolerance to Perkinsus olseni in Grooved Carpet Shell Clam ( Ruditapes decussatus ) Using a Population Genomics Approach

ABSTRACT The grooved carpet shell clam ( Ruditapes decussatus ) is a bivalve of high commercial value distributed throughout the European coast. Its production has suffered a decline caused by different factors, especially by the parasite Perkinsus olsenii . Improving production of R . decussatus requires genomic resources to ascertain the genetic factors underlying resistance/tolerance to P. olseni i . In this study, the first reference genome of R . decussatus was assembled through long‐ and short‐read sequencing (1677 contigs; 1.386 Mb) and further scaffolded at chromosome level with Hi‐C (19 superscaffolds; 95.4% of assembly). Repetitive elements were identified (32%) and masked for annotation of 38,276 coding‐ and 13,056 non‐coding genes. This genome was used as a reference to develop a 2bRAD‐Seq 13,438 SNP panel for a genomic screening on six shellfish beds distributed across the Atlantic Ocean and Mediterranean Sea. Beds were selected by perkinsosis prevalence and the infection level was individually evaluated in all the samples. Genetic diversity was significantly higher in the Mediterranean than in the Atlantic region. The main genetic breakage was detected between those regions (F ST = 0.224), being the Mediterranean more heterogeneous than the Atlantic. Several loci under divergent selection (394 outliers; 261 genomic windows) were detected across shellfish beds. Samples were also inspected to detect signals of selection for resistance/tolerance to P. olseni i by using infection‐level and population‐genomics approaches, and 90 common divergent outliers for resistance/tolerance to perkinsosis were identified and used for gene mining. Candidate genes and markers identified provide invaluable information for controlling perkinsosis and for improving production of the grooved carpet shell clam.

Sambade, Inés M. [Department of Zoology, Genetics ↗
DOE OSTI2024

DeBoinR: Density Boxplots in R

DeBoinR (Density Boxplots in R) takes in a set of Probability Density Functions (PDFs), calculates outliers based on several notions of distance, and visualizes these outliers via functional boxplots. This code is written as a stand-along R package with the hopes of eventually submitting it to CRAN. The package is written in generality; it would be useful to any researching looking to analyze a general ensemble of PDFs.

Murph, Alexander↗
DOE OSTI2024

DISSIDE: Dynamic In Silico Sample Identification for Discrete Evaluation

DISSIDE uses novel unsupervised learning to select samples that best represent the strongest a priori discrete pattern in a given data set. It further removes major outliers and "noisy" samples that do not fit discrete patterns well or represent outliers in groups below a defined n value. It then estimates the fit and strength of the a priori discrete pattern using both unconstrained and constrained methods for raw and cleaned data

LeBrun, Erick↗
DOE OSTI2021

Assessing Prior Emergent Constraints on Surface Albedo Feedback in CMIP6

An emergent constraint (EC) is a popular model evaluation technique, which offers the potential to reduce intermodel variability in projections of climate change. Two examples have previously been laid out for future surface albedo feedbacks (SAF) stemming from loss of Northern Hemisphere (NH) snow cover (SAF snow ) and sea ice (SAF ice ). These processes also have a modern-day analog that occurs each year as snow and sea ice retreat from their seasonal maxima, which is strongly correlated with future SAF across an ensemble of climate models. The newly released CMIP6 ensemble offers the chance to test prior constraints through out-of-sample verification, an important examination of EC robustness. Here, we show that the SAF snow EC is equally strong in CMIP6 as it was in past generations, while the SAF ice EC is also shown to exist in CMIP6, but with different, slightly weaker characteristics. We find that the CMIP6 mean NH SAF exhibits a global feedback of 0.25 ± 0.05 W m -2 K -1 , or ~61% of the total global albedo feedback, largely in line with prior generations despite its increased climate sensitivity. Additionally, the NH SAF can be broken down into similar contributions from snow and sea ice over the twenty-first century in CMIP6. Crucially, intermodel variability in seasonal SAF snow and SAF ice is largely unchanged from CMIP5 because of poor outlier simulations of snow cover, surface albedo, and sea ice thickness. These outliers act to mask the noted improvement from many models when it comes to SAF ice , and to a lesser extent SAF snow .

58 GEOSCIENCES↗
DOE OSTI2025

Data from TropiRoot 1.0 database: tropical root characteristics across environments

TropiRoot 1.0 is a new tropical root database with root characteristics across environment gradients. It has data extracted from 104 new sources, resulting in more than 8000 rows of data (either species or community data). Most of the data in TropiRoot 1.0 includes root characteristics such as root biomass, morphology, root dynamics, mass fraction, architecture, anatomy, physiology and root chemistry. This initiative represents an approximately 30% increase in the currently available data for tropical roots in the Fine Root Ecology Database (FRED). TropiRoot 1.0, contains root characteristics from 25 different countries where seven are located in Asia, six in South America, five in Central America and the Caribbean, four in Africa, two in North America, and 1 in Oceania. Due to the volume of data, when ancillary data was available, including soil data, these data was either extracted and included in the database or their availability was recorded in an additional column. Multiple contributors checked the entries for outliers during the collation process to ensure data quality. For text-based observations, we examined all cells to ensure that their content relates to their specific categories. For numerical observations, we ordered each numerical value from least to greatest and plotted the values, checking apparent outliers against the data in their respective sources and correcting or removing incorrect or impossible values. Some data (soil and aboveground) have different columns for the same variable presented in different units, including originally published units, but root characteristics data had units converted to match the ones reported in FRED. By filling a gap from global databases, TropiRoot 1.0 expands our knowledge of otherwise so far underrepresented regions, and our ability to assess global trends. This advancement can be used to improve tropical forest representation in vegetation models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

COMPASS-FME Terrestrial Ecosystem Manipulation to Probe the Effects of Storm Treatments (TEMPEST) Experiment Level 2 Sensor Data v2-1

This is the version v2-1 Level 2 (L2) data release for COMPASS-FME environmental sensors located at our Terrestrial Ecosystem Manipulation to Probe the Effects of Storm Treatments (TEMPEST) experimental site. This manipulative, ecosystem-scale TEMPEST experiment addresses the potential for freshwater and estuarine-water disturbance events to alter tree function, species composition, and ecosystem processes in a deciduous coastal forest in MD, USA. The experiment uses a large-unit (2000 m2), un-replicated experimental design, with three 50 m × 40 m plots serving as control, freshwater, and estuarine-water treatments. Level 2 (L2) data consist of sensor observations from the COMPASS-FME synoptic sites, TEMPEST, and DELUGE. Compared to the L1 data, these are more consistent (always 15-minute timestamps for the entire year); better QA/QC’d (out of bounds, out of service, and extreme outlier values are removed); and more complete, with a gap-filled time series available alongside the main observations, and additional derived (calculated) variables. L2 data are intended to be rapidly and easily usable in analyses and simulations. However, algorithmic outlier identification always carries the risk of removing valid data, and Level 1 data may be more suitable for analyses that focus on variability or extreme events. This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding variable-specific Parquet (a high performance, space efficient format; see https://parquet.apache.org) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, detailed flood times, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are reported every 15 minutes. Please see v2-1 TEMPEST L2 Sensor Package Quick Start.pdf for detailed information on data package structure, temporal coverage, and versioning. Data files are in Apache Parquet, a high performance, space efficient format for tabular data. These files can be read using R's `arrow` package (https://arrow.apache.org/docs/r/), with similar tools available in other languages. The TEMPEST flood events occurred on the following dates. They lasted for ~10 hours each day and delivered ~80,000 gallons to each plot; many data streams are available at 1 or 5 minute frequency during these periods. * Tests: Aug 25 (fresh plot) and Sep 9 (salt plot), 2021 * TEMPEST 1: June 22, 2022 * TEMPEST 2: June 6-7, 2023 * TEMPEST 3: June 11-13, 2024

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC TEMPERATU↗
DOE OSTI2026

COMPASS-FME Synoptic Sites Level 2 Sensor Data v2-1

This is the version 2-1 Level 2 (L2) data release for COMPASS-FME environmental sensors located at our synoptic field sites. COMPASS-FME is studying sites in two distinct regions, the Chesapeake Bay and the Western Lake Erie Basin. We established the network at seven "synoptic" (observational) sites along the Chesapeake Bay and Lake Erie coastlines, collectively generating over three million observations per month, to track and comprehend environmental changes where land and water intersect. Additionally, the two regions provide an interesting contrast of saltwater and freshwater coasts that allow us to differentiate the impacts of inundation and coastal water chemistries in two nationally important coastal systems. Level 2 (L2) data consist of sensor observations from the COMPASS-FME synoptic sites, TEMPEST, and DELUGE. Compared to the L1 data, these are more consistent (always 15-minute timestamps for the entire year); better QA/QC’d (out of bounds, out of service, and extreme outlier values are removed); and more complete, with a gap-filled time series available alongside the main observations, and additional derived (calculated) variables. L2 data are intended to be rapidly and easily usable in analyses and simulations. However, algorithmic outlier identification always carries the risk of removing valid data, and Level 1 data may be more suitable for analyses that focus on variability or extreme events. This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding variable-specific Parquet (a high performance, space efficient format; see https://parquet.apache.org) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, detailed flood times, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are reported every 15 minutes. Data files are in Apache Parquet, a high performance, space efficient format for tabular data. These files can be read using R's `arrow` package (https://arrow.apache.org/docs/r/), with similar tools available in other languages. Please see v2-1 L2 Sensor Package QStart.pdf for detailed information on data package structure, temporal coverage, and versioning.

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC TEMPERATU↗
DOE OSTI2022

Method for automatic correction of offset drift in online sensors

Abstract Successful operation and optimization of water treatment systems hinge on the availability of high-quality online sensor measurements. Ideally, the available measurements should be simultaneously accurate (i.e., unbiased and precise), representative, voluminous, and timely. This remains a pain-point in current water infrastructures, forming a barrier to a wider adoption of advanced and autonomous control systems. While short-lived symptoms, such as outliers and spikes, can be detected or corrected with state-of-the-art tools for fault detection and identification, it is much more difficult to detect, diagnose, and correct the symptoms of slow faults, such as changes in offset or sensitivity due to drift. The time scale of drift is often longer than the time scales of the system dynamics of interest. Moreover, sensor drift has been shown to occur at the same time and with similar rates when sensors are exposed to the same conditions. This challenges data quality management strategies based on redundancy. In this contribution, we develop a new method, including both a hands-off sensor calibration mechanism and an information-seeking control architecture that can handle the unique challenge of simultaneous and similar drift in online sensors.

Chowdhury, Dhrubajit↗
DOE OSTI2020

TBASS: A Robust Adaptation of Bayesian Adaptive Spline Surfaces

The R package TBASS is an extension of the BASS package created by Francom and Sansó (2019). The package is used to fit a Bayesian multivariate adaptive spline to a dataset that either follows a Student’s t-distribution or has outliers. Much of the framework for TBASS is adapted from the concepts of Bayesian Multivariate Adaptive Regression Splines (BMARS), specifically the work done by Denison, Mallick, and Smith (1998). The spline function is fit using a Reversible-Jump Markov Chain Monte Carlo algorithm,. By including this more robust generalization, a dataset with outliers can be accurately fit using the BMARS model, without the possibility of overfitting or variance inflation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Performance Comparison of Circular and Spherical Error Probable Estimators

This report compares the performance of three Circular Error Probable (CEP) estimators: the Grubbs-Patnaik estimator, a new, non-iterative, radial-integration estimator, and a median estimator. It also compares the performance of two Spherical Error Probable (SEP) estimators. The performance of each estimator is assessed in terms of bias, uncertainty, robustness, and computational complexity. Robustness is evaluated with respect to outliers, variations in the underlying statistical distribution characterizing munition impact positions, and impact-position measurement errors. The performance assessments indicate the radial-integration and Grubbs-Patnaik estimators perform nearly identically providing the statistical distribution of impact-position coordinates is jointly normal with zero means. In that case, both estimators outperform the median estimator by about 2% relative to the true CEP in terms of estimator uncertainty. The bias performance of the radial-integration and median estimators is close to zero for jointly normal impacts, however, the Grubbs-Patnaik estimator can be significantly biased for jointly normal impacts with non-zero means. When the statistical distribution characterizing impact positions is known, but not jointly normal, the radial-integration estimator is superior. In this case, the median estimator also outperforms the Grubbs-Patnaik estimator but is not quite as good as the radial-integration estimator. If the statistical distribution characterizing impacts is unknown and not jointly normal, or if distribution parameters are difficult or impractical to estimate, or if test data is corrupted with outliers, then the median estimator dramatically outperforms the other estimators, especially in terms of estimation bias. Unexpectedly, measurement noise did not significantly degrade the performance of any of the estimators, except for cases with signal to noise ratios less than five. Although the Grubbs-Patnaik estimator has remained the gold standard for CEP estimation for over half a century, the performance assessments indicate the new, non-iterative, radial-integration estimator and the median estimator offer significant advantages and, in most practical real-world conditions, are superior estimators. These estimators are also useful for SEP estimation whereas the Grubbs-Patnaik estimator does not extend to three dimensions.

97 MATHEMATICS AND COMPUTING↗