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DOE OSTI2025

$\bar{\nu}_\mu$ charged-current $\pi^0$ data release

Data release for the NOvA muon antineutrino charged-current (CC) pi^0 cross section presented in arXiv:2511.05807. The signal for this analysis is defined as muon antineutrino CC interactions in the fiducial volume of the NOvA near detector (a 2.7 m × 2.7 m × 9.0 m region) that produce at least one pi^0 in the final state emerging from the nucleus, within the phase space of muon momentum [0.5, 2.5) GeV/c and muon angle [0, 60) degree, as described in arXiv:2511.05807. The released zip file contains two files: NOvA_NumubarCCPi0_DataRelease.root README.txt The ROOT file includes the cross-section results as well as the statistical and systematic covariance matrices for each variable used in this analysis. The README provides a detailed description of the contents of the data release. Official Flux: The flux used in this analysis is available from the NOvA Public Docs: https://publicdocs.fnal.gov/cgi-bin/ShowDocument?docid=8. File structure --- The ROOT file contains the following TDirectories: pi0p - pi^0 momentum distributions pi0dir - pi^0 angular distributions muonp - muon momentum distributions muondir - muon angular distributions Q2 - reconstructed Q^2 distributions Wmass - reconstructed W_mass distributions Each directory contains three histograms: xsec (TH1D): Cross section result cov_stat (TH2D): Statistical covariance matrix cov_syst (TH2D): Systematic covariance matrix Usage notes: - xsec gives the measured differential cross section w.r.t. the corresponding variable. - cov_stat and cov_syst provide the full covariance matrices. - The bin definitions and kinematic phase spaces follow those used in arXiv:2511.05807. Citation --- If you use these data, please cite: NOvA Collaboration, arXiv:2511.05807.

Wu, Wanwei [Pittsburgh U.] (ORCID:0000000326327215↗
NASA NTRS1971

State estimation with small nonlinearities

A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.

Conrad, B.↗
NASA NTRS1972

Decision-directed adaptive recursive estimators - Divergence prevention.

A method is proposed for dealing with the divergence phenomenon problem encountered in applications of minimum-variance recursive estimators when the error covariance calculated by the estimator becomes inconsistent with the actual error covariance. The proposed method differs from previous ones in that the state model and statistics are accepted as given. The form of the optimal estimator is used, but a constant check is made on the consistency of the calculated and actual error covariances. The method is independent of the source of error, whether it be inaccuracies in the system model, incorrect values of the a priori and random process statistics, approximations required in the case of nonlinear systems, or computational roundoff. Several simulated examples, in which inconsistencies in the calculated and actual error covariances exist, show a significant improvement in the performance of the estimator when the given procedure is applied.

Nahi, N. E.↗
NASA NTRS1986

System identification for modeling for control of flexible structures

The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.

Mettler, Edward↗
NASA NTRS1985

A Kalman filter for a two-dimensional shallow-water model

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Parrish, D. F.↗
NASA NTRS1986

Satellite rainfall retrieval by logistic regression

The potential use of logistic regression in rainfall estimation from satellite measurements is investigated. Satellite measurements provide covariate information in terms of radiances from different remote sensors.The logistic regression technique can effectively accommodate many covariates and test their significance in the estimation. The outcome from the logistical model is the probability that the rainrate of a satellite pixel is above a certain threshold. By varying the thresholds, a rainrate histogram can be obtained, from which the mean and the variant can be estimated. A logistical model is developed and applied to rainfall data collected during GATE, using as covariates the fractional rain area and a radiance measurement which is deduced from a microwave temperature-rainrate relation. It is demonstrated that the fractional rain area is an important covariate in the model, consistent with the use of the so-called Area Time Integral in estimating total rain volume in other studies. To calibrate the logistical model, simulated rain fields generated by rainfield models with prescribed parameters are needed. A stringent test of the logistical model is its ability to recover the prescribed parameters of simulated rain fields. A rain field simulation model which preserves the fractional rain area and lognormality of rainrates as found in GATE is developed. A stochastic regression model of branching and immigration whose solutions are lognormally distributed in some asymptotic limits has also been developed.

Chiu, Long S.↗
NASA NTRS1989

Extensions of output variance constrained controllers to hard constraints

Covariance Controllers assign specified matrix values to the state covariance. A number of robustness results are directly related to the covariance matrix. The conservatism in known upperbounds on the H infinity, L infinity, and L (sub 2) norms for stability and disturbance robustness of linear uncertain systems using covariance controllers is illustrated with examples. These results are illustrated for continuous and discrete time systems. **** ONLY 2 BLOCK MARKERS FOUND -- RETRY *****

Skelton, R.↗
NASA NTRS1991

Simplification of the Kalman filter for meteorological data assimilation

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Dee, Dick P.↗
NASA NTRS1991

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed.

Au, Andrew Y.↗
NASA NTRS1992

Incorporation of a priori gravity field information in satellite orbit determination using bin parameters

A method to determine satellite orbits using tracking data and a priori gravitational field is described. The a priori constraint on the orbit dynamics is determined by the covariance matrix of the spherical harmonic coefficients for the gravity model, so that the optimal combination of the measurements and gravitational field is achieved. A set of bin parameters is introduced to represent the perturbation of the gravitational field on the position of the satellite orbit. The covariance matrix of a conventional gravity model is transformed into that for the bin parameters by the variational partial derivatives. The covariance matrices of the bin parameters and the epoch state are combined to form the covariance matrix of the satellite positions at the measurement times. The combined matrix is used as the a priori information to estimate the satellite positions with measurements.

Wu, Jiun-Tsong↗
NASA NTRS1993

Failure modes of reduced-order orbit determination filters and their remedies

Ways in which failure can occur in reduced-order, orbit determination filter, error covariance calculations are discussed. In the context of this article, reduced-order filters denote nonoptimal filters which include fixed levels of uncertainty in some parameters of the measurement models or in the spacecraft dynamical model which are not explicitly estimated in the filter equations. Failure is defined as an increase in the orbit determination covariance with the addition of data or as an unreasonable growth in the covariance with time, i.e., nonasymptotic behavior of the covariance. Some simple, known cases of failure are discussed along with their traditional remedies. In addition, more modern remedies are discussed which are currently under development at the Jet Propulsion Laboratory. The article first describes the known problems of reduced-order filters when they are employed for orbit determination, and their traditional remedies. Then, having defined these, the relevancy and desirability of the more modern remedies are made apparent.

Scheeres, D. J.↗
NASA NTRS1993

Application of the target decomposition theorem to a polarimetric random media model

With advances in polarimetric radar measurements of land surfaces, the need for understanding the underlying scattering mechanisms and dominant target features has become the focus of many studies. In particular, the maximum use of the polarimetric information to identify and/or separate parameters related to the surface features such as vegetation thickness, structure, water content, and soil surface characteristics will enhance the possibility of using polarimetric radars for monitoring the earth's surface from space. In this paper, Cloude's decomposition theorem is applied to a polarimetric random media model to simulate the radar measurements of vegetated canopies. The vegetated canopies are modeled as a three layer discrete random medium with leaves and branches in the first layer, tree trunks in the second layer, and a half space of homogeneous ground with rough interface as the bottom layer. The distorted born approximation (DBA) has been used to compute full Mueller matrix of the canopy, using canonical dielectric objects such as thin discs and cylinders as leaves, branches, and trunks, respectively. The Mueller matrix and the derived covariance matrix contain information on the second order statistics of radar signals at various polarizations from the canopy. To decompose the covariance matrix to its constituent targets, the eigenvalues and eigenvectors of the covariance matrix are computed in terms of the physical parameters of the canopy. In addition, each eigenvector explicitly shows the scattering mechanisms such as odd and even reflections in the canopy. Cloude's decomposition theorem is applied using the Pauli spin matrices as a basis and an expression for the degree of disorder or the entropy for the vegetated surface is found. Then, the physical parameters estimated from in situ measurements are used in the random media to obtain realistic covariance matrices. As a result, the sensitivity of the eigenvalue spectrums and the coefficients resulting from the target decomposition theorem to the physical parameters of the canopy are examined and the possible use of Cloude's theorem to estimate vegetation and soil parameters is discussed.

Saatchi, Sasan S.↗
NASA NTRS1994

Correlated noise in the COBE DMR sky maps

The Cosmic Background Explorer Satellite Differential Radiometer (COBE DMR) sky maps contain low-level correlated noise. We obtain estimates of the amplitude and pattern of the correlated noise from three techniques: angular averages of the covariance matrix, Monte Carlo simulations of two-point correlation functions and direct analysis of the DMR maps. The results from the three methods are mutually consistent. The noise covariance matrix of a DMR sky maps is diagonal to an accuracy of better than 1%. For a given sky pixel, the dominant noise covariance occure with the ring of pixels at an angular separation of 60 deg due to the 60 deg separation of the DMR horns. The mean covariance at 60 deg is 0.45%((sup +0.18)(sub -0.14)) of the mean variance. Additionally, the variance in a given pixel is 0.7% greater than would be expected from a single beam experiment with the same noise properties. Autocorrelation functions suffer from a approximately 1.5 sigma positive bias at 60 deg while cross-correlations have no bias. Published COBE DMR results are not significantly affected by correlated noise.

Lineweaver, C. H.↗
NASA NTRS1999

Adaptive Error Estimation in Linearized Ocean General Circulation Models

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Chechelnitsky, Michael Y.↗
NASA NTRS2001

Design and Implementation of a Parallel Multivariate Ensemble Kalman Filter for the Poseidon Ocean General Circulation Model

A multivariate ensemble Kalman filter (MvEnKF) implemented on a massively parallel computer architecture has been implemented for the Poseidon ocean circulation model and tested with a Pacific Basin model configuration. There are about two million prognostic state-vector variables. Parallelism for the data assimilation step is achieved by regionalization of the background-error covariances that are calculated from the phase-space distribution of the ensemble. Each processing element (PE) collects elements of a matrix measurement functional from nearby PEs. To avoid the introduction of spurious long-range covariances associated with finite ensemble sizes, the background-error covariances are given compact support by means of a Hadamard (element by element) product with a three-dimensional canonical correlation function. The methodology and the MvEnKF configuration are discussed. It is shown that the regionalization of the background covariances; has a negligible impact on the quality of the analyses. The parallel algorithm is very efficient for large numbers of observations but does not scale well beyond 100 PEs at the current model resolution. On a platform with distributed memory, memory rather than speed is the limiting factor.

Keppenne, Christian L.↗
NASA NTRS2002

Orbit Determination Support for the Microwave Anisotropy Probe (MAP)

The Microwave Anisotropy Probe (MAP) is a Medium Class Explorers (MIDEX) mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The main science objective of the MAP mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations anisotropy. MAP was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle at exactly 19:46:46.183 UTC on June 30, 2001. The spacecraft received a nominal direct insertion by the Delta into a 185 km circular orbit. MAP was then maneuvered into a sequence of phasing loops designed to set up a lunar swingby (gravity-assisted acceleration) of the spacecraft onto a transfer trajectory to a Lissajous orbit about the Earth-Sun L2 point. The mission duration is approximately 27 months with 3 to 4 months of transfer time to the final mission orbit about L2. The MAP transfer orbit consisted of 3.5 phasing loops: the first loop has a 7-day period, the second and third loops have a 9-day period, and the last half loop has a 4-day period as illustrated in Figure 1, which also indicates the placement of maneuvers. A Pfinal correction maneuver was performed 18 hours after the last perigee to more closely achieve the targeted lissajous orbit. The lunar encounter or swingby took place approximately 30 days after launch. After the lunar encounter, the spacecraft will cruise for approximately 120 days before it arrives at L2. A Mid-Course Correction (MCC) maneuver was executed seven days after the swingby to further refine the trajectory. Once the MAP satellite is injected into the L2 Lissajous orbit, it will perform occasional stationkeeping maneuvers to maintain the Lissajous orbit for a minimum of two years (and a goal of four years). Because of its complex orbital characteristics, the mission provided a unique challenge to orbit determination (OD) support in many orbital regimes. Extensive trajectory error covariance analysis was performed to predict ephemeris accuracy for the OD process using a Bayesian least-squares technique. The orbit determination error analysis is essential for maneuver planning and maneuver recovery study. Several tracking scenarios were investigated for each phase of the mission. This paper provides a summary of the premission trajectory covariance error analysis, as well as actual real-time OD results. The use and impact of the various tracking stations, systems, and measurements will be discussed. Details of the operational OD support and the inferred OD accuracy will be presented, and the results will be compared to the premission covariance analysis, In addition, there will be a discussion of the challenges presented to OD support including delta-Vs at apogee as well as perigee, and effects due to spacecraft attitude mode, in light of their implications to the OD accuracy and covariance analysis.

Truong, Son H.↗
NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗
NASA NTRS2003

On the Singularity in the Estimation of the Quaternion-of-Rotation

It has been claimed in the archival literature that the covariance matrix of a Kalman filter, which is designed to estimate the quaternion-of-rotation, is necessarily rank deficient because the normality constraint of the quaternion produces dependence between the quaternion elements. In reality, though, this phenomenon does not occur. The covariance matrix is not singular, and the filter is well behaved. Several simple examples are presented that demonstrate the regularity of the covariance matrix. First, estimation cases are presented where a relationship exists between the estimated variables, and yet the covariance matrix is not singular. Then the particular problem of quaternion estimation is analyzed. It is shown that the discrepancy stems from the fact that a functional relationship exists between the elements of the true quaternion but not between its estimated elements.

Bar-Itzhack, Itzhack Y.↗