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NASA NTRS1981

Incorporating partially identified sample segments into acreage estimation procedures: Estimates using only observations from the current year

Several methods of estimating individual crop acreages using a mixture of completely identified and partially identified (generic) segments from a single growing year are derived and discussed. A small Monte Carlo study of eight estimators is presented. The relative empirical behavior of these estimators is discussed as are the effects of segment sample size and amount of partial identification. The principle recommendations are (1) to not exclude, but rather incorporate partially identified sample segments into the estimation procedure, (2) try to avoid having a large percentage (say 80%) of only partially identified segments, in the sample, and (3) use the maximum likelihood estimator although the weighted least squares estimator and least squares ratio estimator both perform almost as well. Sets of spring small grains (North Dakota) data were used.

Sielken, R. L., Jr.↗

NASA NTRS1985

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Murphy, Patrick Charles↗

NASA NTRS2003

Attitude Estimation or Quaternion Estimation?

The attitude of spacecraft is represented by a 3x3 orthogonal matrix with unity determinant, which belongs to the three-dimensional special orthogonal group SO(3). The fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes has led to the use of higher-dimensional nonsingular parameterizations, especially the four-component quaternion. In attitude estimation, we are faced with the alternatives of using an attitude representation that is either singular or redundant. Estimation procedures fall into three broad classes. The first estimates a three-dimensional representation of attitude deviations from a reference attitude parameterized by a higher-dimensional nonsingular parameterization. The deviations from the reference are assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. The second class, which estimates a higher-dimensional representation subject to enough constraints to leave only three degrees of freedom, is difficult to formulate and apply consistently. The third class estimates a representation of SO(3) with more than three dimensions, treating the parameters as independent. We refer to the most common member of this class as quaternion estimation, to contrast it with attitude estimation. We analyze the first and third of these approaches in the context of an extended Kalman filter with simplified kinematics and measurement models.

F Landis Markley↗

DOE OSTI2022

An independent analysis of bias sources and variability in wind plant pre-construction energy yield estimation methods

The wind resource assessment community has long had the goal of reducing the bias between wind plant pre-construction energy yield assessment (EYA) and the observed annual energy production (AEP). This comparison is typically made between the 50% probability of exceedance (P50) value of the EYA and the long-term corrected operational AEP (hereafter OA P50), and is known as the P50 bias. The industry has critically lacked an independent analysis of bias reduction investigated across multiple consultants to identify the greatest sources of uncertainty and variance in the EYA process and the best opportunities for uncertainty reduction. The present study addresses this gap by benchmarking consultant methodologies against each other and against operational data at a scale not seen before in industry collaborations. We consider data from 10 wind plants and evaluate discrepancies between eight consultancies in the steps taken from estimates of gross to net energy. Consultants tend to overestimate the gross energy produced at the turbines and then compensate by further overestimating downstream losses, leading to a mean P50 bias near zero, still with significant variability among the individual wind plants. Within our data sample, we find that consultant estimates of all loss categories, except environmental losses, tend to reduce the project-to-project variability of the P50 bias. The disagreement between consultants, however, remains flat throughout the addition of losses. Finally, we find that differences in consultants’ estimates of project performance can lead to differences up to $10/MWh in the levelized cost of energy for a wind plant.

Todd, Austin C.↗

DOE OSTI2022

Metal Oxide Varistor (MOV) Lifetime Estimation with Impulse-Based Testing in PV Inverter Systems

Surges caused by lightning strikes could damage electrical components in photovoltaic (PV) systems. Metal oxide varistors (MOVs) are commonly used to protect PV systems from lightning strikes. This paper proposes a holistic impulse-based MOV lifetime estimation framework. The impacts of peak current and fault duration induced by lightning events are considered in the MOV lifetime estimation framework. Moreover, the impact of different parameter combinations on MOV lifetime estimation is analyzed. The effectiveness of the proposed work is validated in a PV inverter test system developed in MATLAB/Simulink.

lifetime estimation↗

DOE OSTI2022

Machine Learning for Improving Surface-Layer-Flux Estimates

Abstract Flows in the atmospheric boundary layer are turbulent, characterized by a large Reynolds number, the existence of a roughness sublayer and the absence of a well-defined viscous layer. Exchanges with the surface are therefore dominated by turbulent fluxes. In numerical models for atmospheric flows, turbulent fluxes must be specified at the surface; however, surface fluxes are not known a priori and therefore must be parametrized. Atmospheric flow models, including global circulation, limited area models, and large-eddy simulation, employ Monin–Obukhov similarity theory (MOST) to parametrize surface fluxes. The MOST approach is a semi-empirical formulation that accounts for atmospheric stability effects through universal stability functions. The stability functions are determined based on limited observations using simple regression as a function of the non-dimensional stability parameter representing a ratio of distance from the surface and the Obukhov length scale (Obukhov in Trudy Inst Theor Geofiz AN SSSR 1:95–115, 1946), $$z/L$$ z / L . However, simple regression cannot capture the relationship between governing parameters and surface-layer structure under the wide range of conditions to which MOST is commonly applied. We therefore develop, train, and test two machine-learning models, an artificial neural network (ANN) and random forest (RF), to estimate surface fluxes of momentum, sensible heat, and moisture based on surface and near-surface observations. To train and test these machine-learning algorithms, we use several years of observations from the Cabauw mast in the Netherlands and from the National Oceanic and Atmospheric Administration’s Field Research Division tower in Idaho. The RF and ANN models outperform MOST. Even when we train the RF and ANN on one set of data and apply them to the second set, they provide more accurate estimates of all of the fluxes compared to MOST. Estimates of sensible heat and moisture fluxes are significantly improved, and model interpretability techniques highlight the logical physical relationships we expect in surface-layer processes.

Meteorology & Atmospheric Sciences↗

DOE OSTI2024

Estimates of Southern Hemispheric Gravity Wave Momentum Fluxes across Observations, Reanalyses, and Kilometer-Scale Numerical Weather Prediction Model

Abstract Gravity waves (GWs) are among the key drivers of the meridional overturning circulation in the mesosphere and upper stratosphere. Their representation in climate models suffers from insufficient resolution and limited observational constraints on their parameterizations. This obscures assessments of middle atmospheric circulation changes in a changing climate. This study presents a comprehensive analysis of stratospheric GW activity above and downstream of the Andes from 1 to 15 August 2019, with special focus on GW representation ranging from an unprecedented kilometer-scale global forecast model (1.4 km ECMWF IFS), ground-based Rayleigh lidar (CORAL) observations, modern reanalysis (ERA5), to a coarse-resolution climate model (EMAC). Resolved vertical flux of zonal GW momentum (GWMF) is found to be stronger by a factor of at least 2–2.5 in IFS compared to ERA5. Compared to resolved GWMF in IFS, parameterizations in ERA5 and EMAC continue to inaccurately generate excessive GWMF poleward of 60°S, yielding prominent differences between resolved and parameterized GWMFs. A like-to-like validation of GW profiles in IFS and ERA5 reveals similar wave structures. Still, even at ∼1 km resolution, the resolved waves in IFS are weaker than those observed by lidar. Further, GWMF estimates across datasets reveal that temperature-based proxies, based on midfrequency approximations for linear GWs, overestimate GWMF due to simplifications and uncertainties in GW wavelength estimation from data. Overall, the analysis provides GWMF benchmarks for parameterization validation and calls for three-dimensional GW parameterizations, better upper-boundary treatment, and vertical resolution increases commensurate with increases in horizontal resolution in models, for a more realistic GW analysis. Significance Statement Gravity wave–induced momentum forcing forms a key component of the middle atmospheric circulation. However, complete knowledge of gravity waves, their atmospheric effects, and their long-term trends are obscured due to limited global observations, and the inability of current climate models to fully resolve them. This study combines a kilometer-scale forecast model, modern reanalysis, and a coarse-resolution climate model to first compare the resolved and parameterized momentum fluxes by gravity waves generated over the Andes, and then evaluate the fluxes using a state-of-the-art ground-based Rayleigh lidar. Our analysis reveals shortcomings in current model parameterizations of gravity waves in the middle atmosphere and highlights the sensitivity of the estimated flux to the formulation used.

Meteorology & Atmospheric Sciences↗

NASA NTRS1976

On Schmidt's Vm estimator and other estimators of luminosity functions

Schmidt's (1968) estimator, sometimes used to calculate the luminosity function from a complete sample of observed objects, can be generalized naively to the case in which the maximum distance for detection is a function of the direction. Though unbiased, this estimator then does not have minimum variance and, in some cases, is inferior to the classical estimator. The classical estimator, however, is biased when the magnitude boxes are not infinitesimal. A generalization of Schmidt's estimator is proposed which is unbiased and usually superior to both Schmidt's and the classical estimator. Variance formulas and numerical examples are given. The results can be used in combining several catalogs.

Felten, J. E.↗

NASA NTRS1983

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Source record↗

NASA NTRS1986

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Murphy, P. C.↗

NASA NTRS1991

Estimation of time averages from irregularly spaced observations - With application to coastal zone color scanner estimates of chlorophyll concentration

The sampling error of an arbitrary linear estimate of a time-averaged quantity constructed from a time series of irregularly spaced observations at a fixed located is quantified through a formalism. The method is applied to satellite observations of chlorophyll from the coastal zone color scanner. The two specific linear estimates under consideration are the composite average formed from the simple average of all observations within the averaging period and the optimal estimate formed by minimizing the mean squared error of the temporal average based on all the observations in the time series. The resulting suboptimal estimates are shown to be more accurate than composite averages. Suboptimal estimates are also found to be nearly as accurate as optimal estimates using the correct signal and measurement error variances and correlation functions for realistic ranges of these parameters, which makes it a viable practical alternative to the composite average method generally employed at present.

Chelton, Dudley B.↗

NASA NTRS2015

NASA Software Cost Estimation Model: An Analogy Based Estimation Model

The cost estimation of software development activities is increasingly critical for large scale integrated projects such as those at DOD and NASA especially as the software systems become larger and more complex. As an example MSL (Mars Scientific Laboratory) developed at the Jet Propulsion Laboratory launched with over 2 million lines of code making it the largest robotic spacecraft ever flown (Based on the size of the software). Software development activities are also notorious for their cost growth, with NASA flight software averaging over 50% cost growth. All across the agency, estimators and analysts are increasingly being tasked to develop reliable cost estimates in support of program planning and execution. While there has been extensive work on improving parametric methods there is very little focus on the use of models based on analogy and clustering algorithms. In this paper we summarize our findings on effort/cost model estimation and model development based on ten years of software effort estimation research using data mining and machine learning methods to develop estimation models based on analogy and clustering. The NASA Software Cost Model performance is evaluated by comparing it to COCOMO II, linear regression, and K- nearest neighbor prediction model performance on the same data set.

Hihn, Jairus↗

DOE OSTI2026

Estimators and Fusers for Fiber Delay Estimation Using Environmental Measurements

The properties of deployed network fiber are affected by environmental factors due to their exposure to the elements. Particularly for quantum networks, the resultant delay variations may have significant impacts due to the extreme sensitivity of synchronization, coincidence counting, and other critical operations. In this paper, the delays of 15 km aerial-inground fiber connections are measured, and effects due to temperature, humidity and wind speed are analyzed over multiple periods spanning four seasons of a year. Machine learning methods are first utilized to reveal surprisingly pronounced effects of humidity on the delay, in addition to the expected temperature and its seasonal variations. Estimator and fusion methods are developed to estimate the delay using temperature, humidity and wind speed measurements, by utilizing smooth Gaussian Process Regression (GPR) and nonsmooth Ensemble of Trees (EOT) methods. Measurements from winter and summer periods are temporally fused using twelve different methods, and eight methods provide estimates for the delay throughout the year with median test errors under 1.28%. The results reveal distinct temperature-humidity trends across the seasons, and the ability of estimator and temporal fusion methods to exploit them for estimating the delay. These results constitute a case study of machine learning analytical results, wherein generalization equations explain the performance of various estimator and fuser methods.

Rao, Nageswara [ORNL] (ORCID:0000000234085941)↗

DOE OSTI2023

Estimating Vadose Zone Flow Properties at the 100 K-East Soil Flushing Site Using ERT Monitoring Data: 2023 Interim Report - 100 KE Soil Property Estimation

In situ soil flushing is being using at the Hanford 100 K-East (100 KE) area to transport mobile chromium contamination in the vadose zone to the water table, where it can be collected and treat through pump and treat operations. The efficacy of soil flushing is directly related to the volume of clean water that infiltrates through contaminated soils. In practice, it is infeasible to comprehensively monitor which regions of the vadose zone are being infiltrated through direct sampling of pore water. Consequently, there can be significant uncertainty about which regions of the subsurface have been treated, especially if hydrogeologic conditions are favorable for the development of unstable flows and preferred flow pathways through the vadose zone (Jarvis, Koestel, and Larsbo 2016). Current approaches for quantitative monitoring of soil flushing performance rely on contaminant concentration measurements collected from extractions wells. There is no quantitative information on the volume of flush water delivered to targeted regions of the vadose zone at the Hanford Site, leading to significant uncertainty regarding source term removal and long-term impacts to groundwater. If the subsurface hydrogeologic properties at the 100 KE Area were adequately known, qualitative metrics of soil flushing performance could be simulated, thereby negating expenses required to obtain quantitative performance information through borehole drilling/sampling. However, estimating in situ hydrogeologic properties has long proven elusive, due primarily to a lack of sufficient information to constrain heterogeneous property estimates to a useful degree of certainty. Estimating vadose zone hydrogeologic properties is particularly challenging due the dependence of hydraulic conductivity on saturation. This report describes progress toward a first-of-its-kind demonstration using surface time-lapse 3D electrical resistivity tomography (ERT) monitoring data to estimate the hydrogeologic properties that control flush water transport at the 100 KE soil flushing site. The ultimate objective is (1) to verify sufficient information exists in the ERT monitoring data to adequately resolve vadose zone hydraulic properties, and (2) generate a “digital twin” (i.e., a numerical simulator) that can be used to simulate the amount of flush water that has been delivered to each targeted region of the vadose zone, and thereby assess the efficacy of flush water delivery. Resulting performance estimates can be used in leu of comprehensive borehole drilling and direct sampling (or wellbore logging) that would otherwise be required to obtain the same information.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1975

J-Adaptive estimation with estimated noise statistics

The J-Adaptive estimator described by Jazwinski and Hipkins (1972) is extended to include the simultaneous estimation of the statistics of the unmodeled system accelerations. With the aid of simulations it is demonstrated that the J-Adaptive estimator with estimated noise statistics can automatically estimate satellite orbits to an accuracy comparable with the data noise levels, when excellent, continuous tracking coverage is available. Such tracking coverage will be available from satellite-to-satellite tracking.

Jazwinski, A. H.↗

NASA NTRS2007

Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation

A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.

Rakoczy, John↗

NASA NTRS2008

Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation

Rakoczy, John M.↗

NASA NTRS2009

REFAME: Rain Estimation Using Forward Adjusted-Advection of Microwave Estimates

Sensors flying on satellites provide the only practical means of estimating the precipitation that falls over the entire globe, particularly across the vast unpopulated expanses of Earth s oceans. The sensors that observe the Earth using microwave frequencies provide the best data, but currently these are mounted only on satellites flying in "low Earth orbit". Such satellites constantly move across the Earth s surface, providing snapshots of any given location every 12-36 hours. The entire constellation of low-orbit satellites numbers less than a dozen, and their orbits are not coordinated, so a location will frequently go two or more hours between snapshots. "Geosynchronous Earth orbit" (GEO) satellites continuously observe the same region of the globe, allowing them to provide very frequent pictures. For example, the "satellite movies" shown on television come from GEO satellites. However, the sensors available on GEO satellites cannot match the skill of the low-orbit microwave sensors in estimating precipitation. It is perhaps obvious that scientists should try to combine these very different kinds of data, taking advantage of the strengths of each, but this simple concept has proved to be a huge challenge. The scheme in this paper is "Lagrangian", meaning we follow the storm systems, rather than being tied to a fixed grid of boxes on the Earth s surface. Whenever a microwave snapshot occurs, we gladly use the resulting precipitation estimate. Then at all the times between the microwave snapshots we force the storm system to make a smooth transition from one snapshot s values to the next. We know that a lot more changes occur between the snapshots, but this smooth transition the best we can do with the microwave data alone. The key new contribution in this paper is that we also look at the relative variations in the GEO estimates during these in-between times and force the estimated changes in the precipitation to have similar variations. Preliminary testing shows that this approach has enough promise that it should be developed and studied.

Behrangi, Ali↗