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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

An analysis of estimation of pulmonary blood flow by the single-breath method

The single-breath method represents a simple noninvasive technique for the assessment of capillary blood flow across the lung. However, this method has not gained widespread acceptance, because its accuracy is still being questioned. A rigorous procedure is described for estimating pulmonary blood flow (PBF) using data obtained with the aid of the single-breath method. Attention is given to the minimization of data-processing errors in the presence of measurement errors and to questions regarding a correction for possible loss of CO2 in the lung tissue. It is pointed out that the estimations are based on the exact solution of the underlying differential equations which describe the dynamics of gas exchange in the lung. The reported study demonstrates the feasibility of obtaining highly reliable estimates of PBF from expiratory data in the presence of random measurement errors.

Srinivasan, R.↗
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 NTRS1988

Modeling and measurement of error propagation in a multimodule computing system

An error propagation model has been developed for multimodule computing systems in which the main parameters are the distribution functions of error propagation times. A digraph model is used to represent a multimodule computing system, and error propagation in the system is modeled by general distributions of error propagation times between all pairs of modules. Two algorithms are developed to compute systematically and efficiently the distributions of error propagation times. Experiments are also conducted to measure the distributions of error propagation times with the fault-tolerant microprocessor (FTMP). Statistical analysis of experimental data shows that the error propagation times in FTMP do not follow a well-known distribution, thus justifying the use of general distributions in the present model.

Shin, Kang G.↗
NASA NTRS1980

Determination of instrumentation errors from measured data using maximum likelihood method

The maximum likelihood method is used for estimation of unknown initial conditions, constant bias and scale factor errors in measured flight data. The model for the system to be identified consists of the airplane six-degree-of-freedom kinematic equations, and the output equations specifying the measured variables. The estimation problem is formulated in a general way and then, for practical use, simplified by ignoring the effect of process noise. The algorithm developed is first applied to computer generated data having different levels of process noise for the demonstration of the robustness of the method. Then the real flight data are analyzed and the results compared with those obtained by the extended Kalman filter algorithm.

Keskar, D. A.↗
NASA NTRS2025

Uncertainty Quantification for Empirical X-59 Sonic Boom Loudness Levels

Estimates of the total uncertainty for empirically determined loudness levels are documented when GRS (Ground Recording System) noise monitors are used to record X 59 sonic boom waveforms. The total uncertainty is characterized by combining nine different sources of uncertainty that may affect the apparent gain of the measurement chain. These uncertainty estimates are presented as expected measurement error relative to the true loudness level, and separate error estimates are provided for eight different noise metrics in which NASA has interest. The behavior of the Perceived Level (PL) metric is studied within the report body, while the total uncertainties for the seven other noise metrics are summarized in appendices for brevity. The effects of four sources of uncertainty are estimated simply from information found on hardware specification sheets provided by the manufacturer. However, mock acoustic recordings are created to estimate the effects of other sources because those effects are expected to induce spectral coloration, so they may vary with noise metric type and sound level. These sources are not well modeled by simple gain adjustments. Importantly, measurement error is computable when processing mock recordings since the true levels are knowable, which is not the case when processing data recorded in the field. Specifically, the true levels are knowable because the components of the mock recordings are separable – e.g., loudness levels of booms can be computed with or without superimposed background noise. Mock acoustic recordings also have the benefit of allowing analysis of sonic booms from vehicles that are not yet flying, like the X-59, since the mock recordings are created by combining vehicle-specific predicted waveforms with other audio sources. The estimates of total measurement error are documented as a function of the signal-to-noise ratio (SNR) of the loudness level, where the corrected SNR is computed while accounting for the effects of the method that is used to correct for background noise contamination when computing the noise metric values. The corrected SNR calculations used here can be applied to both mock recordings and in-field measurements, so the uncertainty of in-field recordings can be found using pre-computed lookup tables that identify the relationship between metric type, corrected SNR, and the expected measurement error.

Sonic Boom↗
NASA NTRSDate not supplied

Improving IPATS Channel-to-Channel Registration Assessment

The Image Navigation and Registration (INR) Performance Assessment Tool Set (IPATS) is a primary tool for assessing INR performance of GOES-R series ABI images. IPATS assesses five INR metrics: navigation, channel-to-channel registration (CCR), frame-to-frame registration, within-frame registration, and swath-to-swath registration. It was discovered that CCR assessment results between Visible-Near-Infrared (VNIR) channels and Infrared (IR) channels exhibits an annual oscillation in the north-south (NS) direction and a diurnal oscillation in the east-west (EW) direction, with an amplitude of approximately 5 μrad and 2.5 μrad, respectively. However, differences of navigation assessment results between VNIR and IR channels do not exhibit the annual or diurnal oscillations observed in CCR results. This indicates that the observed oscillations are due to measurement errors. The characteristics of the oscillations imply that cloud shadows are a possible cause of these measurement errors. In this study, several methods are explored to minimize the impact of cloud shadows on VNIR to IR CCR assessments: a) assessment at landmark locations only; b) using navigation assessment results to filter CCR assessments; c) using the ABI clear-sky-ratio product as a cloud mask; and d) smaller CCR assessment windows. In this paper, each method and a combination of several methods are evaluated based on assessment accuracy and the number of successful assessments. The selected approach is then used to reprocess GOES-16 ABI CCR data to show reductions in the annual and diurnal measurement error oscillations.

INR↗
NASA NTRS1997

A Predictive Attitude Determination Algorithm

In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.

Markley, F. Landis↗
NASA NTRS1961

Repeatability of the Over-All Errors of an Airplane Altimeter Installation in Landing-Approach Operations

Flight tests have been conducted to determine the repeatability of the over-all altimetry errors in the landing-approach condition of two sensitive altimeters (Air Force type C-12) installed in the cockpit of a transport airplane and of four precision altimeters (Air Force type MA-1) installed in a photo-observer. Data were obtained through a speed range of 62 to 100 knots during 42 landing-approach operations conducted on four different days. The results of the tests show that the repeatability errors of the two sensitive altimeters are +/- 35 feet and +/- 39 feet. These errors are of the same order as the maximum repeatability error measured in previous tests of eleven airplanes of the same type. For each of the four flights of the present tests the mean values of the data obtained with the two sensitive altimeters shifted by relatively large amounts, apparently because of the interaction of the stability and aftereffect- recovery characteristics of the instruments. For concurrent measurements of the over-all errors of the four precision altimeters, it is concluded that for comparable installations, the repeatability errors measured with these altimeters would be smaller than those measured with the sensitive altimeters.

Gracey, William↗
NASA NTRS1994

Tests of the Tully-Fisher relation. 1: Scatter in infrared magnitude versus 21 cm width

We examine the precision of the Tully-Fisher relation (TFR) using a sample of galaxies in the Coma region of the sky, and find that it is good to 5% or better in measuring relative distances. Total magnitudes and disk axis ratios are derived from H and I band surface photometry, and Arecibo 21 cm profiles define the rotation speeds of the galaxies. Using 25 galaxies for which the disk inclination and 21 cm width are well defined, we find an rms deviation of 0.10 mag from a linear TFR with dI/d(log W(sub c)) = -5.6. Each galaxy is assumed to be at a distance proportional to its redshift, and an extinction correction of 1.4(1-b/a) mag is applied to the total I magnitude. The measured scatter is less than 0.15 mag using milder extinction laws from the literature. The I band TFR scatter is consistent with measurement error, and the 95% CL limits on the intrinsic scatter are 0-0.10 mag. The rms scatter using H band magnitudes is 0.20 mag (N = 17). The low width galaxies have scatter in H significantly in excess of known measurement error, but the higher width half of the galaxies have scatter consistent with measurement error. The H band TFR slope may be as steep as the I band slope. As the first applications of this tight correlation, we note the following: (1) the data for the particular spirals commonly used to define the TFR distance to the Coma cluster are inconsistent with being at a common distance and are in fact in free Hubble expansion, with an upper limit of 300 km/s on the rms peculiar line-of-sight velocity of these gas-rich spirals; and (2) the gravitational potential in the disks of these galaxies has typical ellipticity less than 5%. The published data for three nearby spiral galaxies with Cepheid distance determinations are inconsistent with our Coma TFR, suggesting that these local calibrators are either ill-measured or peculiar relative to the Coma Supercluster spirals, or that the TFR has a varying form in different locales.

Bernstein, Gary M.↗
NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗
NASA NTRS1991

Measurement of precision oscillator phase noise using the two-oscillator coherent down-conversion technique

The characterization of precision frequency standard phase noise and spurious outputs is addressed, using the two-oscillator coherent downconversion technique. Focus is on techniques for making accurate measurements of phase noise and spurious outputs within 100 KHz of a carrier. Significant sources of measurement error related to hardware design problems and inadequate measurement procedures are discussed: measurement errors resulting from system noise sources, phase-locked loop effects, and system bandwidth limitations. In addition, methods and design considerations for minimizing the effects of such errors are presented. Analytic discussions and results are supplemented with actual test data and measurements made using measurement hardware developed at the Ball Corporation, Efratom Division.

Christopher J. Pagnanelli↗
NASA NTRS1986

A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

Melbourne, William G.↗
NASA NTRS2014

A Regional CO2 Observing System Simulation Experiment for the ASCENDS Satellite Mission

Top-down estimates of the spatiotemporal variations in emissions and uptake of CO2 will benefit from the increasing measurement density brought by recent and future additions to the suite of in situ and remote CO2 measurement platforms. In particular, the planned NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) satellite mission will provide greater coverage in cloudy regions, at high latitudes, and at night than passive satellite systems, as well as high precision and accuracy. In a novel approach to quantifying the ability of satellite column measurements to constrain CO2 fluxes, we use a portable library of footprints (surface influence functions) generated by the WRF-STILT Lagrangian transport model in a regional Bayesian synthesis inversion. The regional Lagrangian framework is well suited to make use of ASCENDS observations to constrain fluxes at high resolution, in this case at 1 degree latitude x 1 degree longitude and weekly for North America. We consider random measurement errors only, modeled as a function of mission and instrument design specifications along with realistic atmospheric and surface conditions. We find that the ASCENDS observations could potentially reduce flux uncertainties substantially at biome and finer scales. At the 1 degree x 1 degree, weekly scale, the largest uncertainty reductions, on the order of 50 percent, occur where and when there is good coverage by observations with low measurement errors and the a priori uncertainties are large. Uncertainty reductions are smaller for a 1.57 micron candidate wavelength than for a 2.05 micron wavelength, and are smaller for the higher of the two measurement error levels that we consider (1.0 ppm vs. 0.5 ppm clear-sky error at Railroad Valley, Nevada). Uncertainty reductions at the annual, biome scale range from 40 percent to 75 percent across our four instrument design cases, and from 65 percent to 85 percent for the continent as a whole. Our uncertainty reductions at various scales are substantially smaller than those from a global ASCENDS inversion on a coarser grid, demonstrating how quantitative results can depend on inversion methodology. The a posteriori flux uncertainties we obtain, ranging from 0.01 to 0.06 Pg C yr-1 across the biomes, would meet requirements for improved understanding of long-term carbon sinks suggested by a previous study.

remote sensing↗
NASA NTRS1989

Digitally modulated bit error rate measurement system for microwave component evaluation

The NASA Lewis Research Center has developed a unique capability for evaluation of the microwave components of a digital communication system. This digitally modulated bit-error-rate (BER) measurement system (DMBERMS) features a continuous data digital BER test set, a data processor, a serial minimum shift keying (SMSK) modem, noise generation, and computer automation. Application of the DMBERMS has provided useful information for the evaluation of existing microwave components and of design goals for future components. The design and applications of this system for digitally modulated BER measurements are discussed.

Shalkhauser, Mary Jo W.↗
NASA NTRS2021

A Critical Look at Coulomb Counting Approach for State of Charge Estimation in Batteries

In this paper, we consider the problem of state-of-charge estimation for rechargeable batteries. Coulomb counting is a well-known method for estimating the state of charge, and it is regarded as accurate as long as the battery capacity and the beginning state of charge are known. The Coulomb counting approach, on the other hand, is prone to inaccuracies from a variety of sources, and the magnitude of these errors has not been explored in the literature. We formally construct and quantify the state-of-charge estimate error during Coulomb counting due to four types of error sources: (1) current measurement error; (2) current integration approximation error; (3) battery capacity uncertainty; and (4) timing oscillator error/drift. It is demonstrated that the state-of-charge error produced can be either time-cumulative or state-of-charge-proportional. Time-cumulative errors accumulate over time and have the potential to render the state-of-charge estimation utterly invalid in the long term. The proportional errors of the state of charge rise with the accumulated state of charge and reach their worst value within one charge/discharge cycle. The study presents methods for reducing time-cumulative and state-of-charge-proportional mistakes through simulation analysis.

Battery management system↗
NASA NTRS1972

Pseudorandom noise for telemetry error rate measurement applications and limitations.

A pseudorandom noise (PRN) generator functional design has been developed which is superior to the commercially available instrument in usable bandwidth and in the closeness of fit to the gaussian probability distribution in the 'tails' of the curve. The principal disadvantage of PRN sources for bit error rate (BER) measurements is that the probability distribution is truncated in the tails. This truncation of the probability distribution results in a similar truncation of the BER curve - i.e., there is a minimum BER which can be measured, below which the only possible result is zero. The minimum nonzero BER actually computed with the PRN source developed was 0.00001 with a pseudorandom sequence of 131,071 bits. It is theoretically possible, with a longer sequence, to achieve a minimum BER of 0.000001 with the same design.

Hopkins, P. M.↗