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NASA NTRS1991

Syntactic error modeling and scoring normalization in speech recognition: Error modeling and scoring normalization in the speech recognition task for adult literacy training

The purpose was to develop a speech recognition system to be able to detect speech which is pronounced incorrectly, given that the text of the spoken speech is known to the recognizer. Better mechanisms are provided for using speech recognition in a literacy tutor application. Using a combination of scoring normalization techniques and cheater-mode decoding, a reasonable acceptance/rejection threshold was provided. In continuous speech, the system was tested to be able to provide above 80 pct. correct acceptance of words, while correctly rejecting over 80 pct. of incorrectly pronounced words.

Olorenshaw, Lex↗
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 NTRS2011

An Empirical State Error Covariance Matrix for Batch State Estimation

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. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then 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 will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).

Frisbee, Joseph H., Jr.↗
NASA NTRS2012

Estimating Climatological Bias Errors for the Global Precipitation Climatology Project (GPCP)

A procedure is described to estimate bias errors for mean precipitation by using multiple estimates from different algorithms, satellite sources, and merged products. The Global Precipitation Climatology Project (GPCP) monthly product is used as a base precipitation estimate, with other input products included when they are within +/- 50% of the GPCP estimates on a zonal-mean basis (ocean and land separately). The standard deviation s of the included products is then taken to be the estimated systematic, or bias, error. The results allow one to examine monthly climatologies and the annual climatology, producing maps of estimated bias errors, zonal-mean errors, and estimated errors over large areas such as ocean and land for both the tropics and the globe. For ocean areas, where there is the largest question as to absolute magnitude of precipitation, the analysis shows spatial variations in the estimated bias errors, indicating areas where one should have more or less confidence in the mean precipitation estimates. In the tropics, relative bias error estimates (s/m, where m is the mean precipitation) over the eastern Pacific Ocean are as large as 20%, as compared with 10%-15% in the western Pacific part of the ITCZ. An examination of latitudinal differences over ocean clearly shows an increase in estimated bias error at higher latitudes, reaching up to 50%. Over land, the error estimates also locate regions of potential problems in the tropics and larger cold-season errors at high latitudes that are due to snow. An empirical technique to area average the gridded errors (s) is described that allows one to make error estimates for arbitrary areas and for the tropics and the globe (land and ocean separately, and combined). Over the tropics this calculation leads to a relative error estimate for tropical land and ocean combined of 7%, which is considered to be an upper bound because of the lack of sign-of-the-error canceling when integrating over different areas with a different number of input products. For the globe the calculated relative error estimate from this study is about 9%, which is also probably a slight overestimate. These tropical and global estimated bias errors provide one estimate of the current state of knowledge of the planet's mean precipitation.

Global Precipitation Climatology Project (GPCP)↗
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 NTRS2013

The Role of Model and Initial Condition Error in Numerical Weather Forecasting Investigated with an Observing System Simulation Experiment

A series of experiments that explore the roles of model and initial condition error in numerical weather prediction are performed using an observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO). The use of an OSSE allows the analysis and forecast errors to be explicitly calculated, and different hypothetical observing networks can be tested with ease. In these experiments, both a full global OSSE framework and an 'identical twin' OSSE setup are utilized to compare the behavior of the data assimilation system and evolution of forecast skill with and without model error. The initial condition error is manipulated by varying the distribution and quality of the observing network and the magnitude of observation errors. The results show that model error has a strong impact on both the quality of the analysis field and the evolution of forecast skill, including both systematic and unsystematic model error components. With a realistic observing network, the analysis state retains a significant quantity of error due to systematic model error. If errors of the analysis state are minimized, model error acts to rapidly degrade forecast skill during the first 24-48 hours of forward integration. In the presence of model error, the impact of observation errors on forecast skill is small, but in the absence of model error, observation errors cause a substantial degradation of the skill of medium range forecasts.

Model Error↗
NASA NTRS1992

Error analysis of optical correlators

With the growing interest in using binary phase only filters (BPOF) in optical correlators that are implemented on magnetooptic spatial light modulators, an understanding of the effect of errors in system alignment and optical components is critical in obtaining optimal system performance. We present simulations of optical correlator performance degradation in the presence of eight errors. We break these eight errors into three groups: 1) alignment errors, 2) errors due to a combination of component imperfections and alignment errors, and 3) errors which result solely from non-ideal components. Under the first group, we simulate errors in the distance from the object to the first principle plane of the transform lens, the distance from the second principle plane of the transform lens to the filter plane, and rotational misalignment of the input mask with the filter mask. Next we consider errors which result from a combination of alignment and component imperfections. These include errors in the transform lens, the phase compensation lens, and the inverse Fourier transform lens. Lastly we have the component errors resulting from the choice of spatial light modulator. These include contrast error and phase errors caused by the non-uniform flatness of the masks. The effects of each individual error are discussed, and the result of combining all eight errors under assumptions of reasonable tolerances and system parameters is also presented. Conclusions are drawn as to which tolerances are most critical for optimal system performance.

Ma, Paul W.↗
NASA NTRS2003

Estimation of Model Error Variances During Data Assimilation

Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.

Dee, Dick↗
NASA NTRS2018

An Accurate Method for Correcting Spectral Convolution Errors in Intercalibration of Broadband and Hyperspectral Sensors

The intercalibration between a broadband and a hyperspectral satellite Earth observation system requires the convolution of the hyperspectral data with the spectral response functions (SRFs) of the corresponding broadband channels. There are two potential issues associated with the convolution procedure. First, the finite resolution of a hyperspectral spectrum, that is, the deviation from the highly accurate line-by-line monochromatic radiances, will contribute to convolution errors. The magnitude of the errors depends on the spectral resolution and the SRF shape of the hyperspectral instrument. This type of the convolution error has not been well recognized, and there is a lack of corresponding discussion in most published papers. Although it is small as compared with the instrument accuracy of existing hyperspectral sounders, the error is deemed to be signicant when it is compared with the stringent calibration requirement imposed by future climate missions like the Climate Absolute Radiance and Refractivity Observatory (CLARREO). Second, some broadband channels are insufficiently covered by the hyperspectral data, causing spectral gaps that lead to convolution errors. Although several methods have been developed to fill the spectral gaps and hence compensate for the second type of convolution error, the correction accuracy may still need improvement especially when a large spectral gap needs to be lled. This paper presents a methodology to accurately quantify and compensate for both types of convolution errors. This methodology utilizes the available hyperspectral information to correct the scene-dependent convolution errors due to either the limited spectral resolution or spectral gaps. We use simulations to characterize the intercalibration errors between the Moderate resolution Imaging Spectroradiometer (MODIS) and current operational infrared sounders. We demonstrate that convolution errors can be effectively removed to meet the highly accurate intersatellite calibration requirement proposed by the Climate Absolute Radiance and Refractivity Observatory. Our methodology is also validated using real satellite data for the intercalibration between Aqua MODIS and Aqua Atmospheric Infrared Sounders (AIRS). Our study demonstrates that the accurate characterization and correction for the convolution errors greatly reduces the scene-dependent and spectrally dependent errors, being critical to the consistency check between Infrared Atmospheric Sounding Interferometer (IASI) and AIRS using the double-difference method. The convolution correction also facilitates the evaluation for other intercalibration errors (e.g., the drift of MODIS SRFs). Our derived SRF shift values from MODIS-AIRS (after convolution error corrections) and from MODIS-IASI intercalibration are consistent with each other. We further extend the methodology to study the calibration of a broadband channel which is either completely or largely uncovered bya hyperspectral measurement.The large spectral gap-filling methodology is validated by demonstrating the accurate prediction of the MODIS radiance of band 29 using the Cross-track Infrared Sounder spectra, with the real IASI spectral data being used as the reference.

Correction Method↗
NASA NTRS1994

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗
NASA NTRS2011

Determination of Barometric Altimeter Errors for the Orion Exploration Flight Test-1 Entry

The EFT-1 mission is the unmanned flight test for the upcoming Multi-Purpose Crew Vehicle (MPCV). During entry, the EFT-1 vehicle will trigger several Landing and Recovery System (LRS) events, such as parachute deployment, based on onboard altitude information. The primary altitude source is the filtered navigation solution updated with GPS measurement data. The vehicle also has three barometric altimeters that will be used to measure atmospheric pressure during entry. In the event that GPS data is not available during entry, the altitude derived from the barometric altimeter pressure will be used to trigger chute deployment for the drogues and main parachutes. Therefore it is important to understand the impact of error sources on the pressure measured by the barometric altimeters and on the altitude derived from that pressure. There are four primary error sources impacting the sensed pressure: sensor errors, Analog to Digital conversion errors, aerodynamic errors, and atmosphere modeling errors. This last error source is induced by the conversion from pressure to altitude in the vehicle flight software, which requires an atmosphere model such as the US Standard 1976 Atmosphere model. There are several secondary error sources as well, such as waves, tides, and latencies in data transmission. Typically, for error budget calculations it is assumed that all error sources are independent, normally distributed variables. Thus, the initial approach to developing the EFT-1 barometric altimeter altitude error budget was to create an itemized error budget under these assumptions. This budget was to be verified by simulation using high fidelity models of the vehicle hardware and software. The simulation barometric altimeter model includes hardware error sources and a data-driven model of the aerodynamic errors expected to impact the pressure in the midbay compartment in which the sensors are located. The aerodynamic model includes the pressure difference between the midbay compartment and the free stream pressure as a function of altitude, oscillations in sensed pressure due to wake effects, and an acoustics model capturing fluctuations in pressure due to motion of the passive vents separating the barometric altimeters from the outside of the vehicle.

Brown, Denise L.↗
NASA NTRS1985

An experimental evaluation of error seeding as a program validation technique

A previously reported experiment in error seeding as a program validation technique is summarized. The experiment was designed to test the validity of three assumptions on which the alleged effectiveness of error seeding is based. Errors were seeded into 17 functionally identical but independently programmed Pascal programs in such a way as to produce 408 programs, each with one seeded error. Using mean time to failure as a metric, results indicated that it is possible to generate seeded errors that are arbitrarily but not equally difficult to locate. Examination of indigenous errors demonstrated that these are also arbitrarily difficult to locate. These two results support the assumption that seeded and indigenous errors are approximately equally difficult to locate. However, the assumption that, for each type of error, all errors are equally difficult to locate was not borne out. Finally, since a seeded error occasionally corrected an indigenous error, the assumption that errors do not interfere with each other was proven wrong. Error seeding can be made useful by taking these results into account in modifying the underlying model.

Knight, J. C.↗
NASA NTRS2000

Global Warming Estimation from MSU: Correction for Drift and Calibration Errors

Microwave Sounding Unit (MSU) radiometer observations in Ch 2 (53.74 GHz), made in the nadir direction from sequential, sun-synchronous, polar-orbiting NOAA morning satellites (NOAA 6, 10 and 12 that have approximately 7am/7pm orbital geometry) and. afternoon satellites (NOAA 7, 9, 11 and 14 that have approximately 2am/2pm orbital geometry) are analyzed in this study to derive global temperature trend from 1980 to 1998. In order to remove the discontinuities between the data of the successive satellites and to get a continuous time series, first we have used shortest possible time record of each satellite. In this way we get a preliminary estimate of the global temperature trend of 0.21 K/decade. However, this estimate is affected by systematic time-dependent errors. One such error is the instrument calibration error eo. This error can be inferred whenever there are overlapping measurements made by two satellites over an extended period of time. From the available successive satellite data we have taken the longest possible time record of each satellite to form the time series during the period 1980 to 1998 to this error eo. We find eo can decrease the global temperature trend by approximately 0.07 K/decade. In addition there are systematic time dependent errors ed and ec present in the data that are introduced by the drift in the satellite orbital geometry. ed arises from the diurnal cycle in temperature and ec is the drift related change in the calibration of the MSU. In order to analyze the nature of these drift related errors the multi-satellite Ch 2 data set is partitioned into am and pm subsets to create two independent time series. The error ed can be assessed in the am and pm data of Ch 2 on land and can be eliminated. Observation made in the MSU Ch 1 (50.3 GHz) support this approach. The error ec is obvious only in the difference between the pm and am observations of Ch 2 over the ocean. We have followed two different paths to assess the impact of the error ec on the global temperature trend. In one path the entire error ec is placed in the am data while in the other it is placed in the pm data. Global temperature trend is increased or decreased by approximately 0.03 K/decade depending upon this placement. Taking into account all random errors and systematic errors our analysis of MSU observations leads us to conclude that a conservative estimate of the global warming is 0. 11 (+/-) 0.04 K/decade during 1980 to 1998.

Prabhakara, C.↗