Applied recursive estimation problems and techniques
Semiwideband and adaptive noise variance recursive estimation techniques applicable to spacecraft trajectory analysis
Dennis, A. R.↗
SEARCH · Engineering Papers
Results for “variance estimation”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Effects of sample design and landscape features on a measure of environmental heterogeneity
Environmental heterogeneity, an important influence on organisms and ecological processes, can be quantified by the variance of an environmental characteristic over all locations within a study extent. However on landscapes with autocorrelation and gradient patterns, estimating this variance from a sample of locations may lead to errors that cannot be corrected with statistical techniques. We analytically derived the relative expected sampling error of sample designs on landscapes with particular gradient pattern and autocorrelation features. We applied this closed-form approach to temperature observations from an existing study. The expected heterogeneity differed, both in magnitude and direction, amongst sample designs over the study site's likely range of autocorrelation and gradient features. We conducted a simulation study to understand the effects of (i) landscape variability and (ii) design variability on an average sampling error. On 10 000 simulated landscapes with varying gradient and autocorrelation features, we compared estimates of variance from a variety of structured and random sample designs. While gradient patterns and autocorrelation cause large errors for some designs, others yield near-zero average sampling error. Sample location spacing is a key factor in sample design performance. Random designs have larger range of possible sampling errors than structured designs due to the potential for sample arrangements that over- and under-sample certain areas of the landscape. Furthermore, when implementing a new sample design to quantify environmental heterogeneity via variance, we recommend using a simple structured design with appropriate sample spacing. For existing designs, we recommend calculating the relative expected sampling error via our analytical derivation.
54 ENVIRONMENTAL SCIENCES↗
SU-F-207-16: CT Protocols Optimization Using Model Observer
Purpose: To quantitatively evaluate the performance of different CT protocols using task-based measures of image quality. This work studies the task of size and the contrast estimation of different iodine concentration rods inserted in head- and body-sized phantoms using different imaging protocols. These protocols are designed to have the same dose level (CTDIvol) but using different X-ray tube voltage settings (kVp). Methods: Different concentrations of iodine objects inserted in a head size phantom and a body size phantom are imaged on a 64-slice commercial CT scanner. Scanning protocols with various tube voltages (80, 100, and 120 kVp) and current settings are selected, which output the same absorbed dose level (CTDIvol). Because the phantom design (size of the iodine objects, the air gap between the inserted objects and the phantom) is not ideal for a model observer study, the acquired CT images are used to generate simulation images with four different sizes and five different contracts iodine objects. For each type of the objects, 500 images (100 x 100 pixels) are generated for the observer study. The observer selected in this study is the channelized scanning linear observer which could be applied to estimate the size and the contrast. The figure of merit used is the correct estimation ratio. The mean and the variance are estimated by the shuffle method. Results: The results indicate that the protocols with 100 kVp tube voltage setting provides the best performance for iodine insert size and contrast estimation for both head and body phantom cases. Conclusion: This work presents a practical and robust quantitative approach using channelized scanning linear observer to study contrast and size estimation performance from different CT protocols. Different protocols at same CTDIvol setting could Result in different image quality performance. The relationship between the absorbed dose and the diagnostic image quality is not linear.
60 APPLIED LIFE SCIENCES↗
Development of advanced techniques for rotorcraft state estimation and parameter identification
An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.
Hall, W. E., Jr.↗
Modified fast frequency acquisition via adaptive least squares algorithm
A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error.
Kumar, Rajendra↗
System and method for modeling and forecasting cyclical demand systems with dynamic controls and dynamic incentives
Systems and methods for modeling and forecasting cyclical demand systems in the presence of dynamic control or dynamic incentives. A method for modeling a cyclical demand system comprises obtaining historical data on one or more demand measurements over a plurality of demand cycles, obtaining historical data on incentive signals over the plurality of demand cycles, constructing a model using the obtained historical data on the one or more demand measurements and the incentive signals, wherein constructing the model comprises specifying a state-space model, specifying variance parameters in the model, and estimating unknown variance parameters.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Estimating the Modified Allan Variance
A paper at the 1992 FCS showed how to express the modified Allan variance (mvar) in terms of the third difference of the cumulative sum of time residuals. Although this reformulated definition was presented merely as a computational trick for simplifying the calculation of mvar estimates, it has since turned out to be a powerful theoretical tool for deriving the statistical quality of those estimates in terms of their equivalent degrees of freedom (edf), defined for an estimator V by edf V = 2(EV)2/(var V). Confidence intervals for mvar can then be constructed from levels of the appropriate 2 distribution.
Allan Variance↗
A Frequency-Drift Estimator and Its Removal from Modified Allan Variance
A drift-rate estimator constructed from four values of the cumulative sum of clock residuals is shownn to have good error performance in the presence of the five standard power-law noises.
Allan Variance↗
Estimation of parameters in linear structural relationships: Sensitivity to the choice of the ratio of error variances
Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. The use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio is investigated.
Lakshminarayanan, M. Y.↗
Estimation of parameters in linear structural relationships Sensitivity to the choice of the ratio of error variances
Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. This paper investigates the use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio.
Lakshminarayanan, M. Y.↗
Review of a Draft - Avoiding the Impossible: Re-focusing a Non-Feasible Mission 2-Hrs into a 3-Day Engineering Session
Concurrent engineering offers a great many benefits to engineers and mission designers throughout the world of aerospace. The only downside of concurrent engineering, and this is somewhat unavoidable, is that you don’t know the results of a design session until the end when it is completed. Usually, this is not a problem – you wouldn’t start building a spacecraft before the design is finished. However, within mass and cost constrained systems, you may end up with a final design that although technically sound – is not feasible due to mass or cost limits. Employing in-session mass and cost models with flexible inputs that refine their estimates and variance as more detailed information comes in throughout a design session allows major design changes to be made when the probability of breaching a mass or cost cap exceeds a threshold level. This enables mission designers to re-focus the study, and avoid spending 3-days with 15 engineers designing a non-feasible mission. By understanding key correlations and nested relationships within mass or cost, and specifically mass or cost allocations per mission element by mission type, it’s possible to get flexible-input, statistically based mass and cost estimates very early in the design process. Baseline models are seeded using mission characteristics and general parameters (outer planetary orbiter-probe mission, $500M cost cap for example) to provide a rough estimate of the expected mass or cost. As information gets solidified during the session, it gets added to the model and the estimates are updated. Continuing the orbiter-probe mission example, modeling probe heat shield cost as a percent of total probe cost, and probe cost as a percent of total flight system cost, and total flight system cost as a percent of total mission cost allows a design team to roll-up solidified information to estimate the probability of fitting within a mass or cost constraint early in a concurrent design session. When only the heat shield cost is known, the variance of the final estimate is higher, whereas when the full probe gets defined, naturally, the variance of the estimate decreases. A methodology, model, verification and demo implementation for cost limit breach are presented.
Hihn, Jairus M.↗
Maxar Initial Satellite Characterization
This documents reports on the initial Assessment Specification and Validation (ASV) of Maxar satellite imagery as a geolocation system. Validation is a prerequisite for using geolocation for applications that require quantified uncertainty. A Variance Component Estimation (VCE) calibration of the provider’s co- variance matrices concluded that they were exaggerated. However, we currently lack enough independent validation data to quantify the improvement from the VCE. The current ASV process is slow and expensive. It will not be able to keep up with growing numbers of satellite systems. We proposed a method to automate ASV using controlled imagery. The proposed method will allow us to keep up with new sensors and generate unbounded amounts of calibration data, leading to unprecedented accuracy.
47 OTHER INSTRUMENTATION↗
Smooth empirical Bayes estimation of observation error variances in linear systems.
Abstract missing.
Martz, H. F., Jr.↗
Large Area Crop Inventory Experiment (LACIE). Evaluation of three-category classification
The author has identified the following signficant results. Examination of both machine estimates and stratified areal estimates produced by clustering and classification reveal no significant differences between the proportion estimates and ground truth estimates. When testing the variances of the machine estimates, a significant reduction in the variances was found when the number of starting dots was increased from 30 to 45. The variances were again reduced, although not significantly, when the number of starting dots was increased from 45 to 60. From these results, 60 starting dots are recommended for a three-category classifier. When examining the variances of the estimates for the four estimation procedures (using 60 dots), no significant differences were found between procedures. Thus, only the machine clustering may be used to produce an estimate, and the stratified areal estimate computations and maximum likelihood classification can be deleted.
Havens, K. A.↗
Regularization and Error Characterization of GRACE Mascons
We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.
B. D. Loomis↗
Regularization and Error Characterization of GRACE Mascons
We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.
Loomis, B. D.↗
Estimation of within-stratum variance for sample allocation: Foreign commodity production forecasting
The problem of determining the stratum variances required for an optimum sample allocation for remotely sensed crop surveys is investigated with emphasis on an approach based on the concept of stratum variance as a function of the sampling unit size. A methodology using the existing and easily available information of historical statistics is developed for obtaining initial estimates of stratum variances. The procedure is applied to variance for wheat in the U.S. Great Plains and is evaluated based on the numerical results obtained. It is shown that the proposed technique is viable and performs satisfactorily with the use of a conservative value (smaller than the expected value) for the field size and with the use of crop statistics from the small political division level.
Chhikara, R. S.↗
An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance
Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system.
Keel, Byron M.↗