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At least 109 records · Page 6

A parameterization for downward longwave radiation from satellite meteorological data

An accurate and efficient parameterization is developed which computes clear-atmosphere downward longwave flux in terms of the water vapor burden and water-vapor-weighted average temperature of the surface-700 mb region. The parameterization is based on detailed radiative transfer calculations performed for a wide meteorological data base, consisting of 180 atmospheric models generated from climatological data and 106 radiosonde-measured models. The standard error of the computed fluxes was found to be about 4 percent of the mean value. It is also pointed out that strong heating or cooling of the surface, as shown by many TOVS data sets, caused larger errors in the computed fluxes.

Gupta, S. K.↗

Doppler and range determination for deep space vehicles using active optical transponders

This paper describes and analyzes two types of laser system employing active transponders that could accurately determine Doppler and range to deep space vehicles from earth-orbiting satellites. The first is a noncoherent optical system in which the Doppler effect on an intensity-modulating subcarrier is measured. The second is a coherent optical system in which the Doppler effect of the optical carrier itself is measured. Doppler and range measurement errors are mathematically modeled and, for three example systems, numerically evaluated.

Kinman, Peter W.↗

Extended Kalman filter for attitude estimation of the earth radiation budget satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the Sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗

Extended Kalman Filter for attitude estimation of the Earth Radiation Budget Satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗

Autonomous Navigation Improvements for High-Earth Orbiters Using GPS

The Goddard Space Flight Center is currently developing autonomous navigation systems for satellites in high-Earth orbits where acquisition of the GPS signals is severely limited This paper discusses autonomous navigation improvements for high-Earth orbiters and assesses projected navigation performance for these satellites using Global Positioning System (GPS) Standard Positioning Service (SPS) measurements. Navigation performance is evaluated as a function of signal acquisition threshold, measurement errors, and dynamic modeling errors using realistic GPS signal strength and user antenna models. These analyses indicate that an autonomous navigation position accuracy of better than 30 meters root-mean-square (RMS) can be achieved for high-Earth orbiting satellites using a GPS receiver with a very stable oscillator. This accuracy improves to better than 15 meters RMS if the GPS receiver's signal acquisition threshold can be reduced by 5 dB-Hertz to track weaker signals.

Long, Anne↗

Developing a Fundamental Model for an Integrated GPS/INS State Estimation System with Kalman Filtering

This work will demonstrate the integration of sensor and system dynamic data and their appropriate models using an optimal filter to create a robust, adaptable, easily reconfigurable state (motion) estimation system. This state estimation system will clearly show the application of fundamental modeling and filtering techniques. These techniques are presented at a general, first principles level, that can easily be adapted to specific applications. An example of such an application is demonstrated through the development of an integrated GPS/INS navigation system. This system acquires both global position data and inertial body data, to provide optimal estimates of current position and attitude states. The optimal states are estimated using a Kalman filter. The state estimation system will include appropriate error models for the measurement hardware. The results of this work will lead to the development of a "black-box" state estimation system that supplies current motion information (position and attitude states) that can be used to carry out guidance and control strategies. This black-box state estimation system is developed independent of the vehicle dynamics and therefore is directly applicable to a variety of vehicles. Issues in system modeling and application of Kalman filtering techniques are investigated and presented. These issues include linearized models of equations of state, models of the measurement sensors, and appropriate application and parameter setting (tuning) of the Kalman filter. The general model and subsequent algorithm is developed in Matlab for numerical testing. The results of this system are demonstrated through application to data from the X-33 Michael's 9A8 mission and are presented in plots and simple animations.

Canfield, Stephen↗

An analytic technique for statistically modeling random atomic clock errors in estimation

Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting the observable is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from satellites of the Global Positioning and baseline determination for geodynamic applications. An analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance.

Fell, P. J.↗

Summary and Annotated Bibliography of Measurement Error Corrections with Potential Application in Future Quesst Mission Community Noise Studies

This document is motivated by likely needs of the Quesst mission community response tests, which will culminate in data collection and estimation of dose-response regression relationships for consideration by domestic and international aviation regulators. Furthermore, basic research questions evaluating interactions between rates of community annoyance, dose levels, and indicators of the presence of rattle, vibration, and startle hinge on hypothesis testing in the context of regression models. For a variety of reasons, noise doses may be known only imprecisely and may not reflect the actual level experienced by responding subjects. These differences between true dose and estimated dose, be they systematic or random, constitute covariate measurement error. Available statistics literature speaks to the impacts of measurement error on regression models, both in terms of bias in estimated coefficients and predicted values, and in terms of the loss of statistical power for hypothesis testing. Given the particulars of a categorical annoyance response variable and a continuous noise dose predictor variable subject to measurement error during testing, the emphasis of this report is on findings and methods pertinent to generalized linear (and mixed) models likely to be employed during the Quesst mission community tests. We reach the following conclusions: 1. Of four reviewed methods, structural Bayesian measurement error models and simulation extrapolation (SIMEX) may be the most readily applicable to Quesst mission community noise study objectives. 2. If warranted, a linear measurement model can help model systematic sources of measurement error that the classical measurement error does not. 3. For its ready implementation and small additional input requirements, simulation extrapolation may be ideally suited for addressing secondary research questions involving interactions between annoyance, noise dose, and other factors through hypothesis testing. 4. For their flexibility and ability to propagate uncertainty, structural Bayesian hierarchical models have great appeal for mission purposes; some care may be needed in developing appropriate probability models describing actual noise exposure during testing. An annotated bibliography logs additional papers and resources that may be of value to analysts in other projects and disciplines.

Dose-Response Model↗

A simulation to study the feasibility of improving the temporal resolution of LAGEOS geodynamic solutions by using a sequential process noise filter

A key drawback to estimating geodetic and geodynamic parameters over time based on satellite laser ranging (SLR) observations is the inability to accurately model all the forces acting on the satellite. Errors associated with the observations and the measurement model can detract from the estimates as well. These 'model errors' corrupt the solutions obtained from the satellite orbit determination process. Dynamical models for satellite motion utilize known geophysical parameters to mathematically detail the forces acting on the satellite. However, these parameters, while estimated as constants, vary over time. These temporal variations must be accounted for in some fashion to maintain meaningful solutions. The primary goal of this study is to analyze the feasibility of using a sequential process noise filter for estimating geodynamic parameters over time from the Laser Geodynamics Satellite (LAGEOS) SLR data. This evaluation is achieved by first simulating a sequence of realistic LAGEOS laser ranging observations. These observations are generated using models with known temporal variations in several geodynamic parameters (along track drag and the J(sub 2), J(sub 3), J(sub 4), and J(sub 5) geopotential coefficients). A standard (non-stochastic) filter and a stochastic process noise filter are then utilized to estimate the model parameters from the simulated observations. The standard non-stochastic filter estimates these parameters as constants over consecutive fixed time intervals. Thus, the resulting solutions contain constant estimates of parameters that vary in time which limits the temporal resolution and accuracy of the solution. The stochastic process noise filter estimates these parameters as correlated process noise variables. As a result, the stochastic process noise filter has the potential to estimate the temporal variations more accurately since the constraint of estimating the parameters as constants is eliminated. A comparison of the temporal resolution of solutions obtained from standard sequential filtering methods and process noise sequential filtering methods shows that the accuracy is significantly improved using process noise. The results show that the positional accuracy of the orbit is improved as well. The temporal resolution of the resulting solutions are detailed, and conclusions drawn about the results. Benefits and drawbacks of using process noise filtering in this type of scenario are also identified.

Hartman, Brian Davis↗

Filter Tuning Using the Chi-Squared Statistic

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. Both spacecraft are currently in the science phase of their respective missions. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc. (AGI). This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. It also generates a covariance at each measurement. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. Over estimating or under estimating these error values can have detrimental effects on the overall filter performance. The filter incorporates ground station measurements, which can be tuned based on the accuracy of the individual ground stations. It also includes measurements from the NASA space network (SN), which can be affected by the assumed accuracy of the TDRS satellite state at the time of the measurement.The force modelling in the EKF is also an important factor that affects the propagation accuracy and covariance sizing. The dominant force in the LEO orbit regime is the drag force caused by atmospheric drag. Accurate accounting of the drag force is especially important for the accuracy of the propagated state. The implementation of a box and wing model to improve drag estimation accuracy, and its overall effect on the covariance state is explored.The process of tuning the EKF for Aqua and Aura support is described, including examination of the measurement errors of available observation types (Doppler and range), and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-square statistic, calculated based of the ODTK EKF solutions, are assessed versus accepted norms for the orbit regime.

Covariance Analysis↗

Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.

Sidick, Erkin↗

Absolute flux density calibrations: Receiver saturation effects

The effect of receiver saturation was examined for a total power radiometer which uses an ambient load for calibration. Extension to other calibration schemes is indicated. The analysis shows that a monotonic receiver saturation characteristic could cause either positive or negative measurement errors, with polarity depending upon operating conditions. A realistic model of the receiver was made by using a linear-cubic voltage transfer characteristic. The evaluation of measurement error for this model provided a means for correcting radio source measurements.

Freiley, A. J.↗

Error analysis in the measurement of average power with application to switching controllers

Power measurement errors due to the bandwidth of a power meter and the sampling of the input voltage and current of a power meter were investigated assuming sinusoidal excitation and periodic signals generated by a model of a simple chopper system. Errors incurred in measuring power using a microcomputer with limited data storage were also considered. The behavior of the power measurement error due to the frequency responses of first order transfer functions between the input sinusoidal voltage, input sinusoidal current, and the signal multiplier was studied. Results indicate that this power measurement error can be minimized if the frequency responses of the first order transfer functions are identical. The power error analysis was extended to include the power measurement error for a model of a simple chopper system with a power source and an ideal shunt motor acting as an electrical load for the chopper. The behavior of the power measurement error was determined as a function of the chopper's duty cycle and back EMF of the shunt motor. Results indicate that the error is large when the duty cycle or back EMF is small. Theoretical and experimental results indicate that the power measurement error due to sampling of sinusoidal voltages and currents becomes excessively large when the number of observation periods approaches one-half the size of the microcomputer data memory allocated to the storage of either the input sinusoidal voltage or current.

Maisel, J. E.↗

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

42 ENGINEERING↗

The right conditions for high-precision dynamic temperature and heat capacity measurement via pyrometry and conductivity

The pursuit of accurate bulk temperature T under extreme conditions has been a long-standing goal of the high pressure science community, complicated by a lack of data to inform models. To reach these extremely high-pressure, high-temperature (high P − T) conditions, a combination of dynamic and heated static experiments (e.g., diamond or gem anvil cel experiments) are used. For example, in a diamond anvil cell (DAC) experiment, a sample placed in the DAC is first pressurized. Following pressurization, the sample T is increased either by heating the entire DAC (usually using resistive heating, and limited to ∼1000K) or by applying intense laser power to the sample surfaces. In a dynamic experiment, the process of pressurizing the sample also heats it. In the case of shock physics experiments, such heating is substantial, easily reaching thousands of Kelvin; in our work we have seen T ∼17000K. Most methods of measuring temperature at ambient are not compatible with experiments under these high-pressure, high-temperature conditions: thermocouples break, melt, or have conductivity properties that differ from ambient where they are calibrated; thermometers would melt; both are too slow. As a result most methods are based on non-contact techniques such as x-ray diffraction broadening, neutron scattering, or optical methods. Of these, optical methods using the visible and near-infrared region of the spectrum are the most commonly used as the sources and detectors are readily available. In the case of optical methods the optical depth, and therefore the measurement location, is limited to the surface. When a window or anvil material is used, heat flows from the sample into the window/anvil. Likewise, if the sample undergoes a change in thermodynamic state, such as expansion upon release, different T may be expected. As a result, the surface or apparent temperature T app measurement will differ from the bulk or interior temperature that is desired. This surface measurement must be related to the bulk measurement using thermal transport models and material models. While it is tempting to conclude that one should just use x-ray methods that directly probe the interior, even these methods have been shown to depend on thermal transport and material models. Regardless of the method used to create the high P − T condition, therefore, we must understand the role of thermal transport and material models upon our interpretation of the T measurement, as well as the errors and uncertainties associated with the choice of models used in the analysis. This is a substantial area of research and this paper is by no means a complete survey of the relevant sources of uncertainty. For example, we have yet to begin to address alternate transport models in a detailed manner (e.g., Tan-Ahrens), or the many models that use additional layers to approximate melting, turbulence, or epitaxial phenomena). Likewise, we have not explored the impact upon uncertainty of thermal models that use temperature-dependent thermal transport coefficients, or the wide range of material models that can be applied. Instead, this paper focuses on using one simple model, the Urtiew-Grover model, to understand the sources of error in T measurement so that we may identify how best to focus future research efforts to return the best improvements and avoid working on over-optimizing a single type of measurement. To this end, we work through some of the best and worst case scenarios for T measurement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Temporal Error Correlations in a Terrestrial Carbon Cycle Model Derived by Comparison to Carbon Dioxide Eddy Covariance Flux Tower Measurements

Abstract Atmospheric CO 2 flux inversions require as input an estimate of spatial and temporal correlations of errors in their estimate of the prior mean. Some previous studies have used the differences in CO 2 daily average flux estimates produced by terrestrial carbon cycle models and eddy covariance measurements to constrain the flux error correlations. Since inversions are starting to resolve the daily cycle, we set out to examine the correlations at sub‐daily time scales, as well as the correlations across years. To this end, we examine the autocorrelations in the difference between net ecosystem‐atmosphere exchange measurements from 75 AmeriFlux towers and temporally downscaled high‐spatial‐resolution flux estimates from the Carnegie‐Ames‐Stanford Approach (CASA) terrestrial carbon cycle model. We find that the daily cycle is prominent in these hourly autocorrelations and that these autocorrelations persist across years. We propose a family of functions to model these temporal correlations in atmospheric inversions, and use cross validation to determine which of the correlation functions best fits autocorrelation data from towers not in the training set. Correlation functions with a component that attempts to model the daily cycle in the differences match correlations from other towers better than those without. Those models that reproduce the same correlation structures at 1‐year intervals while modulating the amplitudes of the correlations between those intervals improve the fit still further.

54 ENVIRONMENTAL SCIENCES↗

Measurement-based reliability/performability models

Measurement-based models based on real error-data collected on a multiprocessor system are described. Model development from the raw error-data to the estimation of cumulative reward is also described. A workload/reliability model is developed based on low-level error and resource usage data collected on an IBM 3081 system during its normal operation in order to evaluate the resource usage/error/recovery process in a large mainframe system. Thus, both normal and erroneous behavior of the system are modeled. The results provide an understanding of the different types of errors and recovery processes. The measured data show that the holding times in key operational and error states are not simple exponentials and that a semi-Markov process is necessary to model the system behavior. A sensitivity analysis is performed to investigate the significance of using a semi-Markov process, as opposed to a Markov process, to model the measured system.

Hsueh, Mei-Chen↗

Measurement System Characterization in the Presence of Measurement Errors

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Commo, Sean A.↗