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At least 1,513 records · Page 84
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NASA NTRS1996

Application of Consider Covariance to the Extended Kalman Filter

The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.

Lundberg, John B.↗
NASA NTRS1985

A preliminary look at astrometric accuracy as a function of photon counts

The importance of photon counts as a factor in the accuracy of astrometric positions is illustrated by a preliminary look at data collected with the Allegheny Observatory's photon-counting detector, the Multichannel Astrometric Photometer. Twenty estimates are plotted of the standard errors, per hour, of astrometric positions obtained with the photometer and the blue-light lens of the observatory's 30-inch refractor. The agreement between the estimated standard errors in the X and Y coordinates supports the conclusion that, as predicted by Drake, the accuracy is dependent upon the count rate.

Gatewood, G.↗
NASA NTRS1988

On the appropriateness of applying chi-square distribution based confidence intervals to spectral estimates of helicopter flyover data

The validity of applying chi-square based confidence intervals to far-field acoustic flyover spectral estimates was investigated. Simulated data, using a Kendall series and experimental acoustic data from the NASA/McDonnell Douglas 500E acoustics test, were analyzed. Statistical significance tests to determine the equality of distributions of the simulated and experimental data relative to theoretical chi-square distributions were performed. Bias and uncertainty errors associated with the spectral estimates were easily identified from the data sets. A model relating the uncertainty and bias errors to the estimates resulted, which aided in determining the appropriateness of the chi-square distribution based confidence intervals. Such confidence intervals were appropriate for nontonally associated frequencies of the experimental data but were inappropriate for tonally associated estimate distributions. The appropriateness at the tonally associated frequencies was indicated by the presence of bias error and noncomformity of the distributions to the theoretical chi-square distribution. A technique for determining appropriate confidence intervals at the tonally associated frequencies was suggested.

Rutledge, Charles K.↗
NASA NTRS1991

Demonstration of precise estimation of polar motion parameters with the global positioning system: Initial results

Data from the Global Positioning System (GPS) were used to determine precise polar motion estimates. Conservatively calculated formal errors of the GPS least squares solution are approx. 10 cm. The GPS estimates agree with independently determined polar motion values from very long baseline interferometry (VLBI) at the 5 cm level. The data were obtained from a partial constellation of GPS satellites and from a sparse worldwide distribution of ground stations. The accuracy of the GPS estimates should continue to improve as more satellites and ground receivers become operational, and eventually a near real time GPS capability should be available. Because the GPS data are obtained and processed independently from the large radio antennas at the Deep Space Network (DSN), GPS estimation could provide very precise measurements of Earth orientation for calibration of deep space tracking data and could significantly relieve the ever growing burden on the DSN radio telescopes to provide Earth platform calibrations.

Lichten, S. M.↗
NASA NTRS2010

Estimation of Surface Air Temperature from MODIS 1km Resolution Land Surface Temperature Over Northern China

Surface air temperature is a critical variable to describe the energy and water cycle of the Earth-atmosphere system and is a key input element for hydrology and land surface models. It is a very important variable in agricultural applications and climate change studies. This is a preliminary study to examine statistical relationships between ground meteorological station measured surface daily maximum/minimum air temperature and satellite remotely sensed land surface temperature from MODIS over the dry and semiarid regions of northern China. Studies were conducted for both MODIS-Terra and MODIS-Aqua by using year 2009 data. Results indicate that the relationships between surface air temperature and remotely sensed land surface temperature are statistically significant. The relationships between the maximum air temperature and daytime land surface temperature depends significantly on land surface types and vegetation index, but the minimum air temperature and nighttime land surface temperature has little dependence on the surface conditions. Based on linear regression relationship between surface air temperature and MODIS land surface temperature, surface maximum and minimum air temperatures are estimated from 1km MODIS land surface temperature under clear sky conditions. The statistical errors (sigma) of the estimated daily maximum (minimum) air temperature is about 3.8 C(3.7 C).

Shen, Suhung↗
NASA NTRS1971

State estimation with small nonlinearities

A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.

Conrad, B.↗
NASA NTRS2013

Interpreting SBUV Smoothing Errors: an Example Using the Quasi-biennial Oscillation

The Solar Backscattered Ultraviolet (SBUV) observing system consists of a series of instruments that have been measuring both total ozone and the ozone profile since 1970. SBUV measures the profile in the upper stratosphere with a resolution that is adequate to resolve most of the important features of that region. In the lower stratosphere the limited vertical resolution of the SBUV system means that there are components of the profile variability that SBUV cannot measure. The smoothing error, as defined in the optimal estimation retrieval method, describes the components of the profile variability that the SBUV observing system cannot measure. In this paper we provide a simple visual interpretation of the SBUV smoothing error by comparing SBUV ozone anomalies in the lower tropical stratosphere associated with the quasi-biennial oscillation (QBO) to anomalies obtained from the Aura Microwave Limb Sounder (MLS). We describe a methodology for estimating the SBUV smoothing error for monthly zonal mean (mzm) profiles. We construct covariance matrices that describe the statistics of the inter-annual ozone variability using a 6 yr record of Aura MLS and ozonesonde data. We find that the smoothing error is of the order of 1percent between 10 and 1 hPa, increasing up to 15-20 percent in the troposphere and up to 5 percent in the mesosphere. The smoothing error for total ozone columns is small, mostly less than 0.5 percent. We demonstrate that by merging the partial ozone columns from several layers in the lower stratosphere/troposphere into one thick layer, we can minimize the smoothing error. We recommend using the following layer combinations to reduce the smoothing error to about 1 percent: surface to 25 hPa (16 hPa) outside (inside) of the narrow equatorial zone 20 S-20 N.

ozone profile retrievals↗
NASA NTRS1978

Aircraft parameter estimation in frequency domain

The algorithms for the equation error and output error methods, the two basic procedures for the extraction of aircraft parameters from flight data, are formulated in the frequency domain. The output error method includes the maximum likelihood estimation technique. This is further extended to those cases where the measured data is in the form of frequency response curves and the model of an aircraft includes elastic degrees of freedom and unsteady aerodynamics. Then the generalized maximum likelihood method, which can be applied to the identification of an aircraft subjected to external disturbances, is introduced. Next, all estimation methods mentioned are discussed with emphasis on advantages of the frequency domain analysis. The paper concludes with an example using real flight data.

Klein, V.↗
NASA NTRS1981

Geodesy by radio interferometry - Intercontinental distance determinations with subdecimeter precision

Analysis of very-long-baseline interferometer (VLBI) observations yielded estimates of the distances between three radio telescopes in the United States and one in Sweden, with formal standard errors of a few centimeters: Westford, Massachusetts-Onsala, Sweden: 5,599,714.66 + or - 0.03 m; Green Bank, West Virginia-Onsala, Sweden: 6,319,317.75 + or - 0.03 m; and Owens Valley, California-Onsala, Sweden: 7,914,131.19 + or - 0.04 m, where the earth-fixed reference points are defined in each case with respect to the axes of the telescopes. The actual standard errors are difficult to estimate reliably but are probably not greater than twice the formal errors.

Herring, T. A.↗
NASA NTRS1986

Extended active space CASSCF/MRSD CI calculations of the barrier height for the reaction: O + H2 yields OH + H

The convergence of the barrier height for the O + H2 yields OH + H reaction was studied as a function of the size of the active space and basis set completeness. The barrier height is rapidly convergent with respect to expansion of the active space. Addition of 2p yields 2p' correlation terms to the active space lowers the barrier to the O + H2 reaction by about 2.0 kcal/mole, but addition of 3d and other terms has little additional effect. Multireference singles and doubles contracted CI plus Davidson's correction calculations using a (5s5p3d2f1g/4s3p2d1f) basis set with a 5 sigma 2 pi active space lead to a barrier height of 12.7 kcal/mole. Including an estimate of the CI contraction error and basis set superposition error leads to 12.4 kcal/mole as the best estimate of the barrier height.

Walch, Stephen P.↗
NASA NTRS2018

Incremental States for Precise On-Orbit Relative Knowledge in Formation Flight

High precision and close proximity formation flight is an enabling technology for future space missions and requires an on-board relative navigation capability that is accurate to the mm-level and robust to formation parameters. Common estimation techniques linearize the entire formation about one spacecraft’s position, resulting in degraded accuracy due to linearization errors when separation distances become large. Additionally, methods which decouple absolute and relative state estimates usually require ad-hoc methods to incorporate the estimates together. This work discusses an alternative ”incremental” formulation of the relative navigation problem which is in variant to formation size, robust to coupling between absolute and relative dynamics, and can undergo similarity transformations to smoothly incorporate either absolute or relative information without numerical issues. A specific example of this architecture is presented in the context of formation navigation using Carrier-Differential Global Positioning System measurements, and is compared to a traditional leader-linearized filter. In the presence of accurate measurements, the incremental architecture is shown to reduce linearization errors and mean estimate errors by up to three orders of magnitude without the incorporation of new sensor information.

Seubert, Carl↗
NASA NTRS1985

Improving the absolute positioning accuracy of robot manipulators

The absolute positioning accuracy of robot manipulator can be increased substantially by updating the nominal link parameters in the control software. This paper presents a general method to estimate the link parameter errors for any serial link manipulator (i.e., n links, and any combination of revolute and prismatic joints). The parameters are estimated through a linear kinematic model which relates the link bias errors to the end-effector positioning error. Only end-effector measurements are required instead of individual link measurements to implement this method.

Hayati, S.↗
NASA NTRS2011

Sensitivity of C-Band Polarimetric Radar-Based Drop Size Distribution Measurements to Maximum Diameter Assumptions

The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement Mission (GPM/PMM Science Team)-funded study is to document the sensitivity of DSD measurements, including estimates of D0, from C-band Z(sub dr) and reflectivity to this range of D(sub max) assumptions. For this study, GPM Ground Validation 2DVD's were operated under the scanning domain of the UAHuntsville ARMOR C-band dual-polarimetric radar. Approximately 7500 minutes of DSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSD's were then used as input to a T-matrix model for computation of polarimetric radar moments at C-band. All necessary model parameterizations, such as temperature, drop shape, and drop fall mode, were fixed at typically accepted values while the D(sub max) assumption was allowed to vary in sensitivity tests. By hypothesizing a DSD model with D(sub max) (fit) from which the empirical fit to D0 = F[Z(sub dr)] was derived via non-linear least squares regression and a separate reference DSD model with D(sub max) (truth), bias and standard error in D0 retrievals were estimated in the presence of Z(sub dr) measurement error and hypothesized mismatch in D(sub max) assumptions. Although the normalized standard error for D0 = F[Z(sub dr)r] can increase slightly (as much as from 11% to 16% for all 7500 DSDs) when the D(sub max) (fit) does not match D(sub max) (truth), the primary impact of uncertainty in D(sub max) is a potential increase in normalized bias error in D0 (from 0% to as much as 10% over all 7500 DSDs, depending on the extent of the mismatch between D(sub max) (fit) and D(sub max) (truth)). For DSDs characterized by large Z(sub dr) (Z(sub dr) > 1.5 to 2.0 dB), the normalized bias error for D0 estimation at C-band is sometimes unacceptably large (> 10%), again depending on the extent of the hypothesized D(sub max) mismatch. Modeled errors in D0 retrievals from Z(sub dr) at C-band are demonstrated in detail and comparedo similar modeled retrieval errors at S-band and X-band where the sensitivity to D(sub max) is expected to be less. The impact of D(sub max) assumptions to the retrieval of other DSD parameters such as Nw, the liquid water content normalized intercept parameter, are also explored. Likely implications for DSD retrievals using C-band polarimetric radar for GPM are assessed by considering current community knowledge regarding D(sub max) and quantifying the statistical distribution of Z(sub dr) from ARMOR over a large variety of meteorological conditions. Based on these results and the prevalence of C-band polarimetric radars worldwide, a call for more emphasis on constraining our observational estimate of D(sub max) within a typical radar resolution volume is made

Carey, Lawrence D.↗
NASA NTRS2012

The Surface Water and Ocean Topography Satellite Mission - An Assessment of Swath Altimetry Measurements of River Hydrodynamics

The Surface Water and Ocean Topography (SWOT) satellite mission, scheduled for launch in 2020 with development commencing in 2015, will provide a step-change improvement in the measurement of terrestrial surface water storage and dynamics. In particular, it will provide the first, routine two-dimensional measurements of water surface elevations, which will allow for the estimation of river and floodplain flows via the water surface slope. In this paper, we characterize the measurements which may be obtained from SWOT and illustrate how they may be used to derive estimates of river discharge. In particular, we show (i) the spatia-temporal sampling scheme of SWOT, (ii) the errors which maybe expected in swath altimetry measurements of the terrestrial surface water, and (iii) the impacts such errors may have on estimates of water surface slope and river discharge, We illustrate this through a "virtual mission" study for a approximately 300 km reach of the central Amazon river, using a hydraulic model to provide water surface elevations according to the SWOT spatia-temporal sampling scheme (orbit with 78 degree inclination, 22 day repeat and 140 km swath width) to which errors were added based on a two-dimension height error spectrum derived from the SWOT design requirements. Water surface elevation measurements for the Amazon mainstem as may be observed by SWOT were thereby obtained. Using these measurements, estimates of river slope and discharge were derived and compared to those which may be obtained without error, and those obtained directly from the hydraulic model. It was found that discharge can be reproduced highly accurately from the water height, without knowledge of the detailed channel bathymetry using a modified Manning's equation, if friction, depth, width and slope are known. Increasing reach length was found to be an effective method to reduce systematic height error in SWOT measurements.

Wilson, Matthew D.↗
NASA NTRS1984

A comparison of two position estimate algorithms that use ILS localizer and DME information. Simulation and flight test results

Simulation and flight tests were conducted to compare the accuracy of two algorithms designed to compute a position estimate with an airborne navigation computer. Both algorithms used ILS localizer and DME radio signals to compute a position difference vector to be used as an input to the navigation computer position estimate filter. The results of these tests show that the position estimate accuracy and response to artificially induced errors are improved when the position estimate is computed by an algorithm that geometrically combines DME and ILS localizer information to form a single component of error rather than by an algorithm that produces two independent components of error, one from a DMD input and the other from the ILS localizer input.

Knox, C. E.↗
NASA NTRS1973

An approach to the analysis of performance of quasi-optimum digital phase-locked loops.

An approach to the analysis of performance of quasi-optimum digital phase-locked loops (DPLL's) is presented. An expression for the characteristic function of the prior error in the state estimate is derived, and from this expression an infinite dimensional equation for the prior error variance is obtained. The prior error-variance equation is a function of the communication system model and the DPLL gain and is independent of the method used to derive the DPLL gain. Two approximations are discussed for reducing the prior error-variance equation to finite dimension. The effectiveness of one approximation in analyzing DPLL performance is studied.

Polk, D. R.↗
NASA NTRS1986

Modeling, estimation and identification methods for static shape determination of flexible structures

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Rodriguez, G.↗
NASA NTRS1999

Implication of microdosimetry in estimation of radiation quality in space environment

Errors introduced using a tissue equivalent proportional counter to estimate radiation quality of an arbitrary ion field as related to space radiations are examined. This is accomplished by using a generalized analytic model to calculate the effect of energy loss straggling, track structure, and pathlength distribution on the microdosimetric distribution. The error can be as large as a factor of two, but no systematic trend could be found.

NASA Discipline Radiation Health↗