Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,009 records · Page 56

Robustness of extended-Kalman-type observers

Robustness properties of extended-Kalman-type observers are investigated for linear plants when actuators and sensors have non-linearities or linear dynamics. Sufficient conditions for the stability of the estimation error are obtained for time-varying extended Kalman filters (EKF) for time-varying plants, and for constant-gain, exponentially weighted EKF for time-invariant plants. When the non-linearities are known only within bands of uncertainty, it is proved that the observer is non-divergent.

Joshi, S. M.↗

Elastic lithosphere thickness on the moon from mare tectonic features - A formal inversion

The thickness (T) of the lunar elastic lithosphere at the time (3.6 to 3.8 billion years ago) of the earliest preserved basalt flows in circular mare basins can be estimated by inverting the observed locations of extensional tectonic features in and surrounding the maria. In performing the inversion, the lithosphere is modeled as an elastic shell with a liquid interior, and the basalt load for each mare is approximated by a set of concentric cylinders. To permit solving the forward problem of placing radial limits on the positions of the rilles around a given mare, an additional parameter F, the ratio of the radial stress at the radial limits to the maximum radial stress, is introduced. T and F are chosen to give the best weighted-squares fit of the radial limits to the observations, and are used as the initial values in a linearized matrix inversion to check the resolution and estimate errors. The application of the procedure to three maria with prominent extensional features, Humorum, Orientale, and Serenitatis, gives values of T from about 40 + or - 10 to 50 + or - 10 km, and in each case the linearized matrix equation has an exact inverse.

Comer, R. P.↗

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data]

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts to a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.

47 OTHER INSTRUMENTATION↗

Calibration of TOPEX/POSEIDON at Platform Harvest

We present estimates for the mean bias of the TOPEX/POSEIDON NASA altimeter (ALT) and the Centre National d'Etudes Spatiales altimeter (SSALT) using in-situ data gathered at Platform Harvest during the first 36 cycles of the mission. Data for 21 overflights of the ALT and six overflights of the SSALT have been analyzed. The analysis includes an independent assessment of in-situ measurements of sea level, the radial component of the orbit, wet tropospheric path delay, and ionospheric path delay. (The sign convention used is such that, to correct the geophysical data record values for sea level, add the bias algebraically. Unless otherwise stated, the uncertainty in a given parameter is depicted by +/- sigma(sub x), where sigma(sub x) is the sample standard deviation of x about the mean.) Tide gauges at Harvest provide estimates of sea level with an uncertainty of +/- 1.5 cm. The uncertainty in the radial component of the orbit is estimated to be +/- 1.3 cm. In-situ measurements of tropopsheric path delay at Harvest compare to within +/- 1.3 cm of the TOPEX/POSEIDON microwave radiometer, and in-situ measurements of the ionospheric path delay compare to within -0.4 +/- 0.7 cm of the dual-frequency ALT and 1.1 +/- 0.6 cm of Doppler orbitography and radiopositioning integrated by satellite. We obtain mean bias estimates of -14.5 +/- 2.9 cm for the ALT and +0.9 +/- 3.1 cm for the SSALT (where the uncertainties are based on the standard deviation of the estimated mean (sigma(sub bar x/y), which is derived from sample statistics and estimates for errors that cannot be observed). These results are consistent with independent estimates for the relative bias between the two altimeters. A linear regression applied to the complete set of data shows that there is a discernable secular trend in the time series for the ALT bias estimates. A preliminary analysis of data obtained through cycle 48 suggests that the apparent secular drift may be the result of a poorly sampled annual signal.

Christensen, E. J.↗

A Feasibility Study for Simultaneous Measurements of Water Vapor and Precipitation Parameters using a Three-frequency Radar

The radar return powers from a three-frequency radar, with center frequency at 22.235 GHz and upper and lower frequencies chosen with equal water vapor absorption coefficients, can be used to estimate water vapor density and parameters of the precipitation. A linear combination of differential measurements between the center and lower frequencies on one hand and the upper and lower frequencies on the other provide an estimate of differential water vapor absorption. The coupling between the precipitation and water vapor estimates is generally weak but increases with bandwidth and the amount of non-Rayleigh scattering of the hydrometeors. The coupling leads to biases in the estimates of water vapor absorption that are related primarily to the phase state and the median mass diameter of the hydrometeors. For a down-looking radar, path-averaged estimates of water vapor absorption are possible under rain-free as well as raining conditions by using the surface returns at the three frequencies. Simulations of the water vapor attenuation retrieval show that the largest source of error typically arises from the variance in the measured radar return powers. Although the error can be mitigated by a combination of a high pulse repetition frequency, pulse compression, and averaging in range and time, the radar receiver must be stable over the averaging period. For fractional bandwidths of 20% or less, the potential exists for simultaneous measurements at the three frequencies with a single antenna and transceiver, thereby significantly reducing the cost and mass of the system.

Meneghini, R.↗

The Potential of Water Vapor & Precipitation Estimation with a Differential-frequency Radar

In the presence of rain, the radar return powers from a three-frequency radar, with center frequency at 22.235 GHz and upper and lower frequencies chosen with equal water vapor absorption coefficients, can be used to estimate water vapor density and parameters of the precipitation. A linear combination of differential measurements between the center and lower frequencies on one hand and the upper and lower frequencies on the other provide an estimate of differential water vapor absorption. Conversely, the difference in radar reflectivity factors (in dB) between the upper and lower frequencies is independent of water vapor absorption and can be used to estimate the median mass diameter of the hydrometeors. For a down-looking radar, path-integrated estimates of water vapor absorption may be possible under rain-free as well as raining conditions by using the surface returns at the three frequencies. Cross-talk or interference between the precipitation and water vapor estimates depends on the frequency separation of the channels as well as on the phase state and the median mass diameter of the hydrometeors. Simulations of the retrieval of water vapor absorption show that the largest source of variability arises from the variance in the measured radar return powers while the largest biases occur in the mixed-phase region. Use of high pulse repetition frequencies and signal whitening methods may be needed to obtain the large number of independent samples required. Measurements over a fractional bandwidth, defined as the ratio of the difference between the upper and lower frequencies to the center frequency, up to about 0.2 should be passible in a differential frequency mode, where a single transceiver and antenna are used. Difficulties in frequency allocation may require alternative choices of frequency where the water vapor absorptions at the low and high frequencies are unequal. We consider the degradation in the retrieval accuracy when the frequencies are not optimum.

Meneghini, Robert↗

Estimation of structural parameters from dynamic test data

Parameters for a lumped linear model approximating a distributed elastic structure are determined from dynamic test data comprised of several mode shapes and frequencies. Measurement errors, nonlinear response, and nonmeasurable quantities such as mode slope components are accommodated. Some mass and stiffness parameters may be known accurately, whereas the remainder are to be estimated. The method entails minimizing a quadratic function of the difference between corresponding modes and frequencies of the theoretical model and the test specimen. This technique was applied to some actual vibration test data, and the special techniques that are required to overcome convergence problems are described.

Hall, B. M.↗

Sea ice heat and mass balance measurements from four autonomous buoys during the MOSAiC drift campaign

As part of the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC), four autonomous seasonal ice mass balance buoys were deployed in first- and second-year ice. These buoys measured position, barometric pressure, snow depth, ice thickness, ice growth, surface melt, bottom melt, and vertical profiles of temperature from the air, through the snow and ice, and into the upper ocean. Observed air temperatures were similar at all four sites; however, snow–ice interface temperatures varied by as much as 10°C, primarily due to differences in snow depth. Observed winter ice growth rates (November to May) were <1 cm day -1 , with summer melt rates (June to July) as large as 5 cm day -1 . Air temperatures changed as much as 2°C hour -1 but were dampened to <0.3°C hour -1 at the snow–ice interface. Initial October ice thicknesses ranged from 0.3 m in first-year ice to 1.2 m in second-year ice. By February, this range was only 1.20–1.46 m, due in part to differences in the onset of basal freezing. In second-year ice, this delay was due to large brine-filled voids in the ice; propagating the cold front through this ice required freezing the brine. Mass balance results were similar to those measured by autonomous buoys deployed at the North Pole from 2000 to 2013. Winter average estimates of the ocean heat flux ranged from 0 to 3 W m -2 , with a large increase in June 2020 as the floe moved into warmer water. Estimates of average snow thermal conductivity measured at two buoys during periods of linear temperature profiles were 0.41 and 0.42 W m -1 °C -1 , higher than previously published estimates. Results from these ice mass balance buoys can contribute to efforts to close the MOSAiC heat budget.

54 ENVIRONMENTAL SCIENCES↗

Results of the Magnetometer Navigation (MAGNAV) Inflight Experiment

The Magnetometer Navigation (MAGNAV) algorithm is currently running as a flight experiment as part of the Wide Field Infrarad Explorer Post-Science Engineer- ing Testbed. Initialization of MAGNAV occured on September 4, 2004. MAGNAV is designed to autonomously estimate the spacecraft orbit, attitude, and rate using magnetometer and sun sensor data. Since the earth s magnetic field is a function of time and position, and since time is known quite precisely, the differences between the computed magnetic field and measured magnetic field components, as measured by the magnetometer throughout the entire spacecraft orbit, are a function of the spacecraft trajectory and attitude errors. Therefore, these errors are used to estimate both trajec- tory and attitude. In addition, the time rate of change of the magnetic field vector is used to estimate the spacecraft rotation rate. The estimation of the attitude and tra- jectory is augmented with the rate estimation into an Extended Kalman filter blended with a pseudc-linear Kalman filter. Sun sensor data is also used to improve the accu- racy and observability of the attitude and rate estimates. This test serves to validate MAGNAV as a single low cost navigation system which utilizes reliable, flight qualified sensors. MAGNAV is intended as a backup algorithm, an initialization algorithm, or possibly a prime navigation algorithm for a mission with coarse constraints.

Thienel, Julie↗

Parameter identification for nonlinear aerodynamic systems

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Pearson, Allan E.↗

Vertical wind estimation from horizontal wind measurements

The objective of this study was to assess the ability of simple vertical wind models to improve the hazard prediction capability of an airborne Doppler sensor in a realistic microburst environment. The results indicate that in the altitude region of interest (at or below 300 meters), both the linear and empirical vertical wind models improved the hazard estimate. The radar simulation study showed that the magnitude of the performance improvement was altitude dependent. The altitude of maximum performance improvement occurred at about 300 meters. At the lower altitudes the percent improvement was minimized by the diminished contribution of the vertical wind. The vertical hazard estimate errors from flight tests were less than those of the radar simulation study.

Vicroy, Dan D.↗

Mass center estimation of a drag-free satellite

The mass center location of a spinning drag-free satellite can be estimated because there is control required to accelerate the mass center along the axis of spin as long as there is some nutation in the spinning motion. Linear and nonlinear models are compared and observability discussed. Online estimation fails when nutation is damped so an offline mechanization is proposed. A new sensor has been designed to permit greater relative motion than was possible on the drag-free satellite flown in 1972 (JH-1). Experimental laboratory results using a spinning vehicle with the new sensor mounted 30 cm from a spherical air bearing support are presented which confirm earlier simulation results.

Sanz Fernandez De Cordova, S.↗

Identification evaluation methods

Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.

Klein, V.↗

Sensitivity Analysis of the Human Research Program’s Impact 1.0 Model

Sensitivity analysis estimates the relative contribution of the uncertainty in input values to the uncertainty of model outputs. Partial Rank Correlation Coefficient (PRCC) and Leave One Out (LOO) are methods of conducting sensitivity analysis on non-linear simulation models like the IMPACT Model. The PRCC method estimates the sensitivity using partial correlation of the ranks of the generated input values to each generated output value. The “partial” part is due to the adjustments made for the linear effects of all the other input values in the calculation of correlation between a particular input and each output. LOO removes a medical condition from test suite and calculates the change in the outcome. This is used to identify the influence of the condition input in the model The inputs to the sensitivity procedures include the number of occurrences of each of the one hundred plus IMPACT medical conditions generated over the simulations, and the IMPACT outputs from the MEDPRAT mathematical model. The outputs total task time lost (TTL), number of return to definitive care (RTDC), and number of loss of crew lives (LOCL). The IMPACT team will report the results of using PRCC and LOO on IMPACT 1.0. Tornado plots will assist in the visualization of the condition-related input sensitivities to each of the main outcomes. The outcomes of this sensitivity analysis will drive review focus by identifying conditions where changes in uncertainty, and input values could drive changes in overall model output uncertainty. These efforts are an integral part of the overall verification, validation, and credibility review of IMPACT 1.0.

Sensitivity Anaylsis↗

A Framework for Scaling in Filtering and Linear Covariance Analysis

Scaling is used extensively for numerical optimization and trajectory optimization. Its use in the estimation community is almost nonexistent. This paper creates the framework for practical scaling in space navigation, in general, and linear covariance analysis, in particular.

D'souza, Christopher N.↗

Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.

Park, Michael A.↗

TU-H-BRC-07: Therapeutic Benefit in Spatially Fractionated Radiotherapy (GRID) Using Helical Tomotherapy

Purpose: The aim of this project is to study the therapeutic ratio (TR) for helical Tomotherapy (HT) based spatially fractionated radiotherapy (GRID). Estimation of TR was based on the linear-quadratic cell survival model by comparing the normal cell survival in a HT GRID to that of a uniform dose delivery in an open-field for the same tumor survival. Methods: HT GRID plan was generated using a patient specific virtual GRID block pattern of non-divergent, cylinder shaped holes using MLCs. TR was defined as the ratio of normal tissue surviving fraction (SF) under HT GRID irradiation to an open field irradiation with an equivalent dose that result in the same tumor cell SF. The ratio was estimated from DVH data on ten patient plans with deep seated, bulky tumor approved by the treating radiation oncologist. Dependence of the TR values on radio-sensitivity of the tumor cells and prescription dose were also analyzed. Results: The mean ± standard deviation (SD) of TR was 4.0±0.7 (range: 3.1 to 5.5) for the 10 patients with single fraction dose of 20 Gy and tumor cell SF of 0.5 at 2 Gy. In addition, mean±SD of TR = 1±0.1 and 18.0±5.1 were found for tumor with SF of 0.3 and 0.7, respectively. Reducing the prescription dose to 15 and 10 Gy lowered the TR to 2.0±0.2 and 1.2±0.04 for a tumor cell SF of 0.5 at 2 Gy. In this study, the SF of normal cells was assumed to be 0.5 at 2 Gy. Conclusion: HT GRID displayed a significant therapeutic advantage over uniform dose from an open field irradiation. TR increases with the radioresistance of the tumor cells and with prescription dose.

60 APPLIED LIFE SCIENCES↗

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Kalman filter smoother modeling ocean simulation↗