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NASA NTRS1990

Frequency-Tracking-Error Detector

Frequency-tracking-error detector compares average period of output signal from band-pass tracking filter with average period of signal of frequency 100 f(sub 0) that controls center frequency f(sub 0) of tracking filter. Measures difference between f(sub 0) and frequency of one of periodic components in output of bearing sensor. Bearing sensor is accelerometer, strain gauge, or deflectometer mounted on bearing housing. Detector part of system of electronic equipment used to measure vibrations in bearings in rotating machinery.

Randall, Richard L.↗

NASA NTRS1991

Small convolution kernels for high-fidelity image restoration

An algorithm is developed for computing the mean-square-optimal values for small, image-restoration kernels. The algorithm is based on a comprehensive, end-to-end imaging system model that accounts for the important components of the imaging process: the statistics of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and display reconstruction. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernel values that restore the image with maximum fidelity, that is, the kernel minimizes the expected mean-square restoration error. The algorithm is consistent with the derivation of the spatially unconstrained Wiener filter, but leads to a small, spatially constrained kernel that, unlike the unconstrained filter, can be efficiently implemented by convolution. Simulation experiments demonstrate that for a wide range of imaging systems these small kernels can restore images with fidelity comparable to images restored with the unconstrained Wiener filter.

Reichenbach, Stephen E.↗

NASA NTRS1993

On the 'delta-equations' for vortex sheet evolution

We use a set of equations, sometimes referred to as the 'delta-equations', to approximate the two-dimensional inviscid motion of an initially circular vortex sheet released from rest in a cross-flow. We present numerical solutions of these equations for the case with delta-square = 0 (for which the equations are exact) and for delta-square greater than 0. For small values of the smoothing parameter delta, a spectral filter must be used to eliminate spurious instabilities due to round-off error. Two singularities appear simultaneously in the vortex sheet when delta-square = 0 at a critical time t(c). After t(c), the solutions do not converge as the computational mesh is refined. With delta-square greater than 0, converged solutions were found for all values of delta-square when t is less than t(c), and for all but the two smallest values of delta-square used when t is greater than t(c). Our results show that, when delta-square is greater than 0, the vortex sheet deforms into two doubly branched spirals some time after t(c). The limiting solution as delta approaching 0 clearly exists and equals the delta = 0 solution when t is less than t(c).

Rottman, James W.↗

NASA NTRS1993

Beam-waveguide antenna servo design issues for tracking low earth-orbiting satellites

Upcoming NASA missions will require tracking of low-orbit satellites. As a consequence, NASA antennas will be required to track satellites at higher rates than for the current deep space missions. This article investigates servo design issues for the 34-m beam-waveguide antennas that track low-orbit satellites. This includes upgrading the servo with a feedforward loop, using a monopulse controller design, and reducing tracking errors through either proper choice of elevation pinion location, application of a notch filter, or adjustment of the elevation drive amplifier gain. Finally, improvement of the signal-to-noise ratio through averaging of the over-sampled monopulse signal is described.

Gawronski, W. K.↗

NASA NTRS1997

A Predictive Attitude Determination Algorithm

In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.

Markley, F. Landis↗

NASA NTRS1999

"Novel Techniques in Non-Stationary Analysis of Rotorcraft Vibration Signitures"

This research effort produced new methods to analyze the performance of linear predictors that track non-stationary processes. Specifically, prediction methods have been applied to the vibration pattern of rotorcraft drivetrains. This analysis is part or a larger rotorcraft Health and Usage Monitoring System (HUMS) that can diagnose immediate failures of the subsystems, as indicated by abrupt change in the vibration signature, and prognosticate future health, by examining the vibration patterns against long-term trends. This problem is described by a earlier joint paper co-authored by members of the funding agency and the recipient institutions prior to this grant effort. Specific accomplishments under this grant include the following: (1) Definition of a framework for analysis of non-stationary time-series estimation using the coefficients of an adaptive filter. (2) Description of a novel method of combining short-term predictor error and long-term regression error to analyze the performance of a non-stationary predictor. (3) Formulation of a multi-variate probability density function that quantifies the performance of a adaptive predictor by using the short- and long-term error variables in a Gamma function distribution. and (4) Validation of the mathematical formulations with empirical data from NASA flight tests and simulated data to illustrate the utility beyond the domain of vibrating machinery.

Meng, Teresa↗

NASA NTRS2000

Performance Optimization of a Rotor Alone Nacelle for Acoustic Fan Testing

This paper describes the techniques, equipment, and results from the optimization of a two-axis traverse actuation system used to maintain concentricity between a sting-mounted fan and a wall-mounted nacelle in the 9 x 15 (9 Foot by 15 Foot Test Section) Low Speed Wind Tunnel (LSWT) at the NASA Glenn Research Center (GRC). The Rotor Alone Nacelle (RAN) system, developed at GRC by the Engineering Design and Analysis Division (EDAD) and the Acoustics Branch, used nacelle-mounted lasers and an automated control system to maintain concentricity as thermal and thrust operating loads displace the fan relative to the nacelle. This effort was critical to ensuring rig/facility safety and experimental consistency of the acoustic data from a statorless, externally supported nacelle configuration. Although the tip clearances were originally predicted to be about 0.020 in. at maximum rotor (fan) operating speed, proximity probe measurements showed that the nominal clearance was less than 0.004 in. As a result, the system was optimized through control-loop modifications, active laser cooling, data filtering and averaging, and the development of strict operational procedures. The resultant concentricity error of RAN was reduced to +/- 0.0031 in. in the Y-direction (horizontal) and +0.0035 in./-0.001 3 in. in the Z-direction (vertical), as determined by error analysis and experimental results. Based on the success of this project, the RAN system will be transitioned to other wind tunnel research programs at NASA GRC.

Cunningham, C. C.↗

NASA NTRS2001

Analysis of the Performance Characteristics of the Five-Channel Microtops II Sun Photometer for Measuring Aerosol Optical Thickness and Precipitable Water Vapor

Five Microtops II sun photometers were studied in detail at the NASA Goddard Space Flight Center (GSFC) to determine their performance in measuring aerosol optical thickness (AOT or Tau(sub alphalambda) and precipitable column water vapor (W). Each derives Tau(sub alphalambda) from measured signals at four wavelengths lambda (340, 440, 675, and 870 nm), and W from the 936 nm signal measurements. Accuracy of Tau(sub alphalambda) and W determination depends on the reliability of the relevant channel calibration coefficient (V(sub 0)). Relative calibration by transfer of parameters from a more accurate sun photometer (such as the Mauna-Loa-calibrated AERONET master sun photometer at GSFC) is more reliable than Langley calibration performed at GSFC. It was found that the factory-determined value of the instrument constant for the 936 nm filter (k= 0.7847) used in the Microtops' internal algorithm is unrealistic, causing large errors in V(sub 0(936)), Tau(sub alpha936), and W. Thus, when applied for transfer calibration at GSFC, whereas the random variation of V(aub 0) at 340 to 870 nm is quite small, with coefficients of variation (CV) in the range of 0 to 2.4%, at 936 nm the CV goes up to 19%. Also, the systematic temporal variation of V(sub 0) at 340 to 870 nm is very slow, while at 936 nm it is large and exhibits a very high dependence on W. The algorithm also computes Tau(sub alpha936) as 0.91Tau(sub alpha870), which is highly simplistic. Therefore, it is recommended to determine Tau(sub alpha936) by logarithmic extrapolation from Tau(sub alpha675) and Tau(sub alpha 870. From the operational standpoint of the Microtops, apart from errors that may result from unperceived cloud contamination, the main sources of error include inaccurate pointing to the Sun, neglecting to clean the front quartz window, and neglecting to calibrate correctly. If these three issues are adequately taken care of, the Microtops can be quite accurate and stable, with root mean square (rms) differences between corresponding retrievals from clean calibrated Microtops and the AERONET sun photometer being about +/-0.02 at 340 nm, decreasing down to about +/-0.01 at 870 nm.

Ichoku, Charles↗

NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗

NASA NTRS2014

Assimilation of MODIS Snow Cover Through the Data Assimilation Research Testbed and the Community Land Model Version 4

To improve snowpack estimates in Community Land Model version 4 (CLM4), the Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover fraction (SCF) was assimilated into the Community Land Model version 4 (CLM4) via the Data Assimilation Research Testbed (DART). The interface between CLM4 and DART is a flexible, extensible approach to land surface data assimilation. This data assimilation system has a large ensemble (80-member) atmospheric forcing that facilitates ensemble-based land data assimilation. We use 40 randomly chosen forcing members to drive 40 CLM members as a compromise between computational cost and the data assimilation performance. The localization distance, a parameter in DART, was tuned to optimize the data assimilation performance at the global scale. Snow water equivalent (SWE) and snow depth are adjusted via the ensemble adjustment Kalman filter, particularly in regions with large SCF variability. The root-mean-square error of the forecast SCF against MODIS SCF is largely reduced. In DJF (December-January-February), the discrepancy between MODIS and CLM4 is broadly ameliorated in the lower-middle latitudes (2345N). Only minimal modifications are made in the higher-middle (4566N) and high latitudes, part of which is due to the agreement between model and observation when snow cover is nearly 100. In some regions it also reveals that CLM4-modeled snow cover lacks heterogeneous features compared to MODIS. In MAM (March-April-May), adjustments to snowmove poleward mainly due to the northward movement of the snowline (i.e., where largest SCF uncertainty is and SCF assimilation has the greatest impact). The effectiveness of data assimilation also varies with vegetation types, with mixed performance over forest regions and consistently good performance over grass, which can partly be explained by the linearity of the relationship between SCF and SWE in the model ensembles. The updated snow depth was compared to the Canadian Meteorological Center (CMC) data. Differences between CMC and CLM4 are generally reduced in densely monitored regions.

data assimilation↗

NASA NTRS1987

Investigation, development, and application of optimal output feedback theory. Volume 3: The relationship between dynamic compensators and observers and Kalman filters

Relationships between observers, Kalman Filters and dynamic compensators using feedforward control theory are investigated. In particular, the relationship, if any, between the dynamic compensator state and linear functions of a discrete plane state are investigated. It is shown that, in steady state, a dynamic compensator driven by the plant output can be expressed as the sum of two terms. The first term is a linear combination of the plant state. The second term depends on plant and measurement noise, and the plant control. Thus, the state of the dynamic compensator can be expressed as an estimator of the first term with additive error given by the second term. Conditions under which a dynamic compensator is a Kalman filter are presented, and reduced-order optimal estimaters are investigated.

Broussard, John R.↗

NASA NTRS1983

Autonomous satellite navigation by stellar refraction

This paper describes an error analysis of an autonomous navigator using refraction measurements of starlight passing through the upper atmosphere. The analysis is based on a discrete linear Kalman filter. The filter generated steady-state values of navigator performance for a variety of test cases. Results of these simulations show that in low-earth orbit position-error standard deviations of less than 0.100 km may be obtained using only 40 star sightings per orbit.

Gounley, R.↗

DOE OSTI2020

Radioactive Source Localization via Bayesian Particle Filter

In the event of a misplaced radioactive source or other emergency situation, measuring a radiation field, mapping its distribution, and determining a source location are essential tasks to ameliorating the situation. However, radiation fields may be extremely hazardous to human surveyors and minimizing received radiation doses is just as essential. Robots appear to be a potential solution to these problems. Beyond simply measuring radiation, the robot's computer processing capabilities offer a way to apply complex data analysis methods to radiation measurements in real-time. Methods which predict likely source locations can then feed this information into other processes, potentially improving path planning and enabling more efficient measurements. Given a robot mounted with a gamma-ray detector, can we: develop a methodology to account for detector performance across a wide range of source angles, distances, and photon energies? operate an autonomously navigating robot to effectively survey and characterize an area of interest? implement a data analysis method, conventionally used in measurements of motion, for source localization purposes? An open-source TurtleBot 3 robot, running Robot Operating System (ROS) on Ubuntu 16.04 LTS, was fitted with a Kromek GR1{sup R} Cadmium Zinc Telluride (CZT) solid-state gamma-ray detector. As a part of ROS, the packages OpenSlam, gmapping, and amcl were used to perform Simultaneous Localization and Mapping (SLAM), determining the robot's position and mapping the surrounding area. Data was acquired via Lidar mounted on top the TurtleBot 3. Detector Calibration Fit: The equation was fit to 365 counts of various energies, distances, and angles. A MATLAB{sup R} program was written to simulate measurements taken a robot on a random walk, with count data and positions discretized into finite element pixels. Using this program, a sample of 100 runs was performed on a map with a simulated source at the center, with a total of 200 of 2 pixels each. Similarly, multiple runs of the filter were performed on recorded robot measurement data. In both simulation and real tests, when corrected for errors (particles placed outside of bounds or on the robot, and simulation-specific errors), corresponding t-tests of predicted x and y-coordinates were within a 95% confidence interval of the actual position. For the real trial, these positions are slightly skewed right in the x-axis as the robot remained mainly to the left side of the source within the sample area. These simulations demonstrate potential validity for the usage of a particle filter as method of radioactive source localization. In the future, true real-time implementation and data fusion may further augment the performance of the robot to localize lost sources. Additionally, identification of multiple sources, determination of source types, and usage of a collimator are areas to potentially be explored.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRSDate not supplied

TOWARD A METHOD FOR SCALING HUMAN BODY MODELS IN AN IMU-BASED WORKFLOW

BACKGROUND Scaled biomechanical models can more accurately inform crew health decisions when tailored to the wide range of astronaut sizes. One component to improve scaling of existing models to better represent each unique astronaut’s size is the individual length scaling of limbs. Traditionally, these lengths are determined by motion capture or manual measurement. A new method is herein proposed for length scaling which can be done by measuring linear and angular accelerations at a desired point during isolated motion around a point of rotation, then calculating the distance between the desired point and point of rotation. When an Inertial Measurement Unit (IMU) device is placed at the distal point of a limb, the isolated motion is about that limb’s proximal joint. For example, to measure forearm length, an IMU is placed at the wrist, the point of rotation is at the elbow, and the isolated motion is forearm flexion and extension. These calculated lengths are then used to scale models to each unique astronaut’s size, thereby improving the applicability of the model. This method of scaling limb segments can be used for any limb that has an easily defined proximal joint for the limb to rotate around including hands, arms, legs, feet. Utilizing IMUs for data collection also provides the synergistic ability to record data without a dedicated space in a room with many cameras, therefore reducing the data collection footprint, or record data where optical motion capture is not possible, such as inside a spacesuit. METHODS AND RESULTS To test this method, upper body data collection was performed with 5 Xsens DOT IMUs on a single subject. IMUs consist of an accelerometer, a gyroscope, and a magnetometer which collect linear acceleration, angular velocity, and magnetic fluctuations, respectively. Before any ground-based laboratory collection, the magnetic fluctuations are used to correct the heading of the IMU in space relative to the Earth’s magnetic field. The direct measurement of angular velocity is integrated to calculate angular acceleration. Then the linear acceleration ( a ) and angular acceleration (α) are solved using r = at/α to calculate the radius, which in this case is the distance between the IMU and the point of rotation (i.e., segment length). The IMU must be placed at the most distal point of the limb being measured (i.e., ankle if measuring lower leg length) and the test plan must consist of an isolated motion about that limb’s proximal joint (i.e., knee flexion and extension if measuring lower leg length). The distances (radii) calculated at every time interval were filtered (bandpass filter keeping 5th-90th percentile data) to eliminate outliers and spurious data that occur when the isolated motion was stopped or nearly stopped. The remaining distances were averaged, resulting in the calculated limb length. Scaling factors were then computed by dividing the calculated limb length by the unscaled model’s length. These scale factors are plugged into the Scale Tool in OpenSim [1,2] to apply the scaling to the OpenSim Full Body Rajagopal Model [3,4]. Manual measurements of limb lengths were taken before data collection started and used for comparing against the calculated lengths. The Anthropometric Survey of US Army Personnel (ANSUR II) [5] was also used as a third source of reference for limb length measurements. The following measurements were retrieved from the subject before data collection: 34.5 cm from L1 to C7 (thorax), 25.7 cm from C7 Joint Center (JC) to head vertex (neck and head), 36.3 cm from shoulder JC to elbow JC (humerus), 29.5 cm from elbow JC to wrist JC (forearm), and 16.2 cm from clavicle to acromion (clavicle). Of those five, forearm and humerus lengths were calculated using this proposed method to obtain preliminary results. The forearm length after filtering and averaging was calculated to be 37.6 cm. This is a 28% overestimation from the measured forearm length (29.5 cm). The humerus length after filtering and averaging was calculated to be 47.8 cm. This is a 31% difference from the measured subject length (36.3 cm). Sources of error include imperfect isolated motion (method currently expects that motion should be perfectly circular in a 2D plane, include no rotation of the IMU, and be relatively smooth; a more secure IMU attachment method will help), unrefined filter techniques (removed highest and lowest values with 20% high and low pass filters and no smoothing filters), arbitrary removal of stopped or near stopped data (kept data for only a short range before and after the angular velocity peaking), and a more representative method for removing gravitational acceleration is needed (current method is to zero all accelerations against a baseline taken just before the isolated motion which does not account for the gravitational acceleration changed due to IMU rotation during movement). Addressing these error sources will improve the accuracy of the limb length calculation. Next steps include creating a method for whole-body scaling estimation using individual limb scale factors. Continued pursuit of these techniques is expected to enable acquiring anthropometric information using only IMUs in real-time.

E. K. Marecki↗

NASA NTRS2021

Unsteady Pressure-Sensitive-Paint Shot Noise Reduction

In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.

Lucy Tang↗

NASA NTRS2021

Unsteady Pressure-Sensitive Paint (UPSP) Shot Noise Reduction

Lucy Tang↗

NASA NTRS1976

A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study

The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.

Thornton, C. L.↗

DOE OSTI2023

A comparison of past and present computational methods for shape analysis of double-shell x-ray radiographs

Implosion symmetry is a key requirement in achieving a robust burning plasma in inertial confinement fusion experiments. In double-shell capsule implosions, we are interested in the shape of the inner shell as it pushes on the fuel. Shape analysis is a popular technique for studying said symmetry during implosion. Combinations of filtering and contour-finding algorithms are studied for their promise in reliably recovering Legendre shape coefficients from synthetic radiographs of double-shell capsules with applied levels of noise. A radial lineout max(slope) method when used on an image pre-filtered with non-local means and a variant of the marching squares algorithm are able to recover p 0 , p 2 , and p 4 maxslope Legendre shape coefficients with mean pixel discrepancy errors of 2.81 and 3.06, respectively, for the noisy synthetic radiographs we consider. Here, this improves upon prior radial lineout methods paired with Gaussian filtering, which we show to be unreliable and whose performance is dependent on input parameters that are difficult to estimate.

47 OTHER INSTRUMENTATION↗