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This article presents a case study motivated by a plot of data that suggested an emerging trend that the authors were faced with explaining. When the measurement error of the data is accounted for, it turns out there was no real trend. Furthermore, this article shows how to use a Bayesian modeling approach to account for the measurement error.
A direct inversion method for inverting the temperature profile from satellite-measured radiation is discussed. The nth power of the weighting function in the integral radiative-transfer equation is used as the weight in the averaging process. The vertical resolution of the inverted temperature profile and the response of the inverted temperature profile to the measurement errors are examined in terms of n. It is found that for smaller values of n, the vertical resolution and the effect of measurement errors are reduced. When n = 0, both the vertical resolution and error effect are minimum. The temperature profile is adjusted by a constant; any structure different from the initial shape cannot be resolved. This is equivalent to the case where the entire atmosphere is treated as one layer with a fixed shape of temperature profile. When n approaches infinity, both the vertical resolution and error effect are maximum. This is equivalent to the case where the entire atmosphere is divided into m (the number of spectral channels) layers. Within each layer, the temperatures are adjusted by a constant, and any structure different from the initial shape cannot be resolved. Also, the shape of the final solution is closer to the initial profile if the value of n is smaller.
The effect was examined of aircraft position and attitude, of measurement errors, and of computational approximations on the size, shape, and position of a perspective radar image of an airport runway as might be displayed by an independent landing monitor in transport aircraft. The effect on runway image geometry was examined for different aircraft attitudes and different aircraft positions relative to a standard three degree glide slope. Measurement errors investigated were errors in radar azimuth angle and range, and errors in those aircraft parameters supplied to the radar for use in converting the radar image into a perspective format (namely pitch, roll, and altitude). Also investigated were the effects of using certain mathematical approximations, such as small angle, in the coordinate transformation which converts the image to a perspective format.
The effects of measurement errors appearing during the implementation of the microwave holographic technique are investigated in detail, and many representative results are presented based on computer simulations. The numerical results are tailored for cases applicable to the utilization of the holographic technique for the NASA's Deep Space Network antennas, although the methodology of analysis is applicable to any antenna. Many system measurement topics are presented and summarized.
In this article, we analyze observed count data such as the number of defects in a steel product where the observed counts are the true counts measured with errors. We account for the measurement error by using a measurement error model based on a latent lognormal (LLN) distribution. We consider making inference about a single population (e.g., from samples of a production lot) and a regression model (e.g., from runs of a designed experiment), where the measurement system properties are known, that is, the parameters of the LLN distribution are known. Then, we consider simultaneous inference for the single population and regression model as well as the measurement system. We demonstrate the proposed methodology with both simulated and real observed counts.
Regression analysis procedures for evaluating tracking system measurement errors
Beginning in 2025, the NASA Quesst mission will conduct a series of community response tests involving flyovers of the X-59 aircraft at select localities across the United States. Several waves of a longitudinal survey will be administered over approximately one month of testing in order to capture perceptual responses to low-amplitude sonic booms, or “sonic thumps”. Simultaneously, noise exposure levels will be estimated by fusing model-based predictions with measurements taken from a sparse network of monitors in the region. As one of the aims of the study is to produce a dose-response curve, a regression model relating perceptual response to noise exposure levels, it is important to acknowledge the potential attenuation bias that results from measurement error in the estimated noise exposure levels. In this presentation we review and compare several methods for dealing with measurement error in generalized linear mixed models. The methods are demonstrated on simulated data and real data collected during past NASA risk reduction studies.
Statistical feedback optimization of linear stochastic systems with measurement errors
Abstract In this research, we propose an Error Separation Technique (EST) based on optical fiber sensors for on-machine straightness error measurement. Two fiber optic Fabry–Pérot interferometers have been developed serving as two displacement sensors. The displacement distance is computed according to the reflected spectrum from interferometers, which can achieve a sub-micrometer resolution. The two-point method has been employed to separate the straightness error of the slides and the profile error of a fine-polished standard block. The spacing distance between two interferometers is determined by the diameter of optical fibers so that the EST's resolution has the potential to reach the sub-millimeter scale. In the experiment, the straightness error has been measured on a commercially available computer numerical control machine tool, and the measurement has been conducted on its x-axis. The spacing distance between two optical fiber sensors is 1.5 mm which equals the EST's resolution along the machine tool's x-axis. The separated profile error of the measured standard block is around 30 µm which has been verified by a high precision Coordinate Measurement Machine (CMM). The magnitude of the separated straightness error is around 40 µm. This technique is flexible and simple to be conducted, which can contribute to the micro-machine tool calibration and other straightness error applications.
Deflectometric profilometers are used to precisely measure the form of beam shaping optics of synchrotrons and X-ray free-electron lasers. They often utilize autocollimators which measure slope by evaluating the displacement of a reticle image on a detector. Based on our privileged access to the raw image data of an autocollimator, novel strategies to reduce the systematic measurement errors by using a set of overlapping images of the reticle obtained at different positions on the detector are discussed. It is demonstrated that imaging properties such as, for example, geometrical distortions and vignetting, can be extracted from this redundant set of images without recourse to external calibration facilities. This approach is based on the fact that the properties of the reticle itself do not change – all changes in the reticle image are due to the imaging process. Firstly, by combining interpolation and correlation, it is possible to determine the shift of a reticle image relative to a reference image with minimal error propagation. Secondly, the intensity of the reticle image is analysed as a function of its position on the CCD and a vignetting correction is calculated. Thirdly, the size of the reticle image is analysed as a function of its position and an imaging distortion correction is derived. It is demonstrated that, for different measurement ranges and aperture diameters of the autocollimator, reductions in the systematic errors of up to a factor of four to five can be achieved without recourse to external measurements.
The Ocean Color Instrument on NASA’s PACE mission is a 322 887 nm hyperspectral imager with 1 km x 1 km nadir spatial resolution and 5 nm spectral resolution utilizing charge-coupled devices (CCDs) operating in Time Delay Integration (TDI) mode where each TDI column represents a different wavelength in 0.625 nm increments. After TDI, the charge is moved into serial output pixels and read out. The spatial resolution requires an 8.5 MHz readout rate. This only allows 59 ns for the CCD reset and video to be asserted and settled before sampling. The response exhibits serial pixel-to-pixel readout interference due to the lack of full settling. Each serial pixel value has a dependence on the value of the preceding pixel value. This leads to a spectrally dependent radiometric measurement error of up to 0.3 %. We explain the operation of the detection system, the behavior of the interference, and show the resulting measurement error based on data from both ground testing and on-orbit characterization.
The Ocean Color Instrument on NASA’s PACE mission is a 322 887 nm hyperspectral imager with 1 km x 1 km nadir spatial resolution and 5 nm spectral resolution utilizing charge-coupled devices (CCDs) operating in Time Delay Integration (TDI) mode where each TDI column represents a different wavelength in 0.625 nm increments. After TDI, the charge is moved into serial output pixels and read out. The spatial resolution requires an 8.5 MHz readout rate. This only allows 59 ns for the CCD reset and video to be asserted and settled before sampling. The response exhibits serial pixel-to-pixel readout interference due to the lack of full settling. Each serial pixel value has a dependence on the value of the preceding pixel value. This leads to a spectrally dependent radiometric measurement error of up to 0.3 %. We explain the operation of the detection system, the behavior of the interference, and show the resulting measurement error based on data from both ground testing and on-orbit characterization.
Analysis of effect of design and measurement errors on pump performance parameters
Postflight tracking system measurement error evaluation using regression analysis for Apollo Saturn 1B flight tests
The effects of horizontal and vertical data resolution, data density, data location, different objective analysis algorithms, and measurement error on mesoscale-forecast accuracy are studied with observing-system simulation experiments. Domain-averaged errors are shown to generally decrease with time. It is found that the vertical distribution of error growth depends on the initial vertical distribution of the error itself. Larger gravity-inertia wave noise is produced in forecasts with coarser vertical data resolution. The use of a low vertical resolution observing system with three data levels leads to more forecast errors than moderate and high vertical resolution observing systems with 8 and 14 data levels. Also, with poor vertical resolution in soundings, the initial and forecast errors are not affected by the horizontal data resolution.
System measures timing errors between signals produced by three asynchronous time-code generators. Errors between 1-second clock pulses resolved to 2 microseconds. Basic principle of computation of timing errors as follows: central processing unit in microcontroller constantly monitors time data received from time-code generators for changes in 1-second time-code intervals. In response to any such change, microprocessor buffers count of 16-bit internal timer.
This report describes a study performed by the Colorado Center for Astrodynamics Research (CCAR) on GPS measurement errors in the Codeless GPS Attitude Determination System (CGADS) due to noise and multipath interference. Preliminary simulation models fo the CGADS receiver and orbital multipath are described. The standard FFT algorithms for processing the codeless data is described and two alternative algorithms - an auto-regressive/least squares (AR-LS) method, and a combined adaptive notch filter/least squares (ANF-ALS) method, are also presented. Effects of system noise, quantization, baseband frequency selection, and Doppler rates on the accuracy of phase estimates with each of the processing methods are shown. Typical electrical phase errors for the AR-LS method are 0.2 degrees, compared to 0.3 and 0.5 degrees for the FFT and ANF-ALS algorithms, respectively. Doppler rate was found to have the largest effect on the performance.
A technique is presented for determining the error in diurnal irradiance measurements that results from the non-Lambertian behavior of a reference panel under various irradiance conditions. Spectral biconical reflectance factors of a spray-painted barium sulfate panel, along with simulated sky radiance data for clear and hazy skies at six solar zenith angles, were used to calculate the estimated panel irradiances and true irradiances for a nadir-looking sensor in two wavelength bands. The inherent errors in total spectral irradiance (0.68 microns) for a clear sky were 0.60, 6.0, 13.0, and 27.0% for solar zenith angles of 0, 45, 60, and 75 deg, respectively. The technique can be used to characterize the error of a specific panel used in field measurements, and thus eliminate any ambiguity of the effects of the type, preparation, and aging of the paint.