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Geophysical and remote sensing products that rely on Poisson-distributed measurement signals, such as cosmic-ray neutron sensing (CRNS) and gamma spectrometry, often face challenges due to inherent Poisson noise. Common techniques to enhance signal stability include data aggregation or smoothing (e.g., moving averages and interpolation). However, these methods typically reduce the ability to resolve detailed temporal (stationary data) and spatial (mobile data) features. In this study, we introduced a method for contextual noise suppression tailored to Poisson-distributed data, utilizing a discrete score attribution system. This score filter evaluates each observation against eight different criteria to assess its consistency with surrounding values, assigning a score between 0 (very unlikely) and 8 (very likely) to indicate whether the observation is likely to act as noise. These scores can then be used to flag or remove data points based on user-defined thresholds. We tested the score filter's effectiveness on both stationary and mobile CRNS data, as well as on gamma-ray spectrometry and electromagnetic induction (EMI) recordings. In our examples, the score filter consistently outperformed established filters, for example Savitzky–Golay and Kalman, in direct competition when applied to CRNS time series data. Additionally, the score filter substantially reduced Poisson noise in mobile CRNS, gamma-ray spectrometry and EMI data. The scoring system also provides a context-sensitive evaluation of individual observations or aggregates, assessing their conformity within the dataset. Given its general applicability, customizable criteria and very low computational demands, the proposed filter is easy to implement and holds promise as a valuable tool for denoising geophysical data and applications in other fields.

The scanning of weld seams can be used to evaluate the local weld toe geometry for fatigue assessments. Laser scanned weld seam profiles often contain noise which complicates the accurate measurement of the weld toe geometry. For that reason, filtering of the scanned data is necessary. The issue at hand is that a filtering method can significantly affect the measurement results. Therefore, a calibration of the filter input parameters is needed. In this study, a calibration method for filtered laser-scanned weld profiles is presented by using artificial weld toe geometries. The adjustment of different filter functions is achieved by using an optimization method on predefined weld toes with an artificial noise. The resulting input data for the filter functions is tested on a real specimen to verify the method. Through the calibration method it is possible to achieve satisfactory measurement results with precisely set input parameters for the filter functions. The most suitable filter functions for the measurement of the weld toe are the Gaussian and the Lowpass filter. Both functions are adequate as a universally applicable filter. For the evaluation of the measurement results of the radii and angles, a tolerance range is introduced, which is defined by the theoretically minimum measurable radii and angles. Using an adjusted Lowpass filter and a point distance of 0.07 mm set by the laser scanner, a measurement within the tolerance range of 0.2 mm is achievable for the weld toe radius. For the weld toe angle, the tolerance range of 1.5° is achieved for the majority of measurements.

Clustering forms a major part of showing different relations between data points. Real-time clustering algorithms can visualise relationships between elements in a 3D environment, provide an analysis of data that is separate from the underlying structure and show how the data changes over time. This paper analyses whether conventional clustering algorithms can be adapted to real-time dynamic data while remaining stable over time. By implementing an agglomerative hierarchical clustering algorithm combined with an exponential decay smoothing function, this paper tested several different distance functions and compared their resulting clusterings. It then derives a stable distance function for clustering sailboat competitors during a regatta and compared different smoothing values to see the impact on the final result. The paper shows that an adaptively chosen smoothing value provides the best balance between cluster stability and an intuitive visualisation. This paper concludes this solution can be used and adapted to fit a multitude of applications by changing the distance function and the clustering depth., CSE3000 Research Project, Computer Science and Engineering

Clustering forms a major part of showing different relations between data points. Real-time clustering algorithms can visualise relationships between elements in a 3D environment, provide an analysis of data that is separate from the underlying structure and show how the data changes over time. This paper analyses whether conventional clustering algorithms can be adapted to real-time dynamic data while remaining stable over time. By implementing an agglomerative hierarchical clustering algorithm combined with an exponential decay smoothing function, this paper tested several different distance functions and compared their resulting clusterings. It then derives a stable distance function for clustering sailboat competitors during a regatta and compared different smoothing values to see the impact on the final result. The paper shows that an adaptively chosen smoothing value provides the best balance between cluster stability and an intuitive visualisation. This paper concludes this solution can be used and adapted to fit a multitude of applications by changing the distance function and the clustering depth., CSE3000 Research Project, Computer Science and Engineering

Data smoothing is often required within the environmental data analysis. A number of methods and algorithms that can be applied for data smoothing have been proposed. This paper gives an overview and compares the performance of different smoothing procedures that estimate the trend in the data, based on the surrounding noisy observations that can be applied on environmental data. The considered methods include kernel regression with both global and local bandwidth, moving average, exponential smoothing, robust repeated median regression, trend filtering and approach based on discrete Fourier and discrete wavelet transform. The methods are applied to real data obtained by measurement of PM10 concentrations and compared in a simulation study., info:eu-repo/semantics/openAccess

Data smoothing is often required within the environmental data analysis. A number of methods and algorithms that can be applied for data smoothing have been proposed. This paper gives an overview and compares the performance of different smoothing procedures that estimate the trend in the data, based on the surrounding noisy observations that can be applied on environmental data. The considered methods include kernel regression with both global and local bandwidth, moving average, exponential smoothing, robust repeated median regression, trend filtering and approach based on discrete Fourier and discrete wavelet transform. The methods are applied to real data obtained by measurement of PM10 concentrations and compared in a simulation study., info:eu-repo/semantics/openAccess

Data smoothing is often required within the environmental data analysis. A number of methods and algorithms that can be applied for data smoothing have been proposed. This paper gives an overview and compares the performance of different smoothing procedures that estimate the trend in the data, based on the surrounding noisy observations that can be applied on environmental data. The considered methods include kernel regression with both global and local bandwidth, moving average, exponential smoothing, robust repeated median regression, trend filtering and approach based on discrete Fourier and discrete wavelet transform. The methods are applied to real data obtained by measurement of PM10 concentrations and compared in a simulation study., info:eu-repo/semantics/openAccess

Data smoothing is often required within the environmental data analysis. A number of methods and algorithms that can be applied for data smoothing have been proposed. This paper gives an overview and compares the performance of different smoothing procedures that estimate the trend in the data, based on the surrounding noisy observations that can be applied on environmental data. The considered methods include kernel regression with both global and local bandwidth, moving average, exponential smoothing, robust repeated median regression, trend filtering and approach based on discrete Fourier and discrete wavelet transform. The methods are applied to real data obtained by measurement of PM10 concentrations and compared in a simulation study.

As collective motion plays a crucial role in modern day robotics and engineering, it seems appealing to seek inspiration from nature, which abounds with examples of collective motion (starling flocks, fish schools etc.). This approach towards understanding and reverse-engineering a particular aspect of nature forms the foundation of this dissertation, and its main contribution is threefold. First we identify the importance of appropriate algorithms to extract parameters of motion from sampled observations of the trajectory, and then by assuming an appropriate generative model we turn this into a regularized inversion problem with the regularization term imposing smoothness of the reconstructed trajectory. First we assume a linear triple-integrator model, and by penalizing high values of the jerk path integral we reconstruct the trajectory through an analytical approach. Alternatively, the evolution of a trajectory can be governed by natural Frenet frame equations. Inadequacy of integrability theory for nonlinear systems poses the utmost challenge in having an analytic solution, and forces us to adopt a numerical optimization approach. However, by noting the fact that the underlying dynamics defines a left invariant vector field on a Lie group, we develop a framework based on Pontryagin's maximum principle. This approach toward data smoothing yields a semi-analytic solution. Equipped with appropriate algorithms for trajectory reconstruction we analyze flight data for biological motions, and this marks the second contribution of this dissertation. By analyzing the flight data of big brown bats in two different settings (chasing a free-flying praying mantis and competing with a conspecific to catch a tethered mealworm), we provide evidence to show the presence of a context specific switch in flight strategy. Moreover, our approach provides a way to estimate the behavioral latency associated with these foraging behaviors. On the other hand, we have also analyzed the fli

An ultra-wide bandwidth, full-polarimetric ground penetrating radar (GPR) system operating from 10 MHz to 810 MHz has been applied to the classification of unexploded ordnance (UXO). Late-time radar signatures such as natural resonance and polarization were utilized to separate false alarm objects from UXO-like items with elongated bodies with length-to-diameter ratios greater than three. Additional features such as length, depth and orientation were also extracted from the data. Good classification performance was obtained from the previous Tyndall Test [1] for UXO-like items with inclination angles less than 45 degrees [2], where inclination is measured relative to the approximately horizontal ground surface. That particular test utilized only features extracted from a single radar position, approximately directly above the target. It was later found that this single-position approach contributed to many false alarms and the incapability of classifying UXO s with large inclination angles, such as vertical UXO s. Subsequently, new measurement approaches and additional radar features were developed to reduce the false alarm rate and missed-UXO s. A second field test ( Demo #2), conducted at the Blossom Point UXO Site [3,4], is the subject of this report. An improved system configuration and measurement approach was used to collect GPR data at multiple positions by moving the antenna along a straight line centered at the target spot. Other than 14 known targets, there were 78 blind target positions marked, where either UXO s or clutter items had been emplaced without the test team knowing the target identities. Multiple passes were performed along different orientations through each target position. The new approach provides spatial distributions of scattering response, including both early-time behavior as well as late-time UXO signatures., Prepared in collaboration with the Electroscience Laboratory, the Ohio State University, Columbus.

Three different least-squares methods for processing time-series of satellite sensor data are presented. The first method uses local polynomial functions and can be classified as an adaptive Savitzky–Golay filter. The other two methods are more clear cut least-squares methods, where data are fit to a basis of harmonic functions and asymmetric Gaussian functions, respectively. The methods incorporate qualitative information on cloud contamination from ancillary datasets. The resulting smooth curves are used for extracting seasonal parameters related to the growing seasons. The methods are implemented in a computer program, TIMESAT, and applied to NASA/NOAA Pathfinder AVHRR Land Normalized Difference Vegetation Index data over Africa, giving spatially coherent images of seasonal parameters such as beginnings and ends of growing seasons, seasonally integrated NDVI and seasonal amplitudes. Based on general principles, the TIMESAT program can be used also for other types of satellite-derived time-series data.

Three different least-squares methods for processing time-series of satellite sensor data are presented. The first method uses local polynomial functions and can be classified as an adaptive Savitzky–Golay filter. The other two methods are more clear cut least-squares methods, where data are fit to a basis of harmonic functions and asymmetric Gaussian functions, respectively. The methods incorporate qualitative information on cloud contamination from ancillary datasets. The resulting smooth curves are used for extracting seasonal parameters related to the growing seasons. The methods are implemented in a computer program, TIMESAT, and applied to NASA/NOAA Pathfinder AVHRR Land Normalized Difference Vegetation Index data over Africa, giving spatially coherent images of seasonal parameters such as beginnings and ends of growing seasons, seasonally integrated NDVI and seasonal amplitudes. Based on general principles, the TIMESAT program can be used also for other types of satellite-derived time-series data.

[EN] We use several hydrographic and velocity sections crossing the Gulf Stream to examine how the gradient Richardson number, Ri, is modified due to both vertical smoothing of the hydrographic and/or velocity fields and the assumption of parallel or geostrophic flow. Vertical smoothing of the original (25 m interval) velocity field leads to a substantial increase in the Ri mean value, of the same order as the smoothing factor, while its standard deviation remains approximately constant. This contrasts with very minor changes in the distribution of the Ri values due to vertical smoothing of the density field over similar lengths. Mean geostrophic Ri values remain always above the actual unsmoothed Ri values, commonly one to two orders of magnitude larger, but the standard deviation is typically a factor of five larger in geostrophic than in actual Ri values. At high vertical wavenumbers (length scales below 3 m) the geostrophic shear only leads to near critical conditions in already rather mixed regions. At these scales, hence, the major contributor to shear mixing is likely to come from the interaction of the background flow with internal waves. At low vertical wavenumbers (scales above 25 m) the ageostrophic motions provide the main source for shear, with cross-stream movements having a minor but non-negligible contribution. These large-scale motions may be associated with local accelerations taking place during frontogenetic phases of meanders, [ES] Hemos utilizado varias secciones hidrográficas y de velocidad, que atraviesan la Corriente del Golfo, con el fin de analizar como se modifica el número de gradiente de Richardson, Ri, debido tanto al suavizado vertical de los datos hidrográficos y de velocidad como a la aproximación de flujo geostrófico paralelo. El suavizado vertical de los datos originales de velocidad (intervalo de 25 m) conlleva un aumento substancial del valor medio de Ri, del mismo orden que el factor de suavizado, mientras que la desviación estándar permanece aproximadamente constante. Esto contrasta con los cambios muy pequeños en la distribución de los valores de Ri causados por el suavizado vertical del campo de densidades sobre distancias similares. Los valores medios geostróficos de Ri permanecen siempre por encima de los valores de Ri obtenidos mediante los datos originales de velocidad sin suavizar, típicamente uno o dos órdenes de magnitud mayores, mientras que la desviación estándar de los valores geostróficos usualmente es unas cinco veces mayor que la de los valores reales de Ri. En números de onda verticales altos (escalas de longitud por debajo de 3 m) la cizalla geostrófica solo ocasiona condiciones casi críticas in regiones que ya se encuentran bastante mezcladas. En estas escalas, por tanto, la mayor contribución a la mezcla por cizalla probablemente proviene de la interacción entre el flujo base y las ondas internas. En números de onda verticales bajos (escalas por arriba de 25 m) los movimientos geostróficos proporcionan la fuente principal de cizalla, teniendo los movimientos en la dirección normal al flujo medio una contribución pequeña pero no despreciable. Estos movimientos a escalas largas pueden estar asociados con aceleraciones locales que tienen lugar durante fases frontogenéticas de meandros

The objectives of this report were: (1) to apply off-line post- mission smoothing to raw real-time estimates of the changes in the deflection of the vertical as collected by the Rapid Geodetic Survey System (RGSS) at White Sands; (2) to analyze the residual errors in the smoothed estimates of the changes in the deflection of the vertical for those runs where reference change information was available to determine significant sources of estimate degradation; and (3) to recommend a further course of action as a result of this analysis which should lead to improvement in the deflection recovery accuracy of the RGSS.

A new algorithm for error detection and smoothing, EDS, has been developed for infrared image data. Numerical validation indicates that EDS detects more than 99% of all significant errors. Operating in the time domain, EDS exploits smoothness criteria calculated from laboratory point source measurements, and isolates error bursts via a region-growing approach. EDS is applicable to data from any optical scanner whose output is sampled digitally multiple times per dwell. (Author)

Seismograms were synthesized by the Gaussian beam method and ray trajectories were plotted for a plane wave incident on a 3-D structure obtained from block inversion of teleseismic travel times observed at a local array in central California. The amplitude variations for the given profile are smaller than the order of magnitude variations typically observed. Since amplitudes are sensitive to smaller scale velocity features than travel times, this may indicate that a single scale block model may have difficulty in satisfying both travel time and amplitude. The synthesis of teleseismic body waves by either the Gaussian beam, Maslov, or Kirchhoff techniques entails the integration of dynamic and kinematic ray tracing equations over parts of the model having 3-D as well as 1-D velocity variations. The longest integration intervals are over the 1-D or radially symmetric part of the model. A procedure consisting of the multiplication of propagator matrices can be used to smoothly patch analytic solutions of the dynamic equations obtained over the 1-D or radially symmetric part of the model into numerical solutions obtained over the parts of the model having 3-D velocity variations. (Author)

The FORTRAN program SMOOFF (SMOOthing by a Filtered Fourier transform) smooths a noisy function of two variables on a rectangular domain, by minimizing an appropriate functional subject to a least squares constraint. Keywords: Image processing; Data smoothing; Least squares method; Fourier transformation; SMOOFF computer program; Spate 8000 stress analyzer.

The performance of an extended Kalman filter used to track a maneuvering surface target using HFDF lines-of-bearing is substantially improved by implementing a fixed interval smoothing algorithm and a maneuver detection method that uses a noise variance estimator process. This tracking routine is designed and implemented in a computer program developed for this thesis. The Hall noise model is used to accurately evaluate the performance of the tracking algorithm in a noisy environment. Several tracking scenarios are simulated and analyzed. The application of the Kalman tracker to a tropical storm tracking is investigated. Actual storm tracks obtained from the Joint Typhoon Warning Center in Guam, Mariana Islands are used for this research.

The Algorithm presented in this report is designed for use in smoothing 3-D data at NUWES. It uses fourth-order sequential differences to screen the data for outliers and then a special form of least-squares smoothing is performed to select an appropriate low-order polynomial and fit it to seven-point data segments.

The general track smoothing program (MASM3DRJ) in use at NUWES uses linear, parabolic, and logarithmic functions to fit 3-D data files on torpedo paths by the method of least squares. Polynomial functions of the first (linear), second (parabolic), third, and fourth orders were fitted to data for a variety of path segments of a torpedo run at NUWES using the method of least squares. Results suggest expansion of the program to include higher order polynomials and fitting shorter path segments will provide substantial reduction in residual errors. The method of sequential differences was tried on the data and can be incorporated in the smoothing program as a means of identifying outlier data points and of selecting the appropriate polynomial order for fitting the data.

The formal theory of linear error propagation is applied to the data smoothing and profile inversion routines of the plume diagnostic code EMABIC. In addition to the normal operation of retrieving the radial temperature and concentration profiles of the plume from measured transverse profiles of emission and absorption, EMABIC can now automatically estimate the accuracy of retrieval from estimates of the experimental random error of the measurements. An application of the method is made for a case previously examined with an empirical error propagation method. The present results are essentially in agreement with those of the previous study., See also Rept. no. AFRPL-TR-78-60, ADA068437.

A Kalman filter and smoother which uses data from position measuring instrumentation to estimate changes in position, velocity, and acceleration is derived in detailed analytic form. The filtering and smoothing characteristics are shown to be completely determined by a single nondimensional parameter, which itself is a simple function of the input parameters to the filter. The concept of the bandwidth of the filter and the smoother is examined, and analytic expressions are derived for the bandwidth of the smoother, and of the filter with respect to position. The analysis highlights situations in which the smoother is clearly superior to the filter.

The SHORAD C2 system consists of the equipment necessary to provide command and control capability for Army divisional and non-divisional Air Defense Artillery (ADA). This report describes a technique for smoothing noisy track data using a GHK discrete time-recursive state estimator program. This computer program was developed as part of an analysis of SHORAD track management functions. This system will show how accurately a target can be tracked given the appropriate input values.

The proposed BASIC program for smoothing NUWES data uses the Least-Squares Mehtod to fit a polynomial to a 7-point data segment. It determines the best fitting polynomial of order 1, 2, or 3 and establishes an estimate for the coordinate at the time in the center of the data segment. It also establishes a Figure-of-Merit (FM) for that estimate. This program is designed specifically for treatment of outliers and missing points but it can also be used for smoothing of other observations. It is intended to be used as the basic smoothing program for NUWES data and to provide a value of FM for each observation time for feedback to the Instrumentation Department. Values of the FM's also provide information for other users of the smoothed data on it's quality (i.e., how well the smoothed values can be expected to represent the actual path of a vehicle).

The flexible resolution/truncation baseline version of the AFGL global spectral model as adapted to the CRAY-1 is described. A series of low-resolution (6 layer, rhomboidal 15) and high-resolution (12 layer, rhomboidal 30) forecasts were run and compared to test the performance of the model. In general, higher resolution resulted in improved forecast skill in the 24-to-96-hour range. The only exception to this is the humidity forecast, which shows minimal skill. This characteristic is rather insensitive to the resolution partly because of the poor quality of analyzed humidity fields used for initial data and verification. The original gridded (2.5 X 2.5 deg) topography has been replaced by a smoothed terrain field that has been passed through a nine-point smoother, interpolated to the model's Gaussian grid, and then spectrally truncated. Finally, the effects of initialization have been studied by comparing a series of forecasts subjected to several initialization methods. For forecasts beyond 24 hours, the model is able to supress spurious gravity waves through the combined effects of the semi-implicit time scheme and the subgrid scale diffusion. The impact of normal mode initialization is seen mainly in the very short-range forecasts (less than 24 hours) and is thus important for providing smooth first-guess fields for the analysis/data assimilation cycle. Keywords: Atmospheric models; Spectral models; Weather forecasting; Numerical weather prediction; Global atmospheric circulation.

The Kenyon knotmeter on the R/V ATHENA was calibrated at sea. The calibration method is based on use of the ship's LORAN-C and CC-2 computer to provide a measure of ship speed relative-to-ground. However, the calibration procedure also accounts for ocean current speed and direction. Thus the technique results in an accurate measure of ship speed relative-to-water upon which the knotmeter calibration can be based. Calibration data indicate that the sensor is subject to friction and other factors which results in prior underestimation of speed through the water from about 1.5 knots at low speed (below 15 knots) to 2.25 knots at high speed (15 to 30 knots). This report presents both the method of calibration and the new Kenyon knotmeter calibration curve. The variation in the sensor output data is examined and recommendations are made regarding smoothing of the output data. (Author)

Data obtained during flight trials on a Sea King Mk. 50 helicopter contain significant noise, especially in measurements of components of linear acceleration and angular velocity. Spectral analysis of representative flight data show significant unwanted signal components to be mostly at the rotor frequency and higher harmonics, especially the fifth, which is the blade passing frequency. For channels requiring filtering, two suitable digital Butterworth lowpass filters are designed and their effect demonstrated. Direct representation of the transfer function as a high-order filter is used, in preference to representation as a number of second-order and first-order sub-filters. By using double precision to overcome the usual problems of numerical accuracy with the direct form, the advantages of simplicity and economy of programming effort are realized. For a general-order filter, the mathematical derivation of the filter coefficients in direct form is given. (Author)

The purpose of this study was to assess the value of drifter data taken by NRL for determining horizontal shears in the ocean. The first issue is an evaluation of shears from the smoothed data supplied by NRL along with an assessment of the significance of these evaluations. The other issue is a general assessment of the use of drifters for inferring horizontal shears. It appeared that three tasks were required to resolve these issues. These were: (Task 1) Perform an analysis on drogues 1, 3, 5, 9, 16 and 20 to obtain the differential kinematic properties (shear deformation, normal deformation, vorticity, and horizontal divergence) in a geographic coordinate system (i.e. north and east components); (Task 2) Perform the analysis as stated in Task 1 but with a coordinate system moving with the center of mass of the clusters. Both the large and small scale clusters were analyzed. The results are presented in tables and accompanied by graphs of the functions versus time; and (Task 3) Make a qualitative assessment of the calculation and the effect of turbulent processes.

In relatively recent years, several algorithms for smoothing of time series have been proposed by statisticians. Some of the simpler such algorithms have been also applied in several engineering applications such as Image Processing. The smoothing problem and the implied objective have not been formalized and stated, however. This fact presents a serious handicap when different smoothing algorithms are to be compared in terms of their performance. In this paper, we take a fresh and daring approach to the whole smoothing problem. We formalize the problem as the extraction of a low entropy process from a high entropy process, and as a result we present a constructive theory of parametric and robust data smoothers. We claim that parametric data smoothers are analog-to-digital converters, and that robust data smoothers are stochastic such converters. (Author)

This study extends the technique for computing the smoothed impulse response to the case of scattering from triangular plates, quadrilateral plates, and more refined aircraft models that consist of a cylindrical fuselage with triangular or quadrilateral plates for the wings, stabilizers, and rudder. To the knowledge of Sperry, this is the first time that a successful solution of these problems has been obtained. The numerical techniques developed consisted of the simultaneous solution of two vector space-time integral equations. A major effort was required in order to handle non-rectangular plate geometries. The resulting numerical procedure consisted of a set of local coordinate transformations in the plate edge regions in order to be able to properly satisfy the boundary conditions on the surface currents. Results were computed for several triangular plates, finned cylinders, and a MIG-21 aircraft model. These results were found to be in good agreement with measurements taken on the Sperry time domain scattering range. In addition measured results were obtained for the response of scattering centers when coated with RAM (Radar Abosrbing Materials). These results show that RAM can lower the scattered response but that the amount of reduction is dependent upon the spectrum of the illumination and the aspect angle. Moreover, there were several frequencies where the RCS experienced nulls of an additional 8-10 db.

Techniques for detecting tactical targets on Forward-Looking Infrared (FLIR) imagery are being investigated. The principal topics covered include target and background models, object extraction and classification, and hardware technology applicable to real-time implementation.

It is shown how the problem of estimating a smooth surface on a rectangle in Euclidean p-space, which is measured discretely and with normally distributed errors, reduces to the problem of estimating the mean of a multivariate normal vector. Two empirical Bayes type estimates are noted, and it is observed that cross-validation is useful in certain cases. (Author)

This paper is a survey of methods for fitting a surface to a set of data scattered throughout a plane region. The methods surveyed include interpolation, smoothing, least-squares, and a variety of other direct and approximation methods. The fitting functions include polynomials, rationals, splines, and others. Numerical methods are emphasized, and contouring is also discussed. (Author)

An optimal smoothing technique for processing survey navigation data is described, and a FORTRAN 4 computer program implementation is presented. The technique makes efficient use of navigation redundancy to produce an improved survey plot. The smoothing program, capable of operation in a variety of navigation modes, has been exercised using real and simulated survey data and is shown to have significant accuracy advantages. (Author)

This paper describes a variable smoothing method which was developed to compute closed bomb burning rates. For the variable smoothing method, the smoothing interval is gradually decreased as the pressure increases. The data can be smoothed to within one point of the silvering pressure without any inaccuracies resulting from using data in that region. The variable smoothing method was used for computing burning rates for Navy LOVA and NACO propellant and was found to be preferable over the fixed smoothing method because accurate burning rates could be obtained to much higher pressures. Also in this report, a smoothing routine with a second-degree polynomial fit is compared to a routine with a third-degree polynomial fit. The second-degree polynomial required a considerably smaller smoothing interval than the third-degree polynomial for a smooth pressure-time curve., This article is from JANNAF (Joint Army-Navy-NASA-Air Force) Combustion Meeting (21st) Held at Laurel, Maryland on 1-4 October 1984. Volume 1, AD-A150 981, p335-345.

PCFIT is a user-friendly, menu-driven, curve-fitting utility for minicomputer application. Eleven common functions in addition to data smoothing and data plotting are included. This document is a user's guide to the use of the code, complete with example cases. (Author)

For several years the authors have been evaluating and developing numerical simulation schemes for compressible, two dimensional inviscid or viscous flows in turbomachinery cascades. Numerical schemes considered, all originally classified as time-marching schemes, include: 1) implicit approximate factorization schemes; 2) explicit schemes due to MacCormack; 3) explicit central difference schemes; and 4) the mult-grid scheme of Ni. As we develop these schemes we came to believe that the accuracy of computational results is relatively insensitive to the numerical algorithm chosen but highly sensitive to implementation details such as boundary conditions, consistent flux balancing, grid resolution and numerical smoothing. To illustrate our viewpoint, we present an examination of the relationship between a flux balancing interpretation of the control volume conservation laws and various finite difference formulations and comparisons of the performance of these schemes on three test problems: Ni's bump in a channel, a supersonic nozzle, and flow in a supercritical compressor cascade., Presented at the AIAA Aerospace Sciences Meeting (21st) 10-13 Jan 83, Reno, NV.

The data reduction procedures used in obtaining fully processed data from raw flight data for trials on a Sea King Mk. 50 helicopter are given. The procedures allow various corrections and calibrations to be applied, removal of noise, and calculation of many additional quantities, some of which are used for kinematic consistency checking purposes. Examples are provided on the running of the various computer programs developed. To assist in the use of the data for validation of the Sea King mathematical model, output is obtained in a form allowing ready comparison between trials and model results on the same graphs. (Author)

This report describes and documents an adaptive control algorithm currently used in the Propulsion Wind Tunnel Transonic and Supersonic tunnels for the acquisition of steady-state pressure data using pneumatic commutators. The algorithm employs a classification process to determine whether or not data smoothing is required. If filtering is required, then a self-adjusting arithmetic averaging technique is used. Data obtained using the algorithms are acquired subject to both a settling criterion and a time constraint. The report contains a description of the basic instrumentation system and adaptive control algorithm. (Author)

The purpose of this tutorial report is to allow the reader with a limited background in optimum estimation techniques and/or inertial system theory to achieve a level of competence which will permit his participation in the design and evaluation of aided inertial guidance systems. To this end, the Kalman filter is described in some detail, with full use made of intuitive concepts. Next, the theory of inertial navigation is presented. Based on an understanding of inertial systems and the Kalman filter, the reader is then shown how the two are combined to provide accurate, aided inertial systems. Problems arising in the application of the Kalman filter to practical situations are discussed and common methods for solving them are illustrated. Examples in inertial navigation, gyrocompassing, and alignment transfer are provided in support of the theoretical development.

See also Rept. no. NRL-3959.

A procedure to use the Spline interpolation technique on an arbitrarily prescribed two-dimensional data field is described. In order to use this technique it is necessary to obtain an initial approximation to the data at the grid points. This is achieved by fitting spherical surfaces to the data. Bi-directional Spline interpolation was then applied repeatedly on the grid point estimates of the data to produce convergence to the true surface. The Spline interpolation technique and another objective analysis technique developed by Gilchrist and Cressman are tested against an exact solution and the resulting analyses are compared. Real temperature, geopotential height, and wind data for various pressure surfaces are analysed by the Spline method and the results are compared to the subjective analyses of the same data.

The object of the HITVAL program is to verify the validity (or lack thereof) of mathematical models used to calculate the probability of hit of aircraft fired at by antiaircraft guns. To accomplish this validation of models, a field test was conducted in which aircraft were flown past antiaircraft guns, while their flight paths were recorded by cinetheodolites. The antiaircraft gun crews simulated fire at the aircraft, and instrumentation recorded (among other things) the gun pointing angles. Given the aircraft flight paths, the gun pointing angles, and ballistics data, a probability of hit can be calculated, which can then be used as a standard of comparison for the mathematical models. This paper reports the findings of an analysis of the mount tilt data as recorded by the instrumentation during preliminary trials of the field test. The analysis was conducted to determine if the data need to be smoothed (i.e., whether there is high-frequency noise in the data). The result of the mathematical examination of the spectral structure of the power in the mount tilt data is that the data do contain significant high-frequency noise, and therefore the filtering procedure is necessary.

Two computer programs have been written in the FORTRAN language for use on amino acid chromatographic data obtained by using a multicolumn amino acid analyzer. The first program computes peak areas and the second, final concentrations of individual amino acids. The logic of the programs is presented, including: data collection and editing; data smoothing; location of peaks; baseline identification; correction for baseline drift; peak area computation; peak identification; and comparison of unknown peak areas with corresponding standard peak areas.

In this paper the authors present a local method for data smoothing which is modelled after the manual loft in the ship building industry. The method very effectively solves the outlier problem in statistics, and is superior to the well-known global procedures such as the Schoenberg-Reinsch spline algorithm when it is known that the points have only isolated errors or isolated large errors.

Independent time-series data, consisting of white noise with different degrees of oversampling, have been used to study the effect of oversampling on the time-adaptive prediction filter. If the data are oversampled, false gain occurs in the adaptive prediction results. The false gain depends on the degree of oversampling, the number of channels used in making the prediction, the filter length, and the convergence parameter. Two adaptive algorithms -- one having a constant convergence parameter and the other having a variable convergence parameter -- are discussed in this report. Particular cases of the prediction mean-square-error function of the time- adaptive filter are derived and compared to the empirical results. Although the false gain can be quite severe for high rates of adaption, rates of adaption can be selected in terms of theoretical maximum rates of adaption so that the false gain is not significant -- even for oversampled data cut at 1/20 of the folding frequency.

A comparative analysis was made of five mathematical techniques, capable of computer implementation, for rejection of erroneous data outliers (data points with extreme deviation from the main body of data). For each technique, applications were developed for independent and dependent data. The rejection technique described in the report as one-point iterated rejection proved most effective for both types of data. The best results were achieved when this technique was applied to the sample as a whole rather than to separate subdivisions of the sample. (Author)

An investigation into the possibility of applying statistical analysis of the Fourier transforms of airblast-induced ground motion time-histories in order to predict the most probable spectral characteristics of the motions in terms of known independent variables is presented. The various analytical and empirical procedures used in the development of the prediction technique are discussed. A model Fourier transform equation is postulated to fit actual transforms calculated from measured nuclear and HEST test time-histories. Constants in the model transform equation are found so that the postulated spectra is made to fit the actual spectra for each measured time-history. A set of regression equations using peak overpressure, pressure-impulse, depth and seismic velocity as the independent variables are derived. A linear regression analysis is conducted to calculate new constants for the model spectra which have a mean squared error when compared to the constants fitted to each actual spectra. A statistical analysis of the model Fourier transform constants so calculated is conducted to determine the 95 percent confidence limits on the population mean, variance, and regression and correlation coefficients. Equations are derived for the vertical acceleration, velocity and displacement of the free-field airblast-induced ground motions based on the predicted most probable Fourier transform of the motions. Application of the transform and time-history equations is discussed in terms of an example. (Author)

The selection of the proper filter needed for smoothing any specific data is aided by knowledge of the output truncation error of the filter under consideration. Graphs of this error versus the number of points of the filter are presented for eight main regions of a typical Centaur Twenty-Four Hour Orbit Trajectory. The coordinate system utilized in the investigation was the Azusa tracker coordinates referenced to a tracker centered, north-east rectangular coordinate system. Two tracker locations were necessary in order to track the eight regions involved in the study. These two locations are: (1) Cape, Canaveral, Florida; (2) Kapingamarangi, Solomon Islands. Filters of order one, two and three with midpoint and endpoint prediction for position to position to velocity smoothing are investigated. (Author)