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Results for “polynomial filtering”

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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Boundary implications for frequency response of interval FIR and IIR filters

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials. Subsequently, it is shown that the frequency responses of both interval FIR and IIR filters are bounded by the frequency responses of certain extreme filters. The results apply directly in the evaluation of properties of designed filters, especially because it is more realistic to bound the filter coefficients from above and below instead of determining those with infinite precision because of finite arithmetic effects. Illustrative examples are provided to show how the extreme filters might be easily derived in any specific interval FIR or IIR filter design problem.

Bose, N. K.↗
NASA NTRS1990

Computational tools for multi-linked flexible structures

A software module which designs and tests controllers and filters in Kalman Estimator form, based on a polynomial state-space model is discussed. The user-friendly program employs an interactive graphics approach to simplify the design process. A variety of input methods are provided to test the effectiveness of the estimator. Utilities are provided which address important issues in filter design such as graphical analysis, statistical analysis, and calculation time. The program also provides the user with the ability to save filter parameters, inputs, and outputs for future use.

Lee, Gordon K. F.↗
NASA NTRS1989

An adaptive data-smoothing routine

An adaptive noise reduction algorithm that can be implemented on a microcomputer is developed. Smoothing polynomials are used where the polynomial coefficients are chosen such that the mean-square-error between the noisy and smoothed data is minimized. This approach is equivalent to the implementation of a low-pass finite impulse response filter. The noise reduction depends on the order of the smoothing polynomial. A whiteness test on the error sequence is incorporated to search for the optimal smoothing. Expansion coefficients may be computed via the fast Fourier transform, and the resulting smoothing process is the equivalent of the implementation of an adaptive ideal low-pass filter. Results are obtained for an analytical signal with added white Gaussian noise. The routine may be applied to any smooth signal with additive random noise.

Taylor, Clayborne D.↗
NASA NTRS2011

Radar and Lidar Radar DEM

Using radar and lidar data, the aim is to improve 3D rendering of terrain, including digital elevation models (DEM) and estimates of vegetation height and biomass in a variety of forest types and terrains. The 3D mapping of vegetation structure and the analysis are useful to determine the role of forest in climate change (carbon cycle), in providing habitat and as a provider of socio-economic services. This in turn will lead to potential for development of more effective land-use management. The first part of the project was to characterize the Shuttle Radar Topography Mission DEM error with respect to ICESat/GLAS point estimates of elevation. We investigated potential trends with latitude, canopy height, signal to noise ratio (SNR), number of LiDAR waveform peaks, and maximum peak width. Scatter plots were produced for each variable and were fitted with 1st and 2nd degree polynomials. Higher order trends were visually inspected through filtering with a mean and median filter. We also assessed trends in the DEM error variance. Finally, a map showing how DEM error was geographically distributed globally was created.

remote sensing↗
NASA NTRS1993

Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

Parker, B. Eugene, Jr.↗
NASA NTRS1977

ADDJUST - An automated system for steering Centaur launch vehicles in measured winds

ADDJUST (Automatic Determination and Dissemination of Just-Updated Steering Terms) is an automated computer and communication system designed to provide Atlas/Centaur and Titan/Centaur launch vehicles with booster-phase steering data on launch day. Wind soundings are first obtained, from which a smoothed wind velocity vs altitude relationship is established. Design for conditions at the end of the boost phase with initial pitch and yaw maneuvers, followed by zero total angle of attack through the filtered wind establishes the required vehicle attitude as a function of altitude. Polynomial coefficients for pitch and yaw attitude vs altitude are determined and are transmitted for validation and loading into the Centaur airborne computer. The system has enabled 14 consecutive launches without a flight wind delay.

Swanson, D. C.↗
NASA NTRS1982

MAGSAT and aeromagnetic data of the continental US

The MAGSAT data were used to produce a scalar anomaly map of the U.S. In order to remove the east-west striping anomalies, which are believed to be caused by the low-order polynomials used to reduce the orbital bias errors, a 2-D spectral filtering using the Fourier transform method was applied. The resultant low-pass filtered map, with the east-west stripings removed, resembles much closer the surface aeromagnetic map based on the U.S. MAGNET data. The spectral filtering was also applied to the MAGSAT vector data. Department of Defense gravity data was processed to produce a filtered U.S. gravity map whose spectral contents are comparable to those of the MAGSAT magnetic map.

Won, I. J.↗
NASA NTRS1986

Deriving Two-Dimensional Ocean Wave Spectra and Surface Height Maps from the Shuttle Imaging Radar (SIR-B)

Directional ocean wave spectra were derived from Shuttle Imaging Radar (SIR-B) imagery in regions where nearly simultaneous aircraft-based measurements of the wave spectra were also available as part of the NASA Shuttle Mission 41G experiments. The SIR-B response to a coherently speckled scene is used to estimate the stationary system transfer function in the 15 even terms of an eighth-order two-dimensional polynomial. Surface elevation contours are assigned to SIR-B ocean scenes Fourier filtered using a empirical model of the modulation transfer function calibrated with independent measurements of wave height. The empirical measurements of the wave height distribution are illustrated for a variety of sea states.

Tilley, D. G.↗
NASA NTRS1981

Recursive algorithms for two-dimensional smoothing using bicubic hermite polynomial

It is noted that in the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines gives an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. A derivation is presented here of quarter-plane filtering algorithms that provide smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure sheds light on specific problems encountered in two-dimensional filtering problems. What is more, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Because of certain approximations introduced in its derivation, this recursive processor becomes suboptimal.

Kim, C. S.↗
NASA NTRS2007

Robustness Analysis of Integrated LPV-FDI Filters and LTI-FTC System for a Transport Aircraft

This paper proposes an analysis framework for robustness analysis of a nonlinear dynamics system that can be represented by a polynomial linear parameter varying (PLPV) system with constant bounded uncertainty. The proposed analysis framework contains three key tools: 1) a function substitution method which can convert a nonlinear system in polynomial form into a PLPV system, 2) a matrix-based linear fractional transformation (LFT) modeling approach, which can convert a PLPV system into an LFT system with the delta block that includes key uncertainty and scheduling parameters, 3) micro-analysis, which is a well known robust analysis tool for linear systems. The proposed analysis framework is applied to evaluating the performance of the LPV-fault detection and isolation (FDI) filters of the closed-loop system of a transport aircraft in the presence of unmodeled actuator dynamics and sensor gain uncertainty. The robustness analysis results are compared with nonlinear time simulations.

Khong, Thuan H.↗
NASA NTRS1982

Investigation of Antarctic crust and upper mantle using MAGSAT and other geophysical data

Antarctica is the perfect proving ground for testing data reduction procedures which are alternatives to the standard procedure employing polynomial fitting. Unreduced data (observed values minus corefield model theo each pass) were averaged in 3 degree bins. The resulting map was then high pass filtered using a finite Fourier transform filter so that spectral peaks between 4200 km and 5280 km were diminished by 1/3, peaks corresponding to wavelengths greater than or equal to 5280 km were diminished by 1/2, and the d.c. component was set equal to zero. The surface subtracted in this way differs from the polynomials used in the standard method in that it is static over the 5 north data window. The map produced is presented and the effects of the static model are compared to those of the dynamic mode.

Bentley, C. R.↗
NASA NTRS1982

Crustal interpretation of the MAGSAT data in the continental United States

The processing of MAGSAT scalar data to construct a crustal magnetic anomaly map over the continental U.S. involves removal of the reference field model, a path-by-path subtraction of a low order polynomial through a least-squares fit to reduce orbital offset errors, and a two dimensional spectral filtering to mitigate the spectral bias induced by the path-by-path orbital correction scheme. The resultant anomaly map shows reasonably good correlations with an aeromagnetic map derived from the project MAGNET. Prominent satellite magnetic anomalies are identified in terms of geological provinces and age boundaries. An inversion method was applied to MAGSAT data which produces both the Curie depth topography and laterally varying magnetic susceptibility of the crust. A contoured Curie depth map thus derived shows general agreements with a crustal thickness map based on seismic data.

Won, I. J.↗
NASA NTRS1992

Importance of Geosat orbit and tidal errors in the estimation of large-scale Indian Ocean variations

To improve the estimate accuracy of large-scale meridional sea-level variations, Geosat ERM data on the Indian Ocean for a 26-month period were processed using two different techniques of orbit error reduction. The first technique removes an along-track polynomial of degree 1 over about 5000 km and the second technique removes an along-track once-per-revolution sine wave about 40,000 km. Results obtained show that the polynomial technique produces stronger attenuation of both the tidal error and the large-scale oceanic signal. After filtering, the residual difference between the two methods represents 44 percent of the total variance and 23 percent of the annual variance. The sine-wave method yields a larger estimate of annual and interannual meridional variations.

Perigaud, Claire↗
NASA NTRS1992

Essentially nonoscillatory postprocessing filtering methods

High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

Lafon, F.↗
NASA NTRS2017

Sensitivity Analysis and Uncertainty Quantification of a Mars Ascent Vehicle Concept

The design of a conceptual Mars ascent vehicle is a challenging problem. In order to aid the vehicle and mission concept design it is important to understand the driving design parameters and the expected performance in the presence of model errors and uncertainties. An existing six degree of freedom simulation model is analyzed on a statistical basis using the methods available in the Design Analysis Kit for Optimization and Terascale Applications toolkit. The methods utilized include conventional Monte Carlo techniques, metamodeling via polynomial chaos expansions, and global variance-based sensitivity analyses. Two additional analysis methods referred to as “Monte Carlo filtering” and ”Classification trees” are used to determine which uncertain parameters are driving the performance of the vehicle. Monte Carlo filtering provides a methodology to determine which parameters cause qualitatively different behavior while the classification trees use heuristics to partition the input space and assign probabilities to each partition. These methods serve as qualitative descriptors of model sensitivity while variance-based global sensitivity analysis seeks a quantitative mapping from total output variance to the variance of individual inputs. Application of these techniques to several outputs of a Mars ascent vehicle concept simulation indicates that only a select few input factors dominate their variance.

Noyes, Connor↗
NASA NTRS2012

Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.

Sidick, Erkin↗
NASA NTRS1988

Non-oscillatory spectral Fourier methods for shock wave calculations

A non-oscillatory spectral Fourier method is presented for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order.

Cai, Wei↗
NASA NTRS1989

Essentially nonoscillatory spectral Fourier methods for shock wave calculations

An essentially nonoscillatory spectral Fourier method for the solution of hyperbolic partial differential equations is presented. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that essentially no oscillations develop in the solution.

Cai, Wei↗