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All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

The estimation of the constituent densities of the upper atmosphere by means of a recursive filtering algorithm.

The structure of the upper atmosphere can be indirectly probed by light in order to determine the global density structure of ozone, aerosols, and neutral atmosphere. Scattered and directly transmitted light is measured by a satellite and is shown to be a nonlinear function of the state which is defined to be a point-wise decomposition of the density profiles. Dynamics are imposed on the state vector and a structured estimation problem is developed. The estimation of these densities is then performed using a linearized Kalman-Bucy filter and a linearized Kushner-Stratonovich filter.

Mcgarty, T. P.↗
DOE OSTI2014

Shadow Probability of Detection and False Alarm for Median-Filtered SAR Imagery

Median filtering reduces speckle in synthetic aperture radar (SAR) imagery while preserving edges, at the expense of coarsening the resolution, by replacing the center pixel of a sliding window by the median value. For shadow detection, this approach helps distinguish shadows from clutter more easily, while preserving shadow shape delineations. However, the nonlinear operation alters the shadow and clutter distributions and statistics, which must be taken into consideration when computing probability of detection and false alarm metrics. Depending on system parameters, median filtering can improve probability of detection and false alarm by orders of magnitude. Herein, we examine shadow probability of detection and false alarm in a homogeneous, ideal clutter background after median filter post-processing. Some comments on multi-look processing effects with and without median filtering are also made.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Statistical model based iterative reconstruction (MBIR) in clinical CT systems: Experimental assessment of noise performance

Purpose: To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system. Methods: Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods. Results: (1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a “redder” NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose){sup −β} with the component β ≈ 0.25, which violated the classical σ ∝ (dose){sup −0.5} power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2. Conclusions: The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

A Measurement of the Largest-scale CMB E -mode Polarization with CLASS

We present measurements of large-scale cosmic microwave background E-mode polarization from the Cosmology Large Angular Scale Surveyor 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of 82 μK arcimin, comparable to Planck at similar frequencies (100 and 143 GHz ). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making nonlinearity, being characterized as <3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth τ = $0.053^{+0.018}_{-0.019}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ > 30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck’s measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

A comparison of the effects of small nonlinearities on several estimation schemes.

A variety of techniques are available for estimating the states of nonlinear dynamic systems from noisy data. These procedures are generally equivalent when applied to linear systems. This paper investigates the difference between several of these procedures in the presence of small dynamic and observational nonlinearities. In particular, it examines one least square batch processing algorithm, and three recursive algorithms similar to the Kalman filter. To first order, all the estimators have the same covariance. Expressions for the means, however, show that each estimator has a different bias. The examples presented show that the biases can be a strong function of such parameters as initial covariances and number of data points being considered.

Conrad, B.↗
NASA NTRS1983

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.

Caglayan, A. K.↗
NASA NTRS1983

A bias identification and state estimation methodology for nonlinear systems

A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.

Caglayan, A. K.↗
NASA NTRS1995

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Mei, Chuh↗
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 NTRS2007

Two Mathematical Models of Nonlinear Vibrations

Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

Brugarolas, Paul↗
NASA NTRS2021

Analytical and Numerical Modeling of Sensor Port Acoustics

The purpose of this Technical Publication (TP) is to provide background, relevant theory, and examples for acoustic response analysis of a sensor port. A new approach is devised theoretically and computationally that captures the true acoustic response of a sensor port. This TP summarizes the acoustics back-ground, the port response theoretical development, and provides comparisons of a port acoustic response using an analytical model and computational acoustics. The effects of nonlinear acoustics and acoustic propagation in liquids is also examined. Additionally, this TP describes the design of a specialized filter using the predicted sensor port response that can be applied to data for correction.

sensor port↗
NASA NTRS2017

Precomputing Process Noise Covariance for Onboard Sequential Filters

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

onboard↗
DOE OSTI2015

Terahertz wave electro-optic measurements with optical spectral filtering

We propose electro-optic detection techniques based on variations of the laser pulse spectrum induced during pulse co-propagation with terahertz wave radiation in a nonlinear crystal. Quantitative comparison with two other detection methods is made. Substantial improvement of the sensitivity compared to the standard electro-optic detection technique (at high frequencies) and to the previously shown technique based on laser pulse energy changes is demonstrated in experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2016

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗
NASA NTRS2009

The Principle of Energetic Consistency

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.

Cohn, Stephen E.↗
DOE OSTI2023

Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time–frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton–exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.

Science & Technology - Other Topics↗
DOE OSTI2015

Period–luminosity relations derived from the OGLE-III fundamental mode Cepheids. II. The small magellanic cloud Cepheids

In this paper we present multi-band period–luminosity (P–L) relations for fundamental mode Cepheids in the SMC. The optical VI-band mean magnitudes for these SMC Cepheids were taken from the third phase of the Optical Gravitational Lensing Experiment (OGLE-III) catalog. We also matched the OGLE-III SMC Cepheids to 2MASS and SAGE-SMC catalog to derive mean magnitudes in the JHK-bands and the four Spitzer IRAC bands, respectively. All photometry was corrected for extinction by adopting Zaritsky’s extinction map. Cepheids with periods smaller than ∼2.5 days were removed from the sample. In addition to the extinction corrected P–L relations in nine filters from optical to infrared, we also derived the extinction-free Wesenheit function for these Cepheids. We tested the nonlinearity of these SMC P–L relations (except the 8.0 μm-band P–L relation) at 10 days: none of the P–L relations show statistically significant evidence of nonlinearity. When compared to the P–L relations in the LMC, the t-test results revealed that there is a difference between the SMC/LMC P–L slopes only in the V- and J-band. Further, we found excellent agreement between the SMC/LMC Wesenheit P–L slope. The difference in LMC and SMC Period–Wesenheit relation LMC and SMC zero points was found to be Δμ=0.483±0.015 mag. This amounts to a difference in distance modulus between the LMC and SMC.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

Processor for high-density digital tape-recorded signals

Linear filter and detection theory can bear on problem of reconstructing recorded bit stream. Problem can be taken from realm of nonlinear problems even though basic record process is still recognized as highly nonlinear. Digital tape recorder can be modeled as particular type of linear communication channel with intersymbol interference.

Ashlock, J. C.↗