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Performance tests of signature extension algorithms
Comparative tests were performed on seven signature extension algorithms to evaluate their effectiveness in correcting for changes in atmospheric haze and sun angle in a Landsat scene. Four of the algorithms were cluster matching, and two were maximum likelihood algorithms. The seventh algorithm determined the haze level in both training and recognition segments and used a set of tables calculated from an atmospheric model to determine the affine transformation that corrects the training signatures for changes in sun angle and haze level. Three of the algorithms were tested on a simulated data set, and all of the algorithms were tested on consecutive-day data. The classification performance on the data sets using the algorithms is presented, along with results of statistical tests on the accuracy and proportion estimates. The three algorithms tested on the simulated data produced significant improvements over the results obtained using untransformed signatures. For the consecutive-day data, the tested algorithms produced improvements in most but not all cases. The tests indicated also that no statistically significant differences were noted among the algorithms.
A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations
We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.
Driving mechanism of unsteady separation shock motion in hypersonic interactive flow
Wall pressure fluctuations were measured under the steady separation shock waves in Mach 5 turbulent interactions induced by unswept circular cylinders on a flat plate. The wall temperature was adiabatic. A conditional sampling algorithm was developed to examine the statistics of the shock wave motion. The same algorithm was used to examine data taken in earlier studies in the Princeton University Mach 3 blowdown tunnel. In these earlier studies, hemicylindrically blunted fins of different leading-edge diameters were tested in boundary layers which developed on the tunnel floor and on a flat plate. A description of the algorithm, the reasons why it was developed and the sensitivity of the results to the threshold settings, are discussed. The results from the algorithm, together with cross correlations and power spectral density estimates suggests that the shock motion is driven by the low-frequency unsteadiness of the downstream separated, vortical flow.
Simulation of Long Lived Tracers Using an Improved Empirically-Based Two-Dimensional Model Transport Algorithm
We have developed a new empirically-based transport algorithm for use in our GSFC two-dimensional transport and chemistry assessment model. The new algorithm contains planetary wave statistics, and parameterizations to account for the effects due to gravity waves and equatorial Kelvin waves. We will present an overview of the new algorithm, and show various model-data comparisons of long-lived tracers as part of the model validation. We will also show how the new algorithm gives substantially better agreement with observations compared to our previous model transport. The new model captures much of the qualitative structure and seasonal variability observed methane, water vapor, and total ozone. These include: isolation of the tropics and winter polar vortex, the well mixed surf-zone region of the winter sub-tropics and mid-latitudes, and the propagation of seasonal signals in the tropical lower stratosphere. Model simulations of carbon-14 and strontium-90 compare fairly well with observations in reproducing the peak in mixing ratio at 20-25 km, and the decrease with altitude in mixing ratio above 25 km. We also ran time dependent simulations of SF6 from which the model mean age of air values were derived. The oldest air (5.5 to 6 years) occurred in the high latitude upper stratosphere during fall and early winter of both hemispheres, and in the southern hemisphere lower stratosphere during late winter and early spring. The latitudinal gradient of the mean ages also compare well with ER-2 aircraft observations in the lower stratosphere.
An examination of the assumptions in the POLCAL cross-talk removal algorithm
The POLCAL crosstalk removal algorithm is based on the statistical properties of the image background and does not need any corner reflector or active radar calibrator deployed in the scene. The advantage of being able to remove the crosstalk contamination without using external calibration targets gives rise to the consideration of algorithms based on clutter statistics in polarimetric synthetic aperture radar (SAR) images in more detail. The basic assumption of the POLCAL procedure is the decorrelation of copolarized and cross-polarized backscatter, which is valid for natural targets with azimuthal symmetry. This assumption and others regarding the properties of the imaged surface are examined. An improved version called POLCALII is presented, and its performance is compared with POLCAL.
Simulation of Long Lived Tracers Using an Improved Empirically Based Two-Dimensional Model Transport Algorithm
We have developed a new empirically-based transport algorithm for use in our GSFC two-dimensional transport and chemistry model. The new algorithm contains planetary wave statistics, and parameterizations to account for the effects due to gravity waves and equatorial Kelvin waves. As such, this scheme utilizes significantly more information compared to our previous algorithm which was based only on zonal mean temperatures and heating rates. The new model transport captures much of the qualitative structure and seasonal variability observed in long lived tracers, such as: isolation of the tropics and the southern hemisphere winter polar vortex; the well mixed surf-zone region of the winter sub-tropics and mid-latitudes; the latitudinal and seasonal variations of total ozone; and the seasonal variations of mesospheric H2O. The model also indicates a double peaked structure in methane associated with the semiannual oscillation in the tropical upper stratosphere. This feature is similar in phase but is significantly weaker in amplitude compared to the observations. The model simulations of carbon-14 and strontium-90 are in good agreement with observations, both in simulating the peak in mixing ratio at 20-25 km, and the decrease with altitude in mixing ratio above 25 km. We also find mostly good agreement between modeled and observed age of air determined from SF6 outside of the northern hemisphere polar vortex. However, observations inside the vortex reveal significantly older air compared to the model. This is consistent with the model deficiencies in simulating CH4 in the northern hemisphere winter high latitudes and illustrates the limitations of the current climatological zonal mean model formulation. The propagation of seasonal signals in water vapor and CO2 in the lower stratosphere showed general agreement in phase, and the model qualitatively captured the observed amplitude decrease in CO2 from the tropics to midlatitudes. However, the simulated seasonal amplitudes were attenuated too rapidly with altitude in the tropics. Overall, the simulations with the new transport formulation are in substantially better agreement with observations compared with our previous model transport.
Multiple Component Event-Related Potential (mcERP) Estimation
We show how model-based estimation of the neural sources responsible for transient neuroelectric signals can be improved by the analysis of single trial data. Previously, we showed that a multiple component event-related potential (mcERP) algorithm can extract the responses of individual sources from recordings of a mixture of multiple, possibly interacting, neural ensembles. McERP also estimated single-trial amplitudes and onset latencies, thus allowing more accurate estimation of ongoing neural activity during an experimental trial. The mcERP algorithm is related to informax independent component analysis (ICA); however, the underlying signal model is more physiologically realistic in that a component is modeled as a stereotypic waveshape varying both in amplitude and onset latency from trial to trial. The result is a model that reflects quantities of interest to the neuroscientist. Here we demonstrate that the mcERP algorithm provides more accurate results than more traditional methods such as factor analysis and the more recent ICA. Whereas factor analysis assumes the sources are orthogonal and ICA assumes the sources are statistically independent, the mcERP algorithm makes no such assumptions thus allowing investigators to examine interactions among components by estimating the properties of single-trial responses.
Adaptation of a Fast Optimal Interpolation Algorithm to the Mapping of Oceangraphic Data
A fast, recently developed, multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This algorithm produces solution and error estimates which are consistent with those obtained from exact least squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least squares, that is, problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. In contrast to methods previously proposed for solving large least squares problems, our approach provides estimation error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations. The multiscale algorithm itself, published elsewhere, is not the focus of this paper. However, the algorithm requires statistical models having a very particular multiscale structure; it is the development of a class of multiscale statistical models, appropriate for oceanographic mapping problems, with which we concern ourselves in this paper. The approach is illustrated by mapping temperature in the northeastern Pacific. The number of hydrographic stations is kept deliberately small to show that multiscale and exact least squares results are comparable. A portion of the data were not used in the analysis; these data serve to test the multiscale estimates. A major advantage of the present approach is the ability to repeat the estimation procedure a large number of times for sensitivity studies, parameter estimation, and model testing. We have made available by anonymous Ftp a set of MATLAB-callable routines which implement the multiscale algorithm and the statistical models developed in this paper.
Design and Calibration of Autonomous Coherent Doppler Lidar for Space Missions
Developed a new algorithm for the simulation of three dimensional homogeneous turbulent velocity fields. For typical atmospheric conditions it is impossible to produce a simulated velocity field that simultaneously satisfy a given spatial correlation and the corresponding spatial spectrum because of spectral aliasing. The new algorithms produce a turbulent velocity field which has accurate spatial correlations which is required for performance predictions from space-based systems. Developed a new algorithm for extracting the spatial statistics of the atmospheric velocity field using coherent Doppler lidar. The performance of the algorithm was compared with past methods and the new algorithm produces useful results for space-based data, which was not possible before. Developed new methods for verification of the errors in ground-based and space-based Doppler lidar wind measurements. These new methods do not require independent in situ data. This is an important issue for the verification of space-based Doppler lidar measurements of the global wind field. The performance of the new algorithm was compared with past results for both space-based and ground-based operation. The new algorithm has the best performance and is the only algorithm that performed satisfactory for spacebased operation. The performance of coherent Doppler lidar for a space missions with various scanning geometries was determined using computer simulation which contained the effects of random instrumental velocity errors, wind shear, wind variability along the range-gate and from shot-to-shot, and random variations in atmospheric aerosol backscatter over the measurement volume. The bias in the velocity estimates was small and the accuracy in the is typically less than 0.5 m/s for high signal conditions. For a large number of shot per velocity estimate, the threshold signal level for acceptable estimates is proportional to the number of shots to the minus one half power. This agrees with previous results determined for ground-based measurements. The use of multi-element optical detectors for autonomous operation of coherent Doppler lidar was shown to be a very promising technique. Optimal detector geometries were determined by computer simulation of performance: for ground-based testing with a fixed calibration target and for space-based operation using the random surface returns. The effects of refractive turbulence on ground-based calibration of coherent Doppler lidar was determined by computer simulations and compared with theoretical predictions. New techniques were required to correctly predict performance for the focused beam geometry commonly used for verification of space-based operation. An improved velocity estimator was evaluated for space-based applications were signal shot measurements are used to produce vector wind measurements. This permits more accurate measurements when the signal level is not known a priori or not available from multiple shot measurements. The average Doppler lidar signal spectrum including the effects of velocity turbulence was derived and calculated. This permits new estimation algorithms for turbulence based on spectral estimates. In situ atmospheric measurements were conducted and analyzed using an instrumented kite-platform. This work helps provide the required in situ data for verification of Doppler lidar velocity statistics.
Land Surface Temperature Measurements form EOS MODIS Data
We have developed a physics-based land-surface temperature (LST) algorithm for simultaneously retrieving surface band-averaged emissivities and temperatures from day/night pairs of MODIS (Moderate Resolution Imaging Spectroradiometer) data in seven thermal infrared bands. The set of 14 nonlinear equations in the algorithm is solved with the statistical regression method and the least-squares fit method. This new LST algorithm was tested with simulated MODIS data for 80 sets of band-averaged emissivities calculated from published spectral data of terrestrial materials in wide ranges of atmospheric and surface temperature conditions. Comprehensive sensitivity and error analysis has been made to evaluate the performance of the new LST algorithm and its dependence on variations in surface emissivity and temperature, upon atmospheric conditions, as well as the noise-equivalent temperature difference (NE(Delta)T) and calibration accuracy specifications of the MODIS instrument. In cases with a systematic calibration error of 0.5%, the standard deviations of errors in retrieved surface daytime and nighttime temperatures fall between 0.4-0.5 K over a wide range of surface temperatures for mid-latitude summer conditions. The standard deviations of errors in retrieved emissivities in bands 31 and 32 (in the 10-12.5 micrometer IR spectral window region) are 0.009, and the maximum error in retrieved LST values falls between 2-3 K. Several issues related to the day/night LST algorithm (uncertainties in the day/night registration and in surface emissivity changes caused by dew occurrence, and the cloud cover) have been investigated. The LST algorithms have been validated with MODIS Airborne Simulator (MAS) dada and ground-based measurement data in two field campaigns conducted in Railroad Valley playa, NV in 1995 and 1996. The MODIS LST version 1 software has been delivered.
SeaWiFS technical report series. Volume 32: Level-3 SeaWiFS data products. Spatial and temporal binning algorithms
The level-3 data products from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) are statistical data sets derived from level-2 data. Each data set will be based on a fixed global grid of equal-area bins that are approximately 9 x 9 sq km. Statistics available for each bin include the sum and sum of squares of the natural logarithm of derived level-2 geophysical variables where sums are accumulated over a binning period. Operationally, products with binning periods of 1 day, 8 days, 1 month, and 1 year will be produced and archived. From these accumulated values and for each bin, estimates of the mean, standard deviation, median, and mode may be derived for each geophysical variable. This report contains two major parts: the first (Section 2) is intended as a users' guide for level-3 SeaWiFS data products. It contains an overview of level-0 to level-3 data processing, a discussion of important statistical considerations when using level-3 data, and details of how to use the level-3 data. The second part (Section 3) presents a comparative statistical study of several binning algorithms based on CZCS and moored fluorometer data. The operational binning algorithms were selected based on the results of this study.
Study of photon correlation techniques for processing of laser velocimeter signals
The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.
SeaWiFS technical report series. Volume 4: An analysis of GAC sampling algorithms. A case study
The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) instrument will sample at approximately a 1 km resolution at nadir which will be broadcast for reception by realtime ground stations. However, the global data set will be comprised of coarser four kilometer data which will be recorded and broadcast to the SeaWiFS Project for processing. Several algorithms for degrading the one kilometer data to four kilometer data are examined using imagery from the Coastal Zone Color Scanner (CZCS) in an effort to determine which algorithm would best preserve the statistical characteristics of the derived products generated from the one kilometer data. Of the algorithms tested, subsampling based on a fixed pixel within a 4 x 4 pixel array is judged to yield the most consistent results when compared to the one kilometer data products.
Detection and Modeling of High-Dimensional Thresholds for Fault Detection and Diagnosis
Many Fault Detection and Diagnosis (FDD) systems use discrete models for detection and reasoning. To obtain categorical values like oil pressure too high, analog sensor values need to be discretized using a suitablethreshold. Time series of analog and discrete sensor readings are processed and discretized as they come in. This task isusually performed by the wrapper code'' of the FDD system, together with signal preprocessing and filtering. In practice,selecting the right threshold is very difficult, because it heavily influences the quality of diagnosis. If a threshold causesthe alarm trigger even in nominal situations, false alarms will be the consequence. On the other hand, if threshold settingdoes not trigger in case of an off-nominal condition, important alarms might be missed, potentially causing hazardoussituations. In this paper, we will in detail describe the underlying statistical modeling techniques and algorithm as well as the Bayesian method for selecting the most likely shape and its parameters. Our approach will be illustrated by several examples from the Aerospace domain.
AutoBayes Program Synthesis System System Internals
This lecture combines the theoretical background of schema based program synthesis with the hands-on study of a powerful, open-source program synthesis system (Auto-Bayes). Schema-based program synthesis is a popular approach toward program synthesis. The lecture will provide an introduction into this topic and discuss how this technology can be used to generate customized algorithms. The synthesis of advanced numerical algorithms requires the availability of a powerful symbolic (algebra) system. Its task is to symbolically solve equations, simplify expressions, or to symbolically calculate derivatives (among others) such that the synthesized algorithms become as efficient as possible. We will discuss the use and importance of the symbolic system for synthesis. Any synthesis system is a large and complex piece of code. In this lecture, we will study Autobayes in detail. AutoBayes has been developed at NASA Ames and has been made open source. It takes a compact statistical specification and generates a customized data analysis algorithm (in C/C++) from it. AutoBayes is written in SWI Prolog and many concepts from rewriting, logic, functional, and symbolic programming. We will discuss the system architecture, the schema libary and the extensive support infra-structure. Practical hands-on experiments and exercises will enable the student to get insight into a realistic program synthesis system and provides knowledge to use, modify, and extend Autobayes.
Computing approximate random Delta v magnitude probability densities
This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.
A Coulomb collision algorithm for weighted particle simulations
A binary Coulomb collision algorithm is developed for weighted particle simulations employing Monte Carlo techniques. Charged particles within a given spatial grid cell are pair-wise scattered, explicitly conserving momentum and implicitly conserving energy. A similar algorithm developed by Takizuka and Abe (1977) conserves momentum and energy provided the particles are unweighted (each particle representing equal fractions of the total particle density). If applied as is to simulations incorporating weighted particles, the plasma temperatures equilibrate to an incorrect temperature, as compared to theory. Using the appropriate pairing statistics, a Coulomb collision algorithm is developed for weighted particles. The algorithm conserves energy and momentum and produces the appropriate relaxation time scales as compared to theoretical predictions. Such an algorithm is necessary for future work studying self-consistent multi-species kinetic transport.