Uncertainty Analysis in Signal Detection
Presentation discussed uncertainty analysis in signal detection and the inverse problem for time of arrival (ToA).
97 MATHEMATICS AND COMPUTING↗
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Validity test for linear error analysis
To determine whether estimation process simulated by linear error analysis will converge, criterion has been developed based on extension of classical observability. Particular application of technique is with groups of batched navigation data where statistics of estimation errors are derived with classical minimum-variance methods.
Diamant, L. S.↗
Statistical analysis of failure data on controllers and SSME turbine blade failures
The expressions for the maximum likelihood functions are given when the failure data are censored at a given point or at multiple points, or when the data come in groups. Different models applicable to failure data are presented with their characteristics. A graphical method of distinguishing different models by using cumulative hazard fucnction is discussed. For the failure data on controllers the model is determined by cumulative hazard function and chi-square goodness of fit. Using the Weibull Model the maximum likelihood estimators of the shape parameter and the failure rate parameter are obtained. The confidence intervals, meantime between failures, and B1 are determined. Similarly, for the data on Space Shuttle Main Engine (SSME) blade failures the maximum likelihood estimators are obtained for the Weibull parameters. The variances, confidence intervals, meantime between failures, and reliability are determined. The analysis is performed under assumption of grouped data as well as randomly placed data.
Patil, S. A.↗
On the simultaneous improvement of a satellite orbit and determination of sea surface topography using altimeter data
A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface toography with minimum wavelengths of about 500 km and to reduce the radial orbit errors caused by geopotential uncertainties. The modeling of these errors is made using the linearized Lagrangian perturbation theory. Observation equations are developed using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information can then provide estimates of parametrs representing the sea surface topography and corrections to the orbit. The potential of the method is demonstrated in a solution where simulated geopotential errors and the Levitus sea surface topography are used to generate the observables for a Seasat 3 day arc. The simulation results suggest that the method can be used to efficiently process real altimeter data.
Engelis, Theodossios↗
Estimating aircraft SAR response characteristics and approximating ocean wave spectra in the Labrador Sea
The data processing methods employed to compute estimates of two-dimensional wave height-variance spectra from the ocean imagery obtained in the Labrador Sea by a C-band airborne SAR system are described. The SAR spectra are compared for high and low altitude geometries with large and small elevation angles. A surface contour radar and a radar ocean wave spectrometer aboard an aircraft are used to verify the surface wave spectrum.
Tilley, D. G.↗
Geodetic positioning of the Aerospace Electronics Research Lab (ERL) Osborne Time Transfer Receiver (TTR) using the GPS NAVSTAR Block I satellites
Aerospace has routinely processed the Osborne Time Transfer Receiver (TTR) data for the purpose of monitoring the performance of ground and GPS atomic clocks in near real-time with on-line residual displays and characterizing clock stability with Allan Variance calculations. Recently, Aerospace added the ability to estimate the TTR's location by differentially correcting the TTR's location in the WGS84 reference system. This new feature is exercised on a set of TTR clock phase data and Sub-meter accurate station location estimates of the TTR at the Aerospace Electronic Research Lab (ERL) are obtained.
Liu, Anthony S.↗
Estimation of time averages from irregularly spaced observations - With application to coastal zone color scanner estimates of chlorophyll concentration
The sampling error of an arbitrary linear estimate of a time-averaged quantity constructed from a time series of irregularly spaced observations at a fixed located is quantified through a formalism. The method is applied to satellite observations of chlorophyll from the coastal zone color scanner. The two specific linear estimates under consideration are the composite average formed from the simple average of all observations within the averaging period and the optimal estimate formed by minimizing the mean squared error of the temporal average based on all the observations in the time series. The resulting suboptimal estimates are shown to be more accurate than composite averages. Suboptimal estimates are also found to be nearly as accurate as optimal estimates using the correct signal and measurement error variances and correlation functions for realistic ranges of these parameters, which makes it a viable practical alternative to the composite average method generally employed at present.
Chelton, Dudley B.↗
Masking by Gratings Predicted by an Image Sequence Discriminating Model: Testing Models for Perceptual Discrimination Using Repeatable Noise
Adding noise to stimuli to be discriminated allows estimation of observer classification functions based on the correlation between observer responses and relevant features of the noisy stimuli. Examples will be presented of stimulus features that are found in auditory tone detection and visual vernier acuity. using the standard signal detection model (Thurstone scaling), we derive formulas to estimate the proportion of the observers decision variable variance that is controlled by the added noise. one is based on the probability of agreement of the observer with him/herself on trials with the same noise sample. Another is based on the relative performance of the observer and the model. When these do not agree, the model can be rejected. A second derivation gives the probability of agreement of observer and model when the observer follows the model except for internal noise. Agreement significantly less than this amount allows rejection of the model.
Ahumada, Albert J., Jr.↗
Obliquity Driven Climate Change in Mars' Recent Past
We use the NASA/Ames grid Mars general circulation model with an updated radiation code and cloud nlicrophysics scheme. To speed up the simulations, we run the model at fairly coarse resolution (7.5" latitude x 22.5" longitude). Radiation Code Fluxes and heating rates are calculated from a radiation code based on the two-stream solution to radiative transfer that fully accounts for multiple scattering in the presence of gaseous absorp- tion. The model has 12 spectral intervals. Dust and water ice scattering properties are included. For dust, we use the Ockert-Bell [9] values in the visible, and Forget [IO] values in the infrared. For ice, we can either compute them online as the cloud evolves, or we can specify them. Gaseous opacities for water vapor and CO2 are calculated from correlated k-distributions taken from full line-by-line models. Cloud Microphysics Our cloud scheme is based on momentlorder scheme in which the mass mixing ratio and number density of the cloud ensemble are the advected species. From these we obtain a mean particle size and an estimate or the particle size distribution assuming a variance) which we then divide into 8 bins. Cloud microphysics is performed in each of these bins and includes nucleation, condensation, and gravitational settling. Dust is treated as a tracer and serves as condensation nuclei. The altered size distribution is then converted back into a mean size, a mixing ratio, and a particle number density.
Haberle, R. M.↗
Polarimetric Retrievals of Cloud Droplet Number Concentrations
Cloud droplet number concentration (Nd) is an important parameter of liquid clouds and is crucial to understanding aerosol-cloud interactions. It couples boundary layer aerosol composition, size and concentration with cloud reflectivity. It affects cloud evolution, precipitation, radiative forcing, global climate and, through observation, can be used to partially monitor the first indirect effect. With its unique combination of multi-wavelength, multi-angle, total and polarized reflectance measurements, the Research Scanning Polarimeter (RSP) retrieves Nd with relatively few assumptions. The approach involves measuring cloud optical thickness, mean droplet extinction cross-section and cloud physical thickness. Polarimetric observations are capable of measuring the effective variance, or width, of the droplet size distribution. Estimating cloud geometrical thickness is also an important component of the polarimetric Nd retrieval, which is accomplished using polarimetric measurements in a water vapor absorption band to retrieve the amount of in-cloud water vapor and relating this to physical thickness. We highlight the unique abilities and quantify uncertainties of the polarimetric approach. We validate the approach using observational data from the North Atlantic and Marine Ecosystems Study (NAAMES). NAAMES targets specific phases in the seasonal phytoplankton lifecycle and ocean-atmosphere linkages. This study provides an excellent opportunity for the RSP to evaluate its approach of sensing Nd over a range of concentrations and cloud types with in situ measurements from a Cloud Droplet Probe (CDP). The RSP and CDP, along with an array of other instruments, are flown on the NASA C-130 aircraft, which flies in situ and remote sensing legs in sequence. Cloud base heights retrieved by the RSP compare well with those derived in situ (R=0.83) and by a ceilometer aboard the R.V. Atlantis (R=0.79). Comparing geometric mean values from 12 science flights throughout the NAAMES-1 and NAAMES-2 campaigns, we find a strong correlation between Nd retrieved by the RSP and CDP (R=0.96). A linear least squares fit has a slope of 0.92 and an intercept of 0.3 cm−3. Uncertainty in this comparison can be attributed to cloud 3D effects, nonlinear liquid water profiles, multilayered clouds, measurement uncertainty, variation in spatial and temporal sampling, and assumptions used within the method. Radiometric uncertainties of the RSP measurements lead to biases on derived optical thickness and cloud physical thickness, but these biases largely cancel out when deriving Nd for most conditions and geometries. We find that a polarimetric approach to sensing Nd is viable and the RSP is capable of accurately retrieving Nd for a variety of cloud types and meteorological conditions.
Droplet concentration↗
Global precipitation estimates based on a technique for combining satellite-based estimates, rain gauge analysis, and NWP model precipitation information
The 'satellite-gauge model' (SGM) technique is described for combining precipitation estimates from microwave satellite data, infrared satellite data, rain gauge analyses, and numerical weather prediction models into improved estimates of global precipitation. Throughout, monthly estimates on a 2.5 degrees x 2.5 degrees lat-long grid are employed. First, a multisatellite product is developed using a combination of low-orbit microwave and geosynchronous-orbit infrared data in the latitude range 40 degrees N - 40 degrees S (the adjusted geosynchronous precipitation index) and low-orbit microwave data alone at higher latitudes. Then the rain gauge analysis is brougth in, weighting each field by its inverse relative error variance to produce a nearly global, observationally based precipitation estimate. To produce a complete global estimate, the numerical model results are used to fill data voids in the combined satellite-gauge estimate. Our sequential approach to combining estimates allows a user to select the multisatellite estimate, the satellite-gauge estimate, or the full SGM estimate (observationally based estimates plus the model information). The primary limitation in the method is imperfections in the estimation of relative error for the individual fields. The SGM results for one year of data (July 1987 to June 1988) show important differences from the individual estimates, including model estimates as well as climatological estimates. In general, the SGM results are drier in the subtropics than the model and climatological results, reflecting the relatively dry microwave estimates that dominate the SGM in oceanic regions.
Huffman, George J.↗
A tethered-balloon PTRMS sampling approach for surverying of landscape-scale biogenic VOC fluxes
To survey landscape-scale fluxes of biogenic gases, a100-meterTeflon tube was attached to a tethered balloon as a sampling inlet for a fast response Proton Transfer Reaction Mass Spectrometer (PTRMS). Along with meteorological instruments deployed on the tethered balloon and at 3-mand outputs from a regional weather model, these observations were used to estimate landscape scale biogenic volatile organic compound fluxes with two micrometeorological techniques: mixed layer variance and surface layer gradients. This highly mobile sampling system was deployed at four field sites near Barcelona to estimate landscape-scale BVOC emission factors in a relatively short period (3 weeks). The two micrometeorological techniques agreed within the uncertainty of the flux measurements at all four sites even though the locations had considerable heterogeneity in species distribution and complex terrain. The observed fluxes were significantly different than emissions predicted with an emission model using site-specific emission factors and land-cover characteristics. Considering the wide range in reported BVOC emission factors of VOCs for individual vegetation species (more than an order of magnitude), this flux estimation technique is useful for constraining BVOC emission factors used as model inputs.
Greenberg, Jim↗
Analysis of upper and lower bounds of the frame noise in linear detector arrays
This paper estimates the upper and lower bounds of the frame noise of a linear detector array that uses a one-dimensional scan pattern. Using chi-square distribution, it is analytically shown why it is necessary to use the average of the variances and not the average of the standard deviations to estimate these bounds. Also, a criteria for determining whether any excessively noisy lines exist among the detectors is derived from these bounds. Using a Gaussian standard random variable generator, these bounds are demonstrated to be accurate within the specified confidence interval. A silicon detector array is then used for actual dark current measurements. The criterion developed for determination of noisy detectors is checked on the experimentally obtained data.
Jaggi, S.↗
Magnetopause surface fluctuations observed by Voyager 1
Moving out of the dawnside of the earth's magnetosphere, Voyager 1 crossed the magnetopause apparently seven times, despite the high spacecraft speed of 11 km/sec. Normals to the magnetopause and their associated error cones were estimated for each of the crossings using a minimum variance analysis of the internal magnetic field. The oscillating nature of the ecliptic plane component of these normals indicates that most of the multiple crossings were due to a wave-like surface disturbance moving tailward along the magnetopause. The wave, which was aperiodic, was modeled as a sequence of sine waves. The amplitude, wavelength, and speed were determined for two pairs of intervals from the measured slopes, occurrence times, and relative positions of six magnetopause crossings. The magnetopause thickness was estimated to lie in the range 300 to 700 km with higher values possible. The estimated amplitude of these waves was obviously small compared to their wavelengths.
Lepping, R. P.↗
Supervision of dynamic systems: Monitoring, decision-making and control
Effects of task variables on the performance of the human supervisor by means of modelling techniques are discussed. The task variables considered are: The dynamics of the system, the task to be performed, the environmental disturbances and the observation noise. A relationship between task variables and parameters of a supervisory model is assumed. The model consists of three parts: (1) The observer part is thought to be a full order optimal observer, (2) the decision-making part is stated as a set of decision rules, and (3) the controller part is given by a control law. The observer part generates, on the basis of the system output and the control actions, an estimate of the state of the system and its associated variance. The outputs of the observer part are then used by the decision-making part to determine the instants in time of the observation actions on the one hand and the controls actions on the other. The controller part makes use of the estimated state to derive the amplitude(s) of the control action(s).
White, T. N.↗
Avalanche gain and its effect on energy resolution in GEM-based detectors
Here, we present avalanche gain and associated resolution measurements recorded with a 4 He:CO 2 (70:30) gas mixture and pure SF 6 , a Negative Ion (NI) gas. SF 6 is of particular interest to the directional dark matter detection community, as its low thermal diffusion helps to retain recoil ionization track features over long drift lengths. With the aid of a general form of the reduced first Townsend coefficient (RFTC), multiple GEM-based detector data sets are used to study the high-gain behavior of the 4 He:CO 2 gas mixture. The high-gain data is well described purely in terms of the reduced electric field strength and the number of GEMs, and the robust relationship between the RFTC and the average, reduced, electric field strength across the GEMs is emphasized. The associated (pulse-height) resolution measurements are used to discuss the variance of the avalanche distribution and to describe and estimate the lower limits of energy resolution one should expect to measure using a simple relationship with the RFTC. In the end, a description of avalanche gain, its effect on energy resolution, and the contributing experimental parameters in GEM-based detectors is developed over a broad parameter space for further use.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
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↗
Two biased estimation techniques in linear regression: Application to aircraft
Several ways for detection and assessment of collinearity in measured data are discussed. Because data collinearity usually results in poor least squares estimates, two estimation techniques which can limit a damaging effect of collinearity are presented. These two techniques, the principal components regression and mixed estimation, belong to a class of biased estimation techniques. Detection and assessment of data collinearity and the two biased estimation techniques are demonstrated in two examples using flight test data from longitudinal maneuvers of an experimental aircraft. The eigensystem analysis and parameter variance decomposition appeared to be a promising tool for collinearity evaluation. The biased estimators had far better accuracy than the results from the ordinary least squares technique.
Klein, Vladislav↗