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All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Extensions of the space trajectories error analysis programs

A generalized covariance analysis technique which permits the study of the sensitivity of linear estimation algorithms to errors in a priori statistics has been developed and programed. Several sample cases are presented to illustrate the use of this technique. Modifications to the Simulated Trajectories Error Analysis Program (STEAP) to enable targeting a multiprobe mission of the Planetary Explorer type are discussed. The logic for the mini-probe targeting is presented. Finally, the initial phases of the conversion of the Viking mission Lander Trajectory Reconstruction (LTR) program for use on Venus missions is discussed. An integrator instability problem is discussed and a solution proposed.

Adams, G. L.↗
NASA NTRS1979

Spectrum measurements with laser velocimeters

The length of time or number of samples required for a laser velocimeter experiment to attain a specified variability error level is determined. The study is based on available techniques for estimating turbulence point spectra with a Poisson sampling signal formalism. The discretized lag product technique is found to be the most efficient spectral estimator. The variability error theory developed by Gaster and Roberts (1975) for an exact lag product algorithm provides a practical formula for the discretized lag product algorithm.

Mayo, W. T., Jr.↗
NASA NTRS1993

Stratospheric N2O5, CH4, and N2O profiles from IR solar occultation spectra

Stratospheric volume mixing ratio profiles of N2O5, CH4, and N2O have been retrieved from a set of 0.052/cm resolution (FWHM) solar occultation spectra recorded at sunrise during a balloon flight from Aire sur l'Adour, France (44 N latitude) on 12 October 1990. The N2O5 results have been derived from measurements of the integrated absorption by the 1246/cm band. Assuming a total intensity of 4.32 x 10 exp -17 cm/molecule/sq cm independent of temperature, the retrieved N2O5 volume mixing ratios in ppbv, interpolated to 2 km height spacings, are 1.64 +/- 0.49 at 37.5 km, 1.92 +/- 0.56 at 35.5 km, 2.06 +/- 0.47 at 33.5 km, 1.95 +/- 0.42 at 31.5 km, 1.60 +/- 0.33 at 29.5 km, 1.26 +/- 0.28 at 27.5 km, and 0.85 +/- 0.20 at 25.5 km. Error bars indicate the estimated 1-sigma uncertainty including the error in the total band intensity. The retrieved profiles are compared with previous measurements and photochemical model results.

Camy-Peyret, C.↗
NASA NTRS1992

A preliminary study of the variability and magnitude of the flux of biogenic sulfur gases from a New Hampshire salt marsh

Salt marshes have highly variable spatial and temporal fluxes of hydrogen sulfide, carbonyl sulfide, methane thiol, dimethyl sulfide, and carbon disulfide (H2S, COS, MeSH, DMS, and CS2, respectively). This variability was tested at nine emission sites in a New Hampshire, USA salt marsh: three replicates in each of three vegetation zones, Spartina alterniflora, S. patens, and a transition zone. Three sites were sampled simultaneously, either within or across vegetation zones, using a dynamic flux chamber technique. Difficulties with calibration and field equipment resulted in fluxes with maximum absolute uncertainties of greater than plus or minus 200 percent. However, the relative uncertainty between subsequent samples was closer to plus or minus 20 percent. Chambers are expected to affect the natural flux of gases by altering the humidity, temperature, and composition of the gas inside the chamber. Summertime fluxes are highest for all gases except COS which demonstrated evidence of a springtime peak. A summertime background flux of 5 to 100 x 10(exp -9) g S/m(sup -2) min was observed for all gases, while S alternifora fluxes of MeSH and DMS were approximately 8 fold and approximately 100 fold higher than S. patens, respectively. DMS and MeSH fluxes were higher during the day than at night. Evidence of COS uptake by plants was observed. CS2 appeared to be the quantitatively least important sulfur gas emitted. Improved laboratory and sample collection techniques and further data collection in the field will yield information on the details of salt marsh variability, will improve estimates of the error associated with single flux measurements, and will allow a more accurate estimation of sulfur fluxes from salt marshes based on vegetation and area coverage data. Inability to control the temperature and humidity inside of the chamber remain significant problems with the chamber design.

Morrison, Michael Cope↗
NASA NTRS1996

An Evaluation of the Measurement Requirements for an In-Situ Wake Vortex Detection System

Results of a numerical simulation are presented to determine the feasibility of estimating the location and strength of a wake vortex from imperfect in-situ measurements. These estimates could be used to provide information to a pilot on how to avoid a hazardous wake vortex encounter. An iterative algorithm based on the method of secants was used to solve the four simultaneous equations describing the two-dimensional flow field around a pair of parallel counter-rotating vortices of equal and constant strength. The flow field information used by the algorithm could be derived from measurements from flow angle sensors mounted on the wing-tip of the detecting aircraft and an inertial navigation system. The study determined the propagated errors in the estimated location and strength of the vortex which resulted from random errors added to theoretically perfect measurements. The results are summarized in a series of charts and a table which make it possible to estimate these propagated errors for many practical situations. The situations include several generator-detector airplane combinations, different distances between the vortex and the detector airplane, as well as different levels of total measurement error.

Fuhrmann, Henri D.↗
NASA NTRS2000

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Ballabrera-Poy, Joaquim↗
NASA NTRS2000

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Ballabrera-Poy, J.↗
NASA NTRS2021

Weekly Mapping of Sea Ice Freeboard in the Ross Sea from ICESat-2

NASA’s ICESat-2 has been providing sea ice freeboard measurements across the polar regions since October 2018. In spite of the outstanding spatial resolution and precision of ICESat-2, the spatial sparsity of the data can be a critical issue for sea ice monitoring. This study employs a geostatistical approach (i.e., ordinary kriging) to characterize the spatial autocorrelation of the ICESat-2 freeboard measurements (ATL10) to estimate weekly freeboard variations in 2019 for the entire Ross Sea area, including where ICESat-2 tracks are not directly available. Three variogram models (exponential, Gaussian, and spherical) are compared in this study. According to the cross-validation results, the kriging-estimated freeboards show correlation coefficients of 0.56–0.57, root mean square error (RMSE) of ~0.12 m, and mean absolute error (MAE) of ~0.07 m with the actual ATL10 freeboard measurements. In addition, the estimated errors of the kriging interpolation are low in autumn and high in winter to spring, and low in southern regions and high in northern regions of the Ross Sea. The effective ranges of the variograms are 5–10 km and the results from the three variogram models do not show significant differences with each other. The southwest (SW) sector of the Ross Sea shows low and consistent freeboard over the entire year because of the frequent opening of wide polynya areas generating new ice in this sector. However, the southeast (SE) sector shows large variations in freeboard, which demonstrates the advection of thick multiyear ice from the Amundsen Sea into the Ross Sea. Thus, this kriging-based interpolation of ICESat-2 freeboard can be used in the future to estimate accurate sea ice production over the Ross Sea by incorporating other remote sensing data.

Satellite altimeter↗
NASA NTRS2002

Passive and Active Microwave Remote Sensing of Precipitation and Latent Heating Distributions in the Tropics from TRMM

Passive and active microwave remote sensing data are analyzed to identify signatures of precipitation and vertical motion in tropical convection. A database of cloud/radiative model simulations is used to quantify surface rain rates and latent heating profiles that are consistent with these signatures. At satellite footprint-scale (approximately 10 km), rain rate and latent heating estimates are subject to significant random errors, but by averaging the estimates in space and time, random errors are substantially reduced, Bias errors have been minimized by improving the microphysics in the supporting cloud/radiative model simulations, and by imposing a consistent definition of remotely-sensed and model-simulated convective/stratiform rain coverage. Remotely-sensed precipitation and latent heating distributions in the tropics are derived from Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/ Imager (SSM/ I) sensor data. The prototype Version 6 TRMM passive microwave algorithm typically yields average heating profiles with maxima between 6 and 7 km altitude for organized mesoscale convective systems. Retrieved heating profiles for individual convective systems are compared to coincident estimates based upon a combination of dual-Doppler radar and rawinsonde data. Also, large-scale latent heating distributions are compared to estimates derived from a simpler technique that utilizes observations of surface rain rate and stratiform rain proportion to infer vertical heating structure. Results of these tests will be presented at the conference.

Olson, William S.↗
NASA NTRS1986

Self-adaptive difference method for the effective solution of computationally complex problems of boundary layer theory

An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.

Schoenauer, W.↗
NASA NTRS1987

Intrinsic frequency spectra of short gravity-capillary waves obtained from temporal measurements of wave height on a lake

Intrinsic frequency spectra of water waves in the range of 6-17 Hz were obtained as a function of both wind speed and wind stress from point measurements of wave height. In a lake with a limited fetch, there are two types of surface motions causing Doppler shift in the frequencies of short waves: orbital velocity of long waves and surface wind drift. The former was estimated from long-wave amplitude by using a linear wave theory. The error in this estimate is of the order of the long-wave slope, and for this work it is typically 10 percent. The latter was approximated by the friction velocity. The friction velocity could be either taken as 3 percent of the mean wind speed measured at a height of 10 m or obtained from direct measurements of the wind stress. The surface drift velocities obtained by these two approaches were found to be in close agreement. Doppler frequency shift can be corrected in either the frequency or the equivalent spatial domain. The two techniques were found to produce comparable results. Experimental results showed that the spectral energy of short waves rapidly increased in response to increasing winds and jumped up by an order of magnitude when wave breaking occurred.

Atakturk, S. S.↗
NASA NTRS2013

Spatial Statistical Data Fusion (SSDF)

As remote sensing for scientific purposes has transitioned from an experimental technology to an operational one, the selection of instruments has become more coordinated, so that the scientific community can exploit complementary measurements. However, tech nological and scientific heterogeneity across devices means that the statistical characteristics of the data they collect are different. The challenge addressed here is how to combine heterogeneous remote sensing data sets in a way that yields optimal statistical estimates of the underlying geophysical field, and provides rigorous uncertainty measures for those estimates. Different remote sensing data sets may have different spatial resolutions, different measurement error biases and variances, and other disparate characteristics. A state-of-the-art spatial statistical model was used to relate the true, but not directly observed, geophysical field to noisy, spatial aggregates observed by remote sensing instruments. The spatial covariances of the true field and the covariances of the true field with the observations were modeled. The observations are spatial averages of the true field values, over pixels, with different measurement noise superimposed. A kriging framework is used to infer optimal (minimum mean squared error and unbiased) estimates of the true field at point locations from pixel-level, noisy observations. A key feature of the spatial statistical model is the spatial mixed effects model that underlies it. The approach models the spatial covariance function of the underlying field using linear combinations of basis functions of fixed size. Approaches based on kriging require the inversion of very large spatial covariance matrices, and this is usually done by making simplifying assumptions about spatial covariance structure that simply do not hold for geophysical variables. In contrast, this method does not require these assumptions, and is also computationally much faster. This method is fundamentally different than other approaches to data fusion for remote sensing data because it is inferential rather than merely descriptive. All approaches combine data in a way that minimizes some specified loss function. Most of these are more or less ad hoc criteria based on what looks good to the eye, or some criteria that relate only to the data at hand.

Braverman, Amy J.↗
NASA NTRS1977

SEAHT: A computer program for the use of intersecting arcs of altimeter data for sea surface height refinement

The SEAHT program is designed to process multiple passes of altimeter data with intersecting ground tracks, with the estimation of corrections for orbital errors to each pass such that the data has the best overall agreement at the crossover points. Orbit error for each pass is modeled as a polynomial in time, with optional orders of 0, 1, or 2. One or more passes may be constrained in the adjustment process, thus allowing passes with the best orbits to provide the overall level and orientation of the estimated sea surface heights. Intersections which disagree by more than an input edit level are not used in the error parameter estimation. In the program implementation, passes are grouped into South-North passes and North-South passes, with the North-South passes partitioned out for the estimation of orbit error parameters. Computer core utilization is thus dependent on the number of parameters estimated for the set of South-North arcs, but is independent on the number of North-South passes. Estimated corrections for each pass are applied to the data at its input data rate and an output tape is written which contains the corrected data.

Allen, C. P.↗
NASA NTRS1972

The compensated Kalman filter.

This paper introduces the compensated Kalman filter, a suboptimal state estimator which can be used to eliminate steady-state bias errors when it is used in conjunction with the mismatched steady-state (asymptotic) time-invariant Kalman-Bucy filter. The uncompensated mismatched steady state Kalman-Bucy filter exhibits bias errors whenever the nominal plant parameters used in the filter design are different from the actual plant parameters. The approach used relies on the utilization of the residual (innovations) process of the mismatched filter to estimate, via a Kalman-Bucy filter, the state estimation errors and subsequent improvements of the state estimate. The compensated Kalman filter augments the mismatched steady state Kalman-Bucy filrby the introduction of additional dynamics and feedforward integral compensation channels.

Athans, M.↗
NASA NTRS1987

Efficient computation of parameter confidence intervals

An important step in system identification of aircraft is the estimation of stability and control derivatives from flight data along with an assessment of parameter accuracy. When the maximum likelihood estimation technique is used, parameter accuracy is commonly assessed by the Cramer-Rao lower bound. It is known, however, that in some cases the lower bound can be substantially different from the parameter variance. Under these circumstances the Cramer-Rao bounds may be misleading as an accuracy measure. This paper discusses the confidence interval estimation problem based on likelihood ratios, which offers a more general estimate of the error bounds. Four approaches are considered for computing confidence intervals of maximum likelihood parameter estimates. Each approach is applied to real flight data and compared.

Murphy, Patrick C.↗
NASA NTRS2002

Integrated INS/GPS Navigation from a Popular Perspective

Inertial navigation, blended with other navigation aids, Global Positioning System (GPS) in particular, has gained significance due to enhanced navigation and inertial reference performance and dissimilarity for fault tolerance and anti-jamming. Relatively new concepts based upon using Differential GPS (DGPS) blended with Inertial (and visual) Navigation Sensors (INS) offer the possibility of low cost, autonomous aircraft landing. The FAA has decided to implement the system in a sophisticated form as a new standard navigation tool during this decade. There have been a number of new inertial sensor concepts in the recent past that emphasize increased accuracy of INS/GPS versus INS and reliability of navigation, as well as lower size and weight, and higher power, fault tolerance, and long life. The principles of GPS are not discussed; rather the attention is directed towards general concepts and comparative advantages. A short introduction to the problems faced in kinematics is presented. The intention is to relate the basic principles of kinematics to probably the most used navigation method in the future-INS/GPS. An example of the airborne INS is presented, with emphasis on how it works. The discussion of the error types and sources in navigation, and of the role of filters in optimal estimation of the errors then follows. The main question this paper is trying to answer is 'What are the benefits of the integration of INS and GPS and how is this, navigation concept of the future achieved in reality?' The main goal is to communicate the idea about what stands behind a modern navigation method.

Omerbashich, Mensur↗
NASA NTRS1979

Determination of stability and control parameters of a light airplane from flight data using two estimation methods

Two identification methods, the equation error method and the output error method, are used to estimate stability and control parameter values from flight data for a low-wing, single-engine, general aviation airplane. The estimated parameters from both methods are in very good agreement primarily because of sufficient accuracy of measured data. The estimated static parameters also agree with the results from steady flights. The effect of power different input forms are demonstrated. Examination of all results available gives the best values of estimated parameters and specifies their accuracies.

Klein, V.↗
NASA NTRS1977

Application of microelectronic technology to general aviation flight control

This paper presents several different methods that can be used to determine the aircraft orientation (attitude) without direct measurement. The methods combine state estimation techniques with measurements from solid state pressure sensors, accelerometers, and magnetometers to determine the aircraft state. The paper demonstrates how the estimation algorithms were validated and compared using flight test data, and it presents results of performance sensitivity analyses of sensor error, modeling inaccuracies, and wind disturbance effects on the attitude estimation errors. If implemented, the methods presented could make it possible to eliminate directional and vertical gyros and to change from many isolated sensors to an integrated, small, reliable sensing package for determining the aircraft state.

Sorensen, J. A.↗