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NASA NTRS2002

GPS-Based Navigation and Orbit Determination for the AMSAT Phase 3D Satellite

This paper summarizes the results of processing GPS data from the AMSAT Phase 3D (AP3) satellite for real-time navigation and post-processed orbit determination experiments. AP3 was launched into a geostationary transfer orbit (GTO) on November 16, 2000 from Kourou, French Guiana, and then was maneuvered into its HEO over the next several months. It carries two Trimble TANS Vector GPS receivers for signal reception at apogee and at perigee. Its spin stabilization mode currently makes it favorable to track GPS satellites from the backside of the constellation while at perigee, and to track GPS satellites from below while at perigee. To date, the experiment has demonstrated that it is feasible to use GPS for navigation and orbit determination in HEO, which will be of great benefit to planned and proposed missions that will utilize such orbits for science observations. It has also shown that there are many important operational considerations to take into account. For example, GPS signals can be tracked above the constellation at altitudes as high as 58000 km, but sufficient amplification of those weak signals is needed. Moreover, GPS receivers can track up to 4 GPS satellites at perigee while moving as fast as 9.8 km/sec, but unless the receiver can maintain lock on the signals long enough, point solutions will be difficult to generate. The spin stabilization of AP3, for example, appears to cause signal levels to fluctuate as other antennas on the satellite block the signals. As a result, its TANS Vectors have been unable to lock on to the GPS signals long enough to down load the broadcast ephemeris and then generate position and velocity solutions. AP3 is currently in its eclipse season, and thus most of the spacecraft subsystems have been powered off. In Spring 2002, they will again be powered up and AP3 will be placed into a three-axis stabilization mode. This will significantly enhance the likelihood that point solutions can be generated, and perhaps more important, that the receiver clock can be synchronized to GPS time. This is extremely important for real-time and post-processed orbit determination, where removal of receiver clock bias from the data time tags is needed, for time-tagging of science observations. Current analysis suggests that the inability to generate point solutions has allowed the TANS Vector clock bias to drift freely, being perhaps as large as 5-7 seconds by October, 2001, thus causing up to 50 km of along-track orbit error. The data collected in May, 2002 while in three-axis stabilized mode should provide a significant improvement in the orbit determination results.

Davis, George↗

NASA NTRS2009

Detection of presence of chemical precursors

Methods and systems for determining if one or more target molecules are present in a gas, by exposing a functionalized carbon nanostructure (CNS) to the gas and measuring an electrical parameter value EPV(n) associated with each of N CNS sub-arrays. In a first embodiment, a most-probable concentration value C(opt) is estimated, and an error value, depending upon differences between the measured values EPV(n) and corresponding values EPV(n;C(opt)) is computed. If the error value is less than a first error threshold value, the system interprets this as indicating that the target molecule is present in a concentration C.apprxeq.C(opt). A second embodiment uses extensive statistical and vector space analysis to estimate target molecule concentration.

Li, Jing↗

NASA NTRSDate not supplied

All-sky Microwave Radiance Assimilation in The GEOS Atmospheric Reanalysis for The Early 21st Century (GEOS-21C)

The Goddard Earth Observing System (GEOS) is used for weather, climate, and air quality forecasts and producing reanalysis datasets. Its atmospheric data assimilation system (ADAS) is a hybrid–4DEnVar system. Various satellite radiance, atmospheric motion vector (winds), aircraft, and convectional data are assimilated by this system to produce global atmospheric states. Satellite data assimilation within GEOS ADAS is enhanced by considering correlated observational errors among infrared radiance observations and assimilating new microwave radiance data in all-sky conditions since the release of the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). These new microwave radiance data include brightness temperature measurements made by the Global Precipitation Mission (GPM) microwave imager (GMI) and Advanced Microwave Scanning Radiometer 2 / Global Change Observation Mission 1st – Water (AMSR2/GCOM-W). Historical microwave radiance data made by various Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I) and the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) aboard the Aqua satellite are tested within the all-sky microwave radiance assimilation framework in the preparation of the GEOS enhanced Atmospheric Reanalysis for the early 21st century (GEOS-21C). Assimilation of these data in all-sky conditions enhances use of other satellite data and improves GEOS analysis and forecast. In this talk, we will present the procedures of to assimilate microwave radiance data in all-sky conditions and their impact on atmospheric analysis in the preparation of GEOS-21C.

Jianjun Jin↗

NASA NTRS2022

Assessment of Geo-Kompsat-2A Atmospheric Motion Vector Data and Its Assimilation Impact in the GEOS Atmospheric Data Assimilation System

Korea’s second geostationary meteorological satellite, Geo-Kompsat-2A (Geostationary-Korean Multi-Purpose Satellite-2A, GK2A), was successfully launched on 4 December 2018. GK2Agenerates Atmospheric Motion Vectors (AMVs) every 10 min in the full disk area. This data hasbeen disseminated via Global Telecommunication System (GTS) since 25 October 2019. This articleevaluates the quality of GK2A AMVs in the Goddard Earth Observing System (GEOS) atmosphericdata assimilation system (ADAS). The data show slow wind speed biases at 200–300 hPa and 600–800hPa in the northern and southern hemispheres. These biases are caused by observation heightassignment errors near jet streams. The Equivalent Blackbody Temperature (EBBT) method of GK2Atends to assign clouds at higher altitude, which mainly causes slow wind speed biases, especially inthe lower atmosphere. The IR/WV intercept method of GK2A assigns clouds slightly lower in theatmospheric layers below the altitude of 400 hPa, which causes positive biases. Quality control (QC)criteria to select the most suitable GK2A AMV data for assimilation are presented based on thesequality assessments. A new QC criterion utilizing height errors within the GEOS ADAS is introducedto exclude data with slow wind speed biases and large errors. GEOS forecast accuracy is slightlyimproved after assimilating GK2A AMVs along with other conventional, radiance, and satellitewinds which include AMVs made by the Himawari-8 satellite in nearly the same observational areaof GK2A. Additionally, the present work shows that GEOS forecasts can be significantly improved,especially in the tropics and southern hemisphere after assimilating GK2A data in the absence ofHimawari-8 AMVs. This study demonstrates that GK2A AMV data is a valuable data source toenhance the robustness of GEOS ADAS.

Atmospheric Motion Vectors↗

NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗

NASA NTRS1986

Anisotropic responses to motion toward and away from the eye

When a rigid object moves toward the eye, it is usually perceived as being rigid. However, in the case of motion away from the eye, the motion and structure of the object are perceived nonveridically, with the percept tending to reflect the nonrigid transformations that are present in the retinal image. This difference in response to motion to and from the observer was quantified in an experiment using wire-frame computer-generated boxes which moved toward and away from the eye. Two theoretical systems are developed by which uniform three-dimensional velocity can be recovered from an expansion pattern of nonuniform velocity vectors. It is proposed that the human visual system uses two similar systems for processing motion in depth. The mechanism used for motion away from the eye produces perceptual errors because it is not suited to objects with a depth component.

Perrone, John A.↗

NASA NTRS1991

Development of iterative techniques for the solution of unsteady compressible viscous flows

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Sankar, Lakshmi N.↗

NASA NTRS1992

Dynamic Forms and Their Application to Control

The rigid body model plays a basic role in both mod- and control of many systems, including aircraft flight control. The distinctive feature of the rigid body is that its motion evolves on a curved space, Consequently, the designer must take into account the deterioration of chosen coordinations near their singularities. In these regions the control actions and the sensitivity to modeling and sensor errors become unacceptable. Thus, coordinate patches and patching logic should be a part of the overall control law design and implementation. The various dynamic forms, such as scalar forms, vector forms, matrix forms, rotational forms, Euler angle forms, and Euler parameter forms, described in the paper provide an effective means for coordinate patching and control law implementation. The utility of these forms is illustrated by means of several applications to flight control.

Meyer, George↗

NASA NTRS2007

Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR

An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.

Marcum, David L.↗

NASA NTRS2006

SeaWinds Scatterometer Wind Vector Retrievals Within Hurricanes Using AMSR and NEXRAD to Perform Corrections for Precipitation Effects: Comparison of AMSR and NEXRAD Retrievals of Rain

The opportunity provided by satellite scatterometers to measure ocean surface winds in strong storms and hurricanes is diminished by the errors in the received backscatter (SIGMA-0) caused by the attenuation, scattering and surface roughening produced by heavy rain. Providing a good rain correction is a very challenging problem, particularly at Ku band (13.4 GHz) where rain effects are strong. Corrections to the scatterometer measurements of ocean surface winds can be pursued with either of two different methods: empirical or physical modeling. The latter method is employed in this study because of the availability of near simultaneous and collocated measurements provided by the MIDORI-II suite of instruments. The AMSR was designed to measure atmospheric water-related parameters on a spatial scale comparable to the SeaWinds scatterometer. These quantities can be converted into volumetric attenuation and scattering at the Ku-band frequency of SeaWinds. Optimal estimates of the volume backscatter and attenuation require a knowledge of the three dimensional distribution of reflectivity on a scale comparable to that of the precipitation. Studies selected near the US coastline enable the much higher resolution NEXRAD reflectivity measurements evaluate the AMSR estimates. We are also conducting research into the effects of different beam geometries and nonuniform beamfilling of precipitation within the field-of-view of the AMSR and the scatterometer. Furthermore, both AMSR and NEXRAD estimates of atmospheric correction can be used to produce corrected SIGMA-0s, which are then input to the JPL wind retrieval algorithm.

SeaWinds↗

NASA NTRS1969

Thermal convection at infinite Prandtl number

Numerical solutions are developed for the full scaled three dimensional thermal convection problem, at infinite Prandtl number, and for rigid boundaries. The procedure is designed to give an approximate account of horizontally homogeneous and isotropic flow situations. Results, which included a maximum of 36 horizontal wave number vectors and 20 vertical wave numbers, appear to adequately describe the flow fill up to R = 100,000; beyond this R the results appear to show horizontal wave number truncation error. This error seems to affect the boundary slope of the mean temperature field more than other mean quantities. Despite some numerical uncertainities, certain of the qualitative features of the flow fill are predicted with reasonable confidence.

Herring, J. R.↗

NASA NTRS1977

Updated dispersion analysis for the first Orbital Flight Test (OFT-1) mission

A dispersion analysis considering 3-sigma uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for the first orbital flight test (OFT-1) mission. The dispersion analysis is based on the nominal trajectory for the OFT-1 reference flight profile and was performed to determine state vector and performance dispersions (or variations) which result from the indicated 3 sigma uncertainties. The dispersions are determined at major mission events and fixed times from liftoff (time slices). Principal error contributors to the covariance matrix are listed. The dispersion data indicates that the largest position error occurs in the down range component. At main engine cutoff and circularization, the vehicle performance uncertainties are the major contributors to down range error.

Snow, L. S.↗

NASA NTRS1982

Linear discriminant analysis with misallocation in training samples

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

Chhikara, R.↗

NASA NTRS1984

A comparison of two position estimate algorithms that use ILS localizer and DME information. Simulation and flight test results

Simulation and flight tests were conducted to compare the accuracy of two algorithms designed to compute a position estimate with an airborne navigation computer. Both algorithms used ILS localizer and DME radio signals to compute a position difference vector to be used as an input to the navigation computer position estimate filter. The results of these tests show that the position estimate accuracy and response to artificially induced errors are improved when the position estimate is computed by an algorithm that geometrically combines DME and ILS localizer information to form a single component of error rather than by an algorithm that produces two independent components of error, one from a DMD input and the other from the ILS localizer input.

Knox, C. E.↗

NASA NTRS1988

Estimating residual fault hitting rates by recapture sampling

For the recapture debugging design introduced by Nayak (1988) the problem of estimating the hitting rates of the faults remaining in the system is considered. In the context of a conditional likelihood, moment estimators are derived and are shown to be asymptotically normal and fully efficient. Fixed sample properties of the moment estimators are compared, through simulation, with those of the conditional maximum likelihood estimators. Properties of the conditional model are investigated such as the asymptotic distribution of linear functions of the fault hitting frequencies and a representation of the full data vector in terms of a sequence of independent random vectors. It is assumed that the residual hitting rates follow a log linear rate model and that the testing process is truncated when the gaps between the detection of new errors exceed a fixed amount of time.

Lee, Larry↗

NASA NTRS1997

Predictive Attitude Estimation Using Global Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be non-Gaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-2 spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-2 spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model.

Crassidis, John L.↗

NASA NTRS2003

Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration

It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.

Koshak, William↗

NASA NTRS2005

Estimating moisture transport over oceans using space-based observations

The moisture transport integrated over the depth of the atmosphere (0) is estimated over oceans using satellite data. The transport is the product of the precipitable water and an equivalent velocity (ue), which, by definition, is the depth-averaged wind velocity weighted by humidity. An artificial neural network is employed to construct a relation between the surface wind velocity measured by the spaceborne scatterometer and coincident ue derived using humidity and wind profiles measured by rawinsondes and produced by reanalysis of operational numerical weather prediction (NWP). On the basis of this relation, 0 fields are produced over global tropical and subtropical oceans (40_N- 40_S) at 0.25_ latitude-longitude and twice daily resolutions from August 1999 to December 2003 using surface wind vector from QuikSCAT and precipitable water from the Tropical Rain Measuring Mission. The derived ue were found to capture the major temporal variability when compared with radiosonde measurements. The average error over global oceans, when compared with NWP data, was comparable with the instrument accuracy specification of space-based scatterometers. The global distribution exhibits the known characteristics of, and reveals more detailed variability than in, previous data.

Artificial Neural Network↗