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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

The Impact of Rise of the Andes and Amazon Landscape Evolution on Diversification of Lowland terra-firme Forest Birds

Since the 19th Century, the unmatched biological diversity of Amazonia has stimulated a diverse set of hypotheses accounting for patterns of species diversity and distribution in mega-diverse tropical environments. Unfortunately, the evidence supporting particular hypotheses to date is at best described as ambiguous, and no generalizations have emerged yet, mostly due to the lack of comprehensive comparative phylogeographic studies with thorough trans-Amazonian sampling of lineages. Here we report on spatial and temporal patterns of diversification estimated from mitochondrial gene trees for 31 lineages of birds associated with upland terra-firme forest, the dominant habitat in modern lowland Amazonia. The results confirm the pervasive role of Amazonian rivers as primary barriers separating sister lineages of birds, and a protracted spatio-temporal pattern of diversification, with a gradual reduction of earlier (1st and 2nd) and older (> 2 mya) splits associated with each lineage in an eastward direction. (The easternmost tributaries of the Amazon, the Xingu and Tocantins Rivers, are not associated with any splits older than > 2 mya). For the suboscine passerines, maximum-likelihood estimates of rates of diversification point to an overall constant rate over the past 5 my (up to a significant downturn at 300,000 y ago). This "younging-eastward" pattern may have an abiotic explanation related to landscape evolution. Triggered by a new pulse of Andean uplift, it has been proposed that modern Amazon basin landscapes may have evolved successively eastward, away from the mountain chain, starting approximately 10 mya. This process was likely based on the deposition of vast fluvial sediment masses, known as megafans, that may have extended progressively and in series eastward from Andean sources. This process plausibly explains the progressive extinction of original Pebas wetland of western-central Amazonia by the present fluvial landsurfaces of a more terra-firme type. The youngest landsurfaces thus lie furthest from the mountains. In this scenario major drainages were also reoriented in wholesale fashion away from a northerly orientation generally towards the east and an Atlantic Ocean outlet. The advance of megafans is best seen by the location of axial rivers such as the Orinoco and Mamore which lie against the cratonic margins furthest from the Andes, at the distal ends of major megafan ramparts. More importantly, other major river courses in western-central Amazonia will have been established at progressively younger dates with distance eastward. If this landscape-sequence scenario is accurate, it parallels the progressive younging of the passerine lineages. The bird DNA data appears to confirm strongly the pervasive role of Amazonian rivers--as primary barriers separating sister lineages of birds, and thus probably as facilitaters of bird speciation. We show for the first time that a general spatio-temporal pattern of diversification for terra-firme lineages in the Amazon is associated with rivers ("younging-eastward"), and furthermore parallels a specific scenario of regional drainage evolution.

Aleixo, Alexandre↗
NASA NTRS1981

Selected stability and control derivatives from the first Space Shuttle entry

Primary stability and control derivative estimates garnered from the first Shuttle entry are reported. The craft was the first vehicle to maneuver over a wide range of hypersonic velocities, yielding data on flight characteristics from previously unexplored regimes. The flight envelope was confined to entry and safe landing, with no additional maneuvers to gain control data. Data for a Mach number range of 25-1.5 and altitudes of 515,000-50,000 ft are provided, and functional ranges of the Shuttle control surfaces and attitude jets are outlined. On-board systems gathered data on aerodynamic coefficient identification, flight condition and Euler angles, and jet chamber pressures. A maximum likelihood estimation program, which contained unknown stability and control derivatives, was used for control; a control input determined the value of the unknown derivatives, and the input and spacecraft response were measured. Longitudinal and lateral directional maneuvers and their derivative estimates are described, noting wind contamination of the sideslip measurements below Mach 3. Further maneuvering and stability tests are projected for subsequent flights.

Iliff, K. W.↗
NASA NTRS2007

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗
NASA NTRS1999

How to Estimate Attitude from Vector Observations

In many spacecraft attitude systems, the attitude observations are naturally represented as unit vectors. Typical examples are the unit vectors giving the direction to the sun or a star and the unit vector in the direction of the Earth's magnetic field. In 1965, Grace Wahba, proposed the following problem: Find the orthogonal matrix A with determinant +1 that minimizes the loss function L(A) is identity with 1/2(Sum from i a(sub i) (absolute value of b(sub i - A(r(sub i))(exp 2))) where the set of b(sub i) is a set of unit vectors measured in a spacecraft's body frame, the set of r(sub i) are the corresponding unit vectors in a reference frame, and the set of a(sub i) are non-negative weights. Wahba's problem can be related to Maximum Likelihood Estimation if the weights are chosen to be inverse variances, a(sub i) = sigma((sub -2). Wahba didn't assume this, but it will be convenient to assume it in this paper. Wahba'soptimality condition has provided the basis for many attitude determination algorithms. The purpose of this paper is to give an overview of the most popular and most promising algorithm and to provide accuracy and speed comparisons.

Markley,F. Landis↗
NASA NTRS1994

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Shen, Ji-Yao↗
NASA NTRS1972

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Grove, R. D.↗
NASA NTRS1990

Application of a novel multi-stage signal parameter estimator to high dynamic GPS receivers

The performance of a novel multistage estimator when applied to the estimation of the position, velocity, and acceleration of high dynamic Global Positioning System (GPS) receivers is discussed. For the present application, a two-stage specialization of the more general estimation scheme is considered, wherein the first-stage algorithm is selected to be a modified least-squares algorithm operating upon the differential signal model and referred to as differential least-squares (DLS) and the second stage is simply an extended Kalman filter (EKF). In terms of the threshold on received carrier power-to-noise power spectral density ratio (CNR), when compared to the single-stage EKF algorithm, the DLS-EKF algorithm is about 1.5-2.0 dB better in terms of threshold and outperforms the crossproduct AFC (automatic frequency control) loop by 2-5 dB. For the case when data modulation is present, the proposed scheme provides an improvement of about 6 dB in terms of CNR compared to an earlier approximate MLE (maximum likelihood estimation) scheme. There are also very significant improvements in terms of other performance measures.

Kumar, R.↗
NASA NTRS1985

Post-flight BET products for the 2nd discovery entry, STS-19 (51-A)

The post-flight products for the second Discovery flight, STS-19 (51-A), are summarized. The inertial best estimate trajectory (BET), BT19D19/UN=169750N, was developed using spacecraft dynamic measurements from Inertial Measurement Unit 2 (IMU2) in conjunction with the best tracking coverage available for any of the earlier Shuttle entries. As a consequence of the latter, an anchor epoch was selected which conforms to an initial altitude of greater than a million feet. The Extended BET, ST19BET/UN=274885C, incorporated the previously mentioned inertial reconstructed state information and the Langley Atmospheric Information Retrieval System (LAIRS) atmosphere, ST19MET/UN=712662N, with some minor exceptions. Primary and back-up AEROBET reels are NK0165 and NK0201, respectively. This product was only developed over the lowermost 360 kft altitude range due to atmosphere problems but this relates to altitudes well above meaningful signal in the IMUs. Summary results generated from the AEROBET for this flight are presented with meaningful configuration and statistical comparisons from the previous thirteen flights. Modified maximum likelihood estimation (MMLE) files were generated based on IMU2 and the Rate Gyro Assembly/Accelerometer Assembly (RGA/AA), respectively. Appendices attached define spacecraft and physical constants utilized, show plots of the final tracking data residuals from the post-flight fit, list relevant parameters from the BET at a two second spacing, and retain for archival purpose all relevant input and output tapes and files generated.

Kelly, G. M.↗
NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗
NASA NTRS1967

Computer program reduces calculation time of normal response functions

FORTRAN 2 computer program rapidly calculates parameters of maximum likelihood estimates from sensitivity experiment data populations. The program uses the Newton-Raphson iterative procedure to calculate the mean and standard deviation of portions of the cumulative normal response function.

Alexander, M. J.↗
NASA NTRS1971

The application of signal detection theory to optics

The restoration of images focused on a photosensitive surface is treated from the standpoint of maximum likelihood estimation, taking into account the Poisson distributions of the observed data, which are the numbers of photoelectrons from various elements of the surface. A detector of an image focused on such a surface utilizes a certain linear combination of those numbers as the optimum detection statistic. Methods for calculating the false alarm and detection probabilities are proposed. It is shown that measuring noncommuting observables in an ideal quantum receiver cannot yield a lower Bayes cost than that attainable by a system measuring only commuting observables.

Helstrom, C. W.↗
NASA NTRS1971

A system debugging model.

Consideration of the nature of the 'debugging' process applied to a new complex system during the initial period of its life. During this period failures and errors are corrected as they occur, with resulting improvement in the subsequent performance of the system. One mathematical idealization of this process leads to the assumption that system failure rate is decreasing with time. In practice, the debugging phase is considered completed when the failure rate reaches an equilibrium or constant value. Models are formulated for this phenomenon. Maximum likelihood estimates are obtained for relevant failure rate functions and for the end of the debugging period. A conservative upper confidence bound on the stable failure rate is obtained.

Barlow, R. E.↗
NASA NTRS1972

Two stochastic models useful in petroleum exploration

A model of the petroleum exploration process that tests empirically the hypothesis that at an early stage in the exploration of a basin, the process behaves like sampling without replacement is proposed along with a model of the spatial distribution of petroleum reserviors that conforms to observed facts. In developing the model of discovery, the following topics are discussed: probabilitistic proportionality, likelihood function, and maximum likelihood estimation. In addition, the spatial model is described, which is defined as a stochastic process generating values of a sequence or random variables in a way that simulates the frequency distribution of areal extent, the geographic location, and shape of oil deposits

Kaufman, G. M.↗
NASA NTRS1974

An analysis and demonstration of clock synchronization by VLBI

A prototype of a semi-real time system for synchronizing the Deep Space Net station clocks by radio interferometry was successfully demonstrated on August 30, 1972. The system utilized an approximate maximum likelihood estimation procedure for processing the data, thereby achieving essentially optimum time sync estimates for a given amount of data, or equivalently, minimizing the amount of data required for reliable estimation. Synchronization accuracies as good as 100 ns rms were achieved between Deep Space Stations 11 and 12, both at Goldstone, Calif. The accuracy can be improved by increasing the system bandwidth until the fundamental limitations due to baseline and source position uncertainties and atmospheric effects are reached. These limitations are under 10 ns for transcontinental baselines.

Hurd, W. J.↗
NASA NTRS1972

An analysis and demonstration of clock synchronization by VLBI

A prototype of a semireal-time system for synchronizing the DSN station clocks by radio interferometry was successfully demonstrated. The system utilized an approximate maximum likelihood estimation procedure for processing the data, thereby achieving essentially optimum time synchronization estimates for a given amount of data, or equivalently, minimizing the amount of data required for reliable estimation. Synchronization accuracies as good as 100 nsec rms were achieved between DSS 11 and DSS 12, both at Goldstone, California. The accuracy can be improved by increasing the system bandwidth until the fundamental limitations due to position uncertainties of baseline and source and atmospheric effects are reached. These limitations are under ten nsec for transcontinental baselines.

Hurd, W. J.↗