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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2000

Morphology of Mars North Polar Ice Cap

The northern ice cap of Mars consists of a parabolic dome centered within 13 km of the pole, plus an arm-like ridge extending from the dome between about 135 and 225 east. Chasma Boreale lies between the dome and the extended ridge. The base of the dome is approximately elliptical with a major axis of 1100 km along the 90 east to 270 east direction and minor axis of 700 km along zero east to 180 deg. The heights of the dome and the extended ridge are respectively 2900 inches and 1700 inches above the surrounding basin. Least-squares fitting of a parabola through height profiles of the dome along longitudes 90 deg to 270 deg and zero deg to 180 deg gives an elliptic-paraboloid equation for the dome: Z(m) = 2800 - [(X-x)(exp 2)/113.6] - [(Y-y)(exp 2)/50.3], where X is the 90 deg to 270 deg axis, x = 9.90 km, y = 13.32 km, and the slightly-different fitted heights for the two axes are averaged. The center of the dome is shifted 13.32 km from the pole along zero deg longitude and 9.90 km along 90 deg longitude. Typical mean surface slopes on the ice cap are the order of 1/100 (0.6 deg), A small central portion of the cap, about 100 km by 200 km, extends in elevation about 200 inches above the parabolic shape of the cap. Additional information is contained in the original extended abstract.

Zwally, H. J.↗

NASA NTRS2022

Exploration of an Adaptive Routine for Battery Modeling

The purpose of this document is to explore the use of adaptive routines in battery modeling. The adaptive routines consist of real-time state estimators combined with battery parameter model components that are adjusted in real-time as battery data becomes available. Several aspects are explored. It is shown that model parameter identification is possible for simple battery models using available input/output data measurements. The online system identification used is recursive least squares. Model identification may be combined with a state observer such as the extended Kalman filter or the unscented Kalman filter to form an adaptive model combined with state estimation. However, such a combination is found to be problematic due to uncertainty, observability and stability issues. This paper is organized as follows. Section 1 introduces adaptive routines and possible roles they play in battery modeling. In Section 2 real-time parameter identification is described with results based on battery data. Section 3 reviews various state estimators and results using a simple battery model. In Section 4 parameter identification and state estimation are combined to form an adaptive routine. Finally, in Section 5 conclusions are drawn and future work is suggested.

Adaptive↗

NASA NTRS1974

Helicopter derivative identification from analytic models and flight test data

Recent results of stability derivative identification from helicopter analytic models and flight test data are presented. Six and nine degree-of-freedom (DOF) linear models are identified from an analytic nonlinear helicopter simulation using a least square technique. The identified models are compared with the convectional partial differentiation method for obtaining derivatives to form the basis for interpretation of derivatives identified from flight data. Six degree-of-freedom models are identified from CH-53A and CH-54B flight data, using an extended Kalman filter modified to process several maneuvers simultaneously. The a priori derivative estimate is obtained by optimal filtering of the data and then using a least square method. The results demonstrate that a six DOF identified model is sufficient to determine the low frequency modes of motion, but a nine DOF rotor/body model is necessary for proper representation of short-term response.

Molusis, J. H.↗

NASA NTRS1990

Parameter identification for nonlinear aerodynamic systems

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Pearson, Allan E.↗

NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗

NASA NTRS2003

Real-Time Attitude Independent Three Axis Magnetometer Calibration

In this paper new real-time approaches for three-axis magnetometer sensor calibration are derived. These approaches rely on a conversion of the magnetometer-body and geomagnetic-reference vectors into an attitude independent observation by using scalar checking. The goal of the full calibration problem involves the determination of the magnetometer bias vector, scale factors and non-orthogonality corrections. Although the actual solution to this full calibration problem involves the minimization of a quartic loss function, the problem can be converted into a quadratic loss function by a centering approximation. This leads to a simple batch linear least squares solution. In this paper we develop alternative real-time algorithms based on both the extended Kalman filter and Unscented filter. With these real-time algorithms, a full magnetometer calibration can now be performed on-orbit during typical spacecraft mission-mode operations. Simulation results indicate that both algorithms provide accurate integer resolution in real time, but the Unscented filter is more robust to large initial condition errors than the extended Kalman filter. The algorithms are also tested using actual data from the Transition Region and Coronal Explorer (TRACE).

Crassidis, John L.↗

NASA NTRS1991

Analytical modelling of laminated composites

This paper presents a unique approach to the analysis of thick laminated composites by presenting two simple finite element methods. The first uses the predictor corrector technique to extend the simple Mindlin-type element to achieve greater accuracy, and the second develops a new least squares element which can approximate a C(1) continuous element. The least squares element has the capability to incorporate a simplified higher-order basis into a piecewise continuous displacement field creating an accurate, yet computationally simple, element. These two methods have the potential to significantly upgrade analysis methods with little additional computational cost.

Kouri, Jeffrey V.↗

NASA NTRS2012

Linear Covariance Analysis and Epoch State Estimators

This paper extends in two directions the results of prior work on generalized linear covariance analysis of both batch least-squares and sequential estimators. The first is an improved treatment of process noise in the batch, or epoch state, estimator with an epoch time that may be later than some or all of the measurements in the batch. The second is to account for process noise in specifying the gains in the epoch state estimator. We establish the conditions under which the latter estimator is equivalent to the Kalman filter.

Markley, F. Landis↗

NASA NTRS2014

Linear Covariance Analysis and Epoch State Estimators

Linear covariance analysis↗

NASA NTRS1989

A novel multistage estimation of the signal parameters of a possibly data-modulated sinusoid under very high dynamics

A novel multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data, and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity, acceleration and jerk of the GPS receiver. In the proposed multistage scheme, the first stage estimator operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second state of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. 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. This estimation stage provides relatively coarse estimates of the frequency and its derivatives. The second algorithm is simply an extended Kalman filter which also yields the estimate of the phase along with a more refined estimate of frequency as well. A major advantage of the proposed algorithm is a reduction in the threshold on received carrier power-to-noise power spectral density ratio as compared to the threshold achievable by either of these algorithms alone. In fact, it appears from the simulations that for the case of an unmodulated carrier, the proposed scheme achieves the same threshold as for an almost exact and computationally intensive implementation of the maximum likelihood estimator.

Kumar, Rajendra↗

NASA NTRS2015

Orbit Determination for the Lunar Reconnaissance Orbiter Using an Extended Kalman Filter

Since launch, the FDF has performed daily OD for LRO using the Goddard Trajectory Determination System (GTDS). GTDS is a batch least-squares (BLS) estimator. The tracking data arc for OD is 36 hours. Current operational OD uses 200 x 200 lunar gravity, solid lunar tides, solar radiation pressure (SRP) using a spherical spacecraft area model, and point mass gravity for the Earth, Sun, and Jupiter. LRO tracking data consists of range and range-rate measurements from: Universal Space Network (USN) stations in Sweden, Germany, Australia, and Hawaii. A NASA antenna at White Sands, New Mexico (WS1S). NASA Deep Space Network (DSN) stations. DSN data was sparse and not included in this study. Tracking is predominantly (50) from WS1S. The OD accuracy requirements are: Definitive ephemeris accuracy of 500 meters total position root-mean-squared (RMS) and18 meters radial RMS. Predicted orbit accuracy less than 800 meters root sum squared (RSS) over an 84-hour prediction span.

LRO↗

NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗

NASA NTRSDate not supplied

A 3-D Nodal-Averaged Gradient Approach for Unstructured-Grid Cell-Centered Finite-Volume Methods for Application to Turbulent Hypersonic Flow

A 2-D nodal weighted least-squares gradient method and a related face-averaged nodal gradient approach that were developed for use with triangular grids are extended to 3-D for use with tetrahedral grids. In addition, a method, developed in 2-D, to stabilize the iterative convergence of these methods on quadrilateral cells is described and extended to 3-D and remedies are investigated to determine the nodal gradient averaging approach most suitable for use with grids made up of hexahedral, prismatic, pyramidal and tetrahedral cells. Moreover, due to an interest in hypersonic flow, a robust multidimensional gradient limiter procedure that is consistent with the stencil used to construct the nodal gradients is described. Finally, we demonstrate that the resulting 3-D methods are sufficiently robust for use in scramjet computations through the solution of three canonical turbulent hypersonic flow problems as well as a physically realistic 3-D scramjet inlet geometry.

Jeffery A White↗

NASA NTRS1988

On the Wiener-Masani algorithm for finding the generating function of multivariate stochastic processes

The algorithms developed by Wiener and Masani (1957 and 1958) and Masani (1960) for the characterization of a class of multivariate stationary stochastic processes are investigated analytically. The algorithms permit the determination of (1) the generating function, (2) the prediction-error matrix, and (3) an autoregressive representation of the linear least-squares predictor. A number of theorems and lemmas are proved, and it is shown that the range of validity of the algorithms can be extended significantly beyond that given by Wiener and Masani.

Miamee, A. G.↗

NASA NTRS1992

A new algorithm for L2 optimal model reduction

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗

NASA NTRS1971

The effects of random accelerations on estimation accuracy with applications to the Mariner 1969 relativity experiment

A simple point of view is presented for establishing the relationship between a general modeling error and estimation accuracy. Tentative models are given for the random, nongravitational forces thought likely to affect the Mariner 6 and 7 spacecraft. The navigation data from these spacecraft were used to determine the relativity parameter Gamma. The effect that random accelerations have on the classical least squares filter, which assumes the accelerations do not exist, is calculated, and it is demonstrated that their presence seriously affects the estimates, particularly when an extended data arc is employed. Finally, some preliminary exploration using sequential-type filters, which attempt to model and thus ameliorate the effects of these same accelerations, is reported.

Curkendall, D. W.↗

NASA NTRS1980

Analysis of estimation algorithms for autonomous navigation with TDRSS data

Estimation techniques for onboard orbit determination using Tracking and Data Relay Satellite System (TDRSS) data are investigated. The two user satellite orbits studied are similar to Landsat-D (near-circular, 700 kilometers altitude, near-polar inclination). The following estimation algorithms are identified as candidates for use in autonomous navigation: (1) the extended Kalman filter with process noise, (2) the EKF with consider parameters, (3) the sequential Kalman filter with consider parameters, and (4) the batch least-squares differential correction technique. The candidate estimators are evaluated with respect to their performance with both baseline and worst TDRSS measurement errors and tracking configurations.

Dunham, J.↗

NASA NTRS1978

Time delay occultation data of the Helios spacecraft for probing the electron density distribution in the solar corona

S-band time delay measurements were collected from the spacecraft Helios A and B during three solar occultations in 1975/76 within heliocentric distances of about 3 and 215 earth radius in terms of range, Doppler frequency shift, and electron content. Characteristic features of measurement and data processing are described. Typical data sets are discussed to probe the electron density distribution near the sun (west and east limb as well) including the outer and extended corona. Steady-state and dynamical aspects of the solar corona are presented and compared with earth-bound-K-coronagraph measurements. Using a weighted least squares estimation, parameters of an average coronal electron density profile are derived in a preliminary analysis to yield electron densities at r = 3, 65, 215 earth radius. Transient phenomena are discussed and a velocity of propagation v is nearly equal to 900 km/s is determined for plasma ejecta from a solar flare observed during an extraordinary set of Helios B electron content measurements.

Edenhofer, P.↗