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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 NTRS1992

Frequency domain state-space system identification

An algorithm for identifying state-space models from frequency response data of linear systems is presented. A matrix-fraction description of the transfer function is employed to curve-fit the frequency response data, using the least-squares method. The parameters of the matrix-fraction representation are then used to construct the Markov parameters of the system. Finally, state-space models are obtained through the Eigensystem Realization Algorithm using Markov parameters. The main advantage of this approach is that the curve-fitting and the Markov parameter construction are linear problems which avoid the difficulties of nonlinear optimization of other approaches. Another advantage is that it avoids windowing distortions associated with other frequency domain methods.

Chen, Chung-Wen↗
NASA NTRS1988

International Conference on Advances in Communication and Control Systems, 1st, Washington, DC, June 18-20, 1987, Proceedings

Theoretical models of communication and control systems are discussed in reviews and reports. Topics addressed include smoothing and identification for random fields, the information and coding capacities of mismatched Gaussian channels, recursive least-squares estimation and Kalman filtering by systolic arrays, Kemp echo digital filters, a periodic test-scheduling scheme for communication and queuing processes, and receivers for direct-sequence systems. Consideration is given to a distributed-parameter model for detecting cracks in rotors, active control of aeroelastic systems governed by functional differential equations, robust multivariable control of large space structures, finite-rank relatively bounded perturbations of semigroup generators, and sensitivity analysis of convex optimal-control problems.

Declaris, Nicholas↗
NASA NTRS1998

Efficient and Optimal Attitude Determination Using Recursive Global Positioning System Signal Operations

In this paper, a new and efficient algorithm is developed for attitude determination from Global Positioning System signals. The new algorithm is derived from a generalized nonlinear predictive filter for nonlinear systems. This uses a one time-step ahead approach to propagate a simple kinematics model for attitude determination. The advantages of the new algorithm over previously developed methods include: it provides optimal attitudes even for coplanar baseline configurations; it guarantees convergence even for poor initial conditions; it is a non-iterative algorithm; and it is computationally efficient. These advantages clearly make the new algorithm well suited to on-board applications. The performance of the new algorithm is tested on a dynamic hardware simulator. Results indicate that the new algorithm accurately estimates the attitude of a moving vehicle, and provides robust attitude estimates even when other methods, such as a linearized least-squares approach, fail due to poor initial starting conditions.

Crassidis, John L.↗
NASA NTRS2007

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least-squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

Litt, Jonathan S.↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗
NASA NTRS2013

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS2014

Grail Refinements to Lunar Seismic Structure

To probe a planet's interior, seismology provides the most direct constraints on the variables that govern the dynamic properties of the body. However, the GRAIL (Gravity Recovery and Interior Laboratory) mission's high-resolution measurements of the lunar gravity field provide constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten). These data complement seismic investigations, and joint interpretation permits improved constraints on the Moon's internal structure. Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS1989

Optimum data weighting and error calibration for estimation of gravitational parameters

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least-squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 Goddard Earth Model-T1 (GEM-T1) were employed toward application of this technique for gravity field parameters. Also GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized. The method employs subset solutions of the data associated with the complete solution to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Lerch, Francis J.↗
DOE OSTI2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗
NASA NTRS1993

Identification of integrated airframe-propulsion effects on an F-15 aircraft for application to drag minimization

The application of an adaptive real-time measurement-based performance optimization technique is being explored for a future flight research program. The key technical challenge of the approach is parameter identification, which uses a perturbation-search technique to identify changes in performance caused by forced oscillations of the controls. The controls on the NASA F-15 highly integrated digital electronic control (HIDEC) aircraft were perturbed using inlet cowl rotation steps at various subsonic and supersonic flight conditions to determine the effect on aircraft performance. The feasibility of the perturbation-search technique for identifying integrated airframe-propulsion system performance effects was successfully shown through flight experiments and postflight data analysis. Aircraft response and control data were analyzed postflight to identify gradients and to determine the minimum drag point. Changes in longitudinal acceleration as small as 0.004 g were measured, and absolute resolution was estimated to be 0.002 g or approximately 50 lbf of drag. Two techniques for identifying performance gradients were compared: a least-squares estimation algorithm and a modified maximum likelihood estimator algorithm. A complementary filter algorithm was used with the least squares estimator.

Schkolnik, Gerald S.↗
NASA NTRS1993

Identification of integrated airframe: Propulsion effects on an F-15 aircraft for application to drag minimization

The application of an adaptive real-time measurement-based performance optimization technique is being explored for a future flight research program. The key technical challenge of the approach is parameter identification, which uses a perturbation-search technique to identify changes in performance caused by forced oscillations of the controls. The controls on the NASA F-15 highly integrated digital electronic control (HIDEC) aircraft were perturbed using inlet cowl rotation steps at various subsonic and supersonic flight conditions to determine the effect on aircraft performance. The feasibility of the perturbation-search technique for identifying integrated airframe-propulsion system performance effects was successfully shown through flight experiments and postflight data analysis. Aircraft response and control data were analyzed postflight to identify gradients and to determine the minimum drag point. Changes in longitudinal acceleration as small as 0.004 g were measured, and absolute resolution was estimated to be 0.002 g or approximately 50 lbf of drag. Two techniques for identifying performance gradients were compared: a least-squares estimation algorithm and a modified maximum likelihood estimator algorithm. A complementary filter algorithm was used with the least squares estimator.

Schkolnik, Gerard S.↗
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Liu, Yen↗
NASA NTRS2001

Model-based parameter estimation using cardiovascular response to orthostatic stress

This paper presents a cardiovascular model that is capable of simulating the short-term (< or approximately equal to 3 min) transient hemodynamic response to gravitational stress and a gradient-based optimization method that allows for the automated estimation of model parameters from simulated or experimental data. We perform a sensitivity analysis of the transient heart rate response to determine which parameters of the model impact the heart rate dynamics significantly. We subsequently include only those parameters in the estimation routine that impact the transient heart rate dynamics substantially. We apply the estimation algorithm to both simulated and real data and showed that restriction to the 20 most important parameters does not impair our ability to match the data.

Non-NASA Center↗
NASA NTRS2014

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude, and depth within the Moon. We relate density (p) to seismic velocity (v) using a depth-dependent linear relationship. The corresponding coefficient (B) can reflect a variety of material properties, including temperature and composition. The inversion seeks to recover the set of p, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS1999

Improving Reanalyses Using TRMM and SSM/I-Derived Precipitation and Total Precipitable Water Observations

Global reanalyses currently contain significant errors in the primary fields of the hydrological cycle such as precipitation, evaporation, moisture, and the related cloud fields, especially in the tropics. The Data Assimilation Office (DAO) at the NASA Goddard Space Flight Center has been exploring the use of rainfall and total precipitable water (TPW) observations from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and the Special Sensor Microwave/ Imager (SSM/I) instruments to improve these fields in reanalyses. The DAO has developed a "1+1"D procedure to assimilate 6-hr averaged rainfall and TPW into the Goddard Earth Observing System (GEOS) Data Assimilation System (DAS). The algorithm is based on a 6-hr time integration of a column version of the GEOS DAS. The "1+1" designation refers to one spatial dimension plus one temporal dimension. The scheme minimizes the least-square differences between the satellite-retrieved rain rates and those produced by the column model over the 6-hr analysis window. The control variables are analysis increments of moisture within the Incremental Analysis Update (IAU) framework of the GEOS DAS. This 1+1D scheme, in its generalization to four dimensions, is related to the standard 4D variational assimilation but differs in its choice of the control variable. Instead of estimating the initial condition at the beginning of the assimilation cycle, it estimates the constant IAU forcing applied over a 6-hr assimilation cycle. In doing so, it imposes the forecast model as a weak constraint in a manner similar to the variational continuous assimilation techniques. We present results from an experiment in which the observed rain rate and TPW are assumed to be "perfect". They show that assimilating the TMI and SSM/I-derived surface precipitation and TPW observations improves not only the precipitation and moisture fields but also key climate parameters directly linked to convective activities such as clouds, the outgoing longwave radiation, and the large-scale circulation in the tropics. In particular, assimilating these data types reduce the state-dependent systematic errors in the assimilated products. The improved analysis also leads to a better short-range forecast, but the impact is modest compared with improvements in the time-averaged fields. These results suggest that, in the presence of biases and other errors of the forecast model, it is possible to improve the time-averaged "climate content" in the assimilated data without comparable improvements in the short-range forecast skill. Results of this experiment provide a useful benchmark for evaluating error covariance models for optimal use of these data types.

Hou, Arthur Y.↗