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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Choi, Benjamin B.↗
NASA NTRS1983

Identification of helicopter rotor dynamic models

A recursive, extended Kalman-filter approach is applied to the identifiction of rotor damping levels of representative helicopter dynamic systems. The general formulation of the approach is presented in the context of a typically posed stochastic estimation problem, and the method is analytically applied to determining the damping levels of a coupled rotor-body system. The identified damping covergence characteristics are studied for sensitivity to both constant-coefficient and periodic-coefficient measurement models, process-noise covariance levels, and specified initial estimates of the rotor-system damping. A second application of the method to identifying the plant model for a highly damped, isolated flapping blade with a constant-coefficient state model (hover) and a periodic-coefficient state model (forward flight) is also investigated. The parameter-identification capability is evaluated for the effect of periodicity on the plant model coefficients and the influence of different measurement noise levels.

Molusis, J. A.↗
NASA NTRS1999

An Adaptive Kalman Filter using a Simple Residual Tuning Method

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Harman, Richard R.↗
NASA NTRS1999

An Adaptive Kalman Filter Using a Simple Residual Tuning Method

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Harman, Richard R.↗
NASA NTRS1989

Analysis of modified SMI method for adaptive array weight control

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Dilsavor, R. L.↗
NASA NTRS1995

Analysis of filter tuning techniques for sequential orbit determination

This paper examines filter tuning techniques for a sequential orbit determination (OD) covariance analysis. Recently, there has been a renewed interest in sequential OD, primarily due to the successful flight qualification of the Tracking and Data Relay Satellite System (TDRSS) Onboard Navigation System (TONS) using Doppler data extracted onboard the Extreme Ultraviolet Explorer (EUVE) spacecraft. TONS computes highly accurate orbit solutions onboard the spacecraft in realtime using a sequential filter. As the result of the successful TONS-EUVE flight qualification experiment, the Earth Observing System (EOS) AM-1 Project has selected TONS as the prime navigation system. In addition, sequential OD methods can be used successfully for ground OD. Whether data are processed onboard or on the ground, a sequential OD procedure is generally favored over a batch technique when a realtime automated OD system is desired. Recently, OD covariance analyses were performed for the TONS-EUVE and TONS-EOS missions using the sequential processing options of the Orbit Determination Error Analysis System (ODEAS). ODEAS is the primary covariance analysis system used by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The results of these analyses revealed a high sensitivity of the OD solutions to the state process noise filter tuning parameters. The covariance analysis results show that the state estimate error contributions from measurement-related error sources, especially those due to the random noise and satellite-to-satellite ionospheric refraction correction errors, increase rapidly as the state process noise increases. These results prompted an in-depth investigation of the role of the filter tuning parameters in sequential OD covariance analysis. This paper analyzes how the spacecraft state estimate errors due to dynamic and measurement-related error sources are affected by the process noise level used. This information is then used to establish guidelines for determining optimal filter tuning parameters in a given sequential OD scenario for both covariance analysis and actual OD. Comparisons are also made with corresponding definitive OD results available from the TONS-EUVE analysis.

Lee, T.↗
NASA NTRS1992

Maximum likelihood techniques applied to quasi-elastic light scattering

There is a necessity of having an automatic procedure for reliable estimation of the quality of the measurement of particle size from QELS (Quasi-Elastic Light Scattering). Getting the measurement itself, before any error estimates can be made, is a problem because it is obtained by a very indirect measurement of a signal derived from the motion of particles in the system and requires the solution of an inverse problem. The eigenvalue structure of the transform that generates the signal is such that an arbitrarily small amount of noise can obliterate parts of any practical inversion spectrum. This project uses the Maximum Likelihood Estimation (MLE) as a framework to generate a theory and a functioning set of software to oversee the measurement process and extract the particle size information, while at the same time providing error estimates for those measurements. The theory involved verifying a correct form of the covariance matrix for the noise on the measurement and then estimating particle size parameters using a modified histogram approach.

Edwards, Robert V.↗
NASA NTRS1980

Implicit model following and parameter identification of unstable aircraft

A transformation in the s-plane is described which has utility in implicit model-following optimal control design application and in estimation or parameter identification problems. The objective of the transformation is, for the control problem, to achieve an unstable closed-loop system, and, for the estimation problem, to alleviate algorithm convergence problems that may arise in identifying unstable systems. For the control problem, the transformation is a shift along the real (sigma) axis of the plant and model poles and zeros. This transformation is shown to be equivalent to a modified performance index but offers the advantage of compatibility with existing optimal control solution algorithms. For the estimation problem, the data are multiplied by an exponential function and the assumed measurement and process noise covariances are appropriately modified. Examples of both control and estimation applications are presented.

Lebacqz, J. V.↗
NASA NTRS1991

Characterization of frequency standard instability by estimation of their covariance matrix

The popular 3-cornered hat method used for evaluating the noise contributions of individual frequency standards is revisited. This method is used in several cases, but sometimes the results are not consistent because one or more estimated clock variances turn out to be negative. Different causes of this unacceptable result have been conjectured: among them one regards the hypothesis of uncorrelated clocks, essential in this method. Since recently realistic cases of correlation between clocks, mainly due to the environmental conditions, have been observed, this paper proposes an entirely revisited version of the 3-cornered hat method which permits to evaluate the individual variances and also the possible covariances between clocks, by relaxing the hypothesis of uncorrelation. The uncertainty and the lack of contemporaneity of the measurement series are assumed to be negligible. The lack of the uncorrelation hypothesis calls for a more general mathematical model leading to an underdetermined linear system. The estimates of the (co)variances of the measurement series us well us those of the individual clocks are introduced by means of the scalar product of the related time series and arranged in the respective covariance matrices S and R. Since covariance matrix is positive definite by definition, the problem consists in estimating the unknown R, subject to the constraint of positive definiteness, from the known S. Unfortunately, this constraint is not sufficient to estimate R. Therefore a suitable optimization criterion is proposed, which assures the positive definiteness of R and, at the same time, minimizes the global correlation among clocks. Examples of frequency instability measurements processed by the "classical" 3-cornered hat method and the here-revisited method are presented showing that the solutions are identical only when the uncorrelation hypothesis doesn't violate the positive definiteness of R.

PatriziaTravella↗
NASA NTRS1982

Application of a recursive distortion estimator to the geodetic correction of thematic mapper imagery

It is pointed out that the higher resolution provided by the Thematic Mapper increases the demands on the accuracy needed by the ground processing in correcting for geodetic errors deriving from internal misalignments and uncertainties in the knowledge of spacecraft ephemeris and attitude. In addition, the Thematic Mapper will also process longer imagery intervals than previous missions. The recursive distortion estimator to be used is a Kalman filter. Here, a minimum variance spacecraft state error vector is estimated for known initial covariance of the elements of that vector and known image noise. Tests of the recursive distortion estimator with various spacecraft models carried out using a simulation of real world state vector dynamics are described. A determination is made of the density of control points needed to meet specified geometric correction requirements; it is expressed as a function of imagery interval length and control point measurement error.

Arnold, P.↗
NASA NTRSDate not supplied

From Formal Errors Towards Realistic Uncertainties

Evaluation of uncertainties of geodetic parameter estimates is the problem that is not yet solved in a satisfactory way. A direct evaluation of the uncertainties derived from a least square solution is labeled "formal" and is usually biased, sometimes up to an order of magnitude. Customary, the use of formal errors for scientific analysis is discouraged. We claim that the root of the problem is neglecting off-diagonal elements in the variance-covariance matrix of the noise in the data. A careful reconstruction of the full variance-covariance matrix, including the off-diagonal terms greatly improves realism of uncertainty estimates derived from least squares. We processed the dataset of VLBI group delays and built a prior variance-covariance of the atmosphere-driven noise based on analysis of the output of NASA high-resolution numerical weather models. We found that the uncertainties of parameter estimates derived from this least square solution that uses such variance-covariance matrices become much closer to realistic errors. We consider approaches for implementation of this method in routine data analysis of space geodesy data.

Leonid Petrov↗
DOE OSTI2023

BEYONDPLANCK II. CMB mapmaking through Gibbs sampling

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1974

Square-root algorithm for evaluating mismodeled process noise

As the application of sequential filters has grown, the need has arisen to evaluate the sensitivity of these filters to mismodeling of the random process. A numerically reliable square-root algorithm is developed for calculating the covariances of estimates from a sequential filter which incorrectly models process noise. Mismodeling is restricted to the correlation time and standard deviation of a random process represented as a first-order Gauss-Markov sequence. Using a computer program which employs this algorithm, a sensitivity analysis was performed for several types of earth-based tracking data from an interplanetary spacecraft.

Thornton, C. L.↗
NASA NTRS2002

Partially Decentralized Control Architectures for Satellite Formations

In a partially decentralized control architecture, more than one but less than all nodes have supervisory capability. This paper describes an approach to choosing the number of supervisors in such au architecture, based on a reliability vs. cost trade. It also considers the implications of these results for the design of navigation systems for satellite formations that could be controlled with a partially decentralized architecture. Using an assumed cost model, analytic and simulation-based results indicate that it may be cheaper to achieve a given overall system reliability with a partially decentralized architecture containing only a few supervisors, than with either fully decentralized or purely centralized architectures. Nominally, the subset of supervisors may act as centralized estimation and control nodes for corresponding subsets of the remaining subordinate nodes, and act as decentralized estimation and control peers with respect to each other. However, in the context of partially decentralized satellite formation control, the absolute positions and velocities of each spacecraft are unique, so that correlations which make estimates using only local information suboptimal only occur through common biases and process noise. Covariance and monte-carlo analysis of a simplified system show that this lack of correlation may allow simplification of the local estimators while preserving the global optimality of the maneuvers commanded by the supervisors.

Carpenter, J. Russell↗
NASA NTRS1977

Structured estimation - Sample size reduction for adaptive pattern classification

The Gaussian two-category classification problem with known category mean value vectors and identical but unknown category covariance matrices is considered. The weight vector depends on the unknown common covariance matrix, so the procedure is to estimate the covariance matrix in order to obtain an estimate of the optimum weight vector. The measure of performance for the adapted classifier is the output signal-to-interference noise ratio (SIR). A simple approximation for the expected SIR is gained by using the general sample covariance matrix estimator; this performance is both signal and true covariance matrix independent. An approximation is also found for the expected SIR obtained by using a Toeplitz form covariance matrix estimator; this performance is found to be dependent on both the signal and the true covariance matrix.

Morgera, S.↗
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 NTRS1972

On estimating the Venus spin vector

The improvement in spin vector and probe position estimates one may reasonably expect from the processing of such data is indicated. This was done by duplicating the ensemble calculations associated with a weighed least squares with a priori estimation technique applied to range rate data that were assumed to be unbiased and uncorrelated. The weighting matrix was assumed to be the inverse of the covariance matrix of the noise on the data. Attention is focused primarily on the spin vector estimation.

Argentiero, P. D.↗
NASA NTRS1996

Optimum combining of residual carrier array signals in correlated noises

An array feed combining system for the recovery of signal-to-noise ratio (SNR) loss due to antenna reflector deformation has been implemented and is currently being evaluated on the Jet Propulsion Laboratory 34-m DSS-13 antenna. The current signal-combining system operates under the assumption that the white Gaussian noise processes in the received signals from different array elements are mutually uncorrelated. However, experimental data at DSS 13 indicate that these noise processes are indeed mutually correlated. The objective of this work is to develop a signal-combining system optimized to account for the mutual correlations between these noise processes. The set of optimum combining weight coefficients that maximizes the combined signal SNR in the correlated noises environment is determined. These optimum weights depend on unknown signal and noise covariance parameters. A maximum-likelihood approach is developed to estimate these unknown parameters to obtain estimates of the optimum weight coefficients based on residual carrier signal samples. The actual combined signal SNR using the estimated weight coefficients is derived and shown to converge to the maximum achievable SNR as the number of signal samples increases. These results are also verified by simulation. A numerical example shows a significant improvement in SNR performance can be obtained, especially when the amount of correlation increases.

Liang, R.↗