State estimation errors in navigational state estimation problem Quarterly progress report, 1 Feb. - 1 May 1969
Orbital position estimation error analysis and earth orbital mission simulation
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Development of advanced techniques for rotorcraft state estimation and parameter identification
An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.
Hall, W. E., Jr.↗
Low sensitivity filters for state estimation in the presence of large parameter uncertainties.
Minimax sensitivity criteria used to synthesize filters for estimating state of first order plant subject to dynamic and/or statistical parameters uncertainties
Dappolito, J. A.↗
State estimation with small nonlinearities
A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.
Conrad, B.↗
Parameter estimating state reconstruction
Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and the system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a space shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.
George, E. B.↗
Parameter estimating state reconstruction
Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. These systems must be observable. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a Space Shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.
George, E. B.↗
Applications of state estimation in aircraft flight-data analysis
This paper traces the evolution of the use of state estimation in the analysis of aircraft flight data and discusses some recent applications associated with airline turbulence upsets and high-angle-of-attack flight tests. A unifying mathematical framework for state estimation is reviewed, and several examples are shown that illustrate a general approach for estimating variables that are difficult to measure. It is hoped that the diversity of the applications discussed and the examples presented will make the flight-data analyst mindful of the potential advantages of using state estimation methods.
Bach, R. E., Jr.↗
Stochastic differential games with constrained state estimators
Stochastic differential games with constrained state estimators, involving linear system, quadratic cost functional and white Gaussian noises corrupting output measurements
Luenberger, D. G.↗
A General Simulator Using State Estimation for a Space Tug Navigation System
A general simulation program is presented (GSP) involving nonlinear state estimation for space vehicle flight navigation systems. A complete explanation of the iterative guidance mode guidance law, derivation of the dynamics, coordinate frames, and state estimation routines are given so as to fully clarify the assumptions and approximations involved so that simulation results can be placed in their proper perspective. A complete set of computer acronyms and their definitions as well as explanations of the subroutines used in the GSP simulator are included. To facilitate input/output, a complete set of compatable numbers, with units, are included to aid in data development. Format specifications, output data phrase meanings and purposes, and computer card data input are clearly spelled out. A large number of simulation and analytical studies were used to determine the validity of the simulator itself as well as various data runs.
Boland, J. S., III↗
Parameter identification and state estimation for linear systems
Parameter identification and state estimation for linear systems
Budin, M. A.↗
Large scale state estimation algorithms for DSN tracking station location determination
Estimation of precise tracking station locations for deep space navigation is based on combining state estimates derived from a multitude of planetary encounter missions with planet direction information provided by the planetary ephemeris. Procedures for reducing the dimensionality of the station location estimation problem and for analytically correcting estimates for ephemeris updates have been developed. Using Householder transforms the large scale state estimation problem is decomposed into a sequence of dynamically uncoupled problems of lower dimension. The effect of an ephemeris update is shown to be adequately approximated by Brouwer-Clemence Set III perturbations for the earth-moon barycenter and the target planet for each mission.
Ellis, J.↗
Minimax design of low sensitivity filters for state estimation
Minimax design criteria of linear filters for state estimation in presence of parameter uncertainties
Dappolito, J. A.↗
State estimation and absolute image registration for geosynchronous satellites
Spacecraft state estimation and the absolute registration of Earth images acquired by cameras onboard geosynchronous satellites are described. The basic data type of the procedure consists of line and element numbers of image points called landmarks whose geodetic coordinates, relative to United States Geodetic Survey topographic maps, are known. A conventional least squares process is used to estimate navigational parameters and camera pointing biases from observed minus computed landmark line and element numbers. These estimated parameters along with orbit and attitude dynamic models are used to register images, using an automated grey level correlation technique, inside the span represented by the landmark data. In addition, the dynamic models can be employed to register images outside of the data span in a near real time mode. An important application of this mode is in support of meteorological studies where rapid data reduction is required for the rapid tracking and predicting of dynamic phenomena.
Nankervis, R.↗
Empirical Bayes state estimation in discrete time linear systems
Linear dynamic systems state estimation, using empirical Bayes decision theory to develop filter set
Kamat, S. J.↗
Applications of adaptive state estimation theory
Two main areas of application of adaptive state estimation theory are presented. Following a review of the basic estimation approach, its application to both the control of nonlinear plants and to the problem of tracking maneuvering targets is presented. Results are brought together from these two areas of investigation to provide insight into the wide range of possible applications of the general estimation method.
Moose, R. L.↗
A spline-based parameter and state estimation technique for static models of elastic surfaces
Parameter and state estimation techniques for an elliptic system arising in a developmental model for the antenna surface in the Maypole Hoop/Column antenna are discussed. A computational algorithm based on spline approximations for the state and elastic parameters is given and numerical results obtained using this algorithm are summarized.
Banks, H. T.↗
Recursive state estimation for a set-membership de scription of uncertainty
Linear dynamic system recursive state estimation for set-membership description of uncertainty under unknown input disturbances and observation errors
Bertsekas, D. P.↗
Least-squares sequential parameter and state estimation for large space structures
This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.
Thau, F. E.↗