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NASA NTRS1976

On the design of optimal controllers with certain structural constraints

This paper considers the problem of designing certain structurally constrained optimal regulators for linear systems subjected to additive white process noise and measurement noise. Three types of controller structures are considered, using direct output feedback, prespecified time constant filters, and optimal dynamic compensators. Necessary conditions are obtained for minimizing quadratic performance criteria. The techniques are demonstrated by application to a helicopter/slung load system, and a flexible space station.

Joshi, S. M.↗

NASA NTRS1977

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

NASA NTRS1979

A parameter-estimation subroutine package

Estimation subroutine package comprises fast, efficient, and simple least-squares data-processing algorithms for use in orbit determination and related analyses. Very reliable and general algorithms have been documented. Package contains collection of streamlined subroutines that can be used to solve large variety of parameter-estimation and filtering problems. Special routines are included for problems with colored process noise and covariance (factor) mapping.

Bierman, G.↗

NASA NTRS1977

Range validation using Kalman filter techniques

Range pseudo-residuals may be improved to the level required for data validation by a measurement updating process which utilizes Bierman's adaptation of the Kalman filter measurement updating algorithms together with process noise compensation to account for model errors. This algorithm involves combining the currently available range predictions and measurements to produce an updated range residual measurement whose accuracy is constrained by the range data quality and by the estimated error in the prediction. The algorithm is compact and fast, and is thus suitable for on-line applications in network control or at the station.

Madrid, G. A.↗

NASA NTRS1978

Requirements for Kalman filtering on the GE-701 whole word computer

The results of a study to determine scaling, storage, and word length requirements for programming the Kalman filter on the GE-701 Whole Word Computer are reported. Simulation tests are presented which indicate that the Kalman filter, using a square root formulation with process noise added, utilizing MLS, radar altimeters, and airspeed as navigation aids, may be programmed for the GE-701 computer to successfully navigate and control the Boeing B737-100 during landing approach, landing rollout, and turnoff. The report contains flow charts, equations, computer storage, scaling, and word length recommendations for the Kalman filter on the GE-701 Whole Word computer.

Pines, S.↗

NASA NTRS1978

Kalman filter divergence and aircraft motion estimators

Kalman filters designed for many aerospace systems turn out to be unsatisfactory. The estimate errors become large compared to the errors predicted by the theory ('divergence'). One of the principal causes of this failure is that the system model contains states or modes that are undisturbed by the modeled process noise, and are neutrally stable (NS). One cure for such problems is periodic restarting of a time-varying Kalman filter. Other cures include minimum variance observers with eigenvalue constraints, added noise, pole-shifting, and destabilization. Several examples are given, including effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several NS modes are undisturbed by wind gusts. An interpretation of these estimators as a 'strapdown IMU' without accelerometers, gimbaled gyros, or servos is given.

Bryson, A. E., Jr.↗

NASA NTRS1977

Monte Carlo turbulence simulation

The paper describes turbulence simulation experiments based on the principles of control system theory, that is, the construction of a system characterized by a system function such that upon exciting the system with prescribed noise processes the output of the system is a realization of a random processing the desired statistical attributes of turbulence. An experimental autocorrelation of Jimsphere measurements of wind velocity was approximated to simulate turbulent wind. From the approximate autocorrelation function, the required system function is obtained, and a discrete time system is designed. Another method of simulation is to solve the convolution integral by filter techniques. Other methods include discrete Fourier simulation and self-similar simulation.

Fichtl, G. H.↗

NASA NTRS1978

On-line parameter estimation using a high sensitivity estimator

An on-line parameter identification method is presented. The method is based on a recursive formulation of the maximum likelihood method, with a significant modification on the gains of the state estimator. In the conventional maximum likelihood method, the Kalman gains are used in the state estimator. This produces unbiased, minimum variance parameter estimates in the presence of process noise and measurement noise, but it also slows the convergence rate when the identification is done on-line. Here we suggest choosing the gains to maximize a measure of the sensitivities of the state estimates to parameter variations. One such criterion is to minimize the trace of the inverse information matrix. This increases the convergence rate significantly. After one or two time constants, the gains are switched to the Kalman values to assure unbiased, minimum-variance estimates. The state estimate will initially be nonoptimal, and may not be adequate for control purposes. In this case, a parallel Kalman filter which uses the identifier's parameter estimates can be used. This method is applied here for the identification of a simple first-order system, and for the identification of short-period stability derivatives of an F-8 aircraft from simulated data.

Mishne, D.↗

NASA NTRS1978

Subcarrier phase recovery performance in bent-pipe mode of Shuttle data transmission

The subcarrier phase recovery is analyzed for the bent-pipe mode of Space Shuttle detached-payload data transmission on the Tracking and Data Relay Satellite System (TDRSS) Ku-band return link. The high-power component of the subcarrier modulation is unrestored payload data, either at baseband or modulating another subcarrier. At the receiver a Costas loop recovers the subcarrier phase. To analyze its performance in the baseband case, we obtain the loop S-curve, the power spectral density of the equivalent noise process, and the loop phase error variance.

Mckenzie, T. M.↗

NASA NTRS1980

Design considerations for optical heterodyne receivers: A review

The current state of knowledge concerning optical heterodyne receivers is reviewed. Following a discussion of noise processes in the heterodyne receiver and the manner in which sensitivity is increased through time integration of the detected signal, an expression for the mean square signal current is derived by mixing a coherent local oscillator with a partially coherent, quasimonochromatic source. Then the manner in which the IF signal calculation can be transferred to any convenient plane in the optical front end of the receiver is demonstrated. Using these techniques, a relatively simple equation is obtained for the coherently detected signal from an extended incoherent source and applied to the heterodyne detection of an extended thermal source and to the backscatter lidar problem where the antenna patterns of both the transmitter beam and heterodyne receiver must be taken into account. Finally, the detection of a coherent source is considered and, in particular, a distant point source such as a star or laser transmitter in a long range heterodyne communications system is discussed.

Degnan, J. J.↗

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 NTRS1980

Estimation of Kalman filter model parameters from an ensemble of tests

A methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of nonidentical tests is presented. In addition, the problem of estimating time constants and process noise levels is addressed. Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered.

Gibbs, B. P.↗

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 NTRS1980

Digital preprocessing of SEASAT imagery

A model for radar image data is derived for use in developing enhancement techniques. This model describes the image data as the result of a multiplicative-convolved noise process. This information is then used to design a minimum mean square error (MMSE) filter. The resulting filter is implemented adaptively to change with local statistics. A radar image processing technique which provides the MMSE estimate inside homogeneous areas and tends to preserve edge structure is thus developed. This technique has been implemented and tested using digitally correlated SEASAT-A synthetic aperture radar (SAR) imagery.

Frost, V. S.↗

NASA NTRS1981

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

Saleh, B. E. A.↗

NASA NTRS1982

Observable properties of neutron stars

This paper reviews the information on neutron stars that has been obtained from observations of pulsars and pulsing X-ray stars, with emphasis on results from timing studies. Included are summaries of the most recent theoretical work on neutron star structure and the current evidence concerning neutron star masses and radii. Also included are discussions of large frequency jumps and small-scale timing irregularities, the description of the latter phenomenon in terms of random noise processes, and the use of both as probes of the internal structure and dynamical properties of neutron stars. Finally, some of the most promising directions for future work are briefly noted.

Lamb, F. K.↗

NASA NTRS1983

Identification and stochastic control of helicopter dynamic modes

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.

Molusis, J. A.↗

NASA NTRS1982

Identification and control of spacecraft

Information on the identification and control of spacecraft is given. Maximum likelihood estimation, identification accuracy issues, steady state identifiability analysis and stochastic error with process noise are among the topics addressed.

Greene, C. S.↗