An application of a linear programing technique to nonlinear minimax problems

A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete

Vectorization of linear discrete filtering algorithms

Linear filters, including the conventional Kalman filter and versions of square root filters devised by Potter and Carlson, are studied for potential application on streaming computers. The square root filters are known to maintain a positive definite covariance matrix in cases in which the Kalman filter diverges due to ill-conditioning of the matrix. Vectorization of the filters is discussed, and comparisons are made of the number of operations and storage locations required by each filter. The Carlson filter is shown to be the most efficient of the filters on the Control Data STAR-100 computer

An algorithm for surface smoothing with rational splines

Discussed is an algorithm for smoothing surfaces with spline functions containing tension parameters. The bivariate spline functions used are tensor products of univariate rational-spline functions. A distinct tension parameter corresponds to each rectangular strip defined by a pair of consecutive spline knots along either axis. Equations are derived for writing the bivariate rational spline in terms of functions and derivatives at the knots. Estimates of these values are obtained via weighted least squares subject to continuity constraints at the knots. The algorithm is illustrated on a set of terrain elevation data

Kalman filter estimation of human pilot-model parameters

The parameters of a human pilot-model transfer function are estimated by applying the extended Kalman filter to the corresponding retarded differential-difference equations in the time domain. Use of computer-generated data indicates that most of the parameters, including the implicit time delay, may be reasonably estimated in this way. When applied to two sets of experimental data obtained from a closed-loop tracking task performed by a human, the Kalman filter generated diverging residuals for one of the measurement types, apparently because of model assumption errors. Application of a modified adaptive technique was found to overcome the divergence and to produce reasonable estimates of most of the parameters

Compatibility check of measured aircraft responses using kinematic equations and extended Kalman filter

An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors

Analysis and Monte Carlo simulation of near-terminal aircraft flight paths

The flight paths of arriving and departing aircraft at an airport are stochastically represented. Radar data of the aircraft movements are used to decompose the flight paths into linear and curvilinear segments. Variables which describe the segments are derived, and the best fitting probability distributions of the variables, based on a sample of flight paths, are found. Conversely, given information on the probability distribution of the variables, generation of a random sample of flight paths in a Monte Carlo simulation is discussed. Actual flight paths at Dulles International Airport are analyzed and simulated

A computer program for analyzing unresolved Mossbauer hyperfine spectra

The program for analyzing unresolved Mossbauer hyperfine spectra was written in FORTRAN 4 language for the Control Data CYBER 170 series digital computer system with network operating system 1.1. With the present dimensions, the program requires approximately 36,000 octal locations of core storage. A typical case involving two innermost coordination shells in which the amplitudes and the peak positions of all three components were estimated in 25 iterations requires 30 seconds on CYBER 173. The program was applied to determine the effects of various near neighbor impurity shells on hyperfine fields in dilute FeAl alloys

Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline

Lateral stability and control derivatives extracted from five early flights of the space shuttle Columbia

Flight data taken from the first five flights (STS-2, 3, 4, 5 and 9) of the Space Transportation System Shuttle Columbia during entry are analyzed to determine the Shuttle lateral aerodynamic characteristics. Maximum likelihood estimation is applied to data derived from accelerometer and rate gyro measurements and trajectory, meteorological and control surface data to estimate lateral-directional stability and control derivatives. The estimated parameters are compared across the five flights and to preflight predicted values

Lateral and longitudinal stability and control parameters for the space shuttle discovery as determined from flight test data

The Discovery vehicle was found to have longitudinal and lateral aerodynamic characteristics similar to those of the Columbia and Challenger vehicles. The values of the lateral and longitudinal parameters are compared with the preflight data book. The lateral parameters showed the same trends as the data book. With the exception of C sub l sub Beta for Mach numbers greater than 15, C sub n sub delta r for Mach numbers greater than 2 and for Mach numbers less than 1.5, where the variation boundaries were not well defined, ninety percent of the extracted values of the lateral parameters fell within the predicted variations. The longitudinal parameters showed more scatter, but scattered about the preflight predictions. With the exception of the Mach 1.5 to .5 region of the flight envelope, the preflight predictions seem a reasonable representation of the Shuttle aerodynamics. The models determined accounted for ninety percent of the actual flight time histories