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Management of an inventory the magnitude of that of the Defense Supply Agency makes mandatory the forecast of requirements by computer to the maximum extent possible. Computerized calculations are feasible when standard or uniform procedures are used. The Standard Automated Materiel Management System prescribes use of double exponential smoothing as the technique for forecast of future demands. The study compares the prescribed technique with other prevalent methods and presents the results of penetrating tests.

Sequential algorithms for prediction, filtering, and smoothing are developed for a class of linear distributed parameter systems. The class of systems concerned is that involving noisy measurement data which are obtained from 'averaging' and 'scanner' type sensors. The basic tools of the development are the least-squares estimation viewpoint, the calculus of variations, and the sweep method for two-point boundary-value problems. An example involving the heat equation is presented to illustrate the results. (Author)

The problem of estimating the state of a class of linear distributed parameter systems from noisy measurements is considered from the viewpoint of weighted least-squares estimation over the spatial domain of the system and the time interval of the measurement data. The problem is reduced to a two-point boundary-value problem via the calculus of variations. The two-point boundary-value problem is then solved in closed form via the sweep method to obtain a Kalman-Bucy type filter. Solution of the smoothing problem then follows directly. Cases are considered where measurement data are obtained over the entire spatial domain of the system or at discrete points in this domain, and where the system is subject to internal and external disturbances as well as measurement errors. Some resulting problems for future study are discussed. (Author)

This is a preliminary study which indicates the feasibility and general approach to developing a modular general purpose computer program for the automatic editing, smoothing, and differentiation of multiple time series of constant time interval containing accidental errors and noise. (Author)

Kalman's formal limiting procedure is applied to some recent results in sequential discrete-time nonlinear filtering and smoothing to obtain the corresponding estimation algorithms for continuous-time nonlinear dynamic systems. The resulting filtering algorithm is found to agree with the well-known Detchmendy-Sridhar filter which was obtained via another method. The present smoothing algorithm is a new result. It is argued that the combined filter-smoothing results here lead to an estimation algorithm which is second-order in both system dynamics and measurement function nonlinearity. (Author)

The aim of this project is to provide basic knowledge of the methods which may be used by a man-computer system to detect the presence of a target, using data from a passive sonar receiver. This research consists of analytical studies to evaluate important system parameters and experimental investigations measuring operator performance under various operating conditions. The report contained in this volume investigates the problem of extracting information from a sequence of binary signals. The optimum method of estimating present values of the sequence, predicting future values, and smoothing past values are presented. (Author), See also Volume 2, AD-823 798.

A Newton-Raphson differential correction procedure is developed to solve the nonlinear two-point boundary-value problem of fixed interval data smoothing for noisy nonlinear dynamic systems. A numerical example is included to illustrate the procedure. (Author)

Contents: Spectral analysis of nonstationary random processes; Numerical estimates for averages, variances, and standard deviations; Numerical estimates for the covariance and covariance spectrum; Smoothing, continuous and discrete; Spectral analysis of a single sample function; Calculation of the covariance spectrum for a nonstationary process.

A unified approach to the dynamic nonlinear estimation problem is presented. General algorithms for filtering, smoothing, and prediction for both continuous and discrete nonlinear systems are derived. The continuous problem is treated first by a direct approach which yields an exact solution. A similar approach is then applied to the more complex discrete estimation problem. The discussion provided points out some subtle, but important features of the main results which should be useful when applying the results to practical problems. To provide insight, motivation and background for the technique used in obtaining the solution of the general nonlinear problem, the special case of linear estimation is discussed in the first two appendices. In a third appendix it is shown that in the continuous measurement limit, the derived discrete and continuous nonlinear filtering algorithms are identical. (Author)

It is well known that the problem of estimating the state and parameters of discrete-time nonlinear dynamic systems from noisy measurements can be formulated as a nonlinear two-point boundary-value problem. In this paper, an algorithm is developed for solving the above boundary-value problem. The algorithm, which is based on Newton's method, requires very little storage. A detailed discussion of the algorithm is given and certain extensions of it are indicated. (Author)

The problem of state and parameter estimation for noisy discrete-time nonlinear dynamic systems is examined from the viewpoint of marginal maximum likelihood estimation. Approximate algorithms for sequential prediction, filtering, and smoothing are developed. The former two are in agreement with previous results; the latter is new. A technique for iterative-sequential filtering and smoothing using Newton's method is indicated. A numerical example is included to illustrate the results. (Author)

Second-order, linear, recursive, fixed-weight optimal and critically damped filters are compared on the basis of truncation errors produced by each. The critically damped and optimal filters are derived along with the commonly used parameters which are truncation error and noise ratio. It is shown that when truncation errors are compared on the basis of equal noise ratios for the two filters, the optimal filter yields a significant improvement over the critically damped filter. (Author)

Digital computer filtering provides a data processing technique applicable to a variety of oceanographic problems including: estimating spectra, improving signal to noise, isolating frequency-dependent processes, fitting curves, surfaces-etc., interpolation and data editing. Examples of such uses are given. (Author)