Showing papers on "Sequential algorithm published in 1974"

Sequential Algorithm for the Determination of Maximum Compatibles

Abstract: This correspondence describes an algorithm which finds the maximum compatibles (maximal complete subgraphs of a symmetric graph) sequentially and in lexicographic order. The algorithm is intended for use in digital computers, where it requires only a small program and very little memory space.

A Sequential Algorithm for a Class of Programming Problems with Nonlinear Constraints

Abstract: The purpose of this paper is to furnish a computational scheme for a class of programming problems with nonlinear constraints. The algorithm is sequential in nature, producing a sequence of feasible solutions whose limit points are optimal solutions of the original problem. Further, with a view to accelerating convergence we suggest two variants of the solution procedure.

Comparison of Statistical Orbit Determination Methods

Abstract: HE results obtained in a comparison of the convergence characteristics and accuracy of the batch estimation algorithm and the extended sequential estimation algorithm, as applied to the problem of estimating the state of a near-earth satellite in the presence of geopotential modeling errors, are described. High-accuracy laser range observations of the Beacon Explorer-C satellite, during four consecutive passes, were used in the study. The results indicate that 1) when the solution is iterated, the batch algorithm converges to an estimate which differs from the extended sequential estimate by values less than the observation noise; 2) the extended sequential estimator achieves single iteration convergence whereas several iterations are required by the batch estimator; 3) the convergence rate of the batch algorithm is more dependent on the initial state error than the extended sequential algorithm; 4) the difference in estimates from the two methods produced a predicted position difference of less than one meter after three days; and 5) the radius of convergence of the extended sequential estimation algorithm appears to be about ten times larger than the radius of convergence for the batch estimator. Contents The problem of estimating the state of a nonlinear dynamical system using discrete observations which are corrupted by random observation error was first solved by Gauss 1 using the method of least squares. Since that time, considerable research has been devoted to the problem of improving the classical method of least squares and to placing the state estimation problem on a firm statistical foundation. For the linear estimation problem with Gaussian random errors, it has been shown that the estimation algorithm for the linear, unbiased, minimum variance estimator is identical to the weighted least squares if the weighting matrix is the observation noise covariance matrix.2 Equivalence with a maximum likelihood estimator can also be shown. These methods will subsequently be referred to as "batch processors" since an entire batch of data is processed before an estimate of the state at some epoch is made. The form of the batch processor commonly used in orbit determination uses an a priori state error covariance matrix (for example, see Refs. 3 and 4). This form was used for the comparisons discussed in subsequent paragraphs. The sequential form of the estimator in which state estimates are obtained at each observation time is generally attributed to Kalman and Bucy.5 Since the sequential form can be derived from the batch algorithm through algebraic manipulation, the two are mathematically equivalent. Furthermore, in both formulations, a fixed reference solution is used in