Showing papers on "Recursive least squares filter published in 1975"

How Much Do Gauss-Markov and Least Square Estimates Differ? A Coordinate-Free Approach

Abstract: A simple expression is developed for the difference between the least squares and minimum variance linear unbiased estimators obtained in linear models in which the covariance operator of the observation vector is nonsingular. Bounds and series expansion for this difference are obtained, and bounds for the efficiency of least squares estimates are also obtained.

Fixed memory least squares filtering

Abstract: Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation

Fixed memory least squares filtering (Corresp.)

Abstract: Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data. In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter. The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation.

A Fault-Tolerant Estimator for Redundant Systems

Abstract: This paper proposes a digital estimator for redundant systems which is superior to Kalman Filtering if a failure is present and reduces to Kalman Filtering if no failure is present. Fault tolerant estimation is achieved by defining the non-stationary weighting matrix associated with the nominal least squares estimator (Kalman filter) as a continuous ous nonlinear function of the measurements. Despite the nonlinear character of the failure detection and isolation feature, the estimator equations have closed form and hence require no iterative computations ions or approximations for implementation.

An inverse perturbation theorem for the linear least squares problem

Abstract: Second derivatives of function and first Derivatives of constraints required Second derivatives of both tune, ion and constraints required Integer Programming input/Output Binary octal/Hexadecimal Decimal Character string Graphics, Plotting Batch Interactive Internal File Manipulations Copy or Move File(s) Create a file Sequential Library (-Partltioned Data Set") Other Destroy a file Compare Two Files update a File File Maintenance Program Library Maintenance Language Processors Assemblers Macro Assemblers Other Assemblers (which produce code for the same machine) Cross-Assemblers (i.e., one which runs on one computer but produces code for another computer.) L2.

Least Squares Programs-A Look at the Square Root Procedure

Abstract: Summary Various algorithms are in use on computers to solve least squares problems. Apparently very few programs use the square root procedure. In this paper, results from programs based on the square root procedure are compared with results based on some other algorithms. Remarkably good results are obtained using the square root procedure.

A non-linear filter with higher-order weighting functions via invariant imbedding

Abstract: The problem considered is the sequential estimation of states and parameters in noisy non-linear dynamical systems. The class of systems considered are those in which the dynamical behaviour is described by an ordinary differential equation. No statistical assumptions are required concerning the nature of the unknown inputs to the system or the measurement errors on the output. The equations of the estimator is derived by a least squares criterion and the invariant imbedding approach. The new feature of the algorithms derived lb that a non-linear filter with higher-order weighting functions (higher-order approximated optimal filter) is obtained by using the approximate method in the function space. Simulation results are presented which yield a comparison of the performance of the higher-order approximated optimal filter versus the other nonlinear filters when applied to a chemical batch reactor system. The results indicate that the proposed non-linear estimation scheme is feasible.

Least squares simulation of distributed systems

Abstract: This paper addresses the application of linear optimal control theory to the least squares functional approximation of linear initial-boundary value problems. The method described produces the optimal approximate solution by the realization of a linear quadratic servo configuration imposed on the Galerkin simulation for the problem. It is shown that appropriate formulation of the servo problem guarantees a stable numerical solution, even when the Galerkin simulation itself is unstable, a situation not uncommon with certain hyperbolic partial differential equations. Theoretical least squares and Galerkin properties are comparatively discussed, and numerical examples demonstrating least squares convergence in the face of Galerkin divergence are presented.

A Least Mean Squares Cubic Algorithm for On-Line Differential of Sampled Analog Signals

Abstract: A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementations of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Algorithms for rational discrete least squares approximation

Abstract: In this paper an algorithm for the computation of a locally optimal polefree solution to the discrete rational least squares problem under a mild regularity condition is presented. It is based on an adaptation of projection methods [8], [12], [13], [14], [18], [19] to the modified Gaus-Newton method [4], [10]. A special device makes possible the direct handling of the infinitely many linear constraints present in this problem.

Statistical Properties of a Least Squares Identification Algorithm Used in Modeling Human Operator Performance.

Abstract: : Three methods for identifying the parameters of a linear, autonomous, discrete time single input-single output system are studied. These are a least squares method, known as the output error method, a maximum likelihood method due to Kashyap, and a linear least squares method due to Levin. On the basis of extensive simulation studies, it is concluded that the output error method is the best of the three algorithms. It is shown that if the plant noise and observation noise are independent sequences of independent and identically distributed random variables with finite second moments, then the least squares estimator is consistent. In addition, if the noises have finite third moments, the estimator is asymptotically normal. The output error method is successfully applied to some tracking data.