Showing papers on "Alpha beta filter published in 1975"

A Comparison of Complementary and Kalman Filtering

Abstract: A technique used in the flight control industry for estimation when combining measurements is the complementary filter. This filter is usually designed without any reference to Wiener or Kalman filters, although it is related to them. This paper, which is mainly tutorial, reviews complementary filtering and shows its relationship to Kalman and Wiener filtering.

Design of a zero-sensitive observer

Abstract: The Luenberger observer is frequently used for the state estimator of linear time-invariant control systems However, it cannot be applied directly to the plant which has varying parameters This paper provides an observer for this problem whose structure is not affected by the varying parameters of the plant The results of this paper give the existence condition and the stability condition of such an observer and provide a direct design procedure The extension of this idea to the design of an unknown input observer is also presented

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.

Performance Evaluation of Suboptimal Filters

Abstract: The use of a Kalman filter in an applications problem requires a detailed model of both the system dynamics and the measurement dynamics. The model for many problems may be extremely large in dimensionality. However, in many instances one has a limited computer capability and, thus, must purposely introduce modeling errors into the filter in order to gain a computational advantage. However, as is well known, this may lead to the phenomenon of filter divergence. This paper considers the development of equations which allow one to evaluate a filter of reduced state. The equations are based upon using covariance analysis techniques in order to determine the true root-mean-square estimation error. These equations are computationally more advantageous than others appearing in the literature.

A frequency domain approach to minimal-order observer design for several linear functions of the state

Abstract: A design procedure for minimal-order observers which is applicable to linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state are given.

Real‐time time‐optimal control of a stirred‐tank reactor using Kalman Filtering for state estimation

Abstract: This paper presents the development and real-time implementation of a time-optimal control algorithm for a continuous stirred-tank reactor. A multivariable time-optimal control law is derived and an Extended Kalman Filter formuated for on-line estimation and filtering. The work demonstrates the powerful capability of real-time computation and decision-making in optimal control and optimal estimation of process states.

Kalman filter estimation of human pilot-model parameters

Abstract: 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.

Divergence and the fading memory filter

Abstract: The fading memory filter has been proposed as a substitute for the Kalman filter when model errors exist because it discounts old data, thereby, compensating for the influence of model errors. For model errors in the form of completely unknown inputs, this paper presents computational examples for which the asymptotic error of all fading memory filters will be greater than the Kalman error. This contradicts the assumption that, when the Kalman filter is no longer optimal, there exists a fading memory filter which will achieve lower mean squared error. An explanation for this error behavior and a discussion of its implications are included.

Application of Adaptive Filtering Methods to Maneuvering Trajectory Estimation

Abstract: : The purpose of this report is to examine several modifications of extended Kalman filters which can be used to estimate the position, velocity, and other key parameters associated with maneuvering re-entry vehicles. These filters will be described and discussed in terms of the fundamental problems of modeling accuracy, filter sophistication, and the real-time computational requirements. A nine-state, extended Kalman filter based upon the maneuvering vehicle dynamics is compared with several other candidate filters. These candidate filters include a simple filter based upon polynomial dynamics decoupled with respect to the coordinates and a more complex, fully coupled, seven-state, extended Kalman filter based upon a ballistic re-entry vehicle dynamics. Techniques which adaptively increase the process noise to compensate for modeling errors during the maneuvers are examined.

A certainty equivalence control with a nonlinear filter in the feedback loop

Abstract: The problem of control of a linear stochastic system observed by both linear and hard limited measurements is considered. The control used is the LQG or deterministic linear feedback control where the state estimate is generated by a recursive nonlinear filter. It is shown that the feedback nature of the control induces a natural probing which activates the filter. The results of this feedback system with a nonlinear filter in the feedback loop is compated to a system with an extended Kalman filter in the feedback loop. The state estimation accuracy is also compared to the system without a control to demonstrate how the control activates the nonlinear filter.

Use of Kalman Filtering for Data Resolution Enhancement

Abstract: A method for using Kalman filtering techniques for improving data resolution is presented. The method uses a Taylor series process model which allows one to treat data from a variety of sources. Smoothing can also be included. The potential utility of the method lies in being able to trade off sensor cost versus computer processing. In some cases crude sensors coupled with the estimation techniques may yield as accurate data as would be obtained using more sophisticated sensors.

Optimal estimates in thermal measurements

Abstract: Presented is an analysis of the use of a Kalman filter to improve the accuracy of thermalmeasurement systems and to increase the information which can be obtained from them.