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Showing papers on "Alpha beta filter published in 1980"


Journal ArticleDOI
TL;DR: In this paper, an extended Kalman filter is used for coordinate estimation of a stationary object using bearing measurements taken from a moving platform, and a bound on the Lyapunov function decay rate is given to assist in the design of the modified nonlinearities and in the selection of an appropriate coordinate basis.
Abstract: Extended Kalman filters are here modified for coordinate estimation of a stationary object using bearing measurements taken from a moving platform. The modifications improve significantly the coordinate estimation on the initial period of data collection when otherwise the performance is far from optimal. The modifications are to the nonlinearities and could, in some instances, be implemented by the introduction of a time decreasing amplitude dither signal in the extended Kalman filter prior to the output nonlinearity. A bound on a Lyapunov function decay rate is also given which assists in the design of the modified nonlinearities and in the selection of an appropriate coordinate basis to be used in the extended Kalman filter.

79 citations


DOI
01 May 1980
TL;DR: In this article, the Kalman filter is used to remove the wave motion signals from a dynamically positioned vessel to ensure that the sytem only responds to low-frequency forces that would cause the vessel to move off-station.
Abstract: The position-control systems for dynamically positioned vessels include wave filters to remove the wave motion signals. These ensure that the sytem only responds to low-frequency forces that would cause the vessel to move off-station. Several filters have been proposed and used in this role, and in the following discussion the Kalman filter is considered. The Kalman filter depends upon the model of the vessel, and the development of such a model is described. Simulation results are given to illustrate the performance of the filter and the performance of the combined Kalman filter and optimal state-feedfack control system.

72 citations


Journal ArticleDOI
V. Panuska1
TL;DR: In this paper, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed, based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the extended least squares or Panuska's method.
Abstract: A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least-squares or Panuska's method. Convergence properties of the proposed algorithm are studied, and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed, and an extension to an estimator for randomly varying parameters is outlined.

53 citations


Journal ArticleDOI
TL;DR: In this article, a continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets.
Abstract: A continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets. The track residuals in each coordinate, which are a measure of track quality, are sensed, normalized to unity variance, and then filtered in a single-pole filter. The magnitude Z of the output of this single-pole filter, when it exceeds a threshold Z1 is used to vary the maneuver noise spectral density q in the Kalman filter model in a continuous manner. This has the effect of increasing the tracking filter gains and containing the bias developed by the tracker due to the maneuvering target. The probability of maintaining track, with reasonably sized target gates, is thus increased, The operational characteristic of q versus Z assures that the tracker gains do not change unless there is high confidence that a maneuver is in progress.

49 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a method for the design of an observer capable of reconstucting several linear functionals of the states of a linear, finite-dimensional system, subject to the restriction that the observer eigenvalues be freely assignable.
Abstract: This paper presents a method for the design of an observer capable of reconstucting several linear functionals of the states of a linear, finite-dimensional system. The goal of this method is the design of an observer having minimum order subject to the restriction that the observer eigenvalues be freely assignable. The method is based on the reduction of a state observer formulated from an observable canonic form for the system when the functionals are treated as if they were additional outputs.

42 citations


Journal ArticleDOI
Tony T. Lee1
TL;DR: A new approach is presented for the estimation of the noise covariances associated with the linear discrete Kalman filter.
Abstract: A new approach is presented for the estimation of the noise covariances associated with the linear discrete Kalman filter

35 citations



Journal ArticleDOI
TL;DR: The canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable as mentioned in this paper.
Abstract: Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter

17 citations


Journal ArticleDOI
TL;DR: In this article, the necessary and sufficient condition for constructing the observer for estimating linear functions of the state of a linear system is derived in a geometrical way and its design method is presented.
Abstract: This paper is concerned with the construction of the observer for estimating linear functions of the state of a linear system. The necessary and sufficient condition for constructing the observer is derived in a geometrical way and its design method is presented. The relation between the proposed method and Gopinath's procedure for the state observer is made explicit from the points of minimal realization or the aggregation.

15 citations


Journal ArticleDOI
TL;DR: The problem of designing Luenberger observers for estimating a set of linear functions of the state of a linear time-invariant system under the requirement that the observer function perfectly despite the presence of perturbations of the system parameters from a known class is constructively solved.
Abstract: The problem of designing Luenberger observers for estimating a set of linear functions of the state of a linear time-invariant system under the requirement that the observer function perfectly despite the presence of perturbations of the system parameters from a known class, is constructively solved using notions from the geometric theory of linear systems. The close connection between tins problem and the problem of observer design for linear systems with unknown inputs is pointed out.

14 citations


Journal ArticleDOI
TL;DR: In this article, an identification technique based on the extended Kalman filter and the model reference adaptive approach is proposed. But the technique is not suitable for discrete-time linear systems and it requires noisy measurements.
Abstract: This paper treats an identification technique for discrete-time linear systems whim noisy measurements are taken. The technique is based on the extended Kalman filter and the model reference adaptive approach. Firstly, the extended Kalman filter derived by augmenting unknown parameters as the state variables is modified by neglecting the information between the states and unknown parameters ; and secondly the stability of the modified filter is compensated by the idea of the model reference adaptive approach. Lastly, the convergence of the obtained estimates for unknovm parameters to the exact values is proved. A numerical example shows the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: This paper presents a brief introduction to state estimation techniques, in particular Kalman filtering, and an example employing a three-state K, alman filter is given which highlights the modeling capabilities of the estimation technique.
Abstract: This paper presents a brief introduction to state estimation techniques, in particular Kalman filtering. A description of the Kalman filter and its properties is given. An example employing a three-state K, alman filter is given which highlights the modeling capabilities of the estimation technique. The example, concerned with estimating material loss, is contrasted with the standard CUSUM control chart statistic.

Journal ArticleDOI
TL;DR: The Kalman filter method is applied to the detection of the abrupt change and the trend in electroencephalographic data which is a non-stationary times series and it is shown that the detection can be improved by introducing a feed-back parameter in theKalman filter gain.
Abstract: The objective of this paper is to develop the method of detection of the abrupt change and the trend in electroencephalographic data which is a non-stationary times series. In this paper, the Kalman filter method is applied to the detection of the abrupt change and the trend. It is shown that the detection of the abrupt change can be improved by introducing a feed-back parameter in the Kalman filter gain. For the detection of the slow changes or the trend of the time series, a spectral error measure is applied to the Kalman filter. The amplitude and the frequency changes of the time series are then extracted by the smoothing of the Kalman filter method. Numerical examples illustrate the availability of the filter and verify the methods developed here.


Journal ArticleDOI
TL;DR: In this article, Kalman filtering is used for optimal mixing of continuous-time and discrete-time data, which can be readily accomplished by the theory of Kalman filter, which is briefly reviewed.
Abstract: There is often a need for optimal mixing of continuous-time and discrete-time data. This can be readily accomplished by Kalman filtering, the theory of which is briefly reviewed. In the steady state the filter gains for processing the continuous-time data are generally periodically varying functions of time and cannot be determined by simply solving either the discrete-time or the continuous-time filtering problem, but they can be determined with the aid of the solution of an equivalent discrete-time problem. An illustrative example is given for the system: \ddot{x} = white noise, with discrete-time observations of x and continuous-time observations of \dot{x} .

DOI
01 Mar 1980
TL;DR: In this article, the authors derived an optimal controller for the discrete-time system in the z-domain, which includes direct state-feedback from the measurable states, which improves the performance of the system and reduces the effects of modelling errors.
Abstract: The solution of the l. q. g. regulator problem is given by the separation principle and involves a Kalman filter with the same dimension as that of the plant. It is shown that, for a class of systems where the input subsystem states are measurable, the Kalman filter may be reduced in dimension considerably. An example of a steel-mill shape control problem is discussed where the number of states required in the filter is halved. The proposed optimal system includes direct state-feedback from the measurable states, which improves the performance of the system and reduces the effects of modelling errors.The optimal controller for the discrete-time system is derived in the z-domain. The solution of the above multivariable regulator problem has not previously been obtained in this form. The z-domain controller is particularly suitable for implementation on a microprocessor or digital computer.


Journal ArticleDOI
TL;DR: In this paper, a sequence which has properties similar to the innovation sequence is defined and its properties are used to test whether a particular Kalman filter is performing optimally or not.
Abstract: A sequence which has properties similar to the innovation sequence is defined. Its properties are used to test whether a particular Kalman filter is performing optimally or not. This test also tells whether the transition matrix Φ and the control matrix G, and/or the noise matrices Q and R, are exactly modelled or not. If the filter is not optimal, an identification scheme is developed to estimate those inexact parameters. This scheme is also applicable to determine the steady-state Kalman gain matrix K directly without the immediate determination of the unknown Qand R

Journal ArticleDOI
TL;DR: In this paper, a filter configuration which is distinctly different from the conventional Kalman-Bucy type filter is presented, and it is shown that the performance of this filter is identical to the traditional Kalman filter.
Abstract: A filter configuration which is distinctly different from the conventional Kalman-Bucy type filter is presented. It is shown that the performance of this filter is identical to the conventional Kalman filter.

ReportDOI
16 Jul 1980
TL;DR: Preliminary results indicate that the modified Kalman filter technique is superior in its ability to rapidly develop a reasonable track in the problem of tracking emitters via asynchronous bearing measurements made at two remote sites.
Abstract: : The problem of tracking emitters, via asynchronous bearing measurements made at two remote sites, was addressed. Three algorithms were developed for this purpose; a statistical moving average technique, a modified Kalman filter technique, and an extended Kalman filter technique. The performances of the algorithms in several selected scenarios were compared, with the preliminary results indicating that the modified Kalman filter technique is superior in its ability to rapidly develop a reasonable track. The extended Kalman filter technique demonstrated superior tracking performance once it had settled down; however, for the cases considered this required an unreasonable amount of time. Further investigation is required to assess the performance of the algorithms against maneuvering targets. The effect of varying the time between measurements should also be considered.

ReportDOI
01 Jan 1980
TL;DR: In this article, the authors discuss innovations based on classical transform domain Wiener-Hopf theory to avoid several difficulties occurring in time domain solutions (e.g., those which arise in connection with singular regulator and filter problems).
Abstract: : Most approaches to optimal linear stochastic control problems depend on time domain techniques for both their theoretical foundations and for computational algorithms. In contrast, this paper discusses innovations based on classical transform domain Wiener-Hopf theory. These innovations avoid several difficulties occurring in time domain solutions (e.g., those which arise in connection with singular regulator and filter problems). Emphasis will be upon solution techniques and properties in distinction to derivations. The following points will be demonstrated: linear regulator, filter/observer problems can be solved using linear algebraic equations (in distinction to solving nonlinear Riccati equations); the R weighting matrix need not be positive definite nor is it necessary that 1/R exists; singular regulator and filter/observer problems (e.g., the cheap control problem) can be handled neatly; the weighting matrices, R and Q, can be explicit functions of frequency; and there are some advantages in using non-diagonal Q and R matrices.



Journal ArticleDOI
C. Tye1
TL;DR: In this article, an on-line computer control system for a nuclear reactor using optimal state feedback based on the linear quadratic regulator and state estimation using a Kalman filter is discussed.

01 Oct 1980
TL;DR: In this article, a methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of non-identical tests is presented, and the problem of estimating time constants and process noise levels is addressed Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered
Abstract: A methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of nonidentical tests is presented In addition, the problem of estimating time constants and process noise levels is addressed Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered

Journal ArticleDOI
Takeo Yamada1
TL;DR: In this article, a two-level method of state estimation proposed by Noton is demonstrated to give only an approximate solution, not an exact one, to filtering problems, and it is shown that a two level method of estimation is not the best one for filtering problems.
Abstract: A two-level method of state estimation proposed by Noton is demonstrated to give only an approximate solution, not an exact one, to filtering problems.