Showing papers on "Alpha beta filter published in 1982"

An observer design for linear systems with unknown inputs

Abstract: A method is presented for designing an observer for the state of a linear time-invariant system with unknown inputs. The structure algorithm developed by Silverman is applied to obtain the observer which estimates the maximum estimable subspace of the state. It is shown that the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system. This leads us to the necessary and sufficient condition for the existence of a state observer. An application to the insensitivity observer synthesis is also included.

Two filter smoothing formulae by diagonalization of the Hamiltonian equations

Abstract: We present a new approach to two filter smoothing formulae via diagonalization of the general time variant hamiltonian equations of the linear estimation problem. This approach shows the special role of the famous Mayno-Fraser two filter formulae and also provides insight into certaini nvariance properties of backwards Kalman filter estimates.

A fast Kalman filter for images degraded by both blur and noise

Abstract: An optimal line-by-line recursive Kalman filter is derived for restoring images which are degraded in a deterministic way by linear blur and in a stochastic way by additive white noise. To reduce the computational and storage burden imposed by this line-by-line recursive Kalman filter circulant matrix approximations are made in order to diagonalize - by means of the fast Fourier transform (FFT) - both the model matrices and the distortion matrix in the dynamical model of the total image-recording system. Then the dynamical model reduces to a set of N decoupled equations and the line-by-line recursive Kalman filter based on this model reduces to a set of N scalar Kalman filters suitable for parallel processing of the data in the Fourier domain. Finally, via an inverse FFT the filtered data is presented in the data domain. The total number of computations for an N×N image reduces from the order of 0(N4) to 0(N^{2}\log_{2}N) .

Kalman filter preprocessor

Abstract: An optical signal preprocessor for computing the input functions required to utilize an extended Kalman filter algorithm. An incoming stream of time-varying images is integrated to form a reference image, which is then subtracted from each subsequently sampled image. The result is digitized for use with the extended Kalman filter algorithm. The reference image is also fed through a spatial filter and then input to two light valve image subtraction systems to produce difference image approximations of two partial derivatives. These derivative functions are then digitized and utilized as inputs to the extended Kalman filter algorithm.

Robust Kalman filter design for active flutter suppression systems

Abstract: Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.

A Kalman filter procedure for the processing of the electroencephalogram

Abstract: In the present paper a Kalman filter procedure is illustrated for the reduction of muscular noise superimposed to the electroencephalografic traces (EEG). Such a noise, in fact, has a bandwidth which overlaps the signal carrying the information content useful for the clinical standpoint and, therefore, can not be removed by means of classical digital filtering. A Markov model is used for identifying the signal model (supposed generated by an ARMA process) and the noise model (conceived on the basis of experiments of neurophysiological evidence). The experimental results show a good performance of the filter on the discrete-time EEG signal which is also quantified by the spectral information and the values of the prediction error of the filter itself. Comparison is then carried on with a classical low-pass FIR filter (mostly used in practice) which can not be aggressive enough towards the noise contained in the signal bandwidth but which can undoubtly ameliorate the performance of the Kalman filter.

Real-Time Gravity Gradiometer Utilization to Improve INS Accuracy

Abstract: This paper details a method for deriving approximate low-order filters for estimation of velocity error in an inertial navigation system. The filter inputs are obtained from two sources—a gravity gradiometer and some external velocity reference. It is the intent here to show that these approximate filters are near-optimal. Covariance comparisons are used to evaluate filter performance. The first of these comparisons reveals that the approximate filter gives very nearly the same rms estimate error as the Kalman filter. This result, however, assumes a rational gravity perturbation model which, although unrealistic, is required to implement the Kalman filter. In addition, a multiple-measu rement scheme employing the external velocity reference appears to significantly improve estimation accuracy. A second covariance study compares the rms estimation accuracy of the approximate filters obtained analytically and numerically when an irrational but more realistic gravity perturbation model is assumed. Agreement of these numbers justifies the "Schuler Dominance" assumption used in all the filter derivations and therefore gives greater weight to the claim of filter near-optimality.

Deadbeat observation of linear, time-varying sampled-data systems

Abstract: The paper describes the construction of two types of observers for deadbeat estimation of the state of linear, time-varying systems with vector control and scalar, sampled-data measurements. Expressions for the time-varying gains are obtained in closed form. With a view towards application in a realistic stochastic environment the evolution of the covariance matrices is also described. An application of the estimation of spacecraft attitude motion is worked out in detail. Deadbeat observer performance is compared with Kalman filter performance.

Adaptive filtering in structural dynamics

Abstract: The Kalman filter has been shown to be ideally suited to both the state and parameter estimation problems in structural dynamics. However these exploratory works on the application of Kalman filtering to structural engineering problems, in general only give suboptimal results, relying on assumed statistics to describe the noise sequences. Optimality however can be achieved by adapting onto these statistics (or the filter gain), using output from the filter equations to feed the adaptive algorithm. The present paper details one recently developed adaptive approach which exhibits good computational and convergence properties. This is coupled with a correlation test to show the optimality or nonoptimality of the results in any given application. A seismically excited structure is used to illustrate the required problem formulation and estimation results.

An adaptive tracking observer for failure-detection systems

Abstract: The design problem of adaptive observers applied to linear, constant and variable parameters, multi-input, multi-output systems, is considered. It is shown that, in order to keep the observer's (or Kalman filter) false-alarm rate (FAR) under a certain specified value, it is necessary to have an acceptable proper matching between the observer (or KF) model and the system parameters. An adaptive observer algorithm is introduced in order to maintain desired system-observer model matching, despite initial mismatching and/or system parameter variations. Only a properly designed adaptive observer is able to detect abrupt changes in the system (actuator, sensor failures, etc.) with adequate reliability and FAR. Conditions for convergence for the adaptive process were obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors and accurate and fast parameter identification, in both deterministic and stochastic cases.

A discrete Kalman filter for a class of non-linear stochastic systemsf

Abstract: A class of non-linear systems of the form dx=A(x)x dl + σdW, t>0, XER m , A(x)ERm×m, where W is an Rm-valued standard Wiener process ; together with an observation process given by y(tk) = Mx(tk) + v(tk), y(tk)ERp, t0

Kalman filtering techniques applied to the dynamic ship positioning problem.

Abstract: The dynamic ship positioning problem using Kalman filtering techniques is considered. The main components of the system are discussed. The ship dynamics, based on a linearised model, are represented by state equations. These equations involve low and high frequency subsystems. A simplified design procedure for the implementation of a Kalman filter is described based on the linearised equations of motion. The Kalman filter involves a model of the system and is therefore particularly appropriate for separating the low and high frequency motions of the vessel. The filtering problem is one of estimating the low-frequency motions of the vessel so that control can be applied. An optimal feedback control system simulation based on optimal stochastic control theory is used. The optimal control performance criterion weighting matrices Q, R were pre-selected and the optimal feedback gain matrix was computed. This control scheme involves the low-frequency part of the ship model. The Kalman filter has been simulated on a digital computer for different modelled operating conditions. The computer simulation results showing the behaviour and responses of the Kalman filter applied to the dynamic ship positioning problem were investigated. The system dynamics vary as the weather conditions vary and can be classified from a calm sea condition (Beaufort number 5) to the worst condition (Beaufort number 9). Different tests involving systems modelling and filter mismatching have been carried out. Another field in which the robustness of a Kalman filter has been assessed involved a test in which the system observation noise covariance was increased keeping the filter with the usual noise information. Saving in both computation and computer storage requirement were achieved using a form of semi-constant filter gain and reduced-order Kalman filter respectively. System non-linearities have been considered and a non-linear control algorithm was proposed and implemented using an extended Kalman filter. These non-linearities involve the thruster dynamics and the associated low-frequency part of the system model. All data that have been used within this work for system implementation were obtained from two different models ("Wimpey Sealab" and "Star Hercules" vessels). Our system has been employed by GEC Electrical Projects Limited, Rugby, for a new vessel ("Star Hercules") and this has been commissioned and is currently operating successfully off Brazil.

Minimal order of minimal-time deadbeat function observers†

Abstract: This paper arose from the need for a better understanding of the minimal-order observer problem. A deadbeat function observer is an estimator that estimates exactly a linear function of the state of a deterministic discrete-time linear system via an incomplete state observation. The minimal order of a minimal-time function observer, which exhibits the fastest deadbeat response among deadbeat function observers, was obtained and such an observer was designed. It was shown that the minimal order of a minimal-time function observer is not necessarily the same as the minimal order of a deadbeat function observer.

Reduced Order Observer Design for a linear Map of the State

Abstract: This paper considers the problem of designing an observer to reconstruct a set of linear functionals in the states of a given linear finite-dimensional system. The goal of the present method is the design of least dimension observers having un- restricted spectrum.

An adaptive Kalman window filter to restore degraded images

Abstract: A semicausal model for image representation has been described which accounts for the correlated nature of the pixel data. The model is then used to develop a linear imaging system model suitable for Kalman algorithms. Since the blurring PSF is not known in practice, the system model is modified to include the estimation of the pixels while the noise characteristics are assumed to be known. For restoration, an adaptive Kalman filter is developed whose length of the state vector is shown to be a function of the PSF size resulting in significant savings in computational and storage requirements. Through examples, it is demonstrated that by carefully choosing the initial estimates of the PSF and error covariance terms, results comparable to the case when the PSF is fully known can be obtained. Two criteria to select such initial estimates have been described; one is based on the a priori knowledge about the dominant PSF coefficient and the other is based on the law of conservation of light flux.

On the Kalman-Bucy filter with specified input

Abstract: In a recent paper, Vathsal suggested that a new configuration had been obtained for linear filtering problems, which was distinctly different from the Kalman-Bucy filter. It is shown that this in fact is merely a special case of the filter with a specified input.