Showing papers on "Alpha beta filter published in 1988"
TL;DR: For non-linear MIMO systems, the extended Luenberger observer as discussed by the authors is a nonlinear observer design for all sufficiently smooth and locally observable systems that can be simplified using the degrees of freedom available in the case of multiple outputs.
Abstract: For non-linear multiple-input multiple-output systems [xdot] = f(x, u), y = h(x, u), nonlinear observers are designed using a transformation into the non-linear observer canonical form and an extended linearization The differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory, and dimensioned by eigenvalue assignment With reference to the extended Kalman filter algorithm, this non-linear observer design is called the extended Luenberger observer This observer design is possible for all sufficiently smooth and locally observable systems In comparison with single-output systems, the non-linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs
177 citations
TL;DR: It is proved that an observer pole selection method can be formulated to minimize the observer gain to the system input and is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems.
Abstract: This paper shows that based on the recent development of observer design solution, an observer pole selection method can be formulated to minimize the observer gain to the system input. It is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems.
63 citations
TL;DR: This paper presents, for the first time, a unified, explicit and restriction free set of design formulas for Kalman type and Luenberger type state observers and function observers, with arbitrary poles, for recovering the robustness of a direct state feedback system.
37 citations
TL;DR: In this paper, the Kalman filter is generalized to cover state-space models in which the variance of the observation error depends on the state vector, and derived from two differing viewpoints: linear Bayes theory and Gauss-Markov theory.
Abstract: The Kalman filter is generalized to cover state-space models in which the variance of the observation error depends on the state vector. Derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints: linear Bayes theory and Gauss—Markov theory. The results are applied to a model for which {y t: t = 1, 2, …, n} follow a Poisson distribution with corresponding intensities {θt: t = 1, 2, …,n} that are assumed to follow an autoregressive process of order 1, namely . The steady-state generalized Kalman filter algorithm in the case for which ρ = 1 gives a generalization of exponential smoothing for a Poisson process with time-varying intensity.
31 citations
15 Jun 1988
TL;DR: In this article, a general theory of observer design to achieve LTR is given, which decomposes a given multivariable system into several single input single output subsystems each of which can be designed separately.
Abstract: A general theory of observer design to achieve LTR is given. The method developed decomposes a given multivariable system into several single input single output subsystems each of which can be designed separately. The design method is in the frame work of `asymptotic pole placement', or more completely, it is in the frame work of time-scale structure and eigenvalue assignment. Thus it does not suffer from the inherent drawbacks of "repetitive design" and "stiffness" of design equations common to the existing methods viz observer design via Kalman filter formalism and via eigenstructure assignment. Both full order and reduced order observer designs can be accomplished with in the same frame work. Also, asymptotic LTR design as well as exact LTR design, whenever it can be done, can be formulated with in the same frame work. The developed observer design addresses not only the case when uncertainties are modeled as blocks exterior to the given plant but also the case when uncertainties are prescribed structurally in terms of a state space description. The designed observer can recover the corresponding robustness properties of either a linear or a nonlinear state feedback law. In this sense, this work can be viewed as a theory of a separation principle for uncertain dynamical systems.
28 citations
TL;DR: In this paper, the adaptive fading-memory Kalman filter is used to estimate rigid body motion from radar measurements, with emphasis on their interpretation in the frequency domain, and the stability analysis of an adaptive fading memory Kalman filters is performed.
Abstract: To resolve difficulties encountered in estimating rigid body motion from noisy radar measurements, the behavior of an adaptive fading-memory Kalman filter is studied. How adaptive fading-memory Kalman filters can be constructed to estimate rigid body motion from radar measurements is described. A review of fading-memory Kalman filters is contained, with emphasis on their interpretation in the frequency domain. The stability analysis of an adaptive fading-memory Kalman filter is performed. Sample behavior of the error state vector is also examined. The application of the adaptive fading-memory Kalman filters to rigid-body motion estimation is briefly described. >
25 citations
25 citations
TL;DR: In this article, a design methodology for observers and controllers for a class of single-input, single-output nonlinear systems is developed, where a non-linear observer form is defined, and a corresponding observer using nonlinear observer gains is specified.
Abstract: A design methodology for observers and controllers for a class of single-input, single-output non-linear systems is developed. A non-linear observer form is defined, and a corresponding observer using non-linear observer gains is specified. The resulting error dynamics, which are non-linear, are asymptotically stable for a proper choice of those gains and bounded inputs and outputs. A non-linear controller form is defined and a corresponding controller, which results in linear closed-loop dynamics with arbitrary eigenvalue placement, is devised. Transformations from the class of interest to the defined forms are derived. In the observer case, the transformation to the observer form and the non-linear entries in the state matrix of that form can be determined separately, leading to a system of linear partial-differential equations—a major simplification. In the controller case, a simple, well-known system of linear partial-differential equations is obtained. The efficacy of the developed methodology is sho...
22 citations
TL;DR: The Kalman filter as discussed by the authors is a recursive, digital filtering algorithm which has been used for state and parameter estimation in several areas of chemistry, including the determination of polyaromatic hydrocarbon compounds.
19 citations
TL;DR: The method is shown to be superior to ordinary autoregressive spectral estimation based on stationary theory in recognizing rapid changes in the frequencies of oscillations.
18 citations
01 Sep 1988
TL;DR: In this article, methods for the analysis of the performance of Kalman filters are considered, which are all based on the innovation sequence which has well defined statistical properties if the filter is optimal.
Abstract: Methods for the analysis of the performance of Kalman filters are considered in the paper. The methods are all based on the innovation sequence which has well defined statistical properties if the filter is optimal. Local and global test statistics are presented and discussed. A global slippage test statistic is introduced. This test, which has batch type properties, is given in a recursive form.
11 Apr 1988
TL;DR: A reduced-order model Kalman filter which reduces both the amount and the complexity of the computations is developed.
Abstract: The one-dimensional state-space representation of an image for restoration using a Kalman filter requires a relatively large state vector. For a typical autoregressive signal model with nonsymmetric half-plane support, the dimension of the state is approximately equal to the product of the image model order and the pixel width of the image. This state is large, particularly for practical images and would require excessive computation if the Kalman filter were used directly. Consequently, there have been various filtering approximations which reduce the amount of computation. An alternate approach is to reduce the dimension of the image model and use the corresponding optimal filter directly. To this effect a reduced-order model Kalman filter which reduces both the amount and the complexity of the computations is developed. >
07 Dec 1988
TL;DR: In this paper, the authors propose a design method for a robust controller including a new type of observer called the proportional integral (PI) observer, which differs from the conventional one by an integration path which provides additional degrees of freedom.
Abstract: The authors propose a design method for a robust controller including a new type of observer called the proportional integral (PI) observer. The new observer differs from the conventional one by an integration path which provides additional degrees of freedom. This freedom can be used to make the observer-based controller design less sensitive to parameter variation of the system. It is shown that some of the difficulties that can arise in the exclusive pursuit of a design for the conventional observer-based controller from the point of view of system robustness are resolved in a straightforward manner using the PI observer. A systematic robustness recovery procedure is described for the PI observer-based controller design which asymptotically achieves the same loop transfer functions as the fullstate feedback controller implementation. A design example is included and the effectiveness of the method is illustrated by simulation results. >
TL;DR: In this paper, a one-dimensional Kalman filter algorithm is presented that resolves several overlapped liquid chromatographic peaks without algebraic operations of matrices, and the reliability is shown to be similar to that of the multi-dimensional filter for the resolution of overlapped Gaussian peaks with limited R s and S/N values.
TL;DR: The results presented in the paper help one to understand and be able to predict certain behavior of the Kalman filter when inexact values of noise covariances are used.
11 Apr 1988
TL;DR: Systolic Kalman (SK) filter designs are presented which are based on a triangular array (triarray) configuration, in order to facilitate the systolic design, the original algorithm for the Kalman filter estimation is reformulated in a new least-squares formulation.
Abstract: Systolic Kalman (SK) filter designs are presented which are based on a triangular array (triarray) configuration. In order to facilitate the systolic design, the original algorithm for the Kalman filter estimation is reformulated in a new least-squares formulation. The design has advantages in both numerical accuracy and computational efficiency. For the case of white additive noise, the SK-W filter design uses approximately n/sup 2//2 processors and provides a speed-up of n/sup 2//2, with a nearly 100% utilization rate. For the case of colored additive noise, the SK-C filter design also offers comparable speed-up performance. >
TL;DR: In this article, a state space form of the process step response model is used as the basis for implementing state observer forms and a Kalman filter to predict the residual effects in a servo control application.
01 Jan 1988
TL;DR: In this article, a sequential square root method was proposed to solve the numerical problems of the conventional Kalman filter and a comparison with other square root methods was also provided, and a simple square root algorithm was derived for the Kalman covariance and information filters and for the smoothing equations.
Abstract: This paper describes a sequential square root method which is aimed at solving the numerical problems affecting the conventional Kalman filter. Simple square root algorithms are derived for the Kalman covariance and information filters and for the smoothing equations. A comparison with other square root methods is also provided.
07 Dec 1988
TL;DR: A simple algorithm is suggested to estimate, using a Kalman filter, the unknown process noise variance of an otherwise known linear plant, using the difference between the expected prediction error variance, computed in the Kalman Filter, and the measured predictionerror variance.
Abstract: A simple algorithm is suggested to estimate, using a Kalman filter, the unknown process noise variance of an otherwise known linear plant. The process noise variance estimator is essentially dead beat, using the difference between the expected prediction error variance, computed in the Kalman filter, and the measured prediction error variance. The estimate is used to adapt the Kalman filter. The use of the adaptive filter is demonstrated in a simulated example in which a wildly manoeuvring target is tracked. >
07 Dec 1988
TL;DR: A parallel algorithm for solving an n-state Kalman filter on an (n+1)-cell linear array is described, which is the basis for the mapping of an extended Kalmanfilter on the Warp computer.
Abstract: A parallel algorithm for solving an n-state Kalman filter on an (n+1)-cell linear array is described. The approach is to update the columns of the filter covariance matrix in parallel to balance the computations and minimize the communications. The algorithm is the basis for the mapping of an extended Kalman filter on the Warp computer. The Warp implementation is written in a high-level language and achieves a measured speedup of almost 300 over the same filter running on a Sun workstation. Efficient algorithm mapping is the key to achieve the high-speed filter performance. >
23 May 1988
TL;DR: In this article, it was observed that in minimum MSE (mean square error) linear predictive transform (LPT) coding, a multivariable signal model of the Kalman type inherently arises.
Abstract: It is observed that in minimum MSE (mean square error) linear predictive transform (LPT) coding, a multivariable signal model of the Kalman type inherently arises. This is illustrated with a digital monochrome image example. It is proposed that the Kalman filter could make effective use of this signal model. It then follows that minimum MSE LPT modeling simultaneously addresses relevant coding and filtering problems. >
TL;DR: In this paper, a state estimator can be designed and implemented very easily if the system is output-decoupled, as is often the case in process monitoring and control applications.
Abstract: Most industrial processes are complex systems, characterized by nonlinearity, high order, and even implicit dynamics. The design of a Luenberger-type observer or an extended Kalman filter for state estimation of such systems presents, in general, considerable difficulties. The authors show that a state estimator can be designed and implemented very easily if the system is output-decoupled, as is often the case in process monitoring and control applications. Simulation study and experiments on an experimental water pipeline show that the proposed estimator works very well. Its estimation accuracy is nearly the same as that of an extended Kalman filter, while its computational expenditure is almost as small as the real-time system model. >
Dissertation•
01 Jan 1988
TL;DR: The purpose of this thesis is to study this asymptotic filtering problem and to develop observer designs based on Baras and Krishnaprasad's idea.
Abstract: : An important problem in control theory is the design of observers for nonlinear control systems. By observer we mean a deterministic dynamical system which uses observed information to compute an estimate of the state of the control system in such a way that the error decays to zero. Baras and Krishnaprasad have proposed that an observer design might result from a study of an asymptotic nonlinear filtering problem obtained by adding small noise terms to the equations defining the control system. The purpose of this thesis is to study this asymptotic filtering problem and to develop observer designs based on their idea.
20 Mar 1988
TL;DR: In this article, the steady-state error of a version of the Kalman filter, called the alpha, beta filter, was analyzed under the assumption that missing data may occur.
Abstract: The Kalman filter provides a recursive least-mean-square estimate of parameters in a dynamic system. Because the initial variances of the measurements used in the estimation are uncertain in a practical situation, a tracking filter can be optimum only in steady-state. The steady-state error of a version of the Kalman filter, called the alpha , beta filter, is analyzed under the assumption that missing data may occur. The results are developed for a constant-scan-rate radar. The number of intervals between valid data is modeled as a geometric random variable with the probability of valid data as a parameter. It is shown that missing data can introduce large additional tracking error for slowly scanning radars. >
TL;DR: This paper first presents a state-space representation of a fluid pipeline, then turns the non-linear observer design task into optimization problems in order to bridge the gap between non- linear observer theory and its applications.
Abstract: Observer design for non-linear systems is difficult work, especially for systems of high order. In this paper, we first present a state-space representation of a fluid pipeline. Then we turn the non-linear observer design task into optimization problems in order to bridge the gap between non-linear observer theory and its applications. In applying this method to the discrete high-order model of a pipeline, analytic solutions can easily be obtained. A structural condition for observers to be robust to pipeline friction and diameter variations is also proved through steady-state analysis. Simulation studies and experiments on a water pipeline show that: (a) the observers designed converge rapidly and reliably; (b) the computational expenditure is very small in comparison with the Kalman filter; and (c) friction and diameter variations may have little influence on the estimation accuracy.
11 Apr 1988
TL;DR: 2D Kalman filtering for the restoration of stochastically blurred images is developed and the proposed filters are the best linear estimators for minimizing the mean-square error over the blur process ensemble and observation noise ensemble.
Abstract: 2D Kalman filtering for the restoration of stochastically blurred images is developed. Stochastic blur is treated as the combination of a deterministic blur and correlated random noise. For restoration from single-frame data, an augmented state-vector Kalman filter for stochastic blurs is derived. This filtering scheme is then extended to provide restoration from multiple-frame data also. Kalman filtering for both serial and parallel processing of the frames is proposed. The new filters can take into account the spatio-temporal correlations of the randomly varying blur. For the equivalent 1-D problem, the proposed filters are the best linear estimators for minimizing the mean-square error over the blur process ensemble and observation noise ensemble. Sample results are also provided to show the effectiveness of the proposed filters. >
TL;DR: It is demonstrated that substantial decreases in the computational burden are possible without loss of filter accuracy, which makes possible the application of second‐order filters on large data sets, and they make real‐time filtering possible with a fast processor.
Abstract: The extended Kalman filter has been used to estimate initial reactant concentrations and rate constants for rate-based chemical assays employing a second-order chemical reaction. Application of first- and second-order models to data permits reaction order identification by examining either the filter innovations or the evolution of the filter states. Because of non-linearities in the second-order kinetic model, repetitive filtering is necessary for convergence to reliable state estimates. Reduction of the filter calculation burden is investigated through the use of information-based filter methods, and it is demonstrated that substantial decreases in the computational burden are possible without loss of filter accuracy. These decreases make possible the application of second-order filters on large data sets, and they make real-time filtering possible with a fast processor.
23 May 1988
TL;DR: In this paper, the performance of a decoupled Kalman track filter is analyzed and a steady-state covariance analysis is discussed. But, the analysis is limited to the case where the root-mean-square tracking errors are unbounded.
Abstract: A steady-state covariance analysis is discussed in the study the performance of a six-state, decoupled Kalman track filter. Analytical and numerical results indicate that, for a considerable range of filter gains and target line-of-sight (LOS) rates, the decoupled filter is unstable, and its steady-state root-mean-square tracking errors are unbounded. >
20 Mar 1988
TL;DR: An estimator-subtractor-type line suppressor recently proposed by the author for pseudonoise (PN) spread-spectrum applications or as an adaptive line enhancer in acoustic applications is modeled as a combined discrete state-variable Kalman filter, one-step predictor and optimal linear smoother.
Abstract: An estimator-subtractor-type line suppressor recently (1986) proposed by the author for pseudonoise (PN) spread-spectrum applications or as an adaptive line enhancer in acoustic applications is modeled as a combined discrete state-variable Kalman filter, one-step predictor and optimal linear smoother. It is shown that the adaptive Kalman filter acts as the oscillator. However, the damping and the tuned frequency of this filter oscillator are influenced by the mean-square estimation error. Closed-form expressions are given for the estimation error of a sinusoidal process in the presence of additive broadband noise (the model of a discrete PN spread-spectrum signal). >
01 Jan 1988
TL;DR: In this article, the effects of the finite difference approximation on the performance of Kalman filtering for stochastic dynamic tidal models are investigated. And the degradation of the performance, in case an erroneous filter model is used, is investigated.
Abstract: Kalman filtering for stochastic dynamic tidal models, is a hyperbolic filtering problem. The questions of observability and stability of the filter as well as the effects of the finite difference approximation on the filter performance are studied. The degradation of the performance of the filter, in case an erroneous filter model is used, is investigated. In this paper we discuss these various practical aspects of the application of Kalman filtering for tidal flow identification problems. Filters are derived on the basis of the linear shallow water equations. Analytical methods are used to study the performance of the filters under a variety of circumstances.