Showing papers on "Alpha beta filter published in 1977"
TL;DR: In this article, the problem of observing the state of an unknown, time invariant linear system from measurements of its input and output is considered, and the approach taken here proceeds from a parametrized observer, which is only an alternative, equivalent representation of the Luenberger observer.
Abstract: The problem of observing the state of an unknown, time invariant linear system from measurements of its input and output is considered. Instead of adapting the parameters in a Luenberger observer to solve the problem, as was done by earlier authors, the approach taken here proceeds from a so-called parametrized observer, which is only an alternative, equivalent representation of the Luenberger observer. However, the parametrized observer has a different structure where the state estimate is a linear function (and not a functional) of its parameters. Therefore, adapting the parameters in the parametrized observer results in a complete separation of the observer dynamics from the adaptive loop which substantially simplifies the design of suitable parameter adaptation schemes. Three such schemes are presented and proven to be globally exponentially rather than asymptotically convergent. In particular, the second and the third adaptation schemes allow the construction of adaptive observers with arbitrarily high (exponential) rates of convergence.
701 citations
TL;DR: The reduced update Kalman filter is shown to be optimum in that it minimizes the post update mean-square error (mse) under the constraint of updating only the nearby previously processed neighbors.
Abstract: The Kalman filtering method is extended to two dimensions. The resulting computational load is found to be excessive. Two new approximations are then introduced. One, called the strip processor, updates a line segment at a time; the other, called the reduced update Kalman filter, is a scalar processor. The reduced update Kalman filter is shown to be optimum in that it minimizes the post update mean-square error (mse) under the constraint of updating only the nearby previously processed neighbors. The resulting filter is a general two-dimensional recursive filter.
347 citations
TL;DR: The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs.
139 citations
TL;DR: In this article, a large number of ad hoc modifications are required to prevent divergence, resulting in a rather complex filter and performance is quite good as judged by comparison of Monte Carlo simulations with the Cramer-Rao lower bound, and by the filters ability to track maneuvering targets.
Abstract: It is well known that the extended Kalman filtering methodology works well in situations characterized by a high signal-to-noise ratio, good observability and a valid state trajectory for linearization. This paper considers a problem not characterized by these favorable conditions. A large number of ad hoc modifications are required to prevent divergence, resulting in a rather complex filter. However, performance is quite good as judged by comparison of Monte Carlo simulations with the Cramer-Rao lower bound, and by the filters ability to track maneuvering targets.
78 citations
TL;DR: The Kalman Filter is described, which is used to obtain an “optimal” estimate of the state vector of a linear system with unknown parameters and present value of the mean of the process.
Abstract: This paper describes the use of the Kalman Filter in a certain ciass of forecasting problems. The time series is assumed to be modeled as a time varying mean with additive noise. The mean of the time series is assumed to be a linear combination of known functions. The coefficients appearing in the linear combination are unknown. Under such assumptions, the time series can be described as a linear system with the state vector of the system being the unknown parameters and present value of the mean of the process. The Kalman Filter can be used under these circumstances to obtain an “optimal” estimate of the state vector. One of the distinct advantages of the Kalman Filter is that time varying coefficients can be permitted in the model. Examples using the Kalman Filter in forecasting are presented.
57 citations
01 Aug 1977
TL;DR: Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors and the computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables.
Abstract: An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.
46 citations
43 citations
01 Jan 1977
TL;DR: The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case.
Abstract: The extended Kalman filter is an approximate filter for nonlinear systems, based on first-order linearization. Its use for the joint parameter and state estimation problem for linear systems with unknown parameters is well known and widely spread. Here a convergence analysis of this method is given. It is shown that in general, the estimates may be biased or divergent and the causes for this are displayed. Some common special cases where convergence is guaranteed are also given. The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case. The scheme can then be interpreted as maximization of the likelihood function for the estimation problem, or as a recursive prediction error algorithm.
36 citations
TL;DR: In this article, a new method is proposed that enables well-established Kalman-filter theory to yield a simple 2D filter for images that can be modeled by two-dimensional wide-sense Markov (WSM) random fields.
Abstract: In the recent past considerable attention has been devoted to the application of Kalman filtering to smoothing out observation noise in image data. A generalization of the one-dimensional Kalman filter to two dimensions was earlier suggested by Habibi, but it has since been shown that this generalization is invalid since it does not preserve the optimality of the Kalman filter. A new method is proposed here that enables well-established Kalman-filter theory to yield a simple two-dimensional filter for images that can be modeled by two-dimensional wide-sense Markov (WSM) random fields.
26 citations
TL;DR: In this paper, a method for parameter estimation using the Kalman filter with appropriate initial conditions is presented, which is shown to approximate the minimum-norm weighted least-squares solution to any desired accuracy during all phases of estimation.
Abstract: A method for parameter estimation is presented using the Kalman filter with appropriate initial conditions. The filter solution is shown to approximate the minimum-norm weighted least-squares solution to any desired accuracy during all phases of estimation. Furthermore, the computations are identical for each measurement, irrespective of whether a minimal observable data set has been established. This procedure contrasts with other techniques for parameter estimation that require additional computation when the process is unobservable.
24 citations
TL;DR: In this paper, a reduced order, least squares, state estimator is developed for linear discrete-time systems having both input disturbance noise and output measurement noise with no output being free of measurement noise.
Abstract: A reduced order, least squares, state estimator is developed for linear discrete-time systems having both input disturbance noise and output measurement noise with no output being free of measurement noise. The order reduction is achieved by using a Luenberger observer in connection with some of the system outputs and a Kalman filter to estimate the state of the Luenberger observer. The order of the resulting state estimator is reduced from the order of the usual Kalman filter system state estimator by the number of system outputs selected for use as inputs to the Luenberger Observer. The manner in which the noise associated with the selected system outputs affects the state estimation error covariance provides considerable insight into the compromise being attempted.
TL;DR: In this paper, a two-stage state and parameter estimation algorithm for linear systems has been developed, where stage 1 uses a stochastic approximation method for state estimation, while stage 2 considers parameter estimation through a linear Kalman filter.
Abstract: A two-stage state and parameter estimation algorithm for linear systems has been developed. Stage 1 uses a stochastic approximation method for state estimation, while stage 2 considers parameter estimation through a linear Kalman filter. These two stages are coupled in a bootstrap manner. The algorithm is computationally much simpler than the usual extended Kalman filter. A fourth-order numerical example has been solved, and results have been compared with those obtained using an extended Kalman filter.
TL;DR: In this paper, the numerical stability and accuracy of a new Kalman filtering technique is examined, which is based upon square-root-free Givens transformation methods and involves an upper triangular covariance factorization P = UDUT.
TL;DR: In this article, a second-order observer was proposed to estimate the states of a nonlinear plant based on discrete deterministic measurements, which is obtained by applying the time-varying linear observer theory to the augmented linearized model which was obtained by replacing each quadratic term in the original system with new state variables.
Abstract: This paper presents a second-order observer which estimates the states of a nonlinear plant based on discrete deterministic measurements. The observer is obtained by applying the time-varying linear observer theory to the augmented linearized model which is obtained by replacing each quadratic term in the original system with new state variables. The gain of the observer is evaluated sequentially through a procedure similar to that in the Kalman filter. The comparison between the extended linear observer and this one is made through the computer simulation for two model systems of nonlinear type wherein one of them is an electric power system model. These simulation results indicate that the use of second-order observer leads to improved estimation performance.
TL;DR: In this article, an adaptive observer for linear time-invariant multi-input multi-output (MIMO) systems is proposed, where the observer simultaneously estimates the state vector and the parameter vector of the unknown plant and is globally asymptotically stable.
TL;DR: In this article, the stabilization of an unstable nonlinear distributed chemical reactor system is examined when concentration measurements are not possible, and it is shown that the observability index is equal to two.
TL;DR: In this article, the problem of estimating the state variables and maneuvering parameters for a reentry vehicle was considered and nonlinear filtering results based upon a tuned nine state extended Kalman filter (EKF) were compared with those obtained by a linearized fixed interval smoother, which reprocesses the output of the EKF, using Monte Carlo simulation experiments.
Abstract: This correspondence considers the problem of estimating the state variables and maneuvering parameters for a reentry vehicle. The nonlinear filtering results based upon a tuned nine state extended Kalman filter (EKF) are compared with those obtained by a linearized fixed interval smoother, which reprocesses the output of the EKF, using Monte Carlo simulation experiments.
TL;DR: A method for relating the modeling errors to the selection of the covariance of "process noise" for model error compensation is suggested and a performance ordering for cases when the true system becomes a subsystem of the model used for the filter construction is given.
Abstract: Filter compensation techniques for several special but practical cases are discussed. A general set of bias and covariance equations for linear filters with modeling errors is first summarized. A method for relating the modeling errors to the selection of the covariance of "process noise" for model error compensation is suggested. A performance ordering for cases when the true system becomes a subsystem of the model used for the filter construction is given. A bias correcting filter is derived for the case when the filter is matched only to a subsystem of the actual system.
TL;DR: An iterative sequential observer is presented which enables us to estimate the transient state of power system with high accuracy and an observer gain is introduced which is easily and sequentially evaluated in a similar way as Kalman filter.
Abstract: This paper presents an iterative sequential observer which enables us to estimate the transient state of power system with high accuracy. This observer attempts to reduce the effect of both the dynamic non-linearity and the measurement nonlinearity. The latter is reduced by modifying the estimates iteratively and the former by discretizing the dynamic equation at every short interval of time. Furthermore an observer gain is introduced which is easily and sequentially evaluated in a similar way as Kalman filter. Simulation results, in which the observer is applied to the system of one machine infinite bus, indicate that the state is estimated successfully even in the cases of less available measurements and there is a capability of a real-time estimation using an on-line computer.
TL;DR: In this paper, it has been shown that the satisfaction of the Huddle equations is sufficient for the discrete extended Luenberger observer to be in the form of a Kalman filter.
Abstract: The extended Luenberger observer is considered as an alternative to the Kalman filter for obtaining state estimates in discrete-time linear stochastic systems. In certain conditions both estimators have the same structure. It has been shown that the satisfaction of the Huddle equations [7], [9] is sufficient for the discrete extended Luenberger observer to be in the form of a Kalman filter; here we show necessity.
TL;DR: In this paper, the construction of minimal-order observers for estimating vector functions of the states of linear multivariable systems is considered, and the observer design problem is reduced to a static optimization problem in certain observer parameters.
Abstract: The construction of minimal-order observers for estimating vector functions of the states of linear multivariable systems is considered. By means of geometric arguments, the observer design problem is reduced to a static optimization problem in certain observer parameters. A systematic procedure for designing minimal-order stable observers is proposed that is based on a new lower bound on the required observer order, a special canonical form of the observer matrix that ensures any prescribed degree of stability, and a gradient-type function minimization algorithm. A modified procedure for designing minimal-order observers having arbitrarily specified poles is also described. The techniques developed are illustrated by means of numerical examples.
01 Dec 1977
TL;DR: In this article, a non-linear approximate model for the switching variable is developed and used for the joint estimation of the state vector and the switch variable via a single extended Kalman filter.
Abstract: This paper describes a novel approach to the problems of state estimation in linear, discrete-time systems which switch randomly between two sets of parameters, indicated by a random switching variable. A non-linear approximate model for the switching variable is developed and used for the joint estimation of the state vector and the switching variable via a single extended Kalman filter. The performance of the filter is compared with that of other suboptimal filters known to date. The proposed approach provides comparable accuracy, and saves computational effort in systems of order three or more. In large systems the computational effort is halved.
01 Mar 1977
TL;DR: The development of an adaptive Kalman filter for target tracking and prediction that was subsequently implemented in the digital MARK 68 Gunfire Control System (GFCS) as part of the Gunnery Improvement Program is described.
Abstract: : This report describes the development of an adaptive Kalman filter for target tracking and prediction that was subsequently implemented in the digital MARK 68 Gunfire Control System (GFCS) as part of the Gunnery Improvement Program. The discrete Kalman filter is introduced along with a brief discussion of its selection for this application. The general problem of target modeling was presented with emphasis on conventional polynomial models and their convergence properties. A stochastic target model, a first order Markov process in acceleration, was introduced, and the advantages over the polynomial were models explored. A dual bandwidth adaptation algorithm with associated maneuver detection logic was developed and favorably compared with more conventional adaptation methods. A Kalman filter to handle serially correlated observation error (without state vector augmentation) was found, restructured to improve the computational efficiency and exercised to determine parametric sensitivity to correlation effects. Prefiltering, or data compression techniques, were studied and found to significantly reduce required computation with negligible degradation in performance. Square root covariance propagation (in single precision) was found to be considerably more efficient (by a factor of 4.5) than double precision covariance for the particular filter model and computer for this application. The three-dimensional filtering problem was approached by first developing the optimal nonlinear filter as a standard and then evaluating on a relative basis several suboptimal linearized versions.
TL;DR: In this paper, it was shown that the asymptotic form of the Kalman filter that is obtained by letting the variance matrix of the initial state go to infinity is minimax with respect to the original state if the latter is regarded as an unknown, deterministic quantity.
Abstract: It is proved that both in the discrete-time and the continuous -time case the asymptotic form of the Kalman filter that is obtained by letting the variance matrix of the initial state go to infinity is minimax with respect to the initial state if the latter is regarded as an unknown, deterministic quantity
01 Jul 1977
TL;DR: Linear filters, including the conventional Kalman filter and versions of square root filters devised by Potter and Carlson, are studied for potential application on streaming computers.
Abstract: Linear filters, including the conventional Kalman filter and versions of square root filters devised by Potter and Carlson, are studied for potential application on streaming computers. The square root filters are known to maintain a positive definite covariance matrix in cases in which the Kalman filter diverges due to ill-conditioning of the matrix. Vectorization of the filters is discussed, and comparisons are made of the number of operations and storage locations required by each filter. The Carlson filter is shown to be the most efficient of the filters on the Control Data STAR-100 computer.
TL;DR: The problem of control of a linear stochastic system observed by both linear and hard-limited measurements is considered and it is shown that the feedback nature of the control induces a natural probing which activates the filter.