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Showing papers on "Alpha beta filter published in 1978"


Journal ArticleDOI
TL;DR: In this article, a new decentralized computational structure is developed for optimal state estimation in large scale linear interconnected dynamical systems, which uses a hierarchical structure to perform successive orthogoilalizations on the measurement subspaces of each sub-system in order to provide the optimal estimate.
Abstract: In this paper a new decentralized computational structure is developed for Optimal state estimation in large scale linear interconnected dynamical systems. The new filter uses a hierarchical structure to perform successive orthogoilalizations on the measurement subspaces of each sub-system in order to provide the optimal estimate. This ensures substantial savings in computation time. In addition, since only low-order subsystem equations are manipulated at each stage, numerical inaccuracies are reduced, and the filter remains stable for even high-order systems. This is illustrated on a multimachine example of a system comprising eleven interconnected machines.

70 citations


Journal ArticleDOI
TL;DR: In this article, a general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables.
Abstract: A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.

51 citations


Journal ArticleDOI
TL;DR: In this article, the authors present effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several neutrally stable (NS) modes are undisturbed by wind gusts.
Abstract: Kalman filters designed for many aerospace systems turn out to be unsatisfactory. The estimate errors become large compared to the errors predicted by the theory ('divergence'). One of the principal causes of this failure is that the system model contains states or modes that are undisturbed by the modeled process noise, and are neutrally stable (NS). One cure for such problems is periodic restarting of a time-varying Kalman filter. Other cures include minimum variance observers with eigenvalue constraints, added noise, pole-shifting, and destabilization. Several examples are given, including effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several NS modes are undisturbed by wind gusts. An interpretation of these estimators as a 'strapdown IMU' without accelerometers, gimbaled gyros, or servos is given.

43 citations


Journal ArticleDOI
TL;DR: In this paper, the Kalman filter is applied to the standard linear regression model and the resulting estimator is compared with the classical least-squares estimator, and the applicability and disadvantages of the filter are illustrated by a case study which consists of two parts.
Abstract: In this paper we show how the Kalman filter, which is a recursive estimation procedure, can be applied to the standard linear regression model. The resulting “Kalman estimator” is compared with the classical least-squares estimator. The applicability and (dis)advantages of the filter are illustrated by means of a case study which consists of two parts. In the first part we apply the filter to a regression model with constant parameters and in the second part the filter is applied to a regression model with time-varying stochastic parameters. The prediction-powers of various “Kalman predictors” are compared with “least-squares predictors” by using Theil‘s prediction-error coefficient U.

20 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that if the covariance of a white noise sequence in discrete-time is derived from the accepted mathematical description for the variance of a continuous-time white noise process in continuous time, compatibility between the discrete-and continuous time versions of the Kalman filter is complete.

18 citations


Journal ArticleDOI
K. Tajima1
TL;DR: In this article, an external description of multivariable linear stochastic systems with unknown noise covariances is given, and an estimation method of the steady, state Kalman filter gain for systems with known noise covariance is presented.
Abstract: An external description of multivariable linear stochastic systems gives a new estimation method of the steady, state Kalman filter gain for systems with unknown noise covariances.

17 citations


Journal ArticleDOI
TL;DR: In this paper, a procedure for designing an optimal observer for a linear continuous time invariant system is described, where the parameters of the observer are chosen so as to assign its eigenvalues to desired locations and at the same time a measure of the deviation of the estimate of the observed state from its actual value is minimized.
Abstract: A procedure for designing an optimal observer for a linear continuous time invariant system is described in this paper. The parameters of the observer are chosen so as to assign its eigenvalues to desired locations and at the same time a measure of the deviation of the estimate of the observed state from its actual value is minimized, A numerical example is included to show that the estimate of the state obtained by the optimal observer is much closer to the actual state than the estimate obtained from another observer with the same eigenvalues as the optimal observer.

11 citations


Journal ArticleDOI
TL;DR: In this article, the stationary Kalman filter is approximated by a notch filter together with a low-pass filter in cascade in order to remove unwanted wave motion signals in dynamic ship positioning systems.
Abstract: In dynamic ship positioning systems notch filters have been used mainly to remove the unwanted wave motion signals. Recently, Kalman filters have been introduced for this purpose. It is demonstrated that for this application the stationary Kalman filter is approximated by a notch filter together with a low-pass filter in cascade.

9 citations


Journal ArticleDOI
TL;DR: In this paper, a simple Kalman filter was proposed for optimally aiding a strapdown inertial navigation system (INS) with data from a radiometric area correlator (RAC) onboard a weapon system currently under development.
Abstract: Because of stringent storage restrictions, a very simple Kalman filter has been proposed for optimally aiding a strapdown inertial navigation system (INS) with data from a radiometric area correlator (RAC) onboard a weapon system currently under development. However, the adequacy of two decoupled three-state filters to meet performance specifications was subject to serious question. A set of covariance analyses has been conducted to determine estimation capabilities in a realistic environment generated by accurate *'truth models" of the error characteristics of two competing inertial systems (one using laser gyros and the other, conventional dry gyros) and the RAC system. Despite the simple form, the filters performed well enough to meet system specifications on navigation errors. Because of its extreme precision at low altitudes, the RAC was the dominant factor in attaining this accuracy, with the laser gyro INS providing somewhat better performance than the dry gyro system. Sensitivity analyses revealed that better RAC hardware or RAC error models in the filters would provide the most effective performance enhancement.

8 citations


Journal ArticleDOI
TL;DR: In this article, the optimal control problem of time-delay systems with partial state measurements is studied through the application of a Walsh function expansion, and the main purpose of the paper is to provide a computational technique for determining the expansion coefficient matrices for both the system state and the observer output.
Abstract: The optimal control problem of time-delay systems with partial state measurements is studied through the application of a, Walsh function expansion. The main purpose of the paper is to provide a computational technique for determining the expansion coefficient matrices for both the system state and the observer output. It is shown that the known initial conditions of the state and the observer can be used iteratively to compute the state and the observer at any subsequent time and thus implement the optimal controller. Also, by subdividing the time interval of interest, the procedure is simplified such that it does not involve any matrix inversion.

7 citations


Journal ArticleDOI
TL;DR: The Kalman filter is adapted so that the parameters of stochastic time-invariant systems can be identified by a direct linear process and constants relating to the initial conditions of the unknown system and the characteristics of the noise are determined.


Journal Article
TL;DR: In this paper, an extended Kalman filter is used to estimate the translational position changes of the target in the FLIR field of view due to two effects: actual target motion, and apparent motion caused by atmospheric turbulence.
Abstract: : An extended Kalman filter algorithm, using outputs from a forward looking infrared (FLIR) sensor as measurements, is used to track a point source target in an open loop tracking problem The filter estimates the translational position changes of the target in the FLIR field of view due to two effects: actual target motion, and apparent motion caused by atmospheric turbulence Sixteen cases are examined to determine the performance of the filter as a function of signal-to-noise ratio, Gaussian beam, size, the ratio of RMS target motion to RMS atmospheric jetter, target correlation times, and mismatches between the true shape and the shape assumed by the filter The performance of the extended Kalman filter is compared to the performance of an existing correlation tracker under identical initial conditions A one sigma tracking error of 2 and 8 picture elements is obtained with signal-to-noise ratios of 20 and 1 respectively No degradation in performance is observed when the beam size is decreased or when the target correlation time is increased over a limited range, when filter parameters are adjusted to reflect this knowledge Sensitivity analysis shows that the filter is robust to minor changes in target intensity size (Author)

Proceedings ArticleDOI
F. Nesline1, P. Zarchan1
01 Jan 1978
TL;DR: It is shown for gun fire control applications, the Kalman filter requires at least an order of magnitude more computation to achieve the same performance as a finite memory filter.
Abstract: A finite memory filter is developed for gun fire control and compared to a Kalman filter. As opposed to the Kalman filter, the finite memory filter does not require a priori information concerning measurement or target noise statistics. In addition, the finite memory filter was implemented using a new recursive algorithm which dramatically reduces its computational burden. It is shown for gun fire control applications, the Kalman filter requires at least an order of magnitude more computation to achieve the same performance as a finite memory filter.

Journal ArticleDOI
TL;DR: In this article, a performance measure is suggested for evaluating the performance of a given optimal estimator at other lags than the design lag. And the optimal smoothing improvement is related to optimal improvement and interpreted in terms of input-output transfer function properties.
Abstract: A performance measure is suggested for evaluating the performance of a given optimal estimator at other lags than the design lag. Applying this idea, suboptimal smoothers are found for both continuous-and discrete-time systems, combining low complexity and good performance. Several examples are considered. Suboptimal-smoothing improvement is related to optimal improvement and interpreted in terms of input-output transfer-function properties. A special class of discrete-time systems is also discussed where the optimal smoother is of the same complexity as the zero-lag filter.

Journal ArticleDOI
TL;DR: In this paper, the problem of designing an observer insensitive to the variation of system parameters is considered, and the existence of the K-insensitive observer is examined, where possible, the class of the observers is obtained.


Journal ArticleDOI
TL;DR: In this article, an observer-estimator is derived by using the Luenberger observer relation for the reconstruction of the system state from the uncorrupted system outputs as a constraint on the Kalman filter differential equation for the state estimate.
Abstract: This paper considers the problem of designing an observer-estimator for the state of a continuous-time, finite-dimensional, linear, stochastic system having input disturbance noise and some outputs which are not corrupted by measurement noise. The observer-estimator is derived by using the Luenberger observer relation for the reconstruction of the system state from the uncorrupted system outputs as a constraint on the Kalman filter differential equation for the state estimate which involves the noise-corrupted system outputs. In this fashion both types of system output are utilized by the observer-estimator. The optimal value of the observer-estimator parameter matrices are found by resorting to variational techniques.

Journal ArticleDOI
Hidenori Kimura1
TL;DR: In this article, a new type of function observers is introduced, called a mixed-type observer, in which noisy components of the observation output can be excluded from the static part of the estimation scheme.
Abstract: In this paper a new type of function observers is introduced, in which noisy components of the observation output can be excluded from the static part of the estimation scheme. This type of observer, called a mixed-type observer in this paper, exhibits a better noise performance compared with the conventional Luenberger observer. A simple algorithm for designing mixed-type observers with arbitrarily prescribed poles is derived, as well as an evaluation of its minimal order. Some numerical examples are illustrated in order to show the feasibility of the algorithm.


Journal ArticleDOI
TL;DR: In this paper, it is shown that a method for the identification of deterministic systems derived from the Kalman filter is related to a gradient technique of parameter estimation and that the range of problems to which the gradient method may be applied is thereby extended.

ReportDOI
01 Jul 1978
TL;DR: In this article, Luenberger's minimal-order observer is used as an alternate to the Kalman filter for obtaining state estimates in linear discrete-time stochastic systems, where optimality is in the mean square sense.
Abstract: : This report investigates the idea of utilizing Luenberger's minimal-order observer as an alternate to the Kalman filter for obtaining state estimates in linear discrete time stochastic systems. More specifically, this dissertation presents a solution to the problem of construction as optimal minimal order observer for linear discrete time stochastic systems where optimality is in the mean square sense. The approach taken in this report leads to a completely unified theory for the design of optimal minimal-order observers and is applicable to both time-varying and time-invariant linear systems. To illustrate the theory and application of the observer designs developed in the dissertation, the problem of designing a radar tracking system is considered. Examples are included which illustrate clearly the practicality and usefulness of the proposed optimal observer design technique. Finally, a host of topics for future research is presented in the hope of stimulating further research in the domain of observer theory.

Journal ArticleDOI
TL;DR: The choice of a particular canonical representation for the system is shown to lead to a simple design procedure and the resulting observer is shown also to possess the minimum-time state-estimation property.
Abstract: The problem of constructing an observer for a discrete linear system so as to minimize a quadratic function of the state estimation error is considered. The choice of a particular canonical representation for the system is shown to lead to a simple design procedure. The resulting observer is shown also to possess the minimum-time state-estimation property.

Journal ArticleDOI
TL;DR: It is shown than an estimate generated in a discrete time Kalman filter can, under certain circumstances, give better performance if some delay is allowed in the system.