Showing papers on "Invariant extended Kalman filter published in 1978"
01 Jan 1978
TL;DR: For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramer-Rao lower bound to the estimation error covariance matrix as discussed by the authors.
Abstract: For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramer-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.
199 citations
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
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
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
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
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
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
TL;DR: In this article, the design of linear reduced-order filters and linear full-order filter with reduced complexity is considered, where the objective is to estimate a linear transformation of the state vector with a filter of lower dimension.
Abstract: This short paper considers the design of linear reduced-order filters and linear full-order filters with reduced complexity. The objective of a reduced-order filter is to estimate a linear transformation of the state vector with a filter of lower dimension. This type of filter occurs frequently in applications.
16 citations
13 citations
TL;DR: In this article, an iterative modification of the nonlinear Kalman filter was proposed for the determination of time-variable heat-transfer coefficients, which can be used to calculate the time-varying heat transfer coefficients.
Abstract: An iterative modification of the nonlinear Kalman filter is proposed for the determination of time-variable heat-transfer coefficients.
10 citations
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.
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.
TL;DR: In this paper, the authors apply Kalman filtering techniques to reliability smoothing and find that the estimates of point availability attain a steady-state, while the error variance of the estimate of the steady state availability and the steadystate Kalman gain are zero.
Abstract: This paper applies Kalman filtering techniques to reliability smoothing. Point availability as a function of time is estimated through Kalman filtering techniques. Approximate determination of the sampling interval and the measurement variance is given. The error variance of the estimate of the steady-state availability and the steady-state Kalman gain are zero. From this, it is found that the estimates of point availability attain a steady-state.
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)
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.
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.
TL;DR: Suboptimal filter covariance analysis for problems containing a large number of bias parameters is considered using a decomposition property of the truth model covariance matrix, and the effects of unmodelled bias parameters upon the non-bias parameters can be easily studied, provided the control is impulsive.
Abstract: Suboptimal filter covariance analysis for problems containing a large number of bias parameters is considered Using a decomposition property of the truth model covariance matrix, it is shown that the effects of unmodelled bias parameters upon the non-bias parameters can be easily studied, provided the control is impulsive The results provide a more efficient formulation of the covariance analysis problem and are generalizations of similar results for the optimal estimation problem An alternative proof of bias separation in the Kalman filter is also given
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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.
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.