Showing papers on "Kalman filter published in 1979"
TL;DR: In this paper, a convergence analysis of the extended Kalman filter for nonlinear systems with unknown parameters is given, and it is shown that in general the estimates may be biased or divergent and the causes for this are displayed.
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.
1,021 citations
TL;DR: In this article, a least square estimator is used to estimate the acceleration input vector of a target and a simple Kalman filter is used for tracking the target in constant course and speed mode.
Abstract: Beginning with the derivation of a least squares estimator that yields an estimate of the acceleration input vector, this paper first develops a detector for sensing target maneuvers and then develops the combination of the estimator, detector, and a "simple" Kalman filter to form a tracker for maneuvering targets. Finally, some simulation results are presented. A relationship between the actual residuals, assuming target maneuvers, and the theoretical residuals of the "simple" Kalman filter that assumes no maneuvers, is first formulated. The estimator then computes a constant acceleration input vector that best fits that relationship. The result is a least squares estimator of the input vector which can be used to update the "simple" Kalman filter. Since typical targets spend considerable periods of time in the constant course and speed mode, a detector is used to guard against automatic updating of the "simple" Kalman filter. A maneuver is declared, and updating performed, only if the norm of the estimated input vector exceeds a threshold. The tracking sclheme is easy to implement and its capability is illustrated in three tracking examples.
443 citations
TL;DR: In this paper, the extended Kalman filter applied to bearings-only target tracking is theoretically analyzed, and closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability.
Abstract: The extended Kalman filter applied to bearings-only target tracking is theoretically analyzed. Closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability (i.e., premature covariance collapse and divergence). Further investigation reveals that conventional initialization techniques often precipitate such anomalous behavior. These results have important practical implications and are not presently being exploited to full advantage. In particular, they suggest that substantial improvements in filter stability can be realized by employing alternative initialization and relinearization procedures. Some candidate methods are proposed and discussed.
431 citations
TL;DR: In this paper, a new approach to the three-dimensional airborne maneuvering target tracking problem is presented, which combines the correlated acceleration target model of Singer [3] with the adaptive semi-Markov maneuver model of Gholson and Moose [8].
Abstract: A new approach to the three-dimensional airborne maneuvering target tracking problem is presented. The method, which combines the correlated acceleration target model of Singer [3] with the adaptive semi-Markov maneuver model of Gholson and Moose [8], leads to a practical real-time tracking algorithm that can be easily implemented on a modern fire-control computer. Preliminary testing with actual radar measurements indicates both improved tracking accuracy and increased filter stability in response to rapid target accelerations in elevation, bearing, and range.
231 citations
TL;DR: A model is presented to predict human dynamic spatial orientation in response to multisensory stimuli and computer implementation of the model has shown agreement with several important qualitative characteristics of human spatial orientation.
Abstract: A model is being developed to predict pilot dynamic spatial orientation in response to multisensory stimuli Motion stimuli are first processed by dynamic models of the visual, vestibular, tactile, and proprioceptive sensors Central nervous system function is then modeled as a steady-state Kalman filter which blends information from the various sensors to form an estimate of spatial orientation Where necessary, this linear central estimator has been augmented with nonlinear elements to reflect more accurately some highly nonlinear human response characteristics Computer implementation of the model has shown agreement with several important qualitative characteristics of human spatial orientation, and it is felt that with further modification and additional experimental data the model can be improved and extended Possible means are described for extending the model to better represent the active pilot with varying skill and work load levels
86 citations
TL;DR: A theoretical introduction to the use of Kalman filtering in analytical chemistry is based on multicomponent-analysis computations with the non-recursive least-squares estimation method as a starting point.
85 citations
Dissertation•
01 Jan 1979
62 citations
01 Dec 1979
TL;DR: In this paper, an iterative least square estimation algorithm is applied to the problem of state estimation of ballistic trajectories with angle-only measurements, and a filter initiation procedure is suggested.
Abstract: An iterative least square estimation algorithm is applied to the problem of state estimation of ballistic trajectories with angle-only measurements. A filter initiation procedure is suggested. The application of trajectory a priori knowledge for improving the state estimate is discussed and solved as a constrained estimation problem. A Monte Carlo simulation study was conducted to evaluate these techniques. It was found that the iterative least square filter achieves the Cramer-Rao bound while the extended Kalman filter generally does not.
54 citations
01 Dec 1979
TL;DR: In this paper, an extended Kalman filter is proposed 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 is designed to track a point source target in an open-loop tracking problem, using outputs from a forward-looking infrared (FLIR) sensor as measurements. The filter separately 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. A Monte Carlo analysis is conducted to determine the performance of the filter as a function of signal-to-noise ratio, target spot size, the ratio of rms target motion to rms atmospheric jitter, target correlation times, and mismatches between the true target spot size and the size assumed by the filter. The performance of the extended Kalman filter is compared to the performance of an existing correlation tracker under identical conditions. A one sigma tracking error of 0.2 and 0.8 picture elements is obtained with signal-to-noise ratios of 20:1 and 1:1, respectively. No degradation in performance is observed when the spot 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 spot size.
51 citations
TL;DR: An approximate two-dimensional recursive filtering algorithm that parallels the one-dimensional Kalman filter is presented for a causal system considered by Habibi and a numerical result is shown.
Abstract: An approximate two-dimensional recursive filtering algorithm that parallels the one-dimensional Kalman filter is presented for a causal system considered by Habibi [1]. A numerical result is also shown.
01 Jan 1979
TL;DR: In this paper, a new extended Kalman filtering scheme is introduced which has an improved performance relative to previous designs, compared with one based upon a linear Kalman filter, which is compared with the one based on a non-linear filter.
Abstract: Recent dynamic positioning systems have involved the use of a Kalman filter, in a state estimate feedback control scheme, based upon the separation principle of stochastic optimal control theory. Both linear and non-linear filtering schemes have been proposed for this application. A new extended Kalman filtering scheme is introduced which has an improved performance relative to previous designs. This system is compared with one based upon a linear Kalman filter.
TL;DR: In this paper, a new adaptive filter to reject clutter is derived using autoregressive spectral analysis techniques, resulting in a shorter transient response, and is therefore suitable for radar waveforms containing only a small number of samples.
Abstract: A new adaptive filter to reject clutter is derived using autoregressive spectral analysis techniques. The adaptive filter performs open. Ioop processing, resulting in a shorter transient response, and is therefore suitable for radar waveforms containing only a small number of samples. A number of examples including application to ballistic missile defense are presented to demonstrate the performance capabilities of the new adaptive filter.
01 Apr 1979
TL;DR: The application of the reduced update Kalman filter in the enhancement of two-dimensional images using a composite model description of the image shows considerable improvement in the visual quality compared with linear constant coefficient Kalman filtering.
Abstract: In this paper, we demonstrate the application of the reduced update Kalman filter in the enhancement of two-dimensional images using a composite model description of the image. Typically, for the purpose of simulation, five models corresponding to four predominant correlation directions (at angles of 0°, 45°, 90°, 135° to the horizontal) and one isotropic model, are considered. These models are then used to synthesize a filtering algorithm that estimates the image with near minimum mean square error. The results show considerable improvement in the visual quality compared with linear constant coefficient Kalman filtering.
TL;DR: The results of simulation studies indicate that estimates of the states can be obtained to the accuracy required for control of the industrial process.
TL;DR: In this article, the authors discuss the recursive estimation in regression and time series models, using Kalman filtering techniques to calculate estimates recursively, both for constant and time varying parameters.
Abstract: In this paper we discuss the recursive (or on line) estimation in (i) regression and (ii) autoregressive integrated moving average (ARIMA) time series models. The adopted approach uses Kalman filtering techniques to calculate estimates recursively. This approach is used for the estimation of constant as well as time varying parameters. In the first section of the paper we consider the linear regression model. We discuss recursive estimation both for constant and time varying parameters. For constant parameters, Kalman filtering specializes to recursive least squares. In general, we allow the parameters to vary according to an autoregressive integrated moving average process and update the parameter estimates recursively. Since the stochastic model for the parameter changes will "be rarely known, simplifying assumptions have to be made. In particular we assume a random walk model for the time varying parameters and show how to determine whether the parameters are changing over time. This is illustrated wit...
TL;DR: In this paper, a technique for obtaining low order state estimators for time-invariant, linear systems where estimates of a restricted set of state variables are required is presented, based on reducing the order of the system and then designing a Kalman filter for the reduced order system.
Abstract: A technique is presented for obtaining low order state estimators for time-invariant, linear systems where estimates of a restricted set of state variables are required. The technique is based on reducing the order of the system and then designing a Kalman filter for the reduced order system.
TL;DR: The application of linear filtering techniques is demonstrated to obtain a recursive GLR algorithm so that the requirement for matrix inversions in the previously known GLR algorithms can be reduced or avoided.
Abstract: In this paper, we present a recursive generalized likelihood ratio (GLR) test algorithm for detecting sudden changes in linear discrete systems. We demonstrate the application of linear filtering techniques to obtain a recursive GLR algorithm so that the requirement for matrix inversions in the previously known GLR algorithms can be reduced or avoided. Furthermore, the GLR algorithm is extended to the case when the sudden change follows known linear dynamics. An adaptive filtering scheme which uses the input estimate to correct the state estimate is also presented for the time-varying input case.
TL;DR: In this paper, a state-space representation of the propagating acoustic pulse, required for tractability by Kalman filtering, is described and a recently developed reflection coefficient estimator is applied to simulated and observed data using 2nd, 4th, and 6th order system model approximations.
01 Nov 1979
TL;DR: In this paper, a first-order scalar differential equation is used as a model of the system under test, and a comparison of results from various estimation methods is given, along with numerical examples along with the comparison of the results of various methods.
Abstract: Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.
TL;DR: It is shown how the refined instrumental variable (r.i.v.) method of recursive parameter estimation can be modified simply so that it functions as an optimal adaptive filter and state-estimation algorithm.
Abstract: It is shown how the refined instrumental variable (r.i.v.) method of recursive parameter estimation can be modified simply so that it functions as an optimal adaptive filter and state-estimation algorithm.
TL;DR: In this article, the authors give explicit algorithms in square-root form that allow measurements for the standard state estimation problem to be processed in a highly parallel fashion with little communication between processors, and then blocks of measurements may be incorporated into state estimates with essentially the same computation as usually accompanies the incorporation of a single measurement.
01 Dec 1979
TL;DR: In this article, a simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed, based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the extended least squares or Panuska's method.
Abstract: A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least squares or Panuska's method. Convergence properties of the proposed algorithm are studied and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed and an extension to an estimator for randomly varying parameters is outlined.
TL;DR: This paper shows that the adaptive filtering and forecasting techniques proposed by Makridakis and Wheelwright can be viewed as approximations to a more precise filtering method in which the Kalman filter is applied to a dynamic autoregressive model which is a special case of the models of Harrison and Stevens.
Abstract: This paper shows that the adaptive filtering and forecasting techniques proposed by Makridakis and Wheelwright can be viewed as approximations to a more precise filtering method in which the Kalman filter is applied to a dynamic autoregressive model which is a special case of the models of Harrison and Stevens. The correct "learning" or "training factors" are shown to be data-dependent matrices rather than scalar constants.
01 Jan 1979
TL;DR: In this article, the problem of determining the best estimate of the response or behaviour (equivalently the state) of a dynamic structural system under test is shown to be an optimal smoothing, filtering or prediction problem depending on whether past, present or future values respectively of the state are to be determined.
Abstract: The problem of determining the best estimate of the response or behaviour (equivalently the state) of a dynamic structural system under test is shown to be an optimal smoothing, filtering or prediction problem depending on whether past, present or future values respectively of the state are to be determined. For the filtering problem and for a given random loading and measured random response (including unknown disturbances, errors or noise in the system model and measurements), a best estimate of the state follows from the work of kalman. In the non linear case the 'extended kalman filter' functions by successively linearizing about the best estimate of the state. The identification problem of estimating system model parameters (for example stiffness, damping, etc) may be incorporated within the state estimation problem by suitably augmenting the state vector. State estimation and parameter estimation then proceed simultaneously. Reported tests on the creep of concrete and ground motion effects on a structure are used to illustrate the estimation procedures. Typically the algorithms are recursive and ideally suited to computer usage (a).
01 Jul 1979
TL;DR: In this paper, the design of linear stochastic optimal tracking and regulating systems is considered for systems with time delay, and a transfer function solution for the optimal closed-loop controller is obtained in the s-domain.
Abstract: The design of linear stochastic optimal tracking and regulating systems is considered for systems with time delay. A transfer-function solution for the optimal closed-loop controller is obtained in the s-domain. This solution can be realised physically, but involves the complex-domain delay operator. The state-space realisation of the controller is also obtained. The optimal controllers for both tracking and regulating systems include a Kalman predictor and state estimate feedback. This shows that a form of the separation principle holds for this class of problem. The design technique applies to multivariable systems which may be unstable, nonminimum phase and non-square. The process and measuring system noise terms may be correlated and be coloured or white. The linear quadratic performance criterion to be minimised includes a crossproduct weighting term. The solution to the usual stochastic regulator problem is obtained first and this result is then used to obtain the solution to the optimal tracking problem. Time delays in the control and in the measurement system are shown to have the same effect on the controller design, provided that the performance criterion is chosen appropriately. An expression for the minimum value of the performance criterion, that shows how the minimum cost is increased by the presence of the time delays, is obtained.
TL;DR: A computational method is presented to evaluate the average probability of error of the overall system in the presence of inter-symbol interference, additive noise, and phase-and sampling-synchronization errors, based upon nonclassical one-and two-dimensional quadrature rules.
Abstract: A class of multilevel linear-modulation data-transmission systems, over unknown, slowly time-varying, and bandlimited channels is considered. It is shown how sequence estimation in the presence of Gaussian noise and intersymbol interference can be carried out by means of a discrete Kalman estimator. Moreover, the receiver can be provided with data-aided adaptive loops for performing channel identification, carrier recovery, and timing extraction. A computational method is presented to evaluate the average probability of error of the overall system in the presence of inter-symbol interference, additive noise, and phase-and sampling-synchronization errors. The method is based upon nonclassical one-and two-dimensional quadrature rules, which are outlined in the Appendix. As an example, numerical performance results related to a phase-shift-keying (PSK) system are given. The results are obtained by means of general-purpose and system-oriented computers.
Book•
01 Feb 1979
TL;DR: In this paper, a digital automatic control law for a small jet transport to perform a steep final approach in automatic landings is reported along with the development of a steady-state Kalman filter used to provide smooth estimates to the control law.
Abstract: The development of a digital automatic control law for a small jet transport to perform a steep final approach in automatic landings is reported along with the development of a steady-state Kalman filter used to provide smooth estimates to the control law. The control law performs the functions of localizer and glides capture, localizer and glideslope track, decrab, and place. The control law uses the microwave landing system position data, and aircraft body-mounted accelerators, attitude and attitude rate information. The results obtained from a digital simulation of the aircraft dynamics, wind conditions, and sensor noises using the control law and filter developed are described.