Topic

# Extended Kalman filter

About: Extended Kalman filter is a research topic. Over the lifetime, 25974 publications have been published within this topic receiving 517984 citations.

##### Papers published on a yearly basis

##### Papers

More filters

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TL;DR: Both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters are reviewed.

Abstract: Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

11,409 citations

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01 Apr 1993TL;DR: An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.

Abstract: An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.

8,018 citations

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08 Nov 2004TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.

Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

6,098 citations

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28 Jul 1997TL;DR: It is argued that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.

Abstract: The Kalman Filter (KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearizes all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterize mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet generalizes elegantly to nonlinear systems without the linearization steps required by the EKF. We show analytically that the expected performance of the new approach is superior to that of the EKF and, in fact, is directly comparable to that of the second order Gauss filter. The method is not restricted to assuming that the distributions of noise sources are Gaussian. We argue that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.

5,314 citations

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30 Mar 1990TL;DR: In this article, the Kalman filter and state space models were used for univariate structural time series models to estimate, predict, and smoothen the univariate time series model.

Abstract: List of figures Acknowledgement Preface Notation and conventions List of abbreviations 1. Introduction 2. Univariate time series models 3. State space models and the Kalman filter 4. Estimation, prediction and smoothing for univariate structural time series models 5. Testing and model selection 6. Extensions of the univariate model 7. Explanatory variables 8. Multivariate models 9. Continuous time Appendices Selected answers to exercises References Author index Subject index.

5,071 citations