Novel approach to nonlinear/non-Gaussian Bayesian state estimation
01 Apr 1993-Vol. 140, Iss: 2, pp 107-113
TL;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.
Citations
More filters
TL;DR: This article analyses the recently suggested particle approach to filtering time series and suggests that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution.
Abstract: This article analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Here we tackle the first of these problems.
2,608Â citations
Cites background or methods from "Novel approach to nonlinear/non-Gau..."
...various authors. In particular it is used by Gordon, Salmond, and Smith (1993) on non-Gaussian...
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...The use of this method has been suggested in the particle filter framework by Berzuini et al. (1997), Gordon et al. (1993), Isard and Blake (1996), and Kitagawa (1996)....
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...lihood, just as the original SIR suggestion of Gordon, Salmond, and Smith (1993) ....
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...In particular, it was used by Gordon, Salmond, and Smith (1993) on non-Gaussian sta~ space models....
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...This paper has studied the weaknesses of the very attractive particle filtering method proposed by Gordon, Salmond, and Smith (1993) ....
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TL;DR: A third-degree spherical-radial cubature rule is derived that provides a set of cubature points scaling linearly with the state-vector dimension that may provide a systematic solution for high-dimensional nonlinear filtering problems.
Abstract: In this paper, we present a new nonlinear filter for high-dimensional state estimation, which we have named the cubature Kalman filter (CKF) The heart of the CKF is a spherical-radial cubature rule, which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear Bayesian filter Specifically, we derive a third-degree spherical-radial cubature rule that provides a set of cubature points scaling linearly with the state-vector dimension The CKF may therefore provide a systematic solution for high-dimensional nonlinear filtering problems The paper also includes the derivation of a square-root version of the CKF for improved numerical stability The CKF is tested experimentally in two nonlinear state estimation problems In the first problem, the proposed cubature rule is used to compute the second-order statistics of a nonlinearly transformed Gaussian random variable The second problem addresses the use of the CKF for tracking a maneuvering aircraft The results of both experiments demonstrate the improved performance of the CKF over conventional nonlinear filters
2,597Â citations
Additional excerpts
...For example, the point-mass filter using adaptive grids [13], the Gaussian mixture filter [14], and particle filters using Monte Carlo integrations with the importance sampling [15], [16] fall under this second category....
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TL;DR: This purpose of this introductory paper is to introduce the Monte Carlo method with emphasis on probabilistic machine learning and review the main building blocks of modern Markov chain Monte Carlo simulation.
Abstract: This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.
2,579Â citations
TL;DR: This work addresses the problem of performing Kalman filtering with intermittent observations by showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs.
Abstract: Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.
2,343Â citations
08 May 2019
TL;DR: This paper provides an overview of research and development activities in the field of autonomous agents and multi-agent systems and aims to identify key concepts and applications, and to indicate how they relate to one-another.
Abstract: Model-based Bayesian Reinforcement Learning (BRL) provides a principled solution to dealing with the exploration-exploitation trade-off, but such methods typically assume a fully observable environments. The few Bayesian RL methods that are applicable in partially observable domains, such as the Bayes-Adaptive POMDP (BA-POMDP), scale poorly. To address this issue, we introduce the Factored BA-POMDP model (FBA-POMDP), a framework that is able to learn a compact model of the dynamics by exploiting the underlying structure of a POMDP. The FBA-POMDP framework casts the problem as a planning task, for which we adapt the Monte-Carlo Tree Search planning algorithm and develop a belief tracking method to approximate the joint posterior over the state and model variables. Our empirical results show that this method outperforms a number of BRL baselines and is able to learn efficiently when the factorization is known, as well as learn both the factorization and the model parameters simultaneously.
2,192Â citations
References
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01 Jan 1986
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Abstract: Introduction. Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods. Density Estimation in Action.
15,499Â citations
Book•
14 Mar 1970
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
Abstract: This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective" to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.
6,539Â citations
TL;DR: In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem.
Abstract: Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of the common types of estimates (e.g., minimum variance or maximum a posteriori) can be determined. Except in the linear Gaussian case, it is extremely difficult to determine this density function. In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem. In particular, it is noted that a weighted sum of Gaussian probability density functions can be used to approximate arbitrarily closely another density function. This representation provides the basis for procedure that is developed and discussed.
1,267Â citations
1,214Â citations
Journal Article•
TL;DR: In this article, a sampling-resampling perspective on Bayesian inference is presented, which has both pedagogic appeal and suggests easily implemented calculation strategies, such as sampling-based methods.
Abstract: Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of the numerical integrations required in all but the simplest applications. Moreover, from a teaching perspective, introductions to Bayesian statistics—if they are given at all—are circumscribed by these apparent calculational difficulties. Here we offer a straightforward sampling-resampling perspective on Bayesian inference, which has both pedagogic appeal and suggests easily implemented calculation strategies.
861Â citations