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47
Sequential Monte Carlo Methods for Dynamic Systems
 Journal of the American Statistical Association
, 1998
"... A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ..."
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Cited by 650 (12 self)
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A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We deliver a guideline on how they should be used and under what circumstance each method is most suitable. Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. In addition, we propose a general use of RaoBlackwellization to improve performances. Examples from econometrics and engineering are presented to demonstrate the importance of RaoBlackwellization and to compare different Monte Carlo procedures. Keywords: Blind deconvolution; Bootstrap filter; Gibbs sampling; Hidden Markov model; Kalman filter; Markov...
On sequential simulationbased methods for bayesian filtering
, 1998
"... Abstract. In this report, we present an overview of sequential simulationbased methods for Bayesian filtering of nonlinear and nonGaussian dynamic models. It includes in a general framework numerous methods proposed independently in various areas of science and proposes some original developments. ..."
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Cited by 252 (13 self)
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Abstract. In this report, we present an overview of sequential simulationbased methods for Bayesian filtering of nonlinear and nonGaussian dynamic models. It includes in a general framework numerous methods proposed independently in various areas of science and proposes some original developments.
Mixture Kalman filters
, 2000
"... In treating dynamic systems,sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the online `filtering' task. We propose a special sequential Monte Carlo metho ..."
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Cited by 219 (6 self)
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In treating dynamic systems,sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the online `filtering' task. We propose a special sequential Monte Carlo method,the mixture Kalman filter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for online estimation and prediction of conditional and partial conditional dynamic linear models,which are themselves a class of widely used nonlinear systems and also serve to approximate many others. Compared with a few available filtering methods including Monte Carlo methods,the gain in efficiency that is provided by the mixture Kalman filter can be very substantial. Another contribution of the paper is the formulation of many nonlinear systems into conditional or partial conditional linear form,to which the mixture Kalman filter can be applied. Examples in target tracking and digital communications are given to demonstrate the procedures proposed.
The Unscented Particle Filter
, 2000
"... In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available info ..."
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Cited by 215 (9 self)
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In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.
Particle Filters for Positioning, Navigation and Tracking
, 2002
"... A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the part ..."
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Cited by 212 (23 self)
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A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes lowdimensional. This is of utmost importance for highperformance realtime applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of nonlinear models and nonGaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, realtime implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.
Particle Filters for State Estimation of Jump Markov Linear Systems
, 2001
"... Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filter ..."
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Cited by 174 (15 self)
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Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixedlag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer
Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion
 IEEE Trans. on Signal Processing
, 2002
"... Abstract—The classical particle filter deals with the estimation of one state process conditioned on a realization of one observation process. We extend it here to the estimation of multiple state processes given realizations of several kinds of observation processes. The new algorithm is used to tr ..."
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Cited by 118 (5 self)
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Abstract—The classical particle filter deals with the estimation of one state process conditioned on a realization of one observation process. We extend it here to the estimation of multiple state processes given realizations of several kinds of observation processes. The new algorithm is used to track with success multiple targets in a bearingsonly context, whereas a JPDAF diverges. Making use of the ability of the particle filter to mix different types of observations, we then investigate how to join passive and active measurements for improved tracking. Index Terms—Bayesian estimation, bearingsonly tracking, Gibbs sampler, multiple receivers, multiple targets tracking,
Tracking Multiple Objects with Particle Filtering
, 2000
"... We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the ..."
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Cited by 100 (4 self)
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We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.
Gaussian particle filtering
 IEEE Transactions on Signal Processing
, 2003
"... Abstract—Sequential Bayesian estimation for nonlinear dynamic statespace models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter1. It is base ..."
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Cited by 92 (5 self)
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Abstract—Sequential Bayesian estimation for nonlinear dynamic statespace models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter1. It is based on the particle filtering concept, and it approximates the posterior distributions by single Gaussians, similar to Gaussian filters like the extended Kalman filter and its variants. It is shown that under the Gaussianity assumption, the Gaussian particle filter is asymptotically optimal in the number of particles and, hence, has muchimproved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Simulation results are presented to demonstrate the versatility and improved performance of the Gaussian particle filter over conventional Gaussian filters and the lower complexity than known particle filters. The use of the Gaussian particle filter as a building block of more complex filters is addressed in a companion paper. Index Terms—Dynamic state space models, extended Kalman filter, Gaussian mixture, Gaussian mixture filter, Gaussian particle filter, Gaussian sum filter, Gaussian sum particle filter, Monte Carlo filters, nonlinear nonGaussian stochastic systems, particle filters, sequential Bayesian estimation, sequential sampling methods, unscented Kalman filter. I.
Monte Carlo Filtering for MultiTarget Tracking and Data Association
 IEEE Transactions on Aerospace and Electronic Systems
, 2004
"... In this paper we present Monte Carlo methods for multitarget tracking and data association. The methods are applicable to general nonlinear and nonGaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data associat ..."
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Cited by 85 (5 self)
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In this paper we present Monte Carlo methods for multitarget tracking and data association. The methods are applicable to general nonlinear and nonGaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data association problem that arises due to unlabelled measurements in the presence of clutter, and the curse of dimensionality that arises due to the increased size of the statespace associated with multiple targets. We develop a number of algorithms to achieve this. The first, which we will refer to as the Monte Carlo Joint Probabilistic Data Association Filter (MCJPDAF), is a generalisation of the strategy proposed in [1], [2]. As is the case for the JPDAF, the distributions of interest are the marginal filtering distributions for each of the targets, but these are approximated with particles rather than Gaussians. We also develop two extensions to the standard particle filtering methodology for tracking multiple targets. The first, which we will refer to as the Sequential Sampling Particle Filter (SSPF), samples the individual targets sequentially by utilising a factorisation of the importance weights. The second, which we will refer to as the Independent Partition Particle Filter (IPPF), assumes the associations to be independent over the individual targets, leading to an efficient componentwise sampling strategy to construct new particles. We evaluate and compare the proposed methods on a challenging synthetic tracking problem.