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43
On Sequential Monte Carlo Sampling Methods for Bayesian Filtering
 STATISTICS AND COMPUTING
, 2000
"... In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is develop ..."
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Cited by 976 (75 self)
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In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses RaoBlackwellisation in order to take advantage of the analytic structure present in some important classes of statespace models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.
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 209 (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.
Constraintbased task specification and estimation for sensorbased robot systems in the presence of geometric uncertainty
 Int. J. Robotics Research
, 2007
"... This paper introduces a systematic constraintbased approach to specify complex tasks of general sensorbased robot systems consisting of rigid links and joints. The approach integrates both instantaneous task specification and estimation of geometric uncertainty in a unified framework. Major compone ..."
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Cited by 30 (12 self)
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This paper introduces a systematic constraintbased approach to specify complex tasks of general sensorbased robot systems consisting of rigid links and joints. The approach integrates both instantaneous task specification and estimation of geometric uncertainty in a unified framework. Major components are the use of feature coordinates, defined with respect to object and feature frames, which facilitate the task specification, and the introduction of uncertainty coordinates to model geometric uncertainty. While the focus of the paper is on task specification, an existing velocity based control scheme is reformulated in terms of these feature and uncertainty coordinates. This control scheme compensates for the effect of time varying uncertainty coordinates. Constraint weighting results in an invariant robot behavior in case of conflicting constraints with heterogeneous units. The approach applies to a large variety of robot systems (mobile robots, multiple robot systems, dynamic humanrobot interaction, etc.), various sensor systems, and different robot tasks. Ample simulation and experimental results are presented.
Architectures for Efficient Implementation of Particle Filters
, 2004
"... Particle filters are sequential Monte Carlo methods that are used in numerous problems where timevarying signals must be presented in real time and where the objective is to estimate various unknowns of the signal and/or detect events described by the signals. The standard solutions of such proble ..."
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Cited by 22 (0 self)
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Particle filters are sequential Monte Carlo methods that are used in numerous problems where timevarying signals must be presented in real time and where the objective is to estimate various unknowns of the signal and/or detect events described by the signals. The standard solutions of such problems in many applications are based on the Kalman filters or extended Kalman filters. In situations when the problems are nonlinear or the noise that distorts the signals is nonGaussian, the Kalman filters provide a solution that may be far from optimal. Particle filters are an intriguing alternative to the Kalman filters due to their excellent performance in very di#cult problems including communications, signal processing, navigation, and computer vision. Hence, particle filters have been the focus of wide research recently and immense literature can be found on their theory. Most of these works recognize the complexity and computational intensity of these filters, but there has been no e#ort directed toward the implementation of these filters in hardware. The objective of this dissertation is to develop, design, and build e#cient hardware for particle filters, and thereby bring them closer to practical applications. The fact that particle filters outperform most of the traditional filtering methods in many complex practical scenarios, coupled with the challenges related to decreasing their computational complexity and improving realtime performance, makes this work worthwhile. The main
Kalman Filtering Using Pairwise Gaussian Models
 IN PROCEEDINGS OF THE ICASSP, HONGKONG, APRIL 610 2003
, 2003
"... An important problem in signal processing consists in recursively estimating an unobservable process x = {xn }n#IN from an observed process y = {yn }n#IN . This is done classically in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is giv ..."
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Cited by 20 (12 self)
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An important problem in signal processing consists in recursively estimating an unobservable process x = {xn }n#IN from an observed process y = {yn }n#IN . This is done classically in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the wellknown Kalman filter. In this paper, we consider Pairwise Gaussian Models by assuming that the pair (x, y) is Markovian and Gaussian. We show that this model is strictly more general than the HMM, and yet still enables Kalmanlike filtering.
Bayesian Estimation of DSGE Models: Lessons from SecondOrder Approximations.” Mimeo
, 2006
"... This paper investigates a general procedure to estimate secondorder approximations to a DSGE model and compares the performance with the widely used estimation technique for a loglinearized economy on a version of new Keynesian monetary model. It is done in the context of posterior distributions, ..."
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Cited by 20 (0 self)
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This paper investigates a general procedure to estimate secondorder approximations to a DSGE model and compares the performance with the widely used estimation technique for a loglinearized economy on a version of new Keynesian monetary model. It is done in the context of posterior distributions, welfare cost, and impulse response analysis. Our findings include the followings. First, we find that all the results of An and Schorfheide (2007) are confirmed with U.S. data. With the nonlinear estimation we can identify parameters that are neglected previously; the marginal data density evaluation shows that data support the nonlinear estimation procedure; and parameter estimates that are related to nondeterministic steady states are quite different from the linear estimates. Second, the estimated welfare differentials are more aggressive for the secondorder approximations, that is, the posterior welfare differentials from the linear estimation may underestimate the welfare cost resulted from changes in the monetary policy. Third, the secondorder approximation unveils quite different dynamics which are neglected in a loglinearized economy.
Methods and techniques of complex systems science: An overview
, 2003
"... In this chapter, I review the main methods and techniques of complex systems science. As a ..."
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Cited by 18 (0 self)
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In this chapter, I review the main methods and techniques of complex systems science. As a
Prediction Of Final Data With Use Of Preliminary And/or Revised Data
 Journal of Forecasting
, 1995
"... : In the case of U.S. national accounts, the data are revised for the first few years and every decade, which implies that we do not really have the final data. In this paper, we aim to predict the final data, using the preliminary data and/or the revised data. The following predictors are introduce ..."
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Cited by 13 (4 self)
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: In the case of U.S. national accounts, the data are revised for the first few years and every decade, which implies that we do not really have the final data. In this paper, we aim to predict the final data, using the preliminary data and/or the revised data. The following predictors are introduced and derived from a context of the nonlinear filtering or smoothing problem, which are: (i) prediction of the final data of time t given the preliminary data up to time t
Collision Avoidance for Unmanned Aircraft using Markov Decision Processes ∗
"... Before unmanned aircraft can fly safely in civil airspace, robust airborne collision avoidance systems must be developed. Instead of handcrafting a collision avoidance algorithm for every combination of sensor and aircraft configuration, we investigate the automatic generation of collision avoidanc ..."
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Cited by 7 (2 self)
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Before unmanned aircraft can fly safely in civil airspace, robust airborne collision avoidance systems must be developed. Instead of handcrafting a collision avoidance algorithm for every combination of sensor and aircraft configuration, we investigate the automatic generation of collision avoidance algorithms given models of aircraft dynamics, sensor performance, and intruder behavior. By formulating the problem of collision avoidance as a Markov Decision Process (MDP) for sensors that provide precise localization of the intruder aircraft, or a Partially Observable Markov Decision Process (POMDP) for sensors that have positional uncertainty or limited fieldofview constraints, generic MDP/POMDP solvers can be used to generate avoidance strategies that optimize a cost function that balances flightplan deviation with collision. Experimental results demonstrate the suitability of such an approach using four different sensor modalities and a parametric aircraft performance model. I.
On Nonlinear and Nonnormal Filter Using Rejection Sampling
, 1999
"... In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling. Generating random draws of the statevector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws. In the proposed filter, the random draws ..."
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Cited by 6 (5 self)
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In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling. Generating random draws of the statevector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws. In the proposed filter, the random draws are recursively generated at each time. The MonteCarlo experiments indicate that the proposed nonlinear and nonnormal filter shows a good performance. Keywords Nonlinear, Nonnormal, Filtering, Rejection Sampling, Proposal Density. I. Introduction Nonlinear filters have been investigated for a long time (e.g., Alspach and Sorenson [1], Sorenson and Alspach [18] and Wishner, Tabaczynski and Athans [23]) and we still have numerous densitybased nonlinear filtering algorithms. Kitagawa [13] and Kramer and Sorenson [16] proposed the numerical integration procedure. Tanizaki [20] and Tanizaki and Mariano [22] utilized the MonteCarlo integration with importance sampling for nonlinear and no...