Showing papers on "Particle filter published in 1999"

Filtering via Simulation: Auxiliary Particle Filters

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.

Improved particle filter for nonlinear problems

Abstract: The Kalman filter provides an effective solution to the linear Gaussian filtering problem. However where there is nonlinearity, either in the model specification or the observation process, other methods are required. Methods known generically as 'particle filters' are considered. These include the condensation algorithm and the Bayesian bootstrap or sampling importance resampling (SIR) filter. These filters represent the posterior distribution of the state variables by a system of particles which evolves and adapts recursively as new information becomes available. In practice, large numbers of particles may be required to provide adequate approximations and for certain applications, after a sequence of updates, the particle system will often collapse to a single point. A method of monitoring the efficiency of these filters is introduced which provides a simple quantitative assessment of sample impoverishment and the authors show how to construct improved particle filters that are both structurally efficient in terms of preventing the collapse of the particle system and computationally efficient in their implementation. This is illustrated with the classic bearings-only tracking problem.

Recursive Bayesian Estimation : Navigation and Tracking Applications

Abstract: Recursive estimation deals with the problem of extracting information about parameters, or states, of a dynamical system in real time, given noisy measurements of the system output. Recursive estimation plays a central role in many applications of signal processing, system identification and automatic control. In this thesis we study nonlinear and non-Gaussian recursive estimation problems in discrete time. Our interest in these problems stems from the airborne applications of target tracking, and autonomous aircraft navigation using terrain information.In the Bayesian framework of recursive estimation, both the sought parameters and the observations are considered as stochastic processes. The conceptual solution to the estimation problem is found as a recursive expression for the posterior probability density function of the parameters conditioned on the observed measurements. This optimal solution to nonlinear recursive estimation is usually impossible to compute in practice, since it involves several integrals that lack analytical solutions.We phrase the application of terrain navigation in the Bayesian framework, and develop a numerical approximation to the optimal but intractable recursive solution. The designed point-mass filter computes a discretized version of the posterior filter density in a uniform mesh over the interesting region of the parameter space. Both the uniform mesh resolution and the grid point locations are automatically adjusted at each iteration of the algorithm. This Bayesian point-mass solution is shown to yield high navigation performance in a simulated realistic environment.Even though the optimal Bayesian solution is intractable to implement, the performance of the optimal solution is assessable and can be used for comparative evaluation of suboptimal implementations. We derive explicit expressions for the Cramer-Rao bound of general nonlinear filtering, smoothing and prediction problems. We consider both the cases of random and nonrandom modeling of the parameters. The bounds are recursively expressed and are connected to linear recursive estimation. The newly developed Cramer-Rao bounds are applied to the terrain navigation problem, and the point-mass filter is verified to reach the bound in exhaustive simulations.The uniform mesh of the point-mass filter limits it to estimation problems of low dimension. Monte Carlo methods offer an alternative approach to recursive estimation and promise tractable solutions to general high dimensional estimation problems. We provide a review over the active field of statistical Monte Carlo methods. In particular, we study the particle filters for recursive estimation. Three different particle filters are applied to terrain navigation, and evaluated against the Cramer-Rao bound and the point-mass filter. The particle filters utilize an adaptive grid representation of the filter density and are shown to yield a performance equal to the point-mass method.A Markov Chain Monte Carlo (MCMC) method is developed for a highly complex data association problem in target tracking. This algorithm is compared to previously proposed methods and is shown to yield competitive results in a simulation study.

Bayesian Map Learning in Dynamic Environments

Abstract: We consider the problem of learning a grid-based map using a robot with noisy sensors and actuators. We compare two approaches: online EM, where the map is treated as a fixed parameter, and Bayesian inference, where the map is a (matrix-valued) random variable. We show that even on a very simple example, online EM can get stuck in local minima, which causes the robot to get "lost" and the resulting map to be useless. By contrast, the Bayesian approach, by maintaining multiple hypotheses, is much more robust. We then introduce a method for approximating the Bayesian solution, called Rao-Blackwellised particle filtering. We show that this approximation, when coupled with an active learning strategy, is fast but accurate.

An improved particle filter for non-linear problems

Abstract: The Kalman filter provides an effective solution to the linear Gaussian filtering problem However where there is nonlinearity, either in the model specification or the observation process, other methods are required Methods known generically as `particle filters' are considered These include the condensation algorithm and the Bayesian bootstrap or sampling importance resampling (SIR) filter These filters represent the posterior distribution of the state variables by a system of particles which evolves and adapts recursively as new information becomes available In practice, large numbers of particles may be required to provide adequate approximations and for certain applications, after a sequence of updates, the particle system will often collapse to a single point A method of monitoring the efficiency of these filters is introduced which provides a simple quantitative assessment of sample impoverishment and the authors show how to construct improved particle filters that are both structurally efficient in terms of preventing the collapse of the particle system and computationally efficient in their implementation This is illustrated with the classic bearings-only tracking problem

Some adaptive Monte Carlo methods for Bayesian inference

Abstract: Monte Carlo methods, in particular Markov chain Monte Carlo methods, have become increasingly important as a tool for practical Bayesian inference in recent years A wide range of algorithms is available, and choosing an algorithm that will work well on a specific problem is challenging It is therefore important to explore the possibility of developing adaptive strategies that choose and adjust the algorithm to a particular context based on information obtained during sampling as well as information provided with the problem This paper outlines some of the issues in developing adaptive methods and presents some preliminary results

Tracking through singularities and discontinuities by random sampling

Abstract: Some issues in markerless tracking of human body motion are addressed. Extended Kalman filters have commonly been applied to kinematic variables, to combine predictions consistent with plausible motion, with the incoming stream of visual measurements. Kalman filtering is applicable only when the underlying distribution is approximately Gaussian. Often this assumption proves remarkably robust. There are two pervasive circumstances under which the Gaussianity assumption can break down. The first is kinematic singularity and the second is at joint endstops. Failure of Kalman filtering under these circumstances is illustrated. The non-Gaussian nature of the distributions is demonstrated experimentally by means of Monte Carlo simulation. Random simulation (particle filtering or Condensation) proves to provide a robust alternative algorithm for tracking that can also deal with these difficult conditions.

Interacting particle systems approximations of the Kushner-Stratonovitch equation

Abstract: In this paper we consider the continuous-time filtering problem and we estimate the order of convergence of an interacting particle system scheme presented by the authors in previous works We will discuss how the discrete time approximating model of the Kushner-Stratonovitch equation and the genetic type interacting particle system approximation combine We present quenched error bounds as well as mean order convergence results

Group and extended object tracking

Abstract: Much of the literature on target tracking is based on the assumption that the observing sensor produces a single point measurement of the target. In practice, this is often not the case. For example, a high resolution sensor may be able to resolve features on an extended target. An analogous problem is that of tracking a group of point targets moving in formation. In both cases, there is a strong interdependency between the individual sensor measurements. In this paper, we handle both of these cases via the same model of individual motion superposed on a common “bulk” effect. A common approach to tracking groups of (dependent) points is to perform the update operation in two distinct steps. The first stage is to find the “best” match or registration between the set of measurements and the predicted pattern, while the second step is to generate an estimate based on the assumption that the selected association is correct. The complexity of managing multiple hypotheses with strongly interdependent groups is usually avoided. However, particularly in stressing scenarios, where the measurement-object association is highly uncertain, a multiple hypothesis approach should have significant advantages. We present a Bayesian multiple hypothesis solution using the bootstrap or particle filter technique in which the probability distribution of the problem state vector is represented by a set of random samples or “particles”. The great advantage of this approach is that the sample set implicitly includes information on previous hypotheses and so awkward hypothesis management is avoided. Only the feasible association hypotheses for the current update of the filter need to be considered for construction of the measurement likelihood function. (4 pages)

Monte Carlo Hidden Markov Models: Learning Non-Parametric Models of Partially Observable Stochastic Processes

Abstract: We present a learning algorithm for non-parametric hidden Markov models with continuous state and observation spaces. All necessary probability densities are approximated using samples, along with density trees generated from such samples. A Monte Carlo version of Baum-Welch (EM) is employed to learn models from data. Regularization during learning is achieved using an exponential shrinking technique. The shrinkage factor, which determines the effective capacity of the learning algorithm, is annealed down over multiple iterations of Baum-Welch, and early stopping is applied to select the right model. Once trained, Monte Carlo HMMs can be run in an any-time fashion. We prove that under mild assumptions, Monte Carlo Hidden Markov Models converge to a local maximum in likelihood space, just like conventional HMMs. In addition, we provide empirical results obtained in a gesture recognition domain.

Markov chain Monte Carlo for the Bayesian analysis of evolutionary trees from aligned molecular sequences

Abstract: 2 We show how to quantify the uncertainty in a phylogenetic tree inferred from molecular sequence information. Given a stochastic model of evolution, the Bayesian solution is simply to form a posterior probability distribution over the space of phylogenies. All inferences are derived from this posterior, including tree reconstructions, credible sets of good trees, and conclusions about monophyletic groups, for example. The challenging part is to approximate the posterior, and we do this by constructing a Markov chain having the posterior as its invariant distribution, following the approach of Mau, Newton, and Larget (1998). Our Markov chain Monte Carlo algorithm is based on small but global changes in the phylogeny, and exhibits good mixing properties empirically. We illustrate the methodology on DNA encoding mitochondrial cytochrome oxidase 1 gathered by Hafner et al. (1994) for a set of parasites and their hosts.

On the number of samples to be drawn in particle filtering

Abstract: In this paper we look at the nonlinear filtering problem. In particular we look at filters of the sampling kind, also referred to as particle filters. In a setting where the system is nonlinear, and/or the load disturbance and measurement noise are not Gaussian, the (extended) Kalman filter may exhibit poor performance. In this case one is forced to look at alternative filtering methods. A method that works fine in many situations is the application of a so called sampling filter. The main disadvantage of these sampling types of filter is their computational load, which, especially in real time applications, is of paramount importance. The computation time consuming part of the sampling types of filter is the sampling part. The computational load of this stage of the filter algorithm is determined by two factors, namely: 1. The way in which the sampling stage is implemented. 2. The number of samples that is used. While the first issue has received broad attention in the literature the second one has not. In this report we try to fill this gap and suggest a method to relate the required number of samples in a quantitative way to the accuracy and the level of confidence by which the sampling stage is performed. This method is based on inequalities from probability theory and statistical learning theory. These inequalities then provide bounds for the sample size.

Bayesian Modelling of fMRI lime Series

Abstract: We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte Carlo (MCMC) sampling techniques. The advantage of this method is that detection of short time learning effects between repeated trials is possible since inference is based only on single trial experiments.

Sequential Monte Carlo for maneuvering target tracking in clutter

Abstract: In this paper we consider the problem of tracking a maneuvering target in clutter. We apply an original on-line Monte Carlo filtering algorithm to perform optimal state estimation. Improved performance of the resulting algorithm over standard IMM/PDAF based filters is demonstrated.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Multiple model particle filter

Abstract: This article deals with the ltering problem for multiple dynamical models systems applied to the tracking of a maneuvering target. We chose the particle approach recently proposed for the nonlinear ltering problem. Particle methods can give a non parametric approximation to the signal's conditional distribution even in nonlinear or non Gaussian cases, without depending on the state space dimension. We present a new version of particle lter, called the Multiple Model Particle Filter (MMPF), which is validated by its good behavior during simulations.

Simulation-based optimal filter for maneuvering target tracking

Abstract: While single model filters are sufficient for tracking targets having fixed kinematic behavior, maneuvering targets require the use of multiple models. Jump Markov linear systems whose parameters evolve with time according to a finite state-space Markov chain, have been used in these situations with great success. However, it is well-known that performing optimal estimation for JMLS involves a prohibitive computational cost exponential in the number of observations. Many approximate methods have been proposed in the literature to circumvent this including the well-known GPB and IMM algorithms. These methods are computationally cheap but at the cost of being suboptimal. Efficient off- line methods have recently been proposed based on Markov chain Monte Carlo algorithms that out-perform recent methods based on the Expectation-Maximization algorithms. However, realistic tracking systems need on-line techniques. In this paper, we propose an original on-line Monte Carlo filtering algorithm to perform optimal state estimation of JMLS. The approach taken is loosely based on the bootstrap filter which, wile begin a powerful general algorithm in its original form, does not make the most of the structure of JMLS. The proposed algorithm exploits this structure and leads to a significant performance improvement.

Bayesian neural networks with correlating residuals

Abstract: In a multivariate regression problem it is often assumed that residuals of outputs are independent of each other. In many applications a more realistic model would allow dependencies between the outputs. In this paper we show how a Bayesian treatment using the Markov chain Monte Carlo method can allow for a full covariance matrix with multilayer perceptron neural network.

Adaptive algorithms and Markov chain Monte Carlo methods

Abstract: Many signal processing and control problems are complicated by the presence of unobserved variables and/or auxiliary variables measured with error. In nonlinear settings this causes problems in constructing adaptive parameter estimators. In off-line situations so-called Markov chain Monte Carlo methods have recently become popular for solving these kinds of problems. In this paper we explore the development of online Markov chain Monte Carlo techniques for adaptive parameter estimation.

Non-stationary Bayesian modelling and enhancement of speech signals

Abstract: This report applies time-varying AR (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. For the TVAR coefficients the standard parameterisation, i.e. the coefficients of the TVAR polynomial themselves, and one i.t.o. the characteristic roots of the TVAR polynomial (or system poles) are investigated. The stochastic evolution models for the TVAR parameters are Markovian diffusion processes. The problem and estimation objectives are formulated within a Bayesian framework. Two efficient iterative algorithms are developed to achieve these objectives. The first is a Markov chain Monte Carlo (MCMC) algorithm which generates samples from the posterior distribution based on which the minimum mean square error (MMSE) estimates of the TVAR parameters and clean speech can be computed. The second is a stochastic optimisation algorithm which computes the marginal maximum a posteriori (MMAP) estimate of the TVAR parameters. The clean speech can then be obtained by running a fixed-interval Kalman smoother with this estimate of the TVAR parameters. Contrary to the EM-type algorithms, the estimation schemes work without introducing a set of " missing data " (the clean speech in this case). Nevertheless, at each iteration the computational complexity of the algorithms is still linear in the number of samples in the analysis window. Performance measures based on predictive distributions are used in simulation studies to compare the modelling and signal reconstruction performance of the proposed TVAR models to that of the standard fixed-parameter AR model on both synthetic and real speech data sets.

Efficient particle filters for tracking manoeuvring targets in clutter

Abstract: In this paper, we propose an on-line Monte Carlo (MC) filtering algorithm to perform optimal state estimation for Jump Markov Linear Systems (JMLS). The approach taken is loosely based on the bootstrap filter which, whilst being a powerful general algorithm in its original form, does not make the most of the structure of JMLS. The proposed algorithm exploits this structure and is demonstrated to provide a performance improvement over the IMM-PDA for tracking manoeuvring targets in clutter.

Hybrid sequential Monte Carlo/Kalman methods to train neural networks in non-stationary environments

Abstract: We propose a novel sequential algorithm for training neural networks in non-stationary environments. The approach is based on a Monte Carlo method known as the sampling-importance resampling simulation algorithm. We derive our algorithm using a Bayesian framework, which allows us to learn the probability density functions of the network weights and outputs. Consequently, it is possible to compute various statistical estimates including centroids, modes, confidence intervals and kurtosis. The algorithm performs a global search for minima in parameter space by monitoring the errors and gradients at several points in the error surface. This global optimisation strategy is shown to perform better than local optimisation paradigms such as the extended Kalman filter.

Monte Carlo filters for adaptive detection in fading channels

Abstract: A novel adaptive Bayesian receiver for signal detection in flat-fading channels is developed based on the sequential Monte Carlo methodology. The basic idea is to treat the transmitted signals as missing data and to sequentially impute multiple copies of them based on the observed signals. The imputed signal sequences, together with their importance weights, provide a way to approximate the Bayesian estimate of the transmitted signals and the channel states. It is shown through simulations that the proposed sequential Monte Carlo receivers achieve near-bound performance in fading channels without the aid of any training/pilot symbols or decision feedback. Moreover, the proposed receiver structure exhibits massive parallelism and is ideally suited for high-speed parallel implementation using the VLSI systolic array technology.

Particle methods for multimodal filtering. Application to terrain navigation

Abstract: We consider a target following a noisy dynamical equation which is partially observed. The Extended Kalman Filter (EKF) is widely used to estimate recursively the mean and the variance of the state given the past measurement. The EKF assumes that the conditional density is Gaussian. But, in the case of multimodality, the EKF is inefficient. The goal of the nonlinear filtering is to estimate the whole law of the state. For example, in the tracking context, we will be able to estimate precisely the probability of the presence of a target in any portion of the state space and consequently to estimate the position of the target. For this filter there is no hypothesis concerning the linearity and no conditions about the nature of the noise. We present an application of particle filtering (bootstrap filter and local rejection regularised particle filter) in terrain navigation. (5 pages)

Sequential Bayesian wavelet denoising

Abstract: We propose a wavelet model that incorporates coefficient correlation and is expressed in state-space form, allowing the development and application of sequential estimation algorithms for wavelet denoising. We detail a sequential simulation-based estimation algorithm based on particle filters. This algorithm allows Bayesian wavelet denoising to be performed on-line, enabling it to process a vast dataset, and it is intrinsically parallelizable. The experiments indicate that the algorithm performance is comparable to the majority of Bayesian framework batch-based algorithms.

The MultiBoson method

Abstract: This review describes the MultiBoson algorithm for Monte Carlo simulations of lattice QCD, including its static and dynamical aspects, and presents a comparison with Hybrid Monte Carlo.

The use of bootstrap in computer-intensive Bayesian methods

Abstract: The use of computer-intensive methods in signal processing becomes more frequent as the power of computers continues to increase. Two classes of such methods are Bayesian Monte Carlo sampling and the bootstrap. In general, these types of methods are used in different settings. The Bayesian methods are usually applied in situations where parametric assumptions are made about the densities that generate the observed data, and the bootstrap, in cases where such assumptions are absent. We explore the possibility of combining these methods. The role of the bootstrap is to provide samples for constructing density functions needed for drawing samples which would allow for more accurate integration or optimization carried out by the Bayesian methods.

A Bayesian approach to direction-of-arrival estimation of coherent signals

Abstract: Direction-of-arrival (DOA) estimation is one of the most important problems in array processing. Many existing high resolution methods are based on eigen-decomposition techniques, and they, in many physical scenarios, have excellent performance. In the presence of coherent signals, however, these methods may no longer provide reliable results. In this paper, a Bayesian method is proposed based on a model constructed specifically for coherent signals. In addition, a Markov chain Monte Carlo (MCMC) scheme is proposed to solve some intractable integrals. Finally, simulation results are presented that compare the performance of the Bayesian DOA estimation with some existing approaches.

Sequential Monte Carlo for maneuvering target tracking in clutter

Abstract: In this paper we consider the problem of tracking a maneuvering target in clutter. We apply an original on-line Monte Carlo filtering algorithm to perform optimal state estimation. Improved performance of the resulting algorithm over standard IMM/PDAF based filters is demonstrated.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.