Neil Gordon

Sequential Monte Carlo methods in practice

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

Particle filters for state estimation of jump Markov linear systems

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 simulation-based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed-lag 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 simulations are carried out to evaluate the performance of the proposed algorithms. The problems of on-line deconvolution of impulsive processes and of tracking a maneuvering target are considered. It is shown that our algorithms outperform the current methods.

An Introduction to Sequential Monte Carlo Methods

Many real-world data analysis tasks involve estimating unknown quantities from some given observations. In most of these applications, prior knowledge about the phenomenon being modelled is available. This knowledge allows us to formulate Bayesian models, that is prior distributions for the unknown quantities and likelihood functions relating these quantities to the observations. Within this setting, all inference on the unknown quantities is based on the posterior distribution obtained from Bayes’ theorem. Often, the observations arrive sequentially in time and one is interested in performing inference on-line. It is therefore necessary to update the posterior distribution as data become available. Examples include tracking an aircraft using radar measurements, estimating a digital communications signal using noisy measurements, or estimating the volatility of financial instruments using stock market data. Computational simplicity in the form of not having to store all the data might also be an additional motivating factor for sequential methods.

Bayesian state estimation for tracking and guidance using the bootstrap filter

The bootstrap filter is an algorithm for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples that are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: It may be applied to any state transition or measurement model. A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter. A preliminary investigation of an application of the bootstrap filter to an exoatmospheric engagement with non-Gaussian measurement errors is also given.

Optimal Estimation and Cramér-Rao Bounds for Partial Non-Gaussian State Space Models

Partial non-Gaussian state-space models include many models of interest while keeping a convenient analytical structure. In this paper, two problems related to partial non-Gaussian models are addressed. First, we present an efficient sequential Monte Carlo method to perform Bayesian inference. Second, we derive simple recursions to compute posterior Cramér-Rao bounds (PCRB). An application to jump Markov linear systems (JMLS) is given.

Sequential Monte Carlo for maneuvering target tracking in clutter

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.

Particles and Mixtures for Tracking and Guidance

The guidance algorithm is the central decision and control element of a missile system. It is responsible for taking data from all available missile sensors, together with targeting information and generating a guidance demand. This is usually in the form of an acceleration demand that is passed to the autopilot.

Group tracking with limited sensor resolution and finite field of view

We consider the problem of tracking a group of point targets via a sensor with limited resolution and a finite field of view. Measurement association uncertainty and measurement process non-linearity are major difficulties with such cases. It is shown that a Bayesian estimator can be directly implemented using the particle filter technique.

Tracking in the presence of intermittent spurious objects and clutter

The sampling based bootstrap filter is applied to the problem of maintaining track on a target in the presence of intermittent spurious objects. This problem is formulated in a multiple hypothesis framework and the bootstrap filter is applied to generate the posterior distribution of the state vector of the required target - i.e. to generate the target track. The bootstrap technique facilitates the integration of the available information in a near-optimal fashion without the need to explicitly store and manage hypotheses from previous time steps.

Simulation-based optimal filter for maneuvering target tracking

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.