Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

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A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

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.

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Sequential Monte Carlo methods in practice

Planning and navigation algorithms exploit statistics gleaned from uncertain, imperfect real-world environments to guide robots toward their goals and around obstacles.

Probabilistic Robotics

We report the results of an experimental study aimed at improving the performance of actively Q-switched fiber lasers. Unlike generic design schemes employing photonic crystal fibers, large modal diameter fibers or double-clad fibers, we demonstrate a high-power, actively Q-switched laser based on standard communication erbium doped fibers with peak irradiance beyond the state-of-the-art at 3.1 GW/cm 2. The laser had 2.2 kW peak power, 15.5 ns pulse duration and 36.8 μJ pulse energy. We have also investigated the dynamics of pulse generation and have successfully suppressed pulse instabilities caused by backscattered laser emission reaching the pump laser diodes.

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Optimization of Erbium-Doped Actively Q-Switched Fiber Laser Implemented in Symmetric Configuration

This paper reports on the design, construction and initial testing of a fiber-optic voltage sensor for applications in the field of wide area monitoring, protection and control of high voltage power networks. The 132-kV sensor prototype, combining a capacitive voltage divider (CVD) and an optical low voltage transducer (LVT), was evaluated through laboratory testing and its performance was assessed based on the accuracy requirements specified by the IEC standards for low-power passive voltage transformers. The preliminary results show that the device has the potential to comply with the requirements of the 0,2 class for metering devices, and the 3P and 0,5P classes for protective and multipurpose devices, respectively, as specified by IEC 61869-11. As the device is based on a fiber Bragg grating written in a standard, low-loss, single-mode telecommunication fiber, it has the potential to be deployed as part of a distributed network of sensors along the power network over a wide geographical area, enabling novel power system protection and control strategies.

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132 kV optical voltage sensor for wide area monitoring, protection and control applications

Tracking algorithms are based on models: target dynamic and sensor measurement model. In most practical situations the two models are not known exactly and are typically parametrised by an unknown random vector θ. The paper proposes a Bayesian algorithm based on importance sampling for the estimation of θ. The input are detections/measurements collected by the tracking system from non-cooperative targets. The algorithm relies on the particle filter implementation of the probability density hypothesis (PHD) filter to evaluate the likelihood of the measurement set history conditioned on θ. As a byproduct, the proposed algorithm can also output a multi-target state estimate over time. An application to sensor bias estimation is presented in detail as an illustration. The resulting sensor-bias estimation method is applicable to asynchronous sensors and does not require prior knowledge of measurement-to-track associations.

Calibration of tracking systems using detections from non-cooperative targets

Recursive triangulation, using a bearings-only sensor, is investigated for a fly-by scenario. In a simulation study, several estimators are compared, fundamental estimation limits are calculated for different measurement noise assumptions. The quality of the estimated state distributions is evaluated.

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Recursive Triangulation using Bearings only Sensors

The design, construction and assessment of a CO 2 laser heterodyne receiver based on a Hg 1-x Cd x Te heterostructure is described. The structure has been designed to minimize the leakage currents at high temperatures while maintaining a high quantum efficiency. Measurements show that over 4 dB of shot noise can be obtained with the application of less than 1 mW of laser power. This result can be combined with the measured low-frequency quantum efficiency of 42% to give a noise equivalent power of 7.2 × 10 -20 W Hz -1 . The device is mounted on a single-stage thermoelectric cooler and coupled to an amplifier. It is hoped that the availability of high-performance detectors which do not need to be cooled to cryogenic temperatures will greatly improve the attractiveness of laser heterodyne systems.

Neil Gordon

Papers

Optimization of Erbium-Doped Actively Q-Switched Fiber Laser Implemented in Symmetric Configuration

132 kV optical voltage sensor for wide area monitoring, protection and control applications

Calibration of tracking systems using detections from non-cooperative targets

Recursive Triangulation using Bearings only Sensors

A high-performance CO2 laser heterodyne detector operating at 250 K