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.

/pdf/a-tutorial-on-particle-filters-for-online-nonlinear-non-1rzkwgk2pp.pdf

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.

/pdf/sequential-monte-carlo-methods-in-practice-3kfxeebn8e.pdf

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

Multi-sensor track-before-detect for complementary sensors

The properties of AlxIn1-xSb light-emitting diodes (LEDs) and photodetectors have been investigated to establish their suitability for methane sensing. Using these components it is possible to achieve good signal-to-noise values at both the characteristic absorption wavelength and also at 4 ?m, an attractive wavelength for use as a reference channel. A limit of sensitivity of approximately 400 ppm, with an integration time of 10 s and a path length of 5 cm, was estimated for methane detection.

Mid-Infrared ${\rm Al}_{x}{\rm In}_{1-x}{\rm Sb}$ Light-Emitting Diodes and Photodiodes for Hydrocarbon Sensing

The incorporation of non-imaging optical concentrations in uncooled mid-IR LEDs is described. Novel micromachining methods are used to produce optical concentrators in the growth substrate of epitaxial InSb/InAlSb heterostructures. Resultant large area LED arrays, displaying both positive and negative luminescence, are shown to have optical gains of 3.5 over conventional mesas made form the same material. The LED technology shown also relies on the micromachined substrate being transparent to 3-5 micrometers radiation and to act as a low resistance common contact. The use of degenerate doping in InSb is described, resulting in a shift in the room-temperature transmission to the 3-5micrometers atmospheric window and providing high electrical conductivities.

Optical concentrators for light-emitting diodes

An earlier paper [1] discussed the merits of adaptive coded apertures for use as lensless imaging systems in the thermal
infrared and visible It was shown how diffractive (rather than the more conventional geometric) coding could be used,
and that 2D intensity measurements from multiple mask patterns could be combined and decoded to yield enhanced
imagery Initial experimental results in the visible band were presented Unfortunately, radiosity calculations, also
presented in that paper, indicated that the signal to noise performance of systems using this approach was likely to be
compromised, especially in the infrared
This paper will discuss how such limitations can be overcome, and some of the tradeoffs involved Experimental results
showing tracking and imaging performance of these modified, diffractive, adaptive coded aperture systems in the visible
and infrared will be presented The subpixel imaging and tracking performance is compared to that of conventional
imaging systems and shown to be superior System size, weight and cost calculations indicate that the coded aperture
approach, employing novel photonic MOEMS micro-shutter architectures, has significant merits for a given level of
performance in the MWIR when compared to more conventional imaging approaches

Adaptive coded aperture imaging in the infrared: towards a practical implementation

In a previous paper we presented initial results for sub-detector-pixel imaging in the mid-wave infra-red (MWIR) using
an imager equipped with a coded-aperture based on a re-configurable MOEMS micro-shutter. It was shown in laboratory
experiments that sub-pixel resolution is achievable via this route.
The purpose of the current paper is to provide detail on the reconstruction method and to discuss some challenges which
arise when imaging real-world scenes. The number of different mask patterns required to achieve a certain degree of
super-resolution is also discussed. New results are presented to support the theory.

Neil Gordon

Papers

Multi-sensor track-before-detect for complementary sensors

Mid-Infrared ${\rm Al}_{x}{\rm In}_{1-x}{\rm Sb}$ Light-Emitting Diodes and Photodiodes for Hydrocarbon Sensing

Optical concentrators for light-emitting diodes

Adaptive coded aperture imaging in the infrared: towards a practical implementation

Sub-pixel super-resolution by decoding frames from a reconfigurable coded-aperture camera: theory and experimental verification