In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary

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Narayan Kovvali received the B.Tech. degree in electrical engineering from the Indian Institute of Technology, Kharagpur, India, in 2000, and the M.S. and Ph.D. degrees in electrical engineering from Duke University, Durham, North Carolina, in 2002 and 2005, respectively. In 2006, he joined the Department of Electrical Engineering at Arizona State University, Tempe, Arizona, as Assistant Research Scientist. He currently holds the position of Assistant Research Professor in the School of Electrical, Computer, and Energy Engineering at Arizona State University. His research interests include statistical signal processing, detection, estimation, stochastic filtering and tracking, Bayesian data analysis, multi-sensor data fusion, Monte Carlo methods, and scientific computing. Dr. Kovvali is a Senior Member of the IEEE. Mahesh Banavar is a post-doctoral researcher in the School of Electrical, Computer and Energy Engineering at Arizona State University. He received the B.E. degree in Telecommunications Engineering from Visvesvaraya Technological University, Karnataka, India, in 2005, and the M.S. and Ph.D. degrees in Electrical Engineering from Arizona State University in 2007 and 2010, respectively. His research area is Signal Processing and Communications, and he is specifically working on Wireless Communications and Sensor Networks. He is a member of MENSA and the Eta Kappa Nu honor society. Andreas Spanias is Professor in the School of Electrical, Computer, and Energy Engineering at Arizona State University (ASU). He is also the founder and director of the SenSIP Industry Consortium. His research interests are in the areas of adaptive signal processing, speech processing, and audio sensing. He and his student team developed the computer simulation software Java-DSP. He is author of two text books: Audio Processing and Coding by Wiley and DSP; An Interactive Approach. He served as Associate Editor of the IEEE Transactions on Signal Processing and as General Co-chair ofIEEE ICASSP-99. He also served as the IEEE Signal Processing Vice-President for Conferences. Andreas Spanias is co-recipient of the 2002 IEEE Donald G. Fink paper prize award and was elected Fellow of the IEEE in 2003. He served as Distinguished Lecturer for the IEEE Signal Processing Society in 2004.