Abstract
An introduction to particle filtering is discussed starting with an overview of Bayesian inference from batch to sequential processors. Once the evolving Bayesian paradigm is established, simulation-based methods using sampling theory and Monte Carlo realizations are discussed. Here the usual limitations of nonlinear approximations and non-Gaussian processes prevalent in classical nonlinear processing algorithms (e.g. Kalman filters) are no longer a restriction to perform Bayesian inference. It is shown how the underlying hidden or state variables are easily assimilated into this Bayesian construct. Importance sampling methods are then discussed and shown how they can be extended to sequential solutions implemented using Markovian state-space models as a natural evolution. With this in mind, the idea of a particle filter, which is a discrete representation of a probability distribution, is developed and shown how it can be implemented using sequential importance sampling/resampling methods. Finally, an application is briefly discussed comparing the performance of the particle filter designs with classical nonlinear filter implementations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Candy, J. V. (2006) Model-Based Signal Processing, New Jersey, John Wiley.
Djuric, P., Kotecha, J., Zhang, J., Huang, Y., Ghirmai, T., Bugallo, M., and Miguez, J. (2003) Particle Filtering. IEEE Signal Processing Magazines 20(5), 19–38.
Doucet, A., de Freitas, N., and Gordon, N. (2001) Sequential Monte Carlo Methods in Practice, New York, Springer-Verlag.
Doucet, A. and Wang, X. (2005) Monte Carlo Methods for Signal Processing, IEEE Signal Processing Magazines 24(5), 152–170.
Godsill, S. and Djuric, P. (2002) Special Issue: Monte Carlo methods for statistical signal processing. IEEE Transactions on Signal Processing, 50, 173–449.
Haykin, S. and de Freitas, N. (2004) Special Issue: Sequential State Estimation: From Kalman Filters to Particle Filters. Proceedings of IEEE, 92(3), 399–574.
Liu, J. (2001) Monte Carlo Strategies in Scientific Computing, New York, Springer-Verlag.
Ristic, B., Arulampalam, S., and Gordon, N. (2004) Beyond the Kalman Filter: Particle Filters for Tracking Applications, Boston, Artech House.
Schoen, T. (2006) Estimation of Nonlinear Dynamic Systems: Theory and Applications Linkopings Univ., Linkoping, Sweden PhD Dissertation.
Sullivan, E. J. and Candy, J. V. (1997) Space-time Array Processing: The Model-based Approach, Journal of the Acoustical Society of America, 102(5), 2809–2820.
Tanner, M. (1993) Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 2nd ed.; New York, Springer-Verlag.
van der Merwe, R. (2004) Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models OGI School of Science & Engr., Oregon Health & Science Univ., PhD Dissertation.
West, M. and Harrison, J. (1997) Bayesian Forecasting and Dynamic Models, 2nd ed., New York, Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Candy, J. (2007). NONLINEAR STATISTICAL SIGNAL PROCESSING: A PARTICLE FILTERING APPROACH. In: Byrnes, J. (eds) Imaging for Detection and Identification. NATO Security through Science Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5620-8_7
Download citation
DOI: https://doi.org/10.1007/978-1-4020-5620-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5618-5
Online ISBN: 978-1-4020-5620-8
eBook Packages: EngineeringEngineering (R0)