@inproceedings{Fernandez-Bes2015,
title = {A Probabilistic Least-Mean-Squares Filter},
author = {Fernandez-Bes, Jesus and Elvira, Victor and Van Vaerenbergh, Steven},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178361 http://www.tsc.uc3m.es/~velvira/papers/ICASSP2015_bes.pdf},
doi = {10.1109/ICASSP.2015.7178361},
isbn = {978-1-4673-6997-8},
year = {2015},
date = {2015-04-01},
booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
pages = {2199--2203},
publisher = {IEEE},
address = {Brisbane},
abstract = {We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring somemore Bayesian machine learning techniques to adaptive filtering.},
keywords = {adaptable step size LMS algorithm, Adaptation models, adaptive filtering, Approximation algorithms, Bayesian machine learning techniques, efficient approximation algorithm, filtering theory, Least squares approximations, least-mean-squares, probabilistic least mean squares filter, Probabilistic logic, probabilisticmodels, Probability, Signal processing algorithms, Standards, state-space models},
pubstate = {published},
tppubtype = {inproceedings}
}

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring somemore Bayesian machine learning techniques to adaptive filtering.

@article{Maiz2012,
title = {A Particle Filtering Scheme for Processing Time Series Corrupted by Outliers},
author = {Maiz, Cristina S. and Molanes-Lopez, Elisa M. and Miguez, Joaquin and Djuric, Petar M.},
url = {http://www.tsc.uc3m.es/~jmiguez/papers/P34_2012_A Particle Filtering Scheme for Processing Time Series Corrupted by Outliers.pdf
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6203606},
issn = {1053-587X},
year = {2012},
date = {2012-01-01},
journal = {IEEE Transactions on Signal Processing},
volume = {60},
number = {9},
pages = {4611--4627},
abstract = {The literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data. Most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series. For a target tracking problem described by a nonlinear state-space model, we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm. The outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations, such as a concentration measure or an extreme upper quantile. We also provide asymptotic results about the convergence of the particle approximations of the predictive distribution (and its statistics) and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations.},
keywords = {Kalman filters, Mathematical model, nonlinear state space model, Outlier detection, prediction theory, predictive distribution, Probability density function, State-space methods, state-space models, statistical distributions, Target tracking, time serie processing, Vectors, Yttrium},
pubstate = {published},
tppubtype = {article}
}

The literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data. Most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series. For a target tracking problem described by a nonlinear state-space model, we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm. The outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations, such as a concentration measure or an extreme upper quantile. We also provide asymptotic results about the convergence of the particle approximations of the predictive distribution (and its statistics) and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations.