## 2012 |

## Journal Articles |

Maiz, Cristina S; Molanes-Lopez, Elisa M; Miguez, Joaquin ; Djuric, Petar M A Particle Filtering Scheme for Processing Time Series Corrupted by Outliers Journal Article IEEE Transactions on Signal Processing, 60 (9), pp. 4611–4627, 2012, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: 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 @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. |

## 2010 |

## Journal Articles |

Djuric, Petar M; Miguez, Joaquin Assessment of Nonlinear Dynamic Models by Kolmogorov–Smirnov Statistics Journal Article IEEE Transactions on Signal Processing, 58 (10), pp. 5069–5079, 2010, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Cumulative distributions, discrete random variables, dynamic nonlinear models, Electrical capacitance tomography, Filtering, filtering theory, Iron, Kolmogorov-Smirnov statistics, Kolomogorov–Smirnov statistics, model assessment, nonlinear dynamic models, nonlinear dynamical systems, Permission, predictive cumulative distributions, predictive distributions, Predictive models, Random variables, Robots, statistical analysis, statistical distributions, statistics, Telecommunication control @article{Djuric2010a, title = {Assessment of Nonlinear Dynamic Models by Kolmogorov–Smirnov Statistics}, author = {Djuric, Petar M. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5491124}, issn = {1053-587X}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {58}, number = {10}, pages = {5069--5079}, abstract = {Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov-Smirnov statistics. The technique is based on the generation of discrete random variables that come from a known discrete distribution if the entertained model is correct. We provide simulation examples that demonstrate the performance of the proposed method.}, keywords = {Cumulative distributions, discrete random variables, dynamic nonlinear models, Electrical capacitance tomography, Filtering, filtering theory, Iron, Kolmogorov-Smirnov statistics, Kolomogorov–Smirnov statistics, model assessment, nonlinear dynamic models, nonlinear dynamical systems, Permission, predictive cumulative distributions, predictive distributions, Predictive models, Random variables, Robots, statistical analysis, statistical distributions, statistics, Telecommunication control}, pubstate = {published}, tppubtype = {article} } Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov-Smirnov statistics. The technique is based on the generation of discrete random variables that come from a known discrete distribution if the entertained model is correct. We provide simulation examples that demonstrate the performance of the proposed method. |

## Inproceedings |

Djuric, Petar M; Closas, Pau ; Bugallo, Monica F; Miguez, Joaquin Evaluation of a Method's Robustness Inproceedings 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3598–3601, IEEE, Dallas, 2010, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: Electronic mail, Extraterrestrial measurements, Filtering, Gaussian processes, method's robustness, Random variables, robustness, sequential methods, Signal processing, statistical distributions, Telecommunications, uniform distribution, Wireless communication @inproceedings{Djuric2010, title = {Evaluation of a Method's Robustness}, author = {Djuric, Petar M. and Closas, Pau and Bugallo, Monica F. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5495921}, issn = {1520-6149}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Conference on Acoustics, Speech and Signal Processing}, pages = {3598--3601}, publisher = {IEEE}, address = {Dallas}, abstract = {In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data.}, keywords = {Electronic mail, Extraterrestrial measurements, Filtering, Gaussian processes, method's robustness, Random variables, robustness, sequential methods, Signal processing, statistical distributions, Telecommunications, uniform distribution, Wireless communication}, pubstate = {published}, tppubtype = {inproceedings} } In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data. |

## 2009 |

## Inproceedings |

Maiz, Cristina S; Miguez, Joaquin ; Djuric, Petar M Particle Filtering in the Presence of Outliers Inproceedings 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, pp. 33–36, IEEE, Cardiff, 2009, ISBN: 978-1-4244-2709-3. Abstract | Links | BibTeX | Tags: computer simulations, Degradation, Filtering, multidimensional random variates, Multidimensional signal processing, Multidimensional systems, Nonlinear tracking, Outlier detection, predictive distributions, Signal processing, signal processing tools, signal-power observations, spatial depth, statistical analysis, statistical distributions, statistics, Target tracking, Testing @inproceedings{Maiz2009, title = {Particle Filtering in the Presence of Outliers}, author = {Maiz, Cristina S. and Miguez, Joaquin and Djuric, Petar M.}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278645}, isbn = {978-1-4244-2709-3}, year = {2009}, date = {2009-01-01}, booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing}, pages = {33--36}, publisher = {IEEE}, address = {Cardiff}, abstract = {Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different from the assumed model of the data. Therefore, when handled in the same way as regular observations, outliers may drastically degrade the performance of the particle filter. To address this problem, we introduce an auxiliary particle filtering scheme that incorporates an outlier detection step. We propose to implement it by means of a test involving statistics of the predictive distributions of the observations. Specifically, we investigate the use of a proposed statistic called spatial depth that can easily be applied to multidimensional random variates. The performance of the resulting algorithm is assessed by computer simulations of target tracking based on signal-power observations.}, keywords = {computer simulations, Degradation, Filtering, multidimensional random variates, Multidimensional signal processing, Multidimensional systems, Nonlinear tracking, Outlier detection, predictive distributions, Signal processing, signal processing tools, signal-power observations, spatial depth, statistical analysis, statistical distributions, statistics, Target tracking, Testing}, pubstate = {published}, tppubtype = {inproceedings} } Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different from the assumed model of the data. Therefore, when handled in the same way as regular observations, outliers may drastically degrade the performance of the particle filter. To address this problem, we introduce an auxiliary particle filtering scheme that incorporates an outlier detection step. We propose to implement it by means of a test involving statistics of the predictive distributions of the observations. Specifically, we investigate the use of a proposed statistic called spatial depth that can easily be applied to multidimensional random variates. The performance of the resulting algorithm is assessed by computer simulations of target tracking based on signal-power observations. |

Djuric, Petar M; Bugallo, Monica F; Closas, Pau ; Miguez, Joaquin Measuring the Robustness of Sequential Methods Inproceedings 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, pp. 29–32, IEEE, Aruba, Dutch Antilles, 2009, ISBN: 978-1-4244-5179-1. Abstract | Links | BibTeX | Tags: Additive noise, cumulative distribution functions, data processing method, extended Kalman filtering, Extraterrestrial measurements, Filtering, Gaussian distribution, Gaussian noise, Kalman filters, Kolmogorov-Smirnov distance, Least squares approximation, Noise robustness, nonlinear filters, robustness, sequential methods, statistical distributions, telecommunication computing @inproceedings{Djuric2009a, title = {Measuring the Robustness of Sequential Methods}, author = {Djuric, Petar M. and Bugallo, Monica F. and Closas, Pau and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5413275}, isbn = {978-1-4244-5179-1}, year = {2009}, date = {2009-01-01}, booktitle = {2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop}, pages = {29--32}, publisher = {IEEE}, address = {Aruba, Dutch Antilles}, abstract = {Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper, we propose an approach for constructing such metrics for sequential methods. These metrics are derived from the Kolmogorov-Smirnov distance between the cumulative distribution functions of the actual observations and the ones based on the assumed model. The use of the proposed metrics is demonstrated with simulation examples.}, keywords = {Additive noise, cumulative distribution functions, data processing method, extended Kalman filtering, Extraterrestrial measurements, Filtering, Gaussian distribution, Gaussian noise, Kalman filters, Kolmogorov-Smirnov distance, Least squares approximation, Noise robustness, nonlinear filters, robustness, sequential methods, statistical distributions, telecommunication computing}, pubstate = {published}, tppubtype = {inproceedings} } Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper, we propose an approach for constructing such metrics for sequential methods. These metrics are derived from the Kolmogorov-Smirnov distance between the cumulative distribution functions of the actual observations and the ones based on the assumed model. The use of the proposed metrics is demonstrated with simulation examples. |

## 2008 |

## Inproceedings |

Perez-Cruz, Fernando Kullback-Leibler Divergence Estimation of Continuous Distributions Inproceedings 2008 IEEE International Symposium on Information Theory, pp. 1666–1670, IEEE, Toronto, 2008, ISBN: 978-1-4244-2256-2. Abstract | Links | BibTeX | Tags: Convergence, density estimation, Density measurement, Entropy, Frequency estimation, H infinity control, information theory, k-nearest-neighbour density estimation, Kullback-Leibler divergence estimation, Machine learning, Mutual information, neuroscience, Random variables, statistical distributions, waiting-times distributions @inproceedings{Perez-Cruz2008, title = {Kullback-Leibler Divergence Estimation of Continuous Distributions}, author = {Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4595271}, isbn = {978-1-4244-2256-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE International Symposium on Information Theory}, pages = {1666--1670}, publisher = {IEEE}, address = {Toronto}, abstract = {We present a method for estimating the KL divergence between continuous densities and we prove it converges almost surely. Divergence estimation is typically solved estimating the densities first. Our main result shows this intermediate step is unnecessary and that the divergence can be either estimated using the empirical cdf or k-nearest-neighbour density estimation, which does not converge to the true measure for finite k. The convergence proof is based on describing the statistics of our estimator using waiting-times distributions, as the exponential or Erlang. We illustrate the proposed estimators and show how they compare to existing methods based on density estimation, and we also outline how our divergence estimators can be used for solving the two-sample problem.}, keywords = {Convergence, density estimation, Density measurement, Entropy, Frequency estimation, H infinity control, information theory, k-nearest-neighbour density estimation, Kullback-Leibler divergence estimation, Machine learning, Mutual information, neuroscience, Random variables, statistical distributions, waiting-times distributions}, pubstate = {published}, tppubtype = {inproceedings} } We present a method for estimating the KL divergence between continuous densities and we prove it converges almost surely. Divergence estimation is typically solved estimating the densities first. Our main result shows this intermediate step is unnecessary and that the divergence can be either estimated using the empirical cdf or k-nearest-neighbour density estimation, which does not converge to the true measure for finite k. The convergence proof is based on describing the statistics of our estimator using waiting-times distributions, as the exponential or Erlang. We illustrate the proposed estimators and show how they compare to existing methods based on density estimation, and we also outline how our divergence estimators can be used for solving the two-sample problem. |