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16 results on '"F. LeGland"'

1. Nonlinear system fault detection and isolation based on bootstrap particle filters

Author

F. Legland, Frédéric Cérou, Qinghua Zhang, Fabien Campillo, Applications and Tools of Automatic Control (SOSSO2), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Applications of interacting particle systems to statistics (ASPI), Université de Rennes (UR)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), IEEE--CSS, Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Inria Rennes – Bretagne Atlantique

Subjects
0209 industrial biotechnology, Engineering, business.industry, 020206 networking & telecommunications, 02 engineering and technology, Fault detection and isolation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, 020901 industrial engineering & automation, Discrete time and continuous time, Control theory, Nonlinear dynamic systems, 0202 electrical engineering, electronic engineering, information engineering, Particle filter, business, Particle filtering algorithm
Abstract

International audience; A particle filter based method for nonlinear system fault detection and isolation is proposed in this paper. It is applicable to quite general stochastic nonlinear dynamic systems in discrete time. The main result consists of a new particle filter algorithm, derived from the basic bootstrap particle filter, and capable of rejecting a subset of the faults possibly affecting the considered system. Fault isolation is then achieved by the evaluation of the estimated likelihoods related to the designed filters.

Published
2005

2. Particle filters for partially observed Markov chains

Author

F. LeGland, A. Guyader, N. Caylus, Signal, models, algorithms (SIGMA2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), Département Mathématiques appliquées et sciences sociales - Rennes 2 (MASS), Université de Rennes 2 (UR2), IEEE--SPS, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)

Subjects
Mathematical optimization, Markov chain mixing time, Markov chain, Variable-order Markov model, 020206 networking & telecommunications, 02 engineering and technology, Markov model, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, 0202 electrical engineering, electronic engineering, information engineering, Balance equation, Markov property, Hidden semi-Markov model, Statistical physics, 0101 mathematics, Hidden Markov model, Mathematics
Abstract

Paper WA2―5; International audience; We consider particle filters in a model where the hidden states and the observations form jointly a Markov chain, which means that the hidden states alone do not necessarily form a Markov chain. This model includes as a special case non-linear state-space models with correlated Gaussian noise. Our contribution is to study propagation of errors, stability properties of the filter, and uniform error estimates, using the framework of Le Gland and Oudjane.

Published
2003

3. Integrated short term navigation of a towed underwater body

Author

F. LeGland, G. Damy, M. Joannides, R. Rakotozafy, and M. Prevosto

Subjects
business.industry, Computer science, GPS/INS, Trajectory, Global Positioning System, Synthetic aperture sonar, Underwater, Differential GPS, business, Sonar, Inertial navigation system, Marine engineering
Abstract

An underwater body (the fish) is towed by a ship at the end of a few hundred meters long cable, and uses sidescan sonar to make observations of the sea bottom. To enhance antenna resolution, a virtual antenna is built up by adding up appropriately the echoes received by the moving physical antenna. To carry out this synthetic aperture sonar experiment efficiently, it is necessary to know with an accuracy of a few cms, the trajectory of the fish relative to its otherwise unknown initial position, during a few minutes experiment, so that motion compensation can be performed during the synthetic aperture processing. For this purpose, acceleration measurements provided by an INS (inertial navigation system) located onboard the fish, can be integrated. INS measurements are known to track accurately the high frequency components in the mobile trajectory. However, even on small time intervals, integration of INS measurements can result in unacceptable drifting in position estimates. To prevent this drifting, it is common to use additional measurements which could provide good estimates of the low frequency components of the mobile trajectory. Combining the two types of measurements will improve the trajectory estimates. This can be performed by means of a Kalman filter. The paper investigates the possibility of using position estimates of the ship, provided by differential GPS. An additional difficulty is that the satellites involved in GPS cannot provide any position estimates of an underwater body such as a towed fish, but only position estimates of the surface ship. To overcome this difficulty, the authors introduce a numerical model for the tow cable, to transform GPS position measurements of the surface ship into position and velocity estimates of the towed fish, to combine these estimates with INS measurements. >

Published
2002

4. State and parameter estimation from boundary-crossings

Author

Vikram Krishnamurthy and F. LeGland

Subjects
symbols.namesake, Partial differential equation, Diffusion process, Estimation theory, Mathematical analysis, symbols, Boundary (topology), Feynman diagram, State (functional analysis), Maximum likelihood sequence estimation, Likelihood function, Mathematics
Abstract

We consider the problem of estimating the state, and identifying parameters of a diffusion process, when the only available information is the crossing times of a boundary. By using a partial differential equation approach related with the computation of boundary-crossing probabilities, we derive finite dimensional reconstructors (filters) for the state and Feynman Kac type functionals of the state. These are then used to compute maximum likelihood parameter estimates of the drift coefficient of the diffusion.

Published
2002

5. Small noise asymptotics of nonlinear filters with nonobservable limiting deterministic system

Author

M. Joannides, F. LeGland, Signal, models, algorithms (SIGMA2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), IEEE--CSS, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
Mathematical optimization, Estimation theory, 010102 general mathematics, White noise, 01 natural sciences, Noise (electronics), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, symbols.namesake, Rate of convergence, Gaussian noise, Nonlinear filter, symbols, Applied mathematics, Probability distribution, 0101 mathematics, Deterministic system, Mathematics
Abstract

International audience; We study the asymptotic behaviour of the Bayesian estimator for a deterministic signal in additive Gaussian white noise, in the case where the set of minima of the Kullback-Leibler information is a submanifold of the parameter space. This problem includes as a special case the study of the asymptotic behaviour of the nonlinear filter, when the state equation is noise-free, and when the limiting deterministic system is nonobservable. We present a practical example where this situation occurs. We give an explicit expression of the limit, as the noise intensity goes to zero, of the posterior probability distribution of the parameter, and we study the rate of convergence.

Published
2002

6. Recursive estimation in hidden Markov models

Author

Laurent Mevel and F. LeGland

Subjects
Recursive least squares filter, 0209 industrial biotechnology, Mathematical optimization, Estimation theory, Variable-order Markov model, Estimator, Recursive partitioning, 02 engineering and technology, M-estimator, 01 natural sciences, 010104 statistics & probability, 020901 industrial engineering & automation, Applied mathematics, Hidden semi-Markov model, 0101 mathematics, Recursive Bayesian estimation, Mathematics
Abstract

We consider a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal.

Published
2002

7. A finite dimensional filter with exponential conditional density

Author

Damiano Brigo and F. LeGland

Subjects
Nonlinear system, Exponential family, Exponential growth, Linear system, Mathematical analysis, Filtering problem, Conditional probability distribution, Natural exponential family, Mathematics, Exponential function
Abstract

In this paper we consider the continuous-time nonlinear filtering problem, which has an infinite-dimensional solution in general, as proved by Chaleyat-Maurel and Michel (1984). There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular the Kalman, Benes, and Daum filters. In the present paper, we construct new classes of scalar nonlinear systems admitting finite-dimensional filters. We consider a given (nonlinear) diffusion coefficient for the state equation, a given (nonlinear) observation function, and a given finite-dimensional exponential family of probability densities. We construct a drift for the state equation such that the resulting nonlinear system admits a finite-dimensional filter evolving in the prescribed exponential family, provided the coefficients of the exponential family include the observation function and its square.

Published
2002

8. Recursive identification of HMMs with observations in a finite set

Author

F. LeGland, L. Mevel, Signal Processing and Control (AS), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), IEEE--CSS, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
0209 industrial biotechnology, Mathematical optimization, Markov chain, 020206 networking & telecommunications, 02 engineering and technology, Expression (mathematics), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Maxima and minima, Set (abstract data type), Identification (information), 020901 industrial engineering & automation, Consistency (statistics), 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Hidden Markov model, Finite set, Mathematics
Abstract

International audience; We consider the problem of identification of a partially observed finite-state Markov chain, based on observations in a finite set. We first investigate the asymptotic behaviour of the maximum likelihood estimate (MLE) for the transition probabilities, as the number of observations increases to infinity. In particular, we exhibit the associated contrast function, and discuss consistency issues. Based on this expression, we design a recursive identification algorithm, which converges to the set of local minima of the contrast function.

Published
2002

9. Nonlinear filtering with perfect discrete time observations

Author

F. LeGland, M. Joannides, Department of Mathematics [Imperial College London], Imperial College London, Signal Processing and Control (AS), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), IEEE--CSS, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
Laplace transform, 010102 general mathematics, Mathematical analysis, Perturbation (astronomy), 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Singular value, Geometric measure theory, Diffusion process, Discrete time and continuous time, Singular solution, Observability, 0101 mathematics, Mathematics
Abstract

International audience; We consider the problem of estimating the state of a diffusion process, based on discrete time observations in singular noise. We reduce the problem to a static problem, and we show that the solution is provided by the area or co-area formula of geometric measure theory, provided the observed value is a regular value of the observation function. In order to address the case of singular values, we propose another approach, based on small-noise perturbation and asymptotics of Laplace integrals

Published
2002

10. Efficient particle filters for residual generation in partially observed SDE's

Author

F. LeGland, Frédéric Cérou, Signal, models, algorithms (SIGMA2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), IEEE--CSS, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
0209 industrial biotechnology, Mathematical optimization, Stochastic resonance, Differential equation, Mathematical analysis, 020206 networking & telecommunications, 02 engineering and technology, Residual, Noise (electronics), Electronic mail, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Stochastic differential equation, symbols.namesake, Nonlinear system, 020901 industrial engineering & automation, Gaussian noise, 0202 electrical engineering, electronic engineering, information engineering, symbols, Mathematics
Abstract

International audience; The problem of detecting a change in the drift coefficient of a partially observed stochastic differential equation is addressed. The score function, evaluated at the nominal value, is used as the residual, and only the problem of residual generation is considered. In the special case where the drift coefficient depends on the parameter only in directions that are affected by nondegenerate noise, an efficient numerical approximation of the residual is proposed, using particle filters.

Published
2000

11. Stability and approximation of nonlinear filters using the Hilbert metric, and applications to particle filters

Author

F. LeGland, N. Oudjane, Signal, models, algorithms (SIGMA2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), ONERA - The French Aerospace Lab [Palaiseau], ONERA-Université Paris Saclay (COmUE), IEEE--CSS, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
0209 industrial biotechnology, Uniform convergence, Mathematical analysis, 02 engineering and technology, 01 natural sciences, Adaptive filter, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Filter design, 020901 industrial engineering & automation, Hilbert metric, Filter (video), Metric (mathematics), 0101 mathematics, Network synthesis filters, Particle filter, Mathematics
Abstract

International audience; The stability of the optimal filter w.r.t. its initial condition and w.r.t. the model, is studied in a general hidden Markov model using the Hilbert projective metric. These stability results are then used to prove the uniform convergence of the interacting particle filter to the optimal filter, as the number of particles goes to infinity.

Published
2000

12. Nonlinear filtering with continuous time perfect observations and noninformative quadratic variation

Author

F. LeGland, M. Joannides, Signal, models, algorithms (SIGMA2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), IEEE--CSS, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
0209 industrial biotechnology, Lebesgue measure, 010102 general mathematics, Mathematical analysis, 02 engineering and technology, Conditional probability distribution, State (functional analysis), 16. Peace & justice, 01 natural sciences, Noise (electronics), Quadratic variation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 020901 industrial engineering & automation, Level set, Regular conditional probability, Diffusion process, 0101 mathematics, Mathematics
Abstract

International audience; We consider the problem of estimating the state of a diffusion process, based on continuous time observations in singular noise. As long as the observations are regular values of the observation function, we derive an equation for the density (w.r.t. the canonical Lebesgue measure on the corresponding level set) of the conditional probability distribution of the state, given the past observations. The proof is based on the idea of decomposition of solutions of SDE, as introduced by Kunita (1981)

Published
1997

13. Asymptotic properties of the MLE in hidden Markov models

Author

F. LeGland and Laurent Mevel

Subjects
Statistics::Theory, Markov kernel, Markov chain, Variable-order Markov model, Maximum-entropy Markov model, Markov model, Statistics::Computation, Continuous-time Markov chain, Statistics, Statistics::Methodology, Applied mathematics, Markov property, Hidden semi-Markov model, Mathematics
Abstract

We consider an hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We investigate the asymptotic behaviour of the maximum likelihood estimator (MLE), as the number of observations increases to infinity. We exhibit the associated Kullback-Leibler information, we show that the MLE is consistent, i.e. converges to the set of minima of the Kullback-Leibler information. Finally, we prove that the MLE is asymptotically normal, under standard assumptions.

Published
1997

14. A differential geometric approach to nonlinear filtering: the projection filter

Author

Damiano Brigo, F. LeGland, Bernard Hanzon, Department of Econometrics, Vrije Universiteit Brussel (VUB), Signal, models, algorithms (SIGMA2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), Signal Processing and Control (AS), IEEE--CSS, Department of Mathematics [Imperial College London], Imperial College London, School of Mathematical Sciences [Cork], University College Cork (UCC), INRIA Rennes - Bretagne Atlantique, Econometrics and Operations Research, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes

Subjects
0209 industrial biotechnology, Geometric analysis, Differential equation, Mathematical analysis, 020206 networking & telecommunications, 02 engineering and technology, Computer Science Applications, Adaptive filter, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Filter design, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Filter (video), Nonlinear filter, Kernel adaptive filter, 0202 electrical engineering, electronic engineering, information engineering, Filtering problem, Applied mathematics, Electrical and Electronic Engineering, Network synthesis filters, Projection (set theory), Algorithm, Mathematics
Abstract

This paper deals with a new and systematic method of approximating exact nonlinear filters with finite dimensional filters. The method used here is based on the differential geometric approach to statistics. The projection filter is derived in the case of exponential families. A characterization of the filters is given in terms of an assumed density principle. An a posteriori measure of the performance of the projection filter is defined. Applications to particular systems, and numerical schemes which can be used to implement the projection filter are given in the final part. The results of simulations for the cubic sensor are discussed.; Cet article propose une méthode nouvelle et systématique pour l'approximation d'un filtre non-linéaire exact par un filtre de dimension finie. La méthode repose sur l'utilisation d'outils de géométrie différentielle en statistique. L'équation du filtre par projection est établie dans le cas des familles exponentielles, et on en donne une caractérisation en tant que filtre de forme donnée. On définit également une mesure a posteriori de la qualité de l'approximation. Dans la dernière partie, on étudie quelques exemples, et on propose un schéma numérique pour la mise en œuvre du filtre par projection. Finalement, on présente des résultats de simulations pour le problème du senseur cubique.

Published
1995

15. [Hemangiopericytoma of the ureter]

Author

P, Léger and P F, Legland

Subjects
Male, Ureteral Neoplasms, Humans, Prognosis, Aged, Hemangiopericytoma
Abstract

This report of a case of an exceedingly rare ureteral tumor, i.e. hemangiopericytoma, provides the opportunity for a discussion of the nature, prognosis and management of this lesion.

Published
1987

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