Nouvelles méthodes en filtrage particulaire : application au recalage de navigation inertielle par mesures altimétriques

L'objectif de ce memoire est de developper et d'etudier un nouveau type de filtre particulaire, appele le filtre de Kalman-particulaire a noyaux (KPKF). Le KPKF modelise la densite conditionnelle de l'etat comme un melange de gaussiennes centrees sur les particules et ayant des matrices de covariance de norme petite. L'algorithme du KPKF utilise une correction de l'etat de type Kalman et une correction de type particulaire modifiant les poids des particules. Un nouveau type de re-echantillonnage permet de preserver la structure de cette mixture. Le KPKF combine les avantages du filtre particulaire regularise en terme de robustesse et du filtre de Kalman etendu en terme de precision. Cette nouvelle methode de filtrage a ete appliquee au recalage de navigation inertielle d'un aeronef disposant d'un radio altimetre. Les resultats obtenus montrent que le KPKF fonctionne pour de grandes zones d'incertitude initiale de position.

[1]  D. Pham.  Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems , 2001 .

[2]  D. J. Salmond,et al.  A particle filter for track-before-detect , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[3]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[4]  D. Michel,et al.  Des resultats de non existence de filtre de dimension finie , 1984 .

[5]  B. M. Scherzinger,et al.  Modified strapdown inertial navigator error models , 1994, Proceedings of 1994 IEEE Position, Location and Navigation Symposium - PLANS'94.

[6]  Niclas Bergman,et al.  Recursive Bayesian Estimation : Navigation and Tracking Applications , 1999 .

[7]  P. Pérez,et al.  Tracking multiple objects with particle filtering , 2002 .

[8]  Nadia Oudjane.  Stabilite et approximations particulaires en filtrage non lineaire application au pistage , 2000 .

[9]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[10]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[11]  Donald Benson,et al.  A Comparison of Two Approaches to Pure-Inertial and Doppler-Inertial Error Analysis , 1975, IEEE Transactions on Aerospace and Electronic Systems.

[12]  Dinh-Tuan Pham,et al.  A kalman-particle kernel filter and its application to terrain navigation , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[13]  Y. Bar-Shalom.  Tracking and data association , 1988 .

[14]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[15]  P. Faurre,et al.  Navigation inertielle optimale et filtrage statistique , 1971 .

[16]  Probability of Crashing for a Terrain-Following Missile , 1974 .

[17]  J. Picard.  Asymptotic study of estimation problems with small observation noise , 1987 .

[18]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[19]  Drora Goshen-Meskin,et al.  Unified Approach to Inertial Navigation System Error Modeling , 1990 .

[20]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[21]  S. F. Schmidt,et al.  Application of State-Space Methods to Navigation Problems , 1966 .

[22]  Christian Musso,et al.  Improving Regularised Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[23]  Dinh-Tuan Pham,et al.  Application of the Kalman-particle kernel filter to the updated inertial navigation system , 2004, 2004 12th European Signal Processing Conference.

[24]  Simon J. Godsill,et al.  On sequential simulation-based methods for Bayesian filtering , 1998 .

[25]  Himilcon Carvalho.  Filtrage optimal non-linéaire du signal GPS NAVSTAR en recalage de centrales de navigation , 1995 .

[26]  Kenneth R Britting,et al.  Inertial navigation systems analysis , 1971 .

[27]  F. Gland,et al.  An Adaptive Local Grid Refinement Method for Nonlinear Filtering , 1995 .

[28]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[29]  J.-C. Radix.  Systèmes inertiels à composants liés "Strap-down" , 1980 .

[30]  Jun S. Liu,et al.  Mixture Kalman filters , 2000 .

[31]  Fredrik Gustafsson,et al.  Terrain navigation using Bayesian statistics , 1999 .

[32]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[33]  Christian Musso,et al.  An Efficient Method for Generating Points Uniformly Distributed in Hyperellipsoids , 2001 .

[34]  P. Moral.  Nonlinear filtering : Interacting particle resolution , 1997 .

[35]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[36]  Markus Hürzeler,et al.  Monte Carlo Approximations for General State-Space Models , 1998 .

[37]  P. Nordlund.  Sequential Monte Carlo Filters and Integrated Navigation , 2002 .

[38]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[39]  P. Whittle.  ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[40]  Niclas Bergman,et al.  Posterior Cramér-Rao Bounds for Sequential Estimation , 2001, Sequential Monte Carlo Methods in Practice.

[41]  S. Altmann.  Rotations, Quaternions, and Double Groups , 1986 .

[42]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[43]  N. Oudjane,et al.  Multiple model particle filter , 1999 .

[44]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[45]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[46]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[47]  Alʹbert Nikolaevich Shiri︠a︡ev,et al.  Statistics of random processes , 1977 .

[48]  G. Casella,et al.  Rao-Blackwellisation of sampling schemes , 1996 .

[49]  Babak Azimi-Sadjadi,et al.  Approximate Nonlinear Filtering with Applications to Navigation , 2001 .

[50]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[51]  G. Peters,et al.  Monte Carlo Approximations for General State-Space Models , 1998 .

[52]  Michael Isard,et al.  Active Contours , 2000, Springer London.

[53]  É. Pardoux,et al.  Filtrage Non Lineaire Et Equations Aux Derivees Partielles Stochastiques Associees , 1991 .

[54]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[55]  Approximate Filter for the Conditional Law of a Partially Observed Process in Nonlinear Filtering , 1998 .

[56]  Petar M. Djuric,et al.  Gaussian particle filtering , 2003, IEEE Trans. Signal Process..