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    In brief

  • ECTS credits : 5
  • Code : N9EN21


The objectives of this course is to learn and undestand various way to solve inverse problems. Depending on the student's area, applications wil be oriented toward photographic 3D-reconstruction methods or numerial problems with uncertainty. In the first, case, the problem is to obtain a 3D model of a scene i.e., its shape and its colour.In the second case, the main filtering methods based on the non-linear Bayesian filters (particle filter, Kalman filter, extended Kalman filter, ensemble Kalman filter) will be studied. For a given ODE/SDE, students have to identify the corresponding notion of integration, then should be able to propose an adapted filtering method.


The content is twofold, with a focus on the student's preferred area:

- Filtering methods

    - Introduction to filtering : Bayesian inference ; Filtering and smoothing principles, non-linear filtering ; Application to the linear and Gaussian case: Kalman filter.

    - Uncertainty dynamics for ordinary differential equations (ODE) and stochastic differential equations (SDE): from partial differential equation to ODE (numerical schemes); Lyapunov exponent and chaotic system; stochastic processes; discrete/continuous Markov processes; Observable/measure dynamics duality

     - Stochastic filtering: Particle filter; Ensemble Kalman filter; Stochastic smoother


▪      Jazwinski, A. Stochastic Processes and Filtering Theory Academic Press, 1970

▪      Oksendal, Stochastic differential equations Springer, 2003.

▪      Evensen, G. Data Assimilation: The Ensemble Kalman Filter Springer, 2009.


Optimization, notion of probability and statistics, numerical linear algebra





  • Toulouse


The National Institute of Electrical engineering, Electronics, Computer science,Fluid mechanics & Telecommunications and Networks

2, rue Charles Camichel - BP 7122
31071 Toulouse Cedex 7, France

+33 (0)5 34 32 20 00


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