Kalman Filter - Theory and Hybridation


Present the concept of Kalman Filter as a particular and efficient application of the Least Mean Square error Concept in the Signal Theory. Numerous use of this linear filtering technique could be explored, but the navigation solution in the context of Global Navigation Satellite System will stay the main illustration. Some others examples in Surveillance and in Navigation for positioning an aircraft will be explained. The lecturers will also insist on the possibilities of utilization of merging various sources of measurement (multi-sensor systems).


Engineers or executives, with a knowledge of basic theory of signal processing.


1. State space model, Overview of Continuous and Discrete Problematic.
2. Recall of Random signal, Overview of the Problematic of optimum estimation.
  • Overview and Recall of Random Signal/Processing Theory.

3. Notion of the “Least Mean Square Error (LMSE)“ concept in estimation theory.
4. Kalman filtering Theory and its extension :
  • The main notion in linear and Gaussian noise context. Definition of the Equation System and Kalman filter Algorithm.

  • The extended case (Extended Kalman Filter) in non linear model. Definition of the Equation System and E.K.F Algorithm.

5. Additional of External signal Measurement of information. Illustration with the Inertial Navigation Case :
  • Overview of the problematic of the hybridation and Coupling in Kalman filter theory.

  • Example : GPS/Inertial System Coupling.

6. Case Study and Simulation :
  • Basic example in Surveillance of Aircraft (Radar, Multilateration - Surveillance)

  • Completed Simulation with GPS sensor.

For information only : 30 hours