Invariant particle filtering

A method for estimating a state representative of the movement of a mobile system, the method applying a particle filtering and comprising the following steps applied from a reference particle from among several particles calculated earlier, the reference particle providing an estimation of the state and comprising a first set of variables and a second set of variables, the first set of variables containing at least a bias in satellite radio navigation measurements:

• random mutation (101), by the particle filtering, of the first set of variables in a first mutated set of variables,
• parameterization (102) of an extended Kalman filter by means of the first mutated set of variables,
• application (103) of the extended Kalman filter parameterized in order to produce a new particle from the second set of variables and of data measured by at least one sensor,
• the method being characterized in that the extended Kalman filter is of the invariant type, and in that the second set of variables comprises orientation, velocity and position variables of the mobile system, the invariant extended Kalman filter being configured under the assumption that:
• the pair of the orientation and position variables has an invariance property by applying a rotation or a translation to said pair, and that
• the pair of the orientation and velocity variables has an invariance property by applying a rotation or a translation to said pair.