A method for estimating the state of a moving system, using a particle filter. The method implements on one reference particle an estimation of the state and includes a first set of variables and a second set of variables. A random mutation, by the particle filter, of the first set of variables is performed followed by parameterization of an extended Kalman filter using the mutated first set of variables. The Kalman filter produces a new particle using the second set of variables and data measured by at least one sensor. The second set of variables includes at least the variables: orientation, speed and position of the moving system. The Kalman filter is configured assuming that the pair of variables orientation and position has a property of invariance upon a rotation or translation and their orientation and speed has a property of invariance on application of a rotation or translation.