A method of detecting a substantially invariant rotation axis of a motion of a mobile equipped with at least a magnetic sensor with three sensitive axes and an inertial sensor with three sensitive axes, the method comprising the following steps: - acquiring (E10; E31) physical measurements with respect to the three sensitive axes by the magnetic sensor and the inertial sensor, the physical measurements comprising at least three samples at different times during said motion; - estimating (E11-E15 - E32-E34) the three substantially invariant rotation axes in the physical measurement space of said magnetic sensor and said inertial sensor from said at least three acquired samples, each substantially invariant rotational axis corresponding to the axis for which the standard deviation of the values of said physical measurements projected onto said axis is minimized, said estimating step comprising - a step of calculating by analysis into principal components, the third principal component corresponding to the coordinates of said substantially invariant rotation axis in the physical measurements spaces, respectively of said magnetic sensor and said inertial sensor, or - a step of calculating least squares applied to a linear combination of said physical measurements, respectively of said magnetic sensor and of said inertial sensor; - calculating (E16; E35) an indicator (d) of variations of the rotation axis estimated respectively for the inertial sensor and the magnetic sensor; and - validating, as the substantially invariant rotation axis of said motion, the linear combination of the estimated rotational axis for said physical measurements of the magnetic sensor and the inertial sensor, the coefficients of the combination being comprised not strictly between 0 and 1, the sum being equal to 1, and being function of the values of the indicators of the variations of the rotational axis of the magnetic sensor and/or of the inertial sensor. - acquiring (E10; E31) physical measurements with respect to the three sensitive axes by the magnetic sensor and the inertial sensor, the physical measurements comprising at least three samples at different times during said motion; - estimating (E11-E15 - E32-E34) the three substantially invariant rotation axes in the physical measurement space of said magnetic sensor and said inertial sensor from said at least three acquired samples, each substantially invariant rotational axis corresponding to the axis for which the standard deviation of the values of said physical measurements projected onto said axis is minimized, said estimating step comprising - a step of calculating by analysis into principal components, the third principal component corresponding to the coordinates of said substantially invariant rotation axis in the physical measurements spaces, respectively of said magnetic sensor and said inertial sensor, or - a step of calculating least squares applied to a linear combination of said physical measurements, respectively of said magnetic sensor and of said inertial sensor; - calculating (E16; E35) an indicator (d) of variations of the rotation axis estimated respectively for the inertial sensor and the magnetic sensor; and - validating, as the substantially invariant rotation axis of said motion, the linear combination of the estimated rotational axis for said physical measurements of the magnetic sensor and the inertial sensor, the coefficients of the combination being comprised not strictly between 0 and 1, the sum being equal to 1, and being function of the values of the indicators of the variations of the rotational axis of the magnetic sensor and/or of the inertial sensor.