Abstract: A method for assisting with the navigation of a fleet of vehicles including a main vehicle and a secondary vehicle that is mobile in relation to the main vehicle, the method including receiving relative movement data, acquired by one or more sensors, between the main vehicle and the secondary vehicle, estimating a navigation status of the fleet of vehicles by an invariant Kalman filter using the received data as observations, the navigation status including first variables representing a first rigid transformation linking a location mark associated with the main vehicle to a reference point, and second variables representing a second rigid transformation linking a location mark associated with the main vehicle to a location mark associated with the secondary vehicle, the invariant Kalman filter using, as an internal composition law, a law including a term-by term composition of the first rigid transformation and the second rigid transformation.

Abstract: A method for assisting the navigation of a fleet of vehicles including main vehicle and a secondary vehicle movable relative to the main vehicle includes receiving data acquired by one or more sensors, the received data including relative kinematic data between the main vehicle and the secondary vehicle, and estimating a navigation state of the fleet of vehicles by an invariant Kalman filter using the received data as observations. The navigation state includes first variables representative of a first rigid transformation linking a frame attached to the main vehicle to a reference frame, and second variables representative of a second rigid transformation linking the frame attached to the main vehicle to a frame attached to the secondary vehicle. The invariant Kalman filter uses as binary operation an operation including a term-by-term composition of the first rigid transformation and of the second rigid transformation.

Abstract: The present invention relates to a navigation assistance method for a mobile carrier (1) comprising an inertial navigation unit (10) comprising at least one inertial sensor (12), in which, over a determined observation window, the following steps are implemented by an estimation unit (11) of the inertial navigation unit (10): (E10) parametrisation of a non-linear system configured to estimate a navigation state of the mobile carrier (1) over a given time interval at an iteration n as a function of a kinematic model and/or measurements acquired by at least one inertial sensor (12); (E20) linearisation of the system so that the system expresses a navigation state at iteration n as a function of the state at iteration n?1 and a correction to this navigation state, said system being initialised by a first a priori state; (E21) estimating, by a Kalman filter and stochastic cloning, a first correction of a navigation state at iteration n; (E22) estimating a second correction of the navigation state at iteration n b

Abstract: The invention relates to a method for assisting with the navigation of a fleet of vehicles comprising a main vehicle (1) and a secondary vehicle (2) that is mobile in relation to the main vehicle (1), said method involving the steps of: •receiving relative movement data (Y1, Y2), acquired by at least one sensor (2, 12), between the main vehicle (1) and the secondary vehicle (2); •estimating (100, 200) a navigation status of the fleet of vehicles by an invariant Kalman filter using the received data (Y1, Y2) as observations, the navigation status comprising •first variables representing a first rigid transformation linking a location mark associated with the main vehicle (1) to a reference point, and •second variables representing a second rigid transformation linking a location mark associated with the main vehicle (1) to a location mark associated with the secondary vehicle (2), the invariant Kalman filter using, as an internal composition law, a law comprising a term-by term composition of the first rigid t

Abstract: The invention relates to a method for assisting with the navigation of a first vehicle (1) that is stationary in relation to a second vehicle (2) which is mobile within a reference frame, said method involving acquiring (112) movement data on the first vehicle (1) by at least one proprioceptive sensor (6), and estimating a navigation status (X 1) of the first vehicle (1) by an invariant Kalman filter using a navigation status (X 2) of the second vehicle (2) as an observation, the navigation status of the first vehicle (1) comprising variables that represent a rigid transformation (T 1) linking a first location mark associated with the first vehicle (1) to the reference frame, and variables that represent a rigid transformation (T 21) linking a location mark associated with the second vehicle (2) to the first location mark, the invariant Kalman filter using, as an internal composition taw, a law comprising a term-by-term composition of the two rigid transformations.

Abstract: The invention relates to an alignment method based on a simplified mode allowing processing using an invariant Kalman filter, in which each speed involved in the navigation equations is expressed in a work reference frame (Rt) translated with respect to an inertial reference frame (Ri) and for which the origin moves along a reference inertial trajectory, the carrier of which is assumed to be close (geographic origin for alignment with the sun at known position, GPS trajectory for alignment in-motion, etc.). This simplified mode comprises the repetition of the following steps to estimate a mobile carrier state (P): —propagation (PROP) determining an estimated current state from a preceding estimated state, inertial sensor measurements and theoretical information on the carrier trajectory (P) —updating (MAJ) the estimated state using theoretical information on the carrier trajectory (P). The deterministic uncertainties of the sensors (bias/drift/scale factors, etc.

Abstract: A method of searching for a defect capable of affecting a rotating mechanical power transmission device includes a step of obtaining a signal s that can be modeled by a product of a high frequency signal s1 and a low frequency signal s2, generated by the rotating mechanical power transmission device and acquired by a sensor, a step of determining estimates of the signals s1 and s2, minimizing a difference between all or part of the signal s and a product of these estimates, a step of analyzing the estimates of the signals s1 and s2 in order to detect the presence of a defect affecting the rotating power transmission mechanical device, and, if a defect is detected, a step of locating said defect from at least one of the estimates of the signals s1 and s2.

Abstract: 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.

Abstract: A method for tracking the navigation of a mobile carrier, in which an extended Kalman filter estimates, over successive iterations, a navigation state of the carrier. Each iteration propagates a previous navigation state of the carrier into a propagated state, updates the propagated state according to measurements acquired by at least one navigation sensor. The updating includes: calculating a linear correction term from an innovation representative of a difference between the measurements acquired by the navigation sensor and the propagated state, calculating an exponential of the linear correction in terms of a Lie group, calculating a first correction term expressed in a reference frame that is fixed relative to the carrier, calculating a second correction term expressed in an inertial reference frame in which the carrier is mobile, and adding the second correction term to the value of the variable contained in the propagated state.

Abstract: The invention proposes a method for tracking the navigation of a mobile carrier, in which an extended Kalman filter estimates, over successive iterations, a navigation state of the carrier, one iteration of the filter comprising steps of: propagating a previous navigation state of the carrier into a propagated state according to a kinematic model and/or measurements acquired by at least one inertial sensor, updating the propagated state according to measurements acquired by at least one navigation sensor, in which, for at least one navigation variable of the carrier contained in the propagated state, the updating comprises sub-steps of: calculating a linear correction term from an innovation representative of a difference between the measurements acquired by the navigation sensor and the propagated state, calculating an exponential of the linear correction in terms of a Lie group, calculating a first correction term expressed in a reference frame that is fixed relative to the carrier, the first correction ter

Abstract: A method is provided for estimating the state of a moving system, the method using a particle filter and comprising the following steps implemented on one reference particle among a plurality of previously calculated particles, the reference particle providing an estimation of the state and comprising a first set of variables and a second set of variables: random mutation (101), by the particle filter, of the first set of variables into a mutated first set of variables; parameterization (102) of an extended Kalman filter using the mutated first set of variables; and implementation (103) of the parameterized extended Kalman filter to produce a new particle by way of the second set of variables and data measured by at least one sensor, the method being characterized in that the extended Kalman filter is an invariant extended Kalman filter, and in that the second set of variables comprises at least the variables: orientation, speed and position of the moving system, the invariant extended Kalman filter being con

Abstract: The invention relates to an alignment method based on a simplified mode allowing processing using an invariant Kalman filter, in which each speed involved in the navigation equations is expressed in a work reference frame (Rt) translated with respect to an inertial reference frame (Ri) and for which the origin moves along a reference inertial trajectory, the carrier of which is assumed to be close (geographic origin for alignment with the sun at known position, GPS trajectory for alignment in-motion, etc.). This simplified mode comprises the repetition of the following steps to estimate a mobile carrier state (P): propagation (PROP) determining an estimated current state from a preceding estimated state, inertial sensor measurements and theoretical information on the carrier trajectory (P) updating (MAJ) the estimated state using theoretical information on the carrier trajectory (P). The deterministic uncertainties of the sensors (bias/drift/scale factors, etc.