Method and device for assisting with the navigation of a fleet of vehicles using an invariant Kalman filter

A device for assisting the navigation of a fleet of vehicles comprising a main vehicle and a secondary vehicle movable relative to the main vehicle, the device comprising:

• at least one first sensor onboard the main vehicle, wherein the at least one first sensor is configured to acquire data of the secondary vehicle, the data comprising relative kinematic data between the main vehicle and the secondary vehicle,
• at least one processor configured to implement an invariant Kalman filter to estimate a navigation state of the fleet of vehicles, wherein the invariant Kalman filter is configured to use the received data as observations, wherein the navigation state comprises:
• 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, and
• wherein the invariant Kalman filter is configured to use as a binary operation a term-by-term composition of the first rigid transformation and of the second rigid transformation.