A system for recording a trace performed on a writing surface, including: ∘ a utensil, intended to be handled by a user, provided with a magnetic object, and including a tip intended to come into contact with the writing surface to form the trace to be recorded; ∘ a localisation device, including: • a network of magnetometers (M i), which are secured to the writing surface, and adapted to measure a magnetic field emitted by the magnetic object at different successive measurement times t n, • an electronic calculation unit, adapted to determine a state vector X a representative of at least one position of the magnetic object from the measured magnetic field, and to determine an estimated reference position Č p|c on the writing surface from the state vector X a, ∘ characterised in that it includes a touch matrix sensor including: • a matrix of N distinct pixels (Px i), which are secured to the writing surface, and each adapted to provide an electrical response signal representative of a contact of the tip on the writing surface; • an electronic processing unit, connected to the electronic calculation unit, and adapted to determine a set S px of M pixels, with M less than N, at least partly surrounding said estimated reference position Č p|c, to transmit an electrical control signal to the M pixels of said set S px and receive their electrical response signals; and to detect the contact of the tip on the writing surface from the electrical response signals from said set S px of M pixels, and when the contact is detected, to save successive positions of the tip to form the trace record depending on at least the successive estimated reference positions Č p|c. ∘ a utensil, intended to be handled by a user, provided with a magnetic object, and including a tip intended to come into contact with the writing surface to form the trace to be recorded; ∘ a localisation device, including: • a network of magnetometers (M i), which are secured to the writing surface, and adapted to measure a magnetic field emitted by the magnetic object at different successive measurement times t n, • an electronic calculation unit, adapted to determine a state vector X a representative of at least one position of the magnetic object from the measured magnetic field, and to determine an estimated reference position Č p|c on the writing surface from the state vector X a, • a network of magnetometers (M i), which are secured to the writing surface, and adapted to measure a magnetic field emitted by the magnetic object at different successive measurement times t n, • an electronic calculation unit, adapted to determine a state vector X a representative of at least one position of the magnetic object from the measured magnetic field, and to determine an estimated reference position Č p|c on the writing surface from the state vector X a, ∘ characterised in that it includes a touch matrix sensor including: • a matrix of N distinct pixels (Px i), which are secured to the writing surface, and each adapted to provide an electrical response signal representative of a contact of the tip on the writing surface; • an electronic processing unit, connected to the electronic calculation unit, and adapted to determine a set S px of M pixels, with M less than N, at least partly surrounding said estimated reference position Č p|c, to transmit an electrical control signal to the M pixels of said set S px and receive their electrical response signals; and to detect the contact of the tip on the writing surface from the electrical response signals from said set S px of M pixels, and when the contact is detected, to save successive positions of the tip to form the trace record depending on at least the successive estimated reference positions Č p|c. • a matrix of N distinct pixels (Px i), which are secured to the writing surface, and each adapted to provide an electrical response signal representative of a contact of the tip on the writing surface; • an electronic processing unit, connected to the electronic calculation unit, and adapted to determine a set S px of M pixels, with M less than N, at least partly surrounding said estimated reference position Č p|c, to transmit an electrical control signal to the M pixels of said set S px and receive their electrical response signals; and to detect the contact of the tip on the writing surface from the electrical response signals from said set S px of M pixels, and when the contact is detected, to save successive positions of the tip to form the trace record depending on at least the successive estimated reference positions Č p|c.