An autonomous pointing peripheral unit including, in a casing adapted to be held in hand: - a gyrometer circuit (28, 28'), adapted to produce signals in response to a rotation ( rX, rZ) imparted to the casing according to at least two axes ( X, Z); - an accelerometer circuit (30, 30', 30"), adapted to produce signals in response to an acceleration imparted to the casing according to about two axes (X, Z) out of three (X, Y, Z); - a transmitter, adapted to emit data frames towards a device able to be remote controlled by the pointing peripheral unit as a function of the movements imparted to the casing; - a microcontroller, adapted to operate a periodical polling of the gyrometer and accelerometer circuits and to produce in response data signals applied to the transmitter for emission of data frames; - a battery for the power supply of the gyrometer and accelerometer circuits, the transmitter and the microcontroller; and - battery energy management means with deactivation of the transmitter and of the gyrometer and accelerometer circuits, and putting of the microcontroller in standby state, wherein the management means are means operating by successive steps (I-V), said management means being adapted to: - deactivate the transmitter at the end of a first time out after emission of a data frame, with the gyrometer circuit, the accelerometer circuit and the microcontroller kept active; - deactivate the gyrometer circuit at the end of a second time out in the absence of movement detected by the gyrometer and/or accelerometer circuits after deactivation of the transmitter, with the accelerometer circuit and the microcontroller being active; - deactivate the accelerometer circuit (30, 30', 30") at the end of a third time out in the absence of movement detected by the accelerometer circuit after deactivation of the gyrometer circuit; and - put the microcontroller in standby state at the end of a fourth time out in the absence of movement detected by the accelerometer circuit after deactivation of the gyrometer circuit. - a gyrometer circuit (28, 28'), adapted to produce signals in response to a rotation ( rX, rZ) imparted to the casing according to at least two axes ( X, Z); - an accelerometer circuit (30, 30', 30"), adapted to produce signals in response to an acceleration imparted to the casing according to about two axes (X, Z) out of three (X, Y, Z); - a transmitter, adapted to emit data frames towards a device able to be remote controlled by the pointing peripheral unit as a function of the movements imparted to the casing; - a microcontroller, adapted to operate a periodical polling of the gyrometer and accelerometer circuits and to produce in response data signals applied to the transmitter for emission of data frames; - a battery for the power supply of the gyrometer and accelerometer circuits, the transmitter and the microcontroller; and - battery energy management means with deactivation of the transmitter and of the gyrometer and accelerometer circuits, and putting of the microcontroller in standby state, - deactivate the transmitter at the end of a first time out after emission of a data frame, with the gyrometer circuit, the accelerometer circuit and the microcontroller kept active; - deactivate the gyrometer circuit at the end of a second time out in the absence of movement detected by the gyrometer and/or accelerometer circuits after deactivation of the transmitter, with the accelerometer circuit and the microcontroller being active; - deactivate the accelerometer circuit (30, 30', 30") at the end of a third time out in the absence of movement detected by the accelerometer circuit after deactivation of the gyrometer circuit; and - put the microcontroller in standby state at the end of a fourth time out in the absence of movement detected by the accelerometer circuit after deactivation of the gyrometer circuit.