System for stabilizing a positioner of an equipment item, the positioner being oriented via an orientation command, and installed on a vehicle undergoing motions, the positioner including angular coders producing angular measurements and a set of gyrometric sensors producing measurements of rates of instantaneous rotation, and exhibiting biases, the positioner including a calculation unit with elements of intra-positioner slaving-correction of the instantaneous rates of rotation of the item using measurements and the orientation command to stabilize the item following the line of sight. The vehicle includes an element for measuring the attitude of the vehicle giving vehicle attitude measurements. The system includes calculation elements for controlling the positioner according to a control law to correct the biases by virtue of the vehicle attitude information and by implementing a state observer combining an estimation of attitude of an item and the measurements of rates of rotation of an item of equipment.
