A homing device for a missile, comprising: - an active assembly comprising at least one active sensor configured to transmit and receive signals in order to detect a target with an on-board active radar in a target designation domain corresponding to ranges of values for the distance from the target relative to the device, for the speed of the target relative to the device, and for the angular direction of the target relative to the direction of movement of the device; - a passive assembly comprising at least one passive sensor configured to receive detection signals from the target; - a module for transmitting/receiving high-frequency signals; - a module for transposing a high-frequency signal into a low-frequency signal; - an analogue-to-digital conversion and digital-to-analogue conversion module; and - a computer comprising: - a module for processing data associated with the active assembly; - a module for processing data associated with the passive assembly; - a module for activating/deactivating the active assembly, configured to manage the activation/deactivation of the active assembly during three phases: - during a first phase, called standby phase, for deactivating the active assembly, with the first phase being between the firing of the missile and a first distance from the target that is a homing distance of the missile plus a maximum uncertainty distance value, or being between the firing of the missile and the completion of the self-tests of the homing device; - during a second phase, called search phase, in order to alternately activate and deactivate the active assembly, with the second phase following the first phase, and ending when the power of the signal received by the active assembly when it is activated is greater than a detection power threshold of the target; and - during a third phase, called tracking phase, for activating the active assembly, with the third phase following the second phase; the module for activating/deactivating the active assembly being configured to, during the second phase, alternately activate and deactivate the active assembly, so that the duration (Da) of an activation of the active assembly complies with the following relationship: Da = Dra × OAIa DPAp in which: Da represents the duration of an activation, in s; Dra represents the duration required for the homing device to transmit signals and to receive the signals reflected by a target, in s; OAIa represents the instantaneous angular aperture of the active assembly, in sr; and DPAp represents the angular precision or uncertainty domain of the passive assembly, in sr. - an active assembly comprising at least one active sensor configured to transmit and receive signals in order to detect a target with an on-board active radar in a target designation domain corresponding to ranges of values for the distance from the target relative to the device, for the speed of the target relative to the device, and for the angular direction of the target relative to the direction of movement of the device; - a passive assembly comprising at least one passive sensor configured to receive detection signals from the target; - a module for transmitting/receiving high-frequency signals; - a module for transposing a high-frequency signal into a low-frequency signal; - an analogue-to-digital conversion and digital-to-analogue conversion module; and - a computer comprising: - a module for processing data associated with the active assembly; - a module for processing data associated with the passive assembly; - a module for activating/deactivating the active assembly, configured to manage the activation/deactivation of the active assembly during three phases: - during a first phase, called standby phase, for deactivating the active assembly, with the first phase being between the firing of the missile and a first distance from the target that is a homing distance of the missile plus a maximum uncertainty distance value, or being between the firing of the missile and the completion of the self-tests of the homing device; - during a second phase, called search phase, in order to alternately activate and deactivate the active assembly, with the second phase following the first phase, and ending when the power of the signal received by the active assembly when it is activated is greater than a detection power threshold of the target; and - during a third phase, called tracking phase, for activating the active assembly, with the third phase following the second phase; Da represents the duration of an activation, in s; Dra represents the duration required for the homing device to transmit signals and to receive the signals reflected by a target, in s; OAIa represents the instantaneous angular aperture of the active assembly, in sr; and DPAp represents the angular precision or uncertainty domain of the passive assembly, in sr.