A supplementary device configured to be releasably attached to a distal end of a drug delivery device. The supplementary device comprising primary electronics, a non-contact acceleration sensor and a low power processor. The non-contact acceleration sensor is directed towards a proximal end of the drug delivery device and the low power processor is configured to: receive the signals output from the non-contact acceleration sensor; determine based on the signals that an outer needle cap of the drug delivery device has been removed; and in response to determining that an outer needle cap of the drug delivery device has been removed, send a wake-up signal to the primary electronics of the supplementary device.