The Military Backpack

Stolen from a platoon of soldiers near the outer perimeter around the military base at the centre of the Zone.
When activated it repels the perimeter anomalies and allows safe passage without the disorientation caused by the anomalies.
Activation also sets off a security system with a GPS beacon attached, which prompted an artillery attack the last time it was used.

The backpack comprises four key components.

1. Transmitter. Sends out an anomalous signal in all directions to a range of about 10 metres. This signal is presumably what repels the perimeter anomalies.
2. Shielding. Sends out a signal in all directions to a range of about 50 centimetres. This seems to shield the device from anomalous interference from outside.
3. GPS beacon. Transmits the location of the beacon whenever it is powered up. The GPS also sends out an alert if it cannot detect a specific RFID tag within range, presumably a military ID tag of some kind.
4. Battery and CPU. Runs everything else, seems to operate on a fairly standard OS.

Any of the first three systems can easily be disconnected from the CPU and thus disabled. Reconnecting any of them afterwards will not be very straightforward.

The device emits what can only be described as a form of anti-anomaly radiation. Rather than as per the initial assumption the signal emitted does not repel the perimeter anomaly, it actively cancels it out. The signal seems to be tailored very specifically to the perimeter anomaly, suggesting the device could not be used to mask other anomalies without significant modification. Field studies with the device demonstrate that the emitted field is indeed 10m in radius and appears and disappears instantly when powered up/down. It is also worth noting that the perimeter anomaly signals are weaker at the edges than deeper in, and when the emitter was activated the anomaly just outside the 10m range was as weak as it usually is at its edges.

A physicist may be able to decode the smaller shielding transmission.
A duplicate of the RFID tag could be created to mirror a military ID, at least in electronic terms.