The absolute cheapest thing is just to never update the position unless it significantly changed. Doesn't require anything except the GPS chip.

Bluetooth beacons would need to add an accelerometer, but that undermines their use in pinpointing an object at rest.

Using the GPS signal to detect motion is the most power-expensive path though.

The cheapest in terms of power consumption is a simple Accelerometer/Gyroscope component. The difference can be months or even years in longer battery runtime compared to GPS.

Probably the most effective technique for detection would be attained by spoofing the GPS signals, like the IRGC did to capture multiple US' drones?

https://www.gpsworld.com/gps-circle-spoofing-discovered-in-i...

I wonder how easily GPS can be spoofed, locally ...

https://rntfnd.org/2021/10/28/cheap-and-easy-gps-gnss-spoofi...

Seems someone already had the idea:

https://www.reddit.com/r/hardwarehacking/comments/10na5c8/sp...

I used to have a GPS repeater installed in our lab for RF testing. The FAA did not like it at all and threatened us with action.

Don't go spoofing or broadcasting your own GPS signals unless you have a decent legal team behind you.

Put it in an RF chamber and keep another GPS receiver outside the chamber some distance away to make sure it doesn't lose lock on the real satellites. That's your leakage canary.

We had one of those in an underground parking garage for autonomous vehicle testing at a previous job, but it was a naturally really well shielded room, and it was just repeating surface signals so no one would complain.

Sleeping the CPU until you get an interrupt from an IMU or simple motion detector is a common way to do this. It's not about being stealthy so much as extending battery life.

Whichever one is cheapest energy-wise. My guess is MEMS.