Thucydides wrote:To counter the natural orbital path of a satellite will require some sort of application of energy, which should be obvious to outside observers (especially the orbiting bombardment system).
Using known technology, you wold have to be thrusting constantly with some sort of rocket, or suspended beneath a huge solar sail (Statite). If using anti gravity, you are somehow building a "mountain" out of space/time to lift yourself out of the gravity well, which should have all kinds of odd effects that the enemy AI would notice.
So using some sort of "handwavium" to suspend yourself in space in defiance of orbital mechanics will draw unwanted attention to yourself.
On the other hand, Federation-level technology is not really what the monitoring systems are designed to detect and interfere with.
The monitoring systems are mostly designed to go after the early indicators of technological advancement. Early experimentation on electricity is no doubt on the list of triggers, and electricity production and transmission. They're designed with the preconception that any Federation-level technology is an Angel or Archangel, or one of their trusted agents, and therefore approved. The system may track/monitor/record the activities of Federation-level technologies, but it's not going to trigger an alarm just on movement or communications. It'd probably alert on Federation-level energy-intensive weapons fire (energy weapons, and possibly railguns/mass drivers).