We actually have quite many detectors pointing in every direction and these are for detecting different kinds of interesting stuff. Gamma rays, radio, gravity waves, neutrinos, asteroids, and so forth. There are satellites and ground based detectors to make sure that there is essentially no blind spot, not even behind the Moon or the Sun, and the detectors are very very sensitive. These are all automatic and will report anomalies quite fast. Most of these are even linked to other detectors that would try to capture events in another medium. For instance, when we detect a gamma day burst, we want to detect it in optical and gravity as soon as possible. We also have an army of amateur astronomers with very good telescopes (with wide fields of view) trying to hunt asteroids, comets, and by all means.. aliens too (we've found none yet, in case you were wondering).
So, in an event of an alien fleet would suddenly appear in our solar system, I'd guess that such an agent would register as an anomaly in all kinds of different detectors, and turn pretty much the world's eyes towards it within hours. Astronomers are very keen of detecting new and strange phenomena. I think the alien technology would be pretty advanced to cloak it from detection in such different mediums as broad spectrum electro magnetic (gamma, optical and radio), neutrino and gravity.
I think such technology would have to be so utterly alien that we probably would detect an innovation, even in progress.. we might already be invaded and exploited. And what would be the point of fending off such innovation, if we wouldn't even take notice of it?