I think Overlord's answer is wrong. I think some big governments already have things in place like this.
First of all, we already have enough satellites to cover the entire planet. Look at google earth. Not enough for real time perhaps, but that is because Google is a company looking for profit. If they wanted to, they could assign satellites to this.
But, you do not need to cover the entire planet. After the start up phase, you will have a location on all military personnel, equipment and locations. And then it is a matter of tracking those. You can assign more satellites that cross the earth and scan it, to look for movement you have not logged yet. Aggregate this data with intelligence data, and adding any new movement to the network will be rather quickly.
I also want to point out that the images we see on google maps' satellite view are artificially made of a lesser resolution. The original images are so good that you could very well see a person in their home, through the reflection of a car mirror parked in the street. And these images can further be cleaned by software as well. The reason we do not see this is privacy laws and such.
We also have the infrastructure to process things like this. You just need to be smart about it. If you send all imagery in a data stream to a central point where it will get processed, it won't be possible. But such a system needs to be split up anyway. You will have cells of satellites working together, covering a certain area with their camera's overlapping each other's view. these satellites will have a small computational centre, in space or on ground, that will cover their images, tie it in a single feed AND perform calculations on that.
Again, you do not want to track every square meter of earth. You want to track specific locations and targets. That is what these cell's would do. Since these things are known beforehand, they simply need to track these. If stuff is not moving, there is probably no reason to notify anybody either. So the feed only needs to ring a bell if there is movement or activity happening. This simplifies the system greatly already.
Now all these cells will probably send their data to a bigger hub, which will send it to a bigger hub and so on. Somewhere all this data will be stored, but not in its entirety. Only the relevant bits.
Next to this you would have a separate network of moving satellites that are not in a stationary orbit. They will move across the globe and provide images this way. You can use software to let them look for certain things (and believe me, the stuff we can do with image recognition these days in commercial and hobby projects is amazing. What governments can do is always miles ahead of this.) and flag these. Another system will check these flags (with or without human input) and if desirable add them to the tracking network as a target to keep track off.
You can feed intelligence data to your second network and use that to look for certain things in certain places. eg a spy tells you about a secret base on some island in the pacific at these coordinates. Make network 2 search and locate it, flag it and then add it to network 1 to keep track off.
All of this would cost billions and you will need a large infrastructure. But this is certainly possible. The NSA alone would have the computational infrastructure to process this kind of data and they are only one of many intelligence and security agencies the USA have. If an entire country works on a project such as this; this is possible. If multiple countries (say the UN or an alliance of sorts) work on this, it becomes even more easy.
Heck, if Google or Amazon wanted to, they could do this probably.
If you are curious you should look up what people can do these days with image recognition software. I saw a tech talk from a CEO of a company that is using the windows UWP platform on vending machines in Africa, where they use small camera's to image recognise globally listed criminals. This is image recognition done on vending machine computers. The hardest part was not the image recognition either, it was sending the data over shit internet in the middle of nowhere. So they actively pushed all the processing and such to the machine. With smart algorithms this was possible.
And to get a feel of the difference in tech between what we civilians can use and what governments have, look up the difference between night goggles you or I can buy, and the stuff soldiers have access too. They have optics that can turn a pitch black night into a day light scene.
This applies to almost any technological industry.