How is global greenhouse gas emission calculated?
Your question is simple enough, but the answer depends on what exactly you're looking for.

Who is emitting where right now?

Real-time global monitoring of greenhouse gas emissions with a high spatial resolution is an emerging technology.  We have very useful satellites (see Jean-Marie Privals answer), but they have limitations:


All existing public satellites with instruments for high-resolution GHG measurements are in low Earth orbit, so they only see a particular place when they pass over, not all the time.  So far only the Geostationary Interferometric Infrared Sounder (GIIRS) on the Chinese FengYung (FY)-4A satellite can in theory monitor CO₂ from a geostationary viewpoint, which allows for "continuous" monitoring (probably meaning hourly; it takes a while to scan the area of interest), but from what I've heard GIIRS is not performing very well.  Europe plans to launch the Infra-Red Sounder (IRS) in 2023.  Either way, their spatial resolution will be much worse than for the low Earth orbit satellites, because geostationary orbit is so far away.
They rely on visible radiation.  Although attempts to retrieve from infrared radiation exist, their information content is quite poor (for an Arctic methane example, see Holl et al. (2016)).  In Jean-Marie Privals answer you can see an illustration of how reflected sunlight is used as a retrieval.
They usually need clear skies.  We can't look below the clouds, but even retrieving above the cloud would require a very accurate characterisation of the cloud, and clouds are tricky.  So usually we just assume that the GHG concentration is the same with or without clouds, even when it probably isn't.
Some private satellites exist with a very high spatial resolution, but I can't find much verifiable information about them.  GHGSat claims a spatial resolution of less than 50 metre.  Inevitably, that comes at the cost of field of view (12×12 km² claimed), it will only view a spot when actively pointing, so although it may be able to point anywhere on Earth, it will only view very specific areas and is in that sense not global.  It appears many similar commercial instruments are planned in the near future.



  I can imagine a satellite observation-based model that calculates emissions on a spatial basis but I am not sure if our technology is advanced enough to do that accurately. However, this method would not allow segregation of GHG by source/sectors (electricity generation, cement production, agriculture etc.)


The spatial resolution of about 2 km may be good enough for that, unless the electricity plant is next to the cement producer, the emissions occur at night, the factory is switched off when the satellite happens to pass over, or it's cloudy (there are attempts to retrieve in the presence of clouds, but it's harder).

So while satellites are certainly very useful in GHG monitoring, it's difficult to get everything from satellites alone.

Where were emissions last month?

We can average daytime GHG contentration measurements over the period of a month.  Combined with chemistry and circulation models, we can then try to estimate in what regions of the Earth those emissions may have occurred, but not with a precision high enough to tell "electricity or cement".  This is an average of CO₂ measurements for July 2009:



The limitations are less serious now: the satellite has multiple attempts to capture a particular scene, and will usually see at least one clear-sky overpass per month, probably multiple.  In the image above, there was probably also some form of data fusion to combine with other sources or fill gaps using neighbouring pixels.  The longer the time period we average over, the smoother the distribution will look.

What were global emissions last year?

However, if you are looking for global emissions averaged over a long time period, we can make use of the observation that CO₂, and to a lesser degree CH₄, is a well-mixed gas.  Here, well-mixed means that it stays long enough in the atmosphere to reach pretty much everywhere given enough time.  That means that ultimately, it doesn't matter where you emit.  That's why "global" CO₂ concentrations may be measured at Mauna Kea (Hawaii, USA), even though this is far away from any emissions.  However, that also means that it doesn't tell us whether the CO₂ was emitted in India, Italy, or Idaho.  And much of the emitted CO₂ gets absorbed by the oceans, so the delta between this year and last is not enough to determine global emissions.