Yes and no. At short range there are devices like doppler direction finders [1] that are remarkably affordable and can make quick work out of locating some signals. This is for signals that arrive over a straightforward single path, though.
These shortwave transmissions do not have that convenient property. HF transmissions at high powers will duct through at the atmosphere, bounce off of the geography, and in general propagate in all sorts of strange ways that result in them arriving simultaneously via multiple paths to any given position. This means that standard direction finding methods will not be very effective. Because of the long wavelengths of these signals, very large antennas are also required to even attempt direction finding, usually circular structures hundreds to thousands of feet across, a common type being a Wullenweber antenna [2].
Very few organizations possess substantial HF direction-finding capability. The FCC has monitoring stations that can do this in many cases, and they use it for enforcement purposes, I believe primarily when public safety users report jamming problems. As a fun fact, one of these monitoring stations is located in Livermore, although I believe that station is remote-control and has no staff. The FCC is not very public about how these monitoring stations operate, I believe their positioning is based on differential analysis of the reports from all of their 14 stations across the country though. Most of what I know about them is from a rather outdated source [3] although their locations are listed in 47 CFR s. 0.121 since they are afforded special protections against interference.
On the international scale, if you looked at the Wikipedia article on Wullenwebers you may have noted that that was originally a code name. Various militaries and intelligence agencies operate large direction finding stations, but because of the challenges of locating HF signals even these large facilities have limited efficacy. Nonetheless, I assume that the NSA has confirmed transmitter locations for these signals (probably by a combination of direction-finding and good old fashioned on the ground tradecraft) and has simply chosen not to share.
You can build an antenna with a cardiod pattern, which has a wide range but a very deep, narrow null at one end. When you see the signal strength dip off, the transmitter has to be aligned with the null (sort of, there are also multipath issues to consider)
But, doing this requires you can move freely to track the transmitter. Hunting a transmitter on Russian soil by non-Russian entities might not be viewed very kindly :)
And the location probably wouldn't be too surprising. I remember reading that some number station transmitter was tracked down to a Russian military base. Pretty much where you'd expect it to be.
This confused me too. Unless there are boosters of some kind, the power of a signal seems to follow a pretty predictable decay pattern. You would need to do a sample of the power around a certain radius and find some derivative in that field of where the power is increasing or decreasing the most in proportion to moving across that particular diameter in the circle. Then you've at least established a geodesic line to circumnavigate and hit the station at.
You've also narrowed down the total set of longitudes/latitudes based on the geometry of Russia and with high-confidence, assuming that the station's language can be taken as evidence of anything.
I am not an expert, this is just speculation. But that seems like a reasonable sketch of the problem solving method that would have to be involved.
Some German intelligence officer confirmed some weeks ago that they can locate any FM station in Africa by 100 meters with some radio installation in Germany.
