My understanding is that the idea is one of those where the math and technology required to think that it is worth a try are actually quite old(it’s essentially radio acoustic ranging with a less cooperative sound source; but receivers that aren’t floating around); but where difficulty escalates rapidly once you step out of physics experiment land and into a noisy urban environment with a wide variety of structures that attenuate or reflect sound, nasty multipath reflection issues, and so on. A problem with lots of room for ‘solutions’(even sincere attempts) that don’t actually work all that well; but if you’ve bought one; might as well talk it up and hope for deterrence.
(It would also be interesting to know if whatever New York was doing in the 80s or early 90s was based on the acoustic and other sensors used in IGLOO WHITE during the Vietnam war, shopped around for new markets once that program wound down. The technology would be applicable; but I’m not sure how soon any of the contractors would have been free to pitch it for law enforcement; or whether there is in fact any relation.)
It is telling that, even today, this ‘shot spotter’ system is using trained humans in addition to whatever fancy DSP tricks are involved. I strongly suspect that this is because getting the computer to provide the right answer is hard; not because they like payroll costs.