Cheapest timer for radio trilateration
This IS a  design service, within reason, AND people will close your answer before starting to think (under 5 ns) if you mention commercial alternatives. So, maybe you can't win :-). 

A fast enough comparator (they exist) will allow time of an "edge" relative to a local clock to be turned into a pulse. 

A local clock and counter will allow clocks between start time and trigger time to be determined. 

People make short range time of flight ICs made for cellphone gesture detection (believe it or not) with times approaching what you want. 

You should conceptually look at as many alternatives as you can think of. One or more may even work.

Rotary scanning of a field of sensors with a number of transmitters may be good enough. 

You may be able to do computed tomagraphic position detection by seeing which targets are blocked or affect the signal along a number of paths. 

You say there are "many" devices but you need to be more specific about quantity and blocking characteristic. If there are eg 100 each 1 metre square and 5 metres tall "there may be problems" with some systems. If they are say 300mm x 300mm and 200mm tall so you can "look down on" the field fromm an angle you may be able to use cameras or barcode or similar pattern reading or ...

You say you want them to be passive wrt emission but do not say why or how close to a "MUST" your "want" is. IR LEDs each coded could be very helpful. Transponding LED tx's could be VERY helpfil (Poll and respond.  Resonant circuits in each device that respond to whatever could be helpful but does this violate your radiation objection if passive - or active?

A lot more flesh and blood will help with a good answer.