TANS (Tactical Air Navigation System) was indeed a Helicopter system that was fitted to the Dominie (as well as Sea King and Navy Lynx amongst others).
Quintessentially it was an air data computer with a Doppler Radar feed and a True Air Speed feed (hence the lage 'temperature bulb' on the starboard side of the Dominie's nose) that replaced the earlier 'steam driven' mechanical GPI from the early '80s onwards. It gave a digital read out of the aircraft's position.
Unfortuanately, in the Dominie, it was only as good as the Doppler feed (from the Vucan Mk I which had a drift rate of around 2-3 miles per hour) exacerbated by the Student's interpretation of the Ecko 190 radar.
It was replaced with an all digital system (and colour radar) during the Dominie Avionics Upgrade of the mid '90s.