The oldest aircraft navigational aids to avoid hitting the ground are fairly simple, and predate software (the radar altimeter is a good example, which in its most basic form just tells you your altitude above the ground and works really well in most flight regimes). Ground proximity warning systems are more along the lines of what you're thinking, and rely on the aircraft's flight computer to predict an intersecting flight path with its digital terrain model within a specified period of time (typically relies on GPS and/or INS data). As long as the software isn't integrated into aircraft flight controls (auto-GCAS in fly-by-wire military aircraft, for example) it doesn't necessarily need super-rigorous testing, although when it is connected to automated flight controls it should* have* (looking at you, Boeing...) an extremely rigorous testing process to ensure it behaves deterministically and as the pilot expects under all normal and emergency conditions. This generally involves a lot of bench testing, with a (potentially very large) number of test flights to ensure it works as designed in enough distinct conditions to have full confidence in the system.
TCAS (the family of systems aircraft use to avoid hitting other aircraft) is much simpler and doesn't rely as heavily on GPS/INS data, but generally only gives data on cooperative aircraft transmitting transponder or ADS-B data. A very simple version gives a traffic alert when another aircraft approaches within a specified distance of you, but may not give any other useful information (relative altitude/position, heading, etc.), and the most basic version I can think of just gives a range to a single cooperative aircraft.
I think you'll find that you're off by a few orders of magnitude on the number of submarine navigators out there, and there are few enough certified avionics systems that most are used by a substantial enough audience (and, more importantly, mandated by enough national aviation authorities) to be worth the R&D effort.
That said, military hardware is often decades behind the civilian world when it comes to many of these mandated safety features, so I don't find it surprising that military ships (often with proprietary radar and sonar systems designed primarily for combat, and not wanting to broadcast their location to potential adversaries) don't have good integration with commercial collision avoidance software designed to work in a collaborative environment with off-the-shelf hardware that may have only been installed as an afterthought, if at all.