Note: I am not sure how good these ideas are. I try to make it so they don't give your exact position by building in random modifiers. This might make it pointless and useless, though if you are really lost, it would at least give you a general area you are in.
Idea 1: Naval Action could feature a navigation mini game similar to what I present here and the Sextant Mini game that Nova has here: PBS Nova Sextant Mini Game. This wouldn't actually be based upon the In Game Sun or In Game Horizon. It would bring up a screen similar to what PBS Nova has and you have to place the sun in the correct spot to get the reading. But it won't be exactly easy, because the ship will be pitching in the waves and you will have to try to line it up but it will gradually move back and forth. So basically it will be like a sniper scope in other games. Imagine it will be like the PBS sextant but it will be moving and you will have to use your mouse to try and get the sun at the correct spot. You have 2 hours of In Game Time to take the reading, between 11:00 and 13:00. In real time, this is 96 seconds, but you want to click your mouse with the sun in the correct spot at 12:00pm noon in game time. The closer you are to 12:00, the more accurate your reading. The more off you are in time and the sun not lining up in the correct spot, the more inaccurate your reading.
That covers latitude (z value for the f11 in game coordinates). Longitude is different. Historically, until the marine chronometer, longitude was very difficult to estimate. In the time period of this game, marine chronometers were becoming more popular and less expensive, but it wasn't until the very end of the time period of Naval Action that they became universal. So, we have a few options. #1. The Marine chronometer is a purchased item that takes up an officer slot. It would be very expensive and up to the captain to provide himself. #2. It is assumed everyone has a marine chronometer but the accuracy is random each reading. #3. No one has a marine chronometer (see idea #2). If you have to purchase a marine chronometer, it should not give your exact location but a range, like what I show below.
You then answer a random Navigation question. This could be a random math question for math that was historically used for navigation (angles, degrees, logarithms, etc, etc) or other navigation specific questions. Then, based upon how well you did at the mini game, the question, the time you take your sextant reading, the chronometer reading, the current weather in Open World, and random modifiers to make sure you are not shown your exact spot, you are given a rectangle around which your position could be. Storms will make a huge rectangle around where you are. Cloudy skies will make the rectangle slightly smaller than in a storm. Clear skies will give the smallest rectangle. If you answer the questions wrong or do the mini game poorly, the square will be bigger. Fail at the mini game and the questions during a storm, and the rectangle might take up a quarter of the map or more. This, and allowing you to draw and erase on your map with your dead reckoning, you might be able to better navigate.
Idea 2: Or, you could only take the Latitude Sextant mini game to get your latitude. Leave out the chronometer for longitude; the player has to keep track of that. The Player is only given a rectangle that covers the entire map east to west, but gives an area of latitude that you could be at. It is up to the player to keep track of and figure out their longitude based upon their speed in open world. For this to work, you would need a ruler based upon the in game knot value (400game units per knot). The player would then mark on their map their estimated longitude.
(You won't actually put in f11 coordinates, this is only for the demonstration only. The Game Client would handle this part)
Example: Idea 2
This x/z f11 will show as