There are two primary systems of navigation on Earth today, using maps/compass, and using GPS satellites. It seems unlikely there will be a full constellation of GPS satellites prior to the first humans landing on Mars. In addition, Mars doesn't have a magnetic field like Earth, so a compass is out. It also seems like many long trips will be taken on Mars, even by the first group landing there, requiring accurate navigation. How will this be accomplished?
If long-range navigation is necessary, a combination of inertial navigation with occasional position fixes using stars gives reasonably accurate navigation. Inertial navigation has a few drawbacks: high cost and these systems become less accurate over time (hence the need for occasional position fixes).
For short-range navigation, dead reckoning may be sufficient. For dead reckoning, you use sensors on the wheels of your vehicle to keep track of how far it travels and which way it turns. This was used on the lunar rover.
There are a few things that could be done (Using pretty heavily "A Case for Mars" second edition):
- There will not be full constellation of satellites, but undoubtedly there will be satellites orbiting Mars at that time that are functioning. Each Mars orbiter since Mars Global Surveyor has included some sort of a beacon which could be heard. Measuring Doppler shift and listening to the time you hear it can give you your latitude, and approximate longitude. This could be easily found via a look up table of some sort on the rover.
- Stars could be observed at night, which gives you a reference point. In addition, if you are low enough in latitude, you can use Deimos and Phobos to give you a pretty good latitude/longitude estimate. If you keep careful time, you can use the same trick that mariners have used for a long time to find longitude, in addition, you can use the moons as an additional reference point. In fact, given 2 of the 3 objects (Sun, Phobos, Deimos), a sextant, a clock, and an almanac, one could determine one's location exactly.
- Some sort of a inertial navigation system could be used, as Hobbes mentioned.
- Use the North Star, or best equivalent.
I'm a little surprised nobody has mentioned markers. As in flags, signposts, and splashes of paint on rocks.
Astronauts on the first missions to Mars are not going to go all that far from their base. Vehicles won't have the range and safety considerations would limit them. Vehicle tracks remain visible for a very long time, dust storms lay down a thin layer of dust over them but don't rub them out. So there will quickly be a network of trails to follow.
As activity expands on Mars the network of trails and the distribution of markers will expand with it. These are by far the most reliable navigation tools and I'm sure mission members will be careful to create a dense, easy to use, widely distributed array of them. They don't unexpectedly break, or suffer from interference, or run out of power. Finding them in the reduced visibility of a dust storm might be hard - it might be prudent to set up networks of blinking light posts and beacons for such cases. But any radio-based system would have trouble at such times too.
If you were so far away from any explored area with a base that there were no markers at all, about the only way that could happen is if you landed off course. Even in that case, you probably wouldn't strike out on your own, you'd wait to be found. You'd activate a radio beacon and try to establish radio contact, which you'd likely then use to tell the base where you figure you are based on how you came in and what you can see around you. (And quite likely, figuring out where you were would be the least of your problems.)
If you can afford to get people to Mars, then you can easily afford a navigational satellite or two. Since you asked how it will be accomplished (as opposed to how it perhaps could be accomplished, with lots of interesting answers to that question here), then I can answer with some confidence that they will use navigational satellites for safety and reliability. It won't be much different than GPS here. The main difference will be satellite availability and accuracy. There probably won't be 31 of them flying around Mars.
You could try old school navigation. Like the one they did in the past when sailing ships. They dint have navigation back then so they used a "tool" to calculate the angle of the horizon and the sun. And then according to the specific time they took the angle they could calculate there exact position. Now this is still ment to work only on earth. Because of all the calculation specific to earth and at the beginning it did took a lot of time to calculate where you are.
This video could explain a little more: http://youtu.be/AGCUm_jWtt4
During daylight, it may be possible to adapt a technique used on Earth for locating North that requires an analogue watch/clock and for the sun to be visible. Of course, for Mars, the clock would need to be made for Martian Sols, not Earth days.
The technique for locating North on Earth is:
In the Southern Hemisphere
Hold the watch horizontal with the '12' pointing directly towards the sun. Look at the hour hand, half the angle between '12' and the hour hand points towards north.
In the Northern Hemisphere
Hold the watch horizontal with the hour hand pointing directly towards the sun.
Half the angle between '12' and the hour hand points towards south.
Don't forget to make allowances for daylight savings.
Basically this is a non-problem because any place on Mars is as good as any other. You don't achieve anything by moving to a specific location.
Suppose people settle on Mars. At first, the settlements will probably be close together. Either within sight of each other or nearly so, so that people can go from one to the other by landmarks.
You need a way to explore such that you can find your way to the base, even if you cannot see it and don't recognize landmarks. Building a very tall tower to serve as a beacon could help. It could give off light, or perhaps also a long range radio signal.
A simple navigation device would tell you what direction the beacon signal is coming from.
As for me, being lazy, I will just download the Google Mars Navigation application from the Play Store for my Marsphone.