I've changed my mind. I think the problem is impossible to solve.

Simple reason: no parallax.

Celestial bodies are so far apart that you could move thousands of kilometers without noticing any perceptiable difference in star / galaxy / whatever positions.

The best you could hope for would be determining your heading.

Quote:Original post by Matt Apple
Some thoughts:
If you know where you are now, if you check again in 5 minutes you don't have to start from scratch. You are within a certain radius of your last known position. If you've made no course corrections since your last known position then you can narrow it further(dependent upon how far you are from the nearest gravity well).
Signposts Deploy navigational buoys with unique signals

This is known as dead reckoning navigation, and was the primary method of finding a boats position before the advent of GPS. You can find your position from scratch using a sextant, as long as you have accurate time, (taking elevations from the sun, moon and known stars), but it is much easier if you know approximately where you are from your last position.

In space this would probably be much more accurate, as long as the local gravity fields and solar-winds are mapped, because there is no unpredictable current/weather to throw you off course.

Just though of another point: If you are travelling a relativistic speeds (near light-speed), what can be considered 'accurate' time, i.e. what time frame are you navigating relative to. Since the passage of time is affected by your speed.
And, for that matter, you can't just calculate your position from scratch, you must find your time as well, as the two are inter-related.

SwiftCoder

OK, assuming you are headed straight through space at constant, but unknown, velocity, and have a camera and timer with perfect precision ( so you can get the size of a star and the current time down to the nth decimal place), you won't be able to calculate where you are or how far you've traveled. You would be able to calculate how far you have gone in relation to the distance to the star. Now, you would be able to calculate your position given 3 points of reference ( like 3 nearby stars that have had their position measured). You could measure the ratio of their percieved height vs. their actual height, and using the formula (don't have it right at this moment) that gives the perspective height of an object over distance, you can tell how far you are from each of the stars. Given that, you can pinpoint your position in space. Do it again, some time later, and you can get your velocity. Using this velocity and the perceived height change of the star you are trying to detect the distance to, you can calculate the actual height of that star, and from this you can calculate your distance to it.

Whew!

That wont work because there will be no perceptible difference in the position of the stars. Nearly 0 parallax.

Even on earth with massive high-resolution telescopes, measuring the positions of stars while at opposite sides of our orbit, we cannot do this with any accuracy. (with a few exceptions AFAIK).

I do not think this problem is solvable simply by looking at pictures.

An easier way would be to use a set of gryoscopes, measuring changes in the space-crafts acceleration along all axis. No images required.

Will

If you go with the idea of using a spectrograph instead of a simple camera, and assuming you can identify (or at least classify) the stars you can see, then it would presumably be possible to reckon your speed by measuring the blue shift of the stars in front of you. That's got to be better than trying to measure parallax.