First off, plus/minus a few billion kilometers in any direction actually isn't that terrible, particularly if you have FTL and/or are already dealing with interstellar distances. For comparison, that is on the same order as the distance from the Sun to [Neptune](https://en.wikipedia.org/wiki/Neptune) (Neptune's [semi-major axis](https://en.wikipedia.org/wiki/Semi-major_axis), the diameter between the points farthest from each other in its orbit straight across its orbital plane, is about 4.5 Tm, which is squarely in that range). In other words, metaphorically speaking, it's clearly enough to end up in the correct neighborhood, if not at the correct house.

That said, if you want something better, don't use ordinary stars to try to triangulate your position; **use pulsars.** [Pulsars](https://en.wikipedia.org/wiki/Pulsar) abound in our galaxy (within our immediate neighborhood, out to 300 parsec, we know of [eleven pulsars](https://en.wikipedia.org/wiki/Pulsar#Significant_pulsars)), many have highly specific (down to fractions of a millisecond) periods and pulse lengths, and

> Certain types of pulsars rival atomic clocks in their accuracy in keeping time.

By measuring the angles (you don't need to measure distances to triangulate your position) to a set of pulsars, and measuring their period and pulse length to identify each one, you can use the same principles as used in GPS or ordinary triangulation to determine your position in 3D space to a high degree of accuracy. It stands to reason that the major limiting factor would likely be your ability to accurately measure the angle to a specific pulsar without a platform plane change (changing the attitude of your spacecraft), as well as possibly the accuracy of the on-board data on the location of the pulsars.

The angle to a pulsar could be measured using either optical or radio receivers. With enough directional selectivity (which basically means a large enough antenna relative to the wave length of interest), a sensitive receiver and the capability to measure passage of time to a high degree of accuracy, you can get a sufficiently good idea of the angles to each specific pulsar. This is similar to the early work that led to the discovery of pulsars as radio frequency emitters, and which was awarded a Nobel Prize in physics in 1974, except you wouldn't be looking around at random.

In fact, the reverse has already been done: [the Voyager Golden Records as well as the Pioneer plaques used pulsars as a way of describing the location of the solar system](https://en.wikipedia.org/wiki/Pulsar#Maps) to any potential extraterrestrial intelligent beings that may come across the probes at some time in the future.

By first making a series of shorter trips to map the neighborhood (measuring the angles to pulsars for the purpose of later reference), you could easily make a sort of map that can later be used to determine your position based on the angles from your spacecraft to a handful of pulsars.

Compare also [How might Earth's location be referenced in stellar terms?](https://space.stackexchange.com/q/22383/415) on our sister site Space Exploration.