The Voyager 1 took one last photograph in 1990 and after that, the camera equipment was shut off for power saving. However, the estimates of where the photo was taken in space vary by many hundreds of thousand of miles - not an exact point in space. The Voyager probe is old, however, and I'm wondering, how well can we estimate a point in 3D space today? Would a spacecraft that was built today be able to say exactly where it was when it took a picture?
The precision of position of the space probes depends mostly on the amount of money spent on the navigation sensors and the nav equipment.
Today at any distance of deep space we can invest in X ray pulsar based navigation, for which one test system has been launched on Neutron Star Interior Composition Explorer, NICER. it gives 5km precision using pulsar periods and requires lighter and smaller antenna to capture the x rays.
Other advanced equipments are self contained on-board nav systems made of sensors and celestial models that can self correct the course using optical measures and an onboard sky map of given precision. They are used together with a fixed space coordinate system with origin on the solar barycenter and fixed relative to the constellations.
Prior to 2017, Deep space position was imprecise, and fine control was done relative to the approached object with cameras, where the approached object is unkown to several km/ 100ds of km. it consists of 1/velocity 2/position 3/movement vector 4/space object map... all of those factors are being improved massively all the time, and the precision only depends on the nav equipment budget.
Radio Doppler measurement of the shifted radio signal gives very good precision of radial movement from the terrestrial receivers, to within 1 mm/s, and two radio receivers situated around the planet can determine the movement vector fairly well.
The position is more difficult, for example Cassini's position was known relative to Saturn by 1km and Saturn was know relative to earth by 100km. (after Cassini this was refined to 2km relative to us).
They are checking all kinds of new equipment to increase precision, for example Laser doppler between satellites using optical costas loops and helium-neon laser and other precise wavelengths. A test of optical doppler was done on a previous moon mission to improve positioning and data coms up to a distance of 250,000 miles (>earth-moon distance)
If voyager used a 30 megapixel camera and a very good zoom+moving camera, it could determine it's position many many times more finely than the 1970's version. The sky map is better too. the radio Doppler is still used today but is more precise, and the optical Doppler doesn't go that far. It's position relative to visited objects was much higher resolution than the position of the objects visited.
Current interplanetary spacecraft have no way to determine their own position. Their position is measured from Earth using e.g. the DSN. This gives a position that is very accurate on the Earth-spacecraft axis (~1 m resolution), but has less resolution in the other two axes.
Systems are being investigated to support autonomous positioning, but none of them are in operational use yet.