The position and velocity of crafts is computed almost always on Earth. We use Doppler, radio interferometry and a host of other physics and maths tricks to get the position and velocity. Most of these procedures use the radio signals that these crafts send back to Earth.
The computers we send in space are programmed purposefully for the science mission and it would be far to wasteful to load them up with the heavy computations needed for obtaining a celestial navigation fix.
When these ships have cameras they are usually protected with entry shields and/or folded away during the cruise stage.
If a ship has navigation cameras, pictures are taken of planets and stars (like you theorized) but they are sent back to Earth for processing. Due to the limitations of imaging sensors if you want to see the planet’s edge the stars don’t show up. If you want to see the stars the planet is overexposed and looks like a white orb. Back on earth that can be processed and a precise fix can be calculated.
Thanks. That gives me a lot to think about.
I can see where precise values for speed and acceleration on a line directly away from the earth can be calculated.
One might use transit time of the signal to get absolute distance from the earth, for example.
I'm less clear on how speed and acceleration can be accurately determined at right angles from the line directly away from the earth.
Does the radio interferometry involve comparing the phase of signals received at different stations widely separated on earth, for example.
Is the determination of position and velocity at right angles to the line directly away from earth basically equivalent to viewing a picture of the sky and determining the apparent position of the craft relative to other objects in the field of view?
I think my difficulty may just stem from the possibility that the Doppler and similar techniques are so precise, that I am expecting similar precision for the apparent position in the sky, when perhaps such precision just isn't necessary to do the job.