Saturn is a big target. But it is very far away. How does NASA get a probe like Cassini-Huygens there with any degree of hope that it just isn’t going to head off on it’s own wayward way?
I assume Cassini-Huygens was capable of fine-tuning its trajectory (and certainly capable of slowing), but also that this is controlled from Earth. How do the Earthlings know the position and direction of the probe with sufficient accuracy in order to be able to drop a lander on Titan? Could the probe track its own position accurately enough (and if so, how?), or was it able to be tracked from back here? An inquiring, if incoherent, mind wants to know everything.
They use very precise computer models of: the propulsion, the control loop, and the sensors (on and off board).
At any given moment, they have a precise estimate of the vehicle’s location and velocity based on past sensor readings. Almost always control is done via timed commands; i.e., do these things at a certain time in the future. The models are used to both predict what the commands will do and to determine what the commands should be. As the commands are executed, the sensors are used to update the current location/velocity. Follow-up commands do any adjustments, if needed.
As computers become more powerful, more modeling/prediction is done on-board rather than at mission control. Eventually, vehicles will become very autonomous, with only high level directions given from base.
As for the particular sensors used, I’m not sure. Earth-based radar can work for things near earth, but I think most probes are too small/far. I’d guess star-based navigation could work for orientation, and communication timing could give you distance from Earth.
Jupiter is about 460 million miles from Earth. The speed of light (or radio signals) is about 186,000 miles per second. My math shows a 1-way signal taking about 41 minutes to reach the probe.