Title says it all really: how accurately do they know where the Rosetta space vehicle is at any given time, and how do they know that?
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Rosetta is mainly tracked through radiometric means. They use 3 different methods: range, Doppler and ΔDOR. [2]
Range measurements are conducted by sending a "ping" radio transmission to the spacecraft, which then responds with a "pong". The time it takes for the spacecraft to respond, that is the reaction time of the onboard electronics, is precisely calibrated. The ground observer then can measure the time elapsed between ping and pong. That's the time it takes for the radio waves to propagate back and forth in space plus the calibrated reaction time. Radio waves travel with the speed of light which is precisely known. From this it can be calculated how far the spacecraft is in the line-of-sight direction.
Doppler measurement goes as follows: The spacecraft is transmitting on a known frequency. If it's velocity has a non-zero component along the line-of-sight direction, then the observer will measure in the received transmission in a slightly different frequency. This is called the Doppler effect, and can be used to determine speed with which the spacecraft is approaching or leaving.
∆DOR is best described by this quote from 1:
∆DOR requires two widely separated ground stations to measure the difference in the arrival time of the signal from both Rosetta and a directionally close-by extragalactic radio source (quasar) whose inertial direction is precisely known. It provides a direct measurement of one coordinate of Rosetta's position in the plane-of-sky which is a perfect complement to the line-of-sight Doppler and range measurements.
During the comet flybys and the 67P/Churyumov-Gerasimenko phase Rosetta utilizes its onboard cameras to better track its position relative to the comet nucleus. This is needed because even tough radiometric tracking provides a very accurate position estimate of the spacecraft relative to the solar system, the comets trajectories are not known with sufficient precision. [2][3]
The accuracy of the position estimation varies. When they make more measurements they gain a more precise picture. For example the Mars swing-by paper1 mentions that the altitude at closest approach was known with 3sigma uncertainty of 1.1 kilometer. In that paper Figure 8th provides an illuminating illustration on how the position estimation's accuracy evolved during the days around the swing-by due to frequent measurements.
References:
Rosetta Navigation at Its Mars Swing-By: http://issfd.org/ISSFD_2007/8-4.pdf
Preparations and Strategy for Navigation During Rosetta Comet Phase: http://issfd.org/ISSFD_2012/ISSFD23_IN2_2.pdf
Optical Measurements for the Flyby Navigation of Rosetta at Asteroid Steins: http://issfd.org/ISSFD_2009/AOCSII/Lauer.pdf
