  The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep
space to date. However, while at heliocentric distance of $\sim$ 20--70 AU, the
accuracies of their orbit reconstructions were limited by a small, anomalous,
Doppler frequency drift. This drift can be interpreted as a sunward constant
acceleration of $a_P = (8.74 \pm 1.33)\times 10^{-8}$ cm/s$^2$ which is now
commonly known as the Pioneer anomaly. Here we discuss the Pioneer anomaly and
present the next steps towards understanding of its origin. They are: 1)
Analysis of the entire set of existing Pioneer 10 and 11 data, obtained from
launch to the last telemetry received from Pioneer 10, on 27 April 2002, when
it was at a heliocentric distance of 80 AU. This data could yield critical new
information about the anomaly. If the anomaly is confirmed, 2) Development of
an instrumental package to be operated on a deep space mission to provide an
independent confirmation on the anomaly. If further confirmed, 3) Development
of a deep-space experiment to explore the Pioneer anomaly in a dedicated
mission with an accuracy for acceleration resolution at the level of $10^{-10}$
cm/s$^2$ in the extremely low frequency range. In Appendices we give a summary
of the Pioneer anomaly's characteristics, outline in more detail the steps
needed to perform an analysis of the entire Pioneer data set, and also discuss
the possibility of extracting some useful information from the Cassini mission
cruise data.
