  We introduce a new method to perform preliminary orbit determination for
space debris on low Earth orbits (LEO). This method works with tracks of radar
observations: each track is composed by $n\ge 4$ topocentric position vectors
per pass of the satellite, taken at very short time intervals. We assume very
accurate values for the range $\rho$, while the angular positions (i.e. the
line of sight, given by the pointing of the antenna) are less accurate. We wish
to correct the errors in the angular positions already in the computation of a
preliminary orbit. With the information contained in a pair of radar tracks,
using the laws of the two-body dynamics, we can write 8 equations in 8
unknowns. The unknowns are the components of the topocentric velocity
orthogonal to the line of sight at the two mean epochs of the tracks, and the
corrections $\Delta$ to be applied to the angular positions. We take advantage
of the fact that the components of $\Delta$ are typically small. We show the
results of some tests, performed with simulated observations, and compare this
algorithm with Gibbs' method and the Keplerian integrals method.
