  The task of position and velocity estimation of a moving transmitter (with
either a known or unknown frequency) is a common problem arising in many
different application domains. Based on the Doppler effect, this work presents
a direct solution using only the frequency measured by a multitude of receivers
with a known state. A natural rewriting of the problem as a system of
polynomial equations allows for the use of homotopy continuation to find the
global solution without any a priori information about the frequency source. We
show that the data from six or seven receivers is sufficient in case of known
or unknown frequency, respectively. After a brief development of the
mathematics, two simple examples are provided: (1) position and velocity
estimation of a vocalizing dolphin emitting an acoustic signal and (2) initial
orbit determination of a satellite emitting an electromagnetic signal.
