  In this paper, we present a fast, lightweight odometry method that uses the
Doppler velocity measurements from a Frequency-Modulated Continuous-Wave (FMCW)
lidar without data association. FMCW lidar is a recently emerging technology
that enables per-return relative radial velocity measurements via the Doppler
effect. Since the Doppler measurement model is linear with respect to the
6-degrees-of-freedom (DOF) vehicle velocity, we can formulate a linear
continuous-time estimation problem for the velocity and numerically integrate
for the 6-DOF pose estimate afterward. The caveat is that angular velocity is
not observable with a single FMCW lidar. We address this limitation by also
incorporating the angular velocity measurements from a gyroscope. This results
in an extremely efficient odometry method that processes lidar frames at an
average wall-clock time of 5.64ms on a single thread, well below the 10Hz
operating rate of the lidar we tested. We show experimental results on
real-world driving sequences and compare against state-of-the-art Iterative
Closest Point (ICP)-based odometry methods, presenting a compelling trade-off
between accuracy and computation. We also present an algebraic observability
study, where we demonstrate in theory that the Doppler measurements from
multiple FMCW lidars are capable of observing all 6 degrees of freedom
(translational and angular velocity).
