  The topics of source seeking and Newton-based extremum seeking have
flourished, independently, but never combined. We present the first
Newton-based source seeking algorithm. The algorithm employs forward velocity
tuning, as in the very first source seeker for the unicycle, and incorporates
an additional Riccati filter for inverting the Hessian inverse and feeding it
into the demodulation signal. Using second-order Lie bracket averaging, we
prove convergence to the source at a rate that is independent of the unknown
Hessian of the map. The result is semiglobal and practical, for a map that is
quadratic in the distance from the source. The paper presents a theory and
simulations, which show advantage of the Newton-based over the gradient-based
source seeking.
