We present a novel angular fingerprinting algorithm for detecting changes in
the direction of rotation of a target with a monostatic, stationary sonar
platform. Unlike other approaches, we assume that the target's centroid is
stationary, and exploit doppler multipath signals to resolve the otherwise
unavoidable ambiguities that arise. Since the algorithm is based on an
underlying differential topological theory, it is highly robust to distortions
in the collected data.
This article surveys the Euler calculus - an integral calculus based on Euler
characteristic - and its applications to data, sensing, networks, and imaging.
We introduce the Andre-Quillen cohomology of lambda-rings and Psi-rings, this
is different to the lambda-ring cohomology defined by Yau in 2005. We show that
there is a natural transformation connecting the cohomology of the K-theory of
spheres to the homotopy groups of spheres.