Using Automatic Differentiation to Simplify Ionospheric Specification with Signals From a Network of HF Beacons
Jhassmin A. Aricoche, David Lee Hysell · 2025
A high-frequency (HF) beacon network has been deployed in Peru and another in Alaska. The (HF) beacons and other instruments like GPS and sounder receivers are used to reconstruct the ionospheric electron number density regionally. The continuous wave HF signals employ unquantized random phases code with pseudorandom noise (PRN) encoding, and the observables include propagation time or pseudorange, Doppler shift or beat carrier phase, and amplitude. A forward model based on geometric optics in an inhomogeneous, anisotropic, lossy plasma relates plasma number density to the observables. Plasma number density is parametrized with a modified Chapman profile in the vertical and biquintic B-splines in the horizontal. Sensitivity analysis is needed to model the ray amplitudes and solve the two-point boundary problem for each ray. We perform sensitivity analysis here with reverse-mode automatic differentiation. Specifically, we use an LLVM compiler (Clang), the corresponding OpenMP library, and the Enzyme Automatic Differentiation Framework plugin to compute ray endpoints' sensitivity (gradients) concerning initial bearings. The algorithm exhibits no performance penalty compared to variational sensitivity analysis and is relatively simple to implement.