Ionospheric Radio Beacon Signal Analysis and Parameter Estimation Using Automatic Differentiation

Abstract

Continuous wave signals from a network of high frequency (HF) beacons in Peru and other instruments are used to reconstruct the regional ionospheric electron number density in the volume surrounding the network. The continuous wave (CW) HF signals employ binary phase codes 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 is used to relate plasma number density to the observables. Plasma number density is parametrized in terms of a modified Chapman profile in the vertical and biquintic B‐splines in the horizontal. Sensitivity analysis is required both to model the ray amplitudes and to solve the two‐point boundary problem for each ray. Sensitivity analysis is performed here using reverse‐mode automatic differentiation. In particular, we use an LLVM compiler (Clang), the corresponding OpenMP library, and the Enzyme Automatic Differentiation Framework plugin to compute the sensitivity (gradients) of ray endpoints with respect to their initial bearings. The resulting algorithm exhibits no performance penalty compared to variational sensitivity analysis and is far simpler to implement.