On the Use of Adjoint Methods for Refractivity Estimation in the Troposphere

Abstract

This paper presents a preliminary study of a new inversion strategy combining the method of adjoint applied to the wide-angle parabolic equation and the method of splitstep wavelet for tropospheric refractivity estimation. Our main motivation is to use a gradient based optimization method to infer atmosphere from radio-frequency data, in an effort towards a real-time accurate refractivity-from-clutter system. The proposed adjoint formulation is validated with the method of finite differences. The validation setup is developed for inversion using a tomographic approach.

A Variational Adjoint Approach on Wide-Angle Parabolic Equation for Refractivity Inversion

“…We have proven that the inversion does not fail due to miscomputation of the gradient. Indeed, the gradients may indicate higher ill-posedness due to removal of the phase from synthetic data [54]. Therefore, we are interested in visualizing the extent of non-convexity in the inverse problem.…”

“…The adjoint method properly addresses the highdimensionality of the refractivity inversion for such modern detection systems and it is the backbone method on which our inversion strategy will be built. For this reason, its validation has received emphasis at the initial stage of development [54]. We attach importance to upgrade the forward model to tighten the control on inversion accuracy for this ill-posed inverse problem in real-world scenarios.…”

“…The problem ( 7) is difficult to solve accurately. The inversion results cannot be used for validating the quality of the work except for oversimplified cases (e.g., [54]). Therefore, it is necessary to perform a validation process starting from checking the gradient computation.…”

“…It has width of 5 m and emission frequency f s = 2 GHz at horizontal polarization. This setting yields a φ(z) profile with full shape, which is useful for validation [54]. The ground is accounted with the local image method [18] and a Hanning absorbing window is applied on the top of the domain.…”

A Multiscale Parametrization for Refractivity Estimation in the Troposphere

“…In this section, we validate the proposed methodology and apply it to the inversion of synthetically generated data. More details on the simulation and the validation can be found in [13].…”