Particle MCMC for Bayesian Microwave Control

P Minvielle,P Del Moral,F Caron,A Todeschini

doi:10.1088/1742-6596/542/1/012007

Abstract

We consider the problem of local radioelectric property estimation from global electromagnetic scattering measurements. This challenging ill-posed high dimensional inverse problem can be explored by intensive computations of a parallel Maxwell solver on a petaflopic supercomputer. Then, it is shown how Bayesian inference can be perfomed with a Particle Marginal Metropolis-Hastings (PMMH) approach, which includes a Rao-Blackwellised Sequential Monte Carlo algorithm with interacting Kalman filters. Material properties, including a multiple components "Debye relaxation"/"Lorenzian resonant" material model, are estimated; it is illustrated on synthetic data. Eventually, we propose different ways to deal with higher dimensional problems, from parallelization to the original introduction of efficient sequential data assimilation techniques, widely used in weather forecasting, oceanography, geophysics, etc.

Highlights

Unlike usual electromagnetic (EM) material characterization techniques [1], the microwave control problem involves to determine or check radioelectric properties of materials that are assembled and placed on the full-scaled object or system, from global scattering measurements (Radar Cross Section) [2].An axisymmetrical object or mock-up is illuminated by a monostatic radar that fulfills to a certain extent directivity and far-field conditions [3]
It illuminates the object at a given incidence with a quasi-planar monochromatic continuous wave (CW) of frequency f, the object backscatters a CW to the radar at the same frequency
Various complex scattering coefficients S are measured at different wave frequencies (f ∈ {f1, f2, · · ·, fKf }, for Kf successive discrete frequencies) from a SFCW (Stepped Frequency Continuous Wave) burst, at different incidence angles (θ ∈ {θ1, θ2, · · ·, θKθ }, for Kθ different incidence angles) where the object is rotated with a motorized rotating support, at different transmitted/received linear polarizations 1

Summary

Introduction

Unlike usual electromagnetic (EM) material characterization techniques [1], the microwave control problem involves to determine or check radioelectric properties (i.e. relative dielectric permittivity and magnetic permeability) of materials that are assembled and placed on the full-scaled object or system, from global scattering measurements (Radar Cross Section) [2]. The forward scattering model based on the resolution of Maxwell’s equations can determine the scattering coefficients, given the EM properties, the object geometry and acquisition conditions (i.e. wave frequency, incidence, etc.) It lies in the resolution of Maxwell’s equations, partial derivative equations that represent the electromagnetic scattering problem of an inhomogeneous obstacle. A Bayesian inference approach, based on ”particle MCMC”, is developed It can perform estimation of material properties and determine a multiple components (Debye relaxation/Lorenzian resonant) material model. The parametric material model g(fk, Ψ) depends on the frequency, where Ψ is the associated unknown hyperparameter It is a sum of Debye relaxation/Lorenzian resonant terms (see [5] for details).The deviation (from model) ∆xk can be modeled as an AutoRegressive AR(1) model given frequential correlation ρk (modelled by a Markov process related to a random walk): ∆x1 ∼ N (0, P1) and ∆xk+1 = Mρk · ∆xk + wk, where wk: Gaussian noise (E(wk) = 0). Another way hereinafter developed is to introduce high-dimension oriented adaptations and faster approximations

High dimension adaptation

Conclusion