Cramér-Rao Bound Study of Multiple Scattering Effects in Target Localization

The target position information contained in scattering data is explored in the context of the scalar Helmholtz operator for the basic twopoint scatterer system by means of the statistical estimation framework of the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased position estimation. The CRB results are derived for the exact multiple scattering model and, for reference, also for the single scattering or first Born approximation model applicable to weak scatterers. The roles of the sensing configuration and the scattering parameters in target localization are analyzed. Blind spot conditions under which target localization is impossible are derived and discussed in detail for both the exact and approximate models. It is shown that the sets of sensing configuration and scattering parameters for which localization is impeded are different but equivalent (they have the same size) under the exact multiple scattering model and the Born approximation. Necessary and sufficient conditions for multiple scattering to be useful or detrimental to target localization are derived. Numerical results are given, addressing both single and multiple observation data, which illustrate the dependence of target position estimability on sensing configuration and scattering parameters, as well as the role of multiple scattering in enhancing or diminishing target localizability relative to the baseline provided by the Born approximation.