Model Free Gravimetric Detection

In recent work [1], we introduced a new, linear-programming based method, for detecting underground features based on gravity measurements. The current paper takes this method one important step further, in that it makes it work under realistic conditions, where most of the physical characteristics of the environment are not known. In particular, the ADCS algorithm we introduce works when the following physical parameters are unknown: the spatial variability of the underground density, the amplitude of this variability, the number of the holes (assuming that there are only a few), the shape of the hole(s). The algorithm will construct a map of the unknown holes’ locations and shapes. We achieve this by reformulating our original compressed sensing (CS) which assumes knowledge of the mass density variability. In the new formulation the unknown variable is rescaled for a better balanced optimization problem, and the noise parameter of the problem is calculated based on the input data.