Estimating 3D displacement vectors from line-of-sight observations with application to MIMO-SAR

Displacements in typical monitoring applications occur in 3D but having sensors capable of measuring such 3D deformations with areal coverage is rare. One way could be to combine three or more line-of-sight measurements carried out from different locations at the same time and derive 3D displacement vectors. Automotive Multiple-Input-Multiple-Output Synthetic Aperture Radar (MIMO-SAR) systems are of interest for such monitoring applications as they can acquire line-of-sight displacement measurements with areal coverage and are associated with low cost and high flexibility. In this paper, we present a set of algorithms deriving 3D displacement vectors from line-of-sight displacement measurements while applying spatial and temporal least squares adjustments. We evaluated the algorithms on simulated data and tested them on experimentally acquired MIMO-SAR acquisitions. The results showed that especially spatial parametric and non-parametric least squares adjustments worked very well for typical displacements occurring in geomonitoring and structural monitoring (e.g. tilting, bending, oscillating, etc.). The simulations were confirmed by an experiment, where a corner cube was moved step-wise. The results show that acquisitions of off-the-shelf automotive-grade MIMO-SAR systems can be combined to derive 3D displacement vectors with high accuracy.