A Cramér Rao Based Study of 2-D Fields Retrieval By Measurements From a Random Sensor Network

In this work we present a theoretical study on the performance of retrieving a 2-D field represented as a superposition of B-Spline 2-D patches, using measurements from sensors randomly located in the field. We considered 3 types of sensors: point-projection sensors, line-projection sensors, and surface-projection sensors. We compare the achievable retrieval performance using the different types of sensors, while keeping their nominal locations the same. The non-parametric modeling of the field allows us to present close-form expressions for the Cramér-Rao lower bound (CRLB) on the estimation errors of the field's parameters, which indicate on the best possible performance, independent on the mapping algorithm used. The comparison of the CRLB using different types of sensors indicates on the best sampling strategy. The work was motivated by the problem of rain retrieval using either rain gauges (point-projection sensors) or Commercial Microwave Links - CMLs (line projection sensors). Surface projection sensors can represent CMLs sampling a moving rain field. The results are applied for the problem of estimating the accumulated rain over a given area.