INHERENT LIMITATIONS OF PARAMETER ESTIMATION OF A TEMPO-SPATIAL FIELD USING AN ARRAY OF HETEROGENEOUS SENSORS

Based on an analysis of the Fisher Information Matrix (FIM), this paper presents a study of the inherent limitations in parameter estimation of a localized tempo-spatial field, characterized by a parametric model. The problem is motivated by the need to retrieve rain fields in rural areas, where sudden flash floods are a life-threatening hazard. We first identify the minimum number of sensors necessary for estimating all of the unknown parameters, where two types of sensors are considered: time projection sensors - characterized as a point in space, line-projection in time (such as rain gauges), and spatial projection sensors - characterized as a point in time, line projection in space (such as wireless microwave links). We show that a single spatial projection sensor with one or more sensor of any type are required. Then, we show that the Cramer-Rao bound of each of the unknown parameters is characterized by a U-shape curve as a function of the observation period. By studying the condition number of the FIM we identify the sufficient conditions for the estimation errors to be small (i.e., at the bottom of the U-shape). We demonstrate the results of our analysis with different combinations of sensors.