Lower Bound Analysis of Parameter Estimation of Moving Field by Sensors in Random Locations

In this paper we present an analysis of the performance limits for retrieving a moving 2-D field propagating at a constant velocity. The field is modeled as a spline function, using a superposition of 2-D B-Spline patches. Inspired by near ground rain fields retrieval, measurements from two types of sensors are considered: point-projection sensors (rain gauges) and line-projection sensors (commercial microwave links), each with distinct spatial and temporal characteristics. We derive closed-form expressions for the Cramér-Rao lower bound (CRLB) on the estimation errors of the field's parameters, providing insights into the best possible performance, regardless of the mapping algorithm employed. In particular, the effect of side knowledge of the velocity of the field on the performance is exploited. The derived results are applied to the specific problem of estimating the accumulated rainfall over a defined area and time period.