*Technical Note* **Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation**

**Jack Winkelried 1, Christopher Ruf 1,\* and Scott Gleason <sup>2</sup>**


**Abstract:** Using large constellations of smallsats, mission designers can improve sampling density and coverage. We develop performance metrics that characterize key sampling properties for applications in numerical weather prediction and optimize orbit design parameters of the constellation with respect to those metrics. Orbits are defined by a set of Keplerian elements, and the relationship between those elements and the spatial and temporal coverage metrics are examined in order to maximize global and zonal (latitude-dependent) coverage. Additional optimization is performed by dividing a constellation into multiple orbit planes. An iterative method can be applied to this design process to compare the performance of current and previous designs. The main objective of this work is the design of optimized configurations of satellites in low Earth orbiting constellations to maximize the spatial and temporal sampling and coverage provided by its sensors. The key innovations developed are a new cost function which measures the temporal sampling properties of a satellite constellation, and the use of it together with existing cost functions for spatial sampling to design satellite constellations that optimize performance with respect to both performance metrics.

**Keywords:** constellation design; CYGNSS; GNSS reflectometry; SpOCK
