**1. Introduction**

The proliferation of smallsats and the small but highly capable scientific sensors on them have ushered in a new era of Earth remote sensing from space. Technology development lifecycles have been shortened, new and improved sensors can reach space more quickly, both launch vehicle and satellite costs have been reduced dramatically, and it is now both possible and affordable to consider flying large constellations of remote sensing instruments [1]. Notably, large constellations of smallsats in low Earth orbit have the potential to significantly improve upon the spatial and temporal sampling densities provided by a single traditional large satellite [2]. The improvement in sampling density with number of spacecraft is generally intuitive—more of them spread out around the globe will tend to sample more places at the same time and to sample the same place more frequently. We consider here the optimization problems of:


The optimization is performed with respect to specific orbit parameters of the constellation, namely the number and orientation of orbit planes and the number of satellites in each plane. When quantifying the notion of sampling density, it is helpful to consider a specific type and design of remote sensing instrument. Our optimization study is performed with respect to a Global Navigation Satellite System Reflectometry (GNSS-R) sensor. These sensors are the receiver half of a bistatic radar system in which the transmitters are the

**Citation:** Winkelried, J.; Ruf, C.; Gleason, S. Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation. *Remote Sens.* **2023**, *15*, 333. https:// doi.org/10.3390/rs15020333

Academic Editor: Mehrez Zribi

Received: 21 November 2022 Revised: 22 December 2022 Accepted: 28 December 2022 Published: 5 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

existing constellation of navigation satellites, such as GPS and Galileo. Measurements of GNSS signals scattered back into space from the Earth surface contain information about a wide variety of scientifically valuable geophysical surface conditions [3–7]. The relevant instrument design parameters to be considered are the number of simultaneous GNSS surface reflections observed and the gain and field of view of the antenna through which the observations are made. The former design parameter affects the signal processing complexity and power requirement of the instrument, and the latter parameter affects the size and mass of the antenna. GNSS-R sensors are compatible with smallsats [8,9] and have been demonstrated to provide improved sampling density in small constellations [10], so are a natural type of measurement to consider for this study.

The satellite constellation design space being considered here is an extension of the point design used by the NASA CYGNSS mission [11]. Its constellation consists of 8 identical spacecraft spaced roughly equally around a single orbit plane at an altitude of ~525 km and an inclination angle of 35◦. Each CYGNSS spacecraft carries a GNSS-R sensor capable of measuring 4 simultaneous surface reflections.
