The Validation of the Weight Function in the Leading-Edge-Derivative Path Delay Estimator for Space-Based GNSS-R Altimetry

Abstract

Global Navigation Satellite System Reflectometry (GNSS-R) altimetry uses GNSS-reflected signals off a water body to measure the height of the reflecting surface. The maximum value of the leading-edge derivative (LED) is an important path delay estimator in GNSS-R altimetry. The LED assumes that the weight function representing the power contribution per unit delay is monotonically decreasing with delay. This article focuses on the validation of the LED in space-based GNSS-R altimetry. Two problems of the weight function were studied. First, the monotonicity condition that the weight function requires to meet was theoretically analyzed, reaching the conclusion that the weight function needs to be monotonically nonincreasing. Second, whether the weight function could meet the monotonicity condition was simulated using the orbits of the COSMIC, GRACE, and GPS satellites, and the antenna gain map of the TechDemoSat-1 (TDS-1) mission. Results showed that the monotonicity of the weight function is largely dominated by Doppler, and meets the monotonicity condition because over 97% events decrease with delay. Antenna gain is the only factor that may disobey the monotonicity condition, but has no significant impact on the monotonicity of the weight function for this article. Therefore, the LED is valid for space-based GNSS-R altimetry as studied in this article.