**3. Experiment and Results**

*3.1. Experimental Technical Scheme*

Figure 5 shows the flow chart of the SMC retrieval technique used in this study. The technical route we followed can be divided into three parts: (1) We first preprocessed the GNSS-IR data: the carrier phase, pseudorange observation data, azimuth, elevation angle, and epoch extraction. We extracted other data parameters from the observation (OBS) file and navigation (NAV) file collected by GNSS receivers. (2) We

determined the initial values of phase delay and amplitude attenuation factor, then constructed the dual-frequency carrier phase linear combination multipath error model and dual-frequency pseudorange multipath error model, and then calculated the multipath errors of the two models separately. We fit the ionospheric linear combination (L4), namely the simple difference between *L*<sup>1</sup> and *L*<sup>2</sup> (L4 = *L*<sup>1</sup> − *L*2), with a high order to obtain L4\_IF. We used a 10-degree polynomial fitting. (3) By constructing the error equation, we solved the delay phase. Then, we performed the delayed phase combination representing the variation trend in SMC and the retrieval SMC analysis. (4) Taking the multipath error of the five epochs before and after as the observation value, we calculated the dual-frequency pseudorange multipath error and the dual-frequency carrier-phase combination error and determined the initial phase and the amplitude attenuation factor (AAF). According to Equation (5), we established the model error equation. We used the Lomb–Scargle periodogram (LSP) and least-squares adjustment method to solve the delay phase. In solving the delay phase, the Pearson correlation coefficient (R) between the phase delay and SMC was used to characterize the changing trend between the delay phase and soil moisture.

**Figure 5.** The technical process we followed for multisatellite dual-frequency combined multipath error SMC retrieval. Note: RTKLIB is an open-source program package for standard and precise positioning with GNSS (global navigation satellite system). RTKLIB consists of a portable program library and several APs (application programs) utilizing the library (http://www.rtklib.com/) (accessed on 10 February 2022).
