**1. Introduction**

Soil moisture content (SMC) is the physical quantity that characterizes the degree of soil wetting and drying. As an indispensable environmental factor on the surface, SMC plays an active role in weather forecast, climate research, slope stability prediction, and accurate prediction of flood disasters [1–4]. Global Navigation Satellite System interferometric reflection (GNSS-IR) is a new microwave remote sensing technology that mainly uses the interference effect generated by the direct and surface reflection signals obtained at the GNSS receiver to invert the surface parameters according to the characteristics of the interference signals [5–9].

**Citation:** Nie, S.; Wang, Y.; Tu, J.; Li, P.; Xu, J.; Li, N.; Wang, M.; Huang, D.; Song, J. Retrieval of Soil Moisture Content Based on Multisatellite Dual-Frequency Combination Multipath Errors. *Remote Sens.* **2022**, *14*, 3193. https://doi.org/10.3390/ rs14133193

Academic Editors: Serdjo Kos, José Fernández and Juan F. Prieto

Received: 28 April 2022 Accepted: 1 July 2022 Published: 3 July 2022

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In recent years, many scholars have made remarkable achievements in soil moisture retrieval using GNSS-IR technology. Larson et al. observed that the ground-reflected signal captured by a geodetic-quality Global Positioning System (GPS) antenna is sensitive to soil moisture, so the GPS signals can be used to sense soil moisture. They first proposed using GPS SNR retrieval of soil moisture, confirming the feasibility of SNR data retrieval [10–12]. Zhang et al. used Bei Dou Navigation Satellite System (BDS) and GPS SNR to invert volumetric soil moisture (VSM) changes and wheat growth, and compared the results with the original observation values. The experimental results showed that GPS L1/L2 and BDS B1/B2/B3 frequencies in VSM retrieval are consistent with in situ VSM [13]. Liang et al. estimated the near-surface soil moisture using SNR data, corrected the original phase by obtaining the amplitude and phase of the SNR interferogram, weakened the influence on vegetation change, and established a genetic algorithm back propagation neural network (BPNN) model for soil moisture retrieval. Their experiments showed that the correlation between retrieval results and soil moisture was substantially improved [14]. Han et al. proposed a semiempirical signal-to-noise ratio model as a curve-fitting model to reconstruct direct and reflected signals from SNR data and extract frequency and phase information. The results showed that the soil moisture retrieval effect of the reconstructed signal, with a height angle of 5–15◦, was more accurate, and the fitting quality increased by about 45% [15].

Jin et al. used SNR data to solve the different frequency phases of the SNR sequence by spectrum analysis and the least-squares method and fused the dual-frequency phase observation values with the entropy method. Finally, the fusion results were combined with the measured soil moisture to establish an empirical model to retrieve soil moisture. The results showed that the dual-frequency fusion method can effectively improve retrieval accuracy [16]. Ran et al. used the detrended signal-to-noise ratio (DSNR) sequence and proposed an arc-editing method to edit the DSNR sequence. Only the DSNR data with the typical interference mode chord waveform were retained, and the arc editing method of SMC retrieval was compared with the conventional method. The experimental results showed that the proposed method had higher SMC retrieval accuracy than the traditional method and could improve the retrieval accuracy of SMC in undulating terrain [17]. Han et al. proposed a method to reduce the impact of direct signal components by signal reconstruction and normalization according to the variation law of SNR. The results showed that under the high rough surface conditions, the normalized amplitude strongly correlated with in situ soil moisture. The quadratic model was used to invert soil moisture from the normalized amplitude, and the retrieval error was less than 0.085 cm<sup>3</sup> cm−<sup>3</sup> [18]. Li et al. proposed a new soil moisture estimation method based on SNR data. A solution to SNR AAF was constructed based on the relationship between the amplitude attenuation factor (AAF) of the signal-to-noise ratio in in situ observations and soil moisture. The results showed that the measured soil moisture value was in good agreement with the estimated soil moisture range of 0.35–0.45 cm<sup>3</sup> cm<sup>−</sup>3, and the RMSE was less than 0.012 cm3 cm−<sup>3</sup> [19].

Roussel et al. obtained the amplitude and phase from SNR data and proposed a Global Navigation Satellite System reflectometer interference pattern technique to estimate the temporal variation in soil moisture content around a single earth antenna. Satellite signal-to-noise ratio (SNR) observation data with two satellite altitude angles of 2–30◦ and 30–70◦ were used. The experimental results showed that the method could effectively invert soil moisture [20]. Yu et al. proposed a combined linear method for snow depth retrieval using the phase of GPS triple-frequency signals. This method is independent of geometric freedom and is not affected by the ionospheric delay. The results showed that the accuracy of snow depth retrieval based on triple-frequency multipath error and SNR was high [21]. Zhang et al. proposed two new SMC estimation methods: triple-frequency carrier phase (TRFCP) and triple-frequency pseudorange (TRFP). The experimental results showed that the phase delay estimated by the two methods strongly correlates with Plate boundary observation (PBO) SMC [22]. Shen et al. proposed a BDS Medium Earth Orbit (MEO) and Inclined Geosynchronous Satellite Orbit (IGSO) satellite multisatellite soil moisture retrieval method based on SNR observations. This method weakens the influence of environmental differences in different directions by considering the satellite repetition period. The experimental results showed that the estimation results of BDS IGSO and MEO soil moisture agreed with the in situ soil moisture fluctuation. They verified that the BDS MEO satellite could effectively capture sudden rainfall [23].

According to the above research results, most scholars have focused on analysing SNR data for GNSS-IR soil moisture retrieval. However, GNSS-IR soil moisture retrieval based on SNR observations has the following problems: SNR is useless for most GNSS users, as SNR does not always exist in the original GNSS file [9]; the performance of GNSS-IR with SNR as the system input depends, to a large extent, on the observation quality of SNR and whether the direct component (trend term) of SNR is successfully removed [21]. However, the actual SNR is often impure by abnormal noise, so the multipath SNR was obtained using a low-order polynomial to draw the trend term to characterize multipath information. Owing to the above two reasons, GNSS-IR performance based on SNR time series may be seriously inaccurate. At present, some scholars have used the triple-frequency signal combination for GNSS-IR snow depth detection and soil moisture retrieval, but the number of triple-frequency signal observation satellites is small, resulting in the time resolution of GNSS-IR retrieval of surface physical parameters being low. The duration of the signal-to-noise ratio for the effective satellite elevation angle is shorter, which is basically maintained at about 0.5–2 h, which is not conducive to enabling highly dynamic monitoring of soil moisture.

Based on the above problems, to compensate for the shortcomings of SNR observation, including too few triple-frequency signal satellites and low time resolution, by combining the current multimode and multifrequency development pattern of GNSS, GNSS can play a positive role in environmental monitoring. As such, GNSS-IR soil moisture retrieval based on multifrequency linear combination observation has not yet been studied. In this study, we constructed a soil moisture retrieval method based on multisatellite dual-frequency combined multipath error by constructing the dual-frequency pseudorange (DFP) and the dual-frequency carrier phase (L4 Ionosphere Free, L4\_IF) multipath error calculation model affected by deionosphericity. We selected the five epochs before and after the time point of the effective satellite period and used a total of eleven epoch data to construct the multipath error model and error equation. We solved the delay phase for soil moisture retrieval. We used Plate Boundary Observatory (PBO) P041 (Boulder, CO, USA) site data to verify the proposed method and further verified the method by using the soil moisture data of MFLE station close to P041 station, which effectively improves the time resolution of GNSS-IR soil moisture estimation. To realize the high dynamic monitoring of soil moisture, this paper uses the multipath error of fewer epochs to calculate the delay phase for SMC inversion. Because soil moisture is often affected by vegetation cover, soil temperature, air humidity and other factors, to better improve the inversion accuracy of GNSS-IR soil moisture, we use ULR, BPNN and RBFNN to construct soil moisture prediction models and evaluate the accuracy of each model.

### **2. Materials and Methods**
