Preliminary inquiry on the linear relationship between the height of the station and the ground height error retrieved by GNSS-IR with low-cost smart electronic equipment

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) ground height retrieval technology is based on global navigation satellite system (GNSS) signal reflection, which can achieve efficient and high-precision ground retrieval. However, errors cannot be avoided. And whether there is a linear relationship between the height of the station and the error is unknown. This research uses Hi-Target geodetic GNSS receivers, smart phone devices (Honor 60) and smart tablet devices (Huawei MatePad Pro) to collect a total of 5 d data from DOY65 to DOY69 in 2023, with the station heights of 0.8 m, 1.0 m, 1.2 m, 1.4 m and 1.6 m, respectively. The experimental results show that each satellite can effectively establish a linear relationship between the inversion error and the station height, which can be used in the error compensation research of different station heights under the limitation that the height of reflector is between 0.8 m and 1.6 m. Simultaneously, the error is related to the influence of comprehensive factors such as reflector type, satellite number, and data-receiving equipment. Secondly, two clustering methods, k-means and k-media, are introduced to cluster a and b in the linear relationship y = ax + b of each satellite, and it is proved that the linear relationship between inversion error and station height is obviously related to ground reflection surface (plastic track and concrete ground). Finally, it is verified that the height measurement accuracy of low-cost smart electronic equipment (Root Mean Square Error (RMSE): 0.047 m and 0.042 m) is worse than that of GNSS (RMSE: 0.010 m), but it still has good measurement performance. All in all, this study provides an essential technical reference for the error compensation of different station heights and for the application of GNSS-IR with low-cost smart electronic equipment. Due to its low-cost advantage, it has great potential in developing other surface parameter inversion of GNSS-IR technology.