The study established a theoretical relation between weighted position dilution of precision (WPDOP) and standard deviation (STD) of positioning error ( $\epsilon /\sigma _{R})$ derived by linear Kalman filter (KF). The obtained results exposed a rectangular hyperbolic relationship of WPDOP and STD of error. The RTK Drone data were collected around 50 min of interval (07:37 to 08:28 A.M.) on May 12, 2021, with respect to the base station located at 13.841°N; 100.288°E over Thailand region, and a numerical test has been carried out to demonstrate the proposed algorithm. The simulation results verified the theoretical hyperbolic relationship with the distinct flatness of the curve at the base and drone receiver. This different flatness from the experiments was anticipated because of the position errors for the highly nonlinear dynamics motion of the drone receiver while the base receiver is fixed at one location.

中文翻译：

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加权 PDOP 对 RTK 无人机数据线性卡尔曼滤波器性能的影响

该研究建立了加权位置精度稀释（WPDOP）与定位误差标准差（STD）之间的理论关系（ $\epsilon /\sigma _{R})$由线性卡尔曼滤波器 (KF) 导出。所得结果揭示了 WPDOP 和 STD 误差的矩形双曲线关系。RTK Drone 数据是在 2021 年 5 月 12 日大约 50 分钟间隔（07:37 到 08:28 AM）收集的，相对于位于 13.841°N 的基站；泰国地区上空 100.288°E，并进行了数值测试以演示所提出的算法。仿真结果验证了理论双曲线关系与基地和无人机接收器处曲线的明显平坦度。这种与实验不同的平坦度是预期的，因为无人机接收器的高度非线性动态运动的位置误差，而基地接收器固定在一个位置。