Geographical distribution of global navigation satellite system (GNSS) ground monitoring stations affects the accuracy of satellite orbit, earth rotation parameters (ERP), and real-time satellite clock offset determination. The geometric dilution of precision (GDOP) is an important metric used to measure the uniformity of the stations distribution. However, it is difficult to find the optimal configuration with the lowest GDOP when taking the 71% ocean limitation into account, because the ground stations are hardly uniformly distributed on the whole of the Earth surface. The station distribution geometry needs to be optimized and besides the stability and observational quality of the stations should also be taken into account. Based on these considerations, a method of configuring global station tracking networks based on grid control probabilities is proposed to generate optimal configurations that approximately have the minimum GDOP. A random optimization algorithm method is proposed to perform the station selection. It is shown that an optimal subset of the total stations can be obtained in limited iterations by assigning selecting probabilities for the global stations and performing a Monte Carlo sampling. By applying the proposed algorithm for observation data of 201 International GNSS Service (IGS) stations for 3 consecutive days, an experiment of ultra-rapid orbit determination and real-time clock offset estimation is conducted. The distribution effects of stations on the products accuracy are analyzed. It shows that (1) the accuracies of GNSS ultra-rapid observed and predicted orbits and real-time clock offset achieved using the proposed algorithm are higher than those achieved with the traditional method having the drawbacks of lacking evaluation indicators and being time-consuming, corresponding to the improvements 17.15%, 19.30%, and 31.55%, respectively. Only using 30 stations selected by the proposed method, the accuracies achieved reach 2.01 cm (RMS), 4.93 cm (RMS), and 0.20 ns (STD), respectively. Using 60 stations, the accuracies are 1.47 cm, 3.50 cm, and 0.17 ns, respectively. (2) With the increasing number of stations, the accuracies of the Global Positioning System (GPS) orbit and clock offset improve continuously, but more than 60 stations, the improvement on the orbit determination becomes more gradual, while for more than 30 stations, there is no appreciable increase in the accuracy of the real-time clock offset.
Ground surface monitoring (GSM) points collect information for mining surface subsidence monitoring and environmental governance. However, GSM points submerge in high groundwater mining areas, preventing the collection of monitoring data. The application of machine learning (ML) algorithms to subsidence prediction ignores the uncertainty and irregularity in subsidence changes. Thus, an innovative GSM point information prediction model, which improves the multikernel support vector machine (GA-MK-SVM) using chaos residual theory commonly used for capturing GSM point information, is proposed. The mean relative errors (MREs) between the predicted and observed results of GA-SVM and GA-MK-SVM were 8.2% and 6.1% during active periods, respectively. The GA-MK-SVM also performed better than the GA-SVM during stable periods. The residual error accumulates as the ML algorithms progress, resulting in imprecise predictions of the GSM points. Thus, the GA-MK-SVM model was improved using chaotic theory (Chaos-GA-MK-SVM), with MREs of 5.0% and 0.9% during the active and stable periods, respectively. The accuracy of the proposed model was improved by 1.1% and 3.2% compared with the unimproved GA-MK-SVM, respectively. The proposed approach provides practical GSM point information for mining subsidence studies and governance in high groundwater mines.
Real-time solution of Global Navigation Satellite System (GNSS) epoch-differenced ionospheric delay (DID) is of great significance for real-time cycle slip detection and repair of multi-GNSS dual-frequency or trifrequency undifferenced measurements under high ionospheric activity. We construct a dynamic model of DID and perform a real-time estimate of the noise level of DID based on estimating the variance component. The estimated and predicted values of DID are obtained by designing a new adaptive Kalman filter algorithm with colored noise. Combining the predicted value and the detection method for cycle slips for Melbourne-Wübbena (MW) and Geometry-Free (GF) combination and taking into account the correlation between the predicted value and the carrier signal, we estimate the cycle slip, N2, on the second frequency of the carrier signal. The prediction and estimate of DID and detection and repair of dual-frequency cycle slip of multisystem undifferenced phase observations are measured with the GNSS multisystem observational data at different sampling rates (30 s, 15 s, 10 s, and 1 s). The results show that the DID model constructed in this paper is correct. The predicted value of DID has a high accuracy, which can effectively assist in dual-frequency cycle slip detection and repair. (1) The obtained predicted values, the estimated value, and the difference value between the two values of DID are less than 1.2 cm (STD), 1.2 cm (STD), and 0.6 cm (STD), respectively; (2) the precisions of the detection of cycle slip for MW, GF, and N2 are less than 0.083 cycles (STD), 0.4 cm (STD), and 0.071 cycles (STD), respectively; (3) with the obtained predicted value of DID to aid the detection and repair of cycle slip in GNSS double-frequency signals, a success rate of 100% can be reached.
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