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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

Nowadays, GNSS (global navigation satellite systems) postprocessed and real-time precise satellite orbits and clock offsets, long-term and short-term Earth rotation parameters (ERP), interfrequency deviation parameters, and troposphere and ionosphere correction parameters, are produced using the observation data of ground monitoring stations to meet the needs of PNT (positioning navigation and timing) users. Usually we select a subset of well-distributed stations of high quality to obtain the products required by users. Dvorkin and Karutin [

The grid control method is widely used to obtain uniformly distributed global stations [

As to the importance of the GDOP metric, GDOP minimization has been widely concerned in the past [

A stochastic optimization method based on grid control probability proposed in this paper aims for quickly and automatically selecting the list of stations with dominant geometric distribution and station quality. It is believed that this method with potential high efficiency and optimization selection results can provide an optimized solution for the management of the over-size tracking station network (see for example

This paper first applies the grid method to the candidate stations to allocate the initial probabilities, and then, considering the quality factors of the stations, probabilities are reassigned to the candidate stations. A comprehensive indicator for measuring the uniformity of distribution of ground stations and the observation quality is introduced to justify the selected subset of stations. It is shown that the proposed approach can quickly and automatically select high quality and well-distributed stations, improving the accuracy of ultra-rapid orbit determination and real-time clock offset estimation and the calculation of ERP.

When the stations as known points are evenly distributed on the Earth surface, the GDOP at the geocenter can get the minimum [

The station-geocenter positioning configuration can be recorded as

Considering the GDOP minimization condition expressed in (_{i,k} or_{i,k} is the element of the vector _{i. }The condition (

As is well known, the geometry of the station distribution is only one of impact factors affecting the GNSS products, e.g., some of stations improve the geometric configuration obviously, but their quality may be poor, leading to bad GNSS products. For this, we further introduce the following weighted station-geocenter DOP as_{1} and_{2} are, respectively, the medians of all station variances and multipath errors.

In general, the WSDOP would lead to an overall indicator by combining the station geometry with the station quality factors, thereby an effectiveness indicator.

The station selection is performed to solve two problems: (1) model incompleteness, such as that due to system error (i.e., station stability or observation quality) and (2) compromise between the calculation cost and the accuracy (i.e., the fast positioning of low-performance terminals or fast automatic selection when a certain accuracy is guaranteed). However, the above SDOP or WSDOP minimization may face with various limitations and the NP problem, i.e., optimally selecting P points from N points. For this, we propose a probabilistic approach to search the optimal station configuration by minimizing WSDOP; that is,

Owing to the extremely uneven global distribution of the stations, the number of stations is different in each cell. At this time, it is generally necessary to comprehensively consider the position and quality of each station and to select the ideal orbital station configuration in each cell. To improve the stochastic optimization convergence ability and to avoid the selected stations being concentrated in a certain area, it is necessary to control the allocation probabilities of stations by the grid. On the basis of (

The method mainly considers the distribution of stations, and it is difficult to weigh the information of station stability and station observation quality at the same time. There are also many artificial control factors in the selection process. The factors usually refer to artificially determining the appropriate number of grid division by multiple grid scaling, and artificially selecting one station from multiple stations in each grid because of lacking corresponding evaluation indicators. Addressing these drawbacks, we propose a stochastic combinatorial optimization algorithm to obtain the optimal solution from the huge number of candidate configurations for all combinations. On the basis of the above problems, a method of station screening under the grid control probability is used, and the idea of probability statistics is introduced into the station selection. That is to say, on the basis of the grid method and by considering the data quality, stability, and geographical distribution of the station, each station is assigned a certain probability. A station is assigned a high probability when the stability and observation quality of the station are high. The probability allocation formula reads

_{j} is the probability of station

Taking all stations as the experimental population in each random sampling,

Experimental data for a total of 201 ground stations are downloaded from the IGS website. IGS has provided a high-precision tracking station coordinates in the SINEX (Software INdependent EXchange) format since 1999. The coordinates are obtained through a combination of at least seven AC (analysis-center) products [

Flow of the station selection algorithm and orbit and clock offset solution process.

Figure

It is noted that the station selection in this paper is only performed in the preprocessing stages of each ultra-rapid and real-time clock offset solutions rather than the processing stages. The weight

The experiment conducted in this paper mainly investigates the effects of the station distribution and number on the accuracy of ultra-rapid orbit determination and real-time clock offset estimation using the WSDOP value. After optimizing the station selection, using the orbit and clock software of CUM, IGS observation data (i.e., 24-h observation arc data merged with hourly observation files) for 3 consecutive days, from the 68th day to the 70th day of 2017, are used for the determination and prediction of the ultra-rapid orbit. The ultra-rapid orbit is determined once at GPST 00-h, 06-h, 12-h, and 18-h on each day to generate four 6-h predictions of the ultra-rapid orbit. When 90 stations are used in orbit determination on each day, the orbital prediction file of the day is generated by concatenating the four 6-h predictions of the ultra-rapid orbit. Using the prediction files and corresponding three-day observation data (day file data; sampling interval of 30 s), the real-time clock offset is solved by employing a square-root information filter algorithm [

In this paper, the orbit accuracy is the root-mean-square error (RMSE), while the clock accuracy is the mean Standard Deviations of Errors (STDE). The twice difference comparison method calculated in two steps is used to obtain the STDE [

The calculation strategy of the orbit determination and real-time clock offset estimation is presented in Table

Calculation strategy of the ultra-rapid orbit determination and real-time clock offset estimation.

Parameter | Ultra-rapid orbit handing strategy | Real-time clock offset handing strategy | |
---|---|---|---|

Observation information | Observation | Undifferenced ionosphere-free | Undifferenced ionosphere-free |

phase and code combination: | phase and code combination: | ||

L1 and L2(GPS) | L1 and L2(GPS) | ||

Elevation mask angle | 7°; height angle | 7°; height angle | |

weight determination | weight determination | ||

Observation arc | 24h arc | - | |

| |||

Error correction | Phase winding | Model correction | Model correction |

PCO/PCV | IGS08 Model | IGS08 Model | |

Gravity field | EGM96 model (8×8) | - | |

Ocean, solid earth and pole tide | IERS conventions 2010 | IERS conventions 2010 | |

Relativistic effect | IERS conventions 2010 | IERS conventions 2010 | |

Solar light pressure model | ECOM9 Model | - | |

| |||

Parameter estimation | Satellite orbit | Estimation | Fixed as ultra-rapid predicted |

orbit of CUM | |||

Site coordinates | Estimation | Fixed as IGS week solution | |

ERP | IERS prior constraint + | Fixed as IERS result | |

parameter estimation | |||

Troposphere | SAAS model / GMF projection | SAAS model / GMF projection | |

+ random walk estimation | + random walk estimation | ||

Clock offset of satellite | Estimation (white noise) | SRIF estimation | |

Clock error of receiver | Estimation (white noise) | Estimation (white noise) | |

Ambiguity | Estimation | Estimation |

Relationship between the number of stations and DOP value.

Variations in WSDOP and SDOP values for each group’s experiment.

Frequency histograms and probability density functions of WSDOP and SDOP values for the third-group, sixth-group, and ninth-group experiments.

Figure

Figure

Figure

Twenty experiments of orbit and clock offset determination are conducted for each group above. Figure

Variations in the GPS orbit determination accuracy (RMS) for each group’s experiments.

Variations in the GPS real-time clock offset accuracy (STD) in each group’s experiments.

Figures

Figures

Average accuracy and calculation time statistics of 3 consecutive days for probability and traditional methods.

Number of stations | GRID observed | GRID predicted orbit (cm) | GRID real-time clock offset(ns) | WSDOP observed orbit (cm) | WSDOP predicted orbit (cm) | WSDOP real-time clock offset (ns) | Increasing rates of observed orbit (%) | Increasing rates of predicted orbit (%) | Increasing rates of real-time clock offset (ns) | Computation time of WSDOP station selection (min) | Computation time of orbit determination (min) | Computation time of clock offset estimation (min) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

10 | 22.93 | 43.73 | 0.89 | 9.37 | 19.10 | 0.37 | 59.16 | 56.33 | 58.43 | 2.22 | 5.88 | 1.23 |

20 | 4.57 | 9.40 | 0.36 | 3.77 | 8.03 | 0.21 | 17.52 | 14.54 | 42.20 | 3.34 | 6.57 | 4.84 |

30 | 2.27 | 5.70 | 0.30 | 2.01 | 4.93 | 0.20 | 11.40 | 13.45 | 32.58 | 4.38 | 7.41 | 12.33 |

40 | 2.13 | 5.40 | 0.28 | 1.76 | 4.47 | 0.20 | 17.65 | 17.28 | 28.92 | 5.52 | 8.62 | 27.82 |

50 | 1.87 | 4.67 | 0.26 | 1.73 | 4.13 | 0.19 | 7.14 | 11.43 | 27.85 | 6.65 | 9.81 | 56.43 |

60 | 1.53 | 3.77 | 0.26 | 1.47 | 3.50 | 0.17 | 4.12 | 7.08 | 33.77 | 8.02 | 11.39 | 103.57 |

70 | 1.37 | 3.73 | 0.23 | 1.20 | 2.93 | 0.19 | 11.99 | 21.43 | 17.65 | 9.97 | 12.63 | 170.33 |

80 | 1.37 | 4.00 | 0.22 | 1.15 | 3.17 | 0.18 | 15.59 | 20.83 | 19.40 | 12.71 | 14.68 | 259.76 |

90 | 1.27 | 3.53 | 0.23 | 1.14 | 3.13 | 0.18 | 9.75 | 11.32 | 23.19 | 14.15 | 16.82 | 358.04 |

Note: the station selection is performed with a conventional computer while the orbit and clock calculations are made with a graphics workstation.

Selection results for 30 (a), 60 (c), and 90 (c) stations on the 68th day obtained with the probability (black) and traditional (red) methods, where blue points indicate all candidate stations.

Accuracy statistics of ultra-rapid observed (a) and predicted (b) orbits and real-time clock offset (c) of the nine groups of experiments on 3 consecutive days for probability and traditional methods.

(1) Figure

(2) Table

(3) Figure

(4) Table

A random optimization algorithm for the selection of GNSS global monitoring stations based on the selection judgment index WSDOP was proposed. After analyzing optimized ground station distribution obtained by the proposed probabilistic algorithm, it is shown that the proposed algorithm quickly and automatically produces a desirable subset of total stations with regard to the geometric distribution factor and the quality factors about the station observations. By applying this algorithm to the calculation of ultra-rapid orbit determination and real-time clock offset, we find that the accuracies of the orbit and clock offset for 3 consecutive days achieved are better than that of the traditional grid method. The conclusions are drawn as follows.

(1) In general, irrespective of whether the number of stations is the same or different, while the geometric configuration of the stations is improved, the accuracy of the orbit and real-time clock offset are both improved with the decreasing WSDOP values.

(2) There is an obvious improvement in the station geometric configuration with an increase in the number of stations. The improvement in the orbital geometric structure information is gradual when there are more than 60 stations. When using 30 stations selected by the proposed method, the accuracies of the GPS ultra-rapid orbit observation and prediction and the real-time clock offset can reach 2.01 cm, 4.93 cm, and 0.20 ns, respectively. When using 30 stations, the accuracies are, respectively, 1.47 cm, 3.5 cm, and 0.17 ns. For more than 60 stations, the accuracy improvement of the orbit determination will be limited; meanwhile, 30 stations may achieve an extreme accuracy of the clock estimation.

(3) The GNSS product accuracies from the proposed algorithm are overall higher than those of the traditional grid method, with the observation and prediction orbit and clock offset accuracies improving by 4.12–59.16%, 7.08–56.33%, and 17.65–58.43% over the latter method with the average increasing rates of 17.15%, 19.30%, and 31.55%. When few stations are selected (e.g., 20 stations or fewer), the improvements are more remarkable both in the orbit and clock offset.

(4) The calculation times of station selection, ultra-rapid orbit determination, and real-time clock offset estimation increase gradually with the number of stations; in particular, the calculation time of the clock offset sharply increases. When the number of station selection is 90 stations are selected, the respective calculation times are 14.15, 16.82, and 358.04 min.

Combined with the neural network method or ant colony algorithm, the probability method presented in this paper is expected to be further improved. Considering that the monitoring stations of the Beidou system are unevenly and less distributed presently, the method can provide an effective approach for orbit determination, real-time clock offset estimation, ERP solutions, and construction of global stations of the Beidou system.

See Table

Names and longitudes and latitudes of station selection lists for 30, 60, and 90 stations on the 68th day obtained with the probability and traditional methods, respectively. A tick indicates whether or not the station belongs to the 30, 60, or 90 set. If the longitude or latitude of a station is negative, it indicates the station locates in the western or southern hemisphere of the Earth. If the longitude or latitude of a station is a positive number, it indicates the station locates in the eastern or northern hemisphere of the Earth. It is noted that the longitudes and latitudes of some stations, such as “areg” and “areq”, are the same due to the very close distance between the stations and the rounding error of the calculation.

Station Name | Longitude (degree) | GRID-30 | WSDOP-30 | GRID-60 | WSDOP-60 | GRID-90 | WSDOP-90 | Station Name | Longitude (degree) | Latitude (degree) | GRID-30 | WSDOP-30 | GRID-60 | WSDOP-60 | GRID-90 | WSDOP-90 | Station Name | Longitude (degree) | Latitude (degree) | GRID-30 | WSDOP-30 | GRID-60 | WSDOP-60 | GRID-90 | WSDOP-90 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

adis | 9.04 | √ | √ | √ | √ | hueg | 47.83 | 7.60 | pie1 | 34.30 | -108.12 | √ | √ | √ | |||||||||||

ajac | 41.93 | hyde | 17.42 | 78.55 | pimo | 14.64 | 121.08 | √ | √ | √ | √ | √ | |||||||||||||

albh | 48.39 | √ | irkj | 52.22 | 104.32 | √ | √ | √ | pngm | -2.04 | 147.37 | √ | √ | ||||||||||||

algo | 45.96 | ispa | -27.12 | -109.34 | √ | √ | √ | √ | polv | 49.60 | 34.54 | √ | |||||||||||||

alic | -23.67 | √ | √ | √ | ista | 41.10 | 29.02 | pots | 52.38 | 13.07 | |||||||||||||||

alrt | 82.49 | √ | √ | √ | √ | jfng | 30.52 | 114.49 | pove | -8.71 | -63.90 | √ | √ | ||||||||||||

ankr | 39.89 | jog2 | -7.76 | 110.37 | √ | √ | prds | 50.87 | -114.29 | √ | |||||||||||||||

areg | -16.47 | √ | √ | karr | -20.98 | 117.10 | √ | ptgg | 14.54 | 121.04 | |||||||||||||||

areq | -16.47 | kely | 66.99 | -50.94 | √ | √ | √ | √ | ptvl | -17.75 | 168.32 | √ | √ | √ | |||||||||||

artu | 56.43 | √ | √ | √ | √ | kerg | -49.35 | 70.26 | √ | √ | √ | qiki | 67.56 | -64.03 | √ | ||||||||||

ascg | -7.92 | √ | √ | √ | kir8 | 67.88 | 21.06 | ramo | 30.60 | 34.76 | √ | √ | |||||||||||||

aspa | -14.33 | √ | √ | √ | kiri | 1.35 | 172.92 | √ | √ | √ | √ | recf | -8.05 | -34.95 | √ | √ | |||||||||

auck | -36.60 | kokb | 22.13 | -159.66 | √ | √ | reso | 74.69 | -94.89 | √ | √ | √ | |||||||||||||

bjco | 6.38 | √ | √ | √ | kokv | 22.13 | -159.66 | √ | reun | -21.21 | 55.57 | √ | √ | √ | √ | ||||||||||

bjfs | 39.61 | √ | √ | √ | kouc | -20.56 | 164.29 | √ | √ | reyk | 64.14 | -21.96 | √ | √ | |||||||||||

bor1 | 52.28 | koug | 5.10 | -52.64 | √ | rgdg | -53.79 | -67.75 | √ | √ | √ | ||||||||||||||

brew | 48.13 | √ | krgg | -49.35 | 70.26 | √ | √ | riga | 56.95 | 24.06 | |||||||||||||||

brft | -3.88 | √ | lama | 53.89 | 20.67 | √ | rio2 | -53.79 | -67.75 | √ | |||||||||||||||

brmu | 32.37 | √ | √ | √ | laut | -17.61 | 177.45 | √ | √ | riop | -1.65 | -78.65 | √ | √ | √ | √ | |||||||||

brst | 48.38 | √ | √ | √ | √ | leij | 51.35 | 12.37 | roap | 36.46 | -6.21 | √ | √ | √ | |||||||||||

brux | 50.80 | lhaz | 29.66 | 91.10 | √ | √ | √ | salu | -2.59 | -44.21 | |||||||||||||||

bucu | 44.46 | lmmf | 14.59 | -61.00 | √ | √ | samo | -13.85 | -171.74 | √ | |||||||||||||||

cas1 | -66.28 | √ | √ | √ | √ | √ | √ | lpal | 28.76 | -17.89 | √ | √ | √ | sant | -33.15 | -70.67 | |||||||||

cedu | -31.87 | √ | lpgs | -34.91 | -57.93 | √ | √ | √ | savo | -12.94 | -38.43 | √ | √ | ||||||||||||

chpg | -22.68 | √ | √ | mag0 | 59.58 | 150.77 | √ | √ | √ | sch2 | 54.83 | -66.83 | √ | ||||||||||||

chum | 43.00 | √ | √ | maju | 7.12 | 171.36 | √ | √ | √ | scrz | -17.80 | -63.16 | √ | ||||||||||||

chur | 58.76 | √ | mana | 12.15 | -86.25 | √ | √ | √ | scub | 20.01 | -75.76 | √ | |||||||||||||

ckis | -21.20 | √ | √ | √ | √ | mar6 | 60.60 | 17.26 | √ | √ | √ | √ | seyg | -4.68 | 55.53 | √ | √ | √ | √ | ||||||

cnmr | 15.23 | √ | √ | mar7 | 60.60 | 17.26 | sgoc | 6.89 | 79.87 | √ | √ | √ | √ | ||||||||||||

coco | -12.19 | √ | √ | √ | √ | mars | 43.28 | 5.35 | shao | 31.10 | 121.20 | √ | √ | √ | |||||||||||

cpvg | 16.73 | √ | √ | √ | mate | 40.65 | 16.70 | sofi | 42.56 | 23.39 | √ | √ | |||||||||||||

crao | 44.41 | √ | matg | 40.65 | 16.70 | ssia | 13.70 | -89.12 | √ | √ | |||||||||||||||

darw | -12.84 | √ | maw1 | -67.60 | 62.87 | √ | √ | √ | √ | sthl | -15.94 | -5.67 | √ | √ | √ | √ | |||||||||

dav1 | -68.58 | √ | √ | √ | √ | mayg | -12.78 | 45.26 | √ | √ | √ | stjo | 47.60 | -52.68 | √ | √ | |||||||||

djig | 11.53 | √ | mcm4 | -77.84 | 166.67 | √ | √ | √ | √ | sutm | -32.38 | 20.81 | √ | √ | √ | ||||||||||

dlf1 | 51.99 | medi | 44.52 | 11.65 | syog | -69.01 | 39.58 | √ | √ | √ | |||||||||||||||

drao | 49.32 | metg | 60.24 | 24.38 | √ | √ | tehn | 35.70 | 51.33 | √ | √ | ||||||||||||||

dubo | 50.26 | √ | √ | mizu | 39.14 | 141.13 | √ | √ | √ | √ | thtg | -17.58 | -149.61 | √ | √ | √ | |||||||||

dund | -45.88 | mkea | 19.80 | -155.46 | √ | √ | √ | √ | √ | thti | -17.58 | -149.61 | √ | √ | |||||||||||

dyng | 38.08 | mobs | -37.83 | 144.98 | √ | √ | √ | √ | thu3 | 76.54 | -68.83 | √ | √ | √ | |||||||||||

ebre | 40.82 | morp | 55.21 | -1.69 | tixi | 71.63 | 128.87 | √ | √ | ||||||||||||||||

fair | 64.98 | √ | √ | √ | √ | nano | 49.29 | -124.09 | √ | tlse | 43.56 | 1.48 | √ | ||||||||||||

falk | -51.69 | √ | √ | √ | nico | 35.14 | 33.40 | √ | √ | √ | tow2 | -19.27 | 147.06 | √ | √ | √ | |||||||||

ffmj | 50.09 | nium | -19.08 | -169.93 | √ | √ | tsk2 | 36.11 | 140.09 | ||||||||||||||||

flin | 54.73 | √ | √ | √ | nklg | 0.35 | 9.67 | √ | √ | tskb | 36.11 | 140.09 | √ | √ | |||||||||||

flrs | 39.45 | √ | √ | nnor | -31.05 | 116.19 | tuva | -8.53 | 179.20 | ||||||||||||||||

ftna | -14.31 | not1 | 36.88 | 14.99 | √ | √ | twtf | 24.95 | 121.16 | √ | |||||||||||||||

ganp | 49.03 | novm | 55.03 | 82.91 | √ | ufpr | -25.45 | -49.23 | √ | ||||||||||||||||

glps | -0.74 | √ | √ | √ | √ | √ | nrc1 | 45.45 | -75.62 | √ | unbj | 45.95 | -66.64 | ||||||||||||

glsv | 50.36 | √ | nrmd | -22.23 | 166.48 | √ | √ | unbn | 45.95 | -66.64 | |||||||||||||||

gmsd | 30.56 | nrmg | -22.23 | 166.48 | unsa | -24.73 | -65.41 | √ | √ | √ | |||||||||||||||

gode | 39.02 | √ | √ | nya1 | 78.93 | 11.87 | √ | urum | 43.81 | 87.60 | √ | √ | |||||||||||||

gold | 35.43 | √ | √ | √ | nya2 | 78.93 | 11.86 | √ | √ | voim | -21.91 | 46.79 | √ | √ | √ | √ | |||||||||

gop6 | 49.91 | nyal | 78.93 | 11.87 | wark | -36.43 | 174.66 | √ | √ | √ | |||||||||||||||

gop7 | 49.91 | obe4 | 48.08 | 11.28 | whit | 60.75 | -135.22 | √ | √ | √ | |||||||||||||||

grac | 43.75 | √ | ohi2 | -63.32 | -57.90 | √ | √ | √ | will | 52.24 | -122.17 | √ | |||||||||||||

graz | 47.07 | ohi3 | -63.32 | -57.90 | √ | √ | wsrt | 52.91 | 6.60 | ||||||||||||||||

guat | 14.59 | √ | ons1 | 57.40 | 11.92 | wtzz | 49.14 | 12.88 | |||||||||||||||||

guug | 13.43 | √ | onsa | 57.40 | 11.93 | √ | wuh2 | 30.53 | 114.36 | ||||||||||||||||

harb | -25.89 | √ | ous2 | -45.87 | 170.51 | √ | √ | yakt | 62.03 | 129.68 | √ | √ | √ | √ | |||||||||||

hers | 50.87 | √ | pado | 45.41 | 11.90 | √ | yar2 | -29.05 | 115.35 | √ | |||||||||||||||

hlfx | 44.68 | √ | √ | palm | -64.78 | -64.05 | √ | √ | √ | √ | yell | 62.48 | -114.48 | √ | |||||||||||

hnpt | 38.59 | parc | -53.14 | -70.88 | √ | √ | √ | ykro | 6.87 | -5.24 | √ | √ | √ | ||||||||||||

hob2 | -42.80 | √ | √ | pdel | 37.75 | -25.66 | √ | √ | zamb | -15.43 | 28.31 | √ | √ | ||||||||||||

hofn | 64.27 | √ | pen2 | 47.79 | 19.28 | zeck | 43.79 | 41.57 | √ | √ | |||||||||||||||

holm | 70.74 | √ | √ | √ | pert | -31.80 | 115.89 | √ | √ | zimj | 46.88 | 7.47 | |||||||||||||

hrao | -25.89 | √ | √ | √ | √ | pets | 53.02 | 158.65 | √ | √ | √ | √ | zimm | 46.88 | 7.47 |

The data used to support the findings of this study are available from the first or the corresponding author upon request.

The authors declare no conflicts of interest.

Qianxin Wang, Shuqiang Xue, and Xu Yang conceived and defined the research scheme. Xu Yang and Shuqiang Xue verified the feasibility of the method and implemented the software algorithm; Xu Yang and Qianxin Wang checked the data processing results and wrote the manuscript; Qianxin Wang and Shuqiang Xue helped to revise the manuscript and modified some figures and tables.

This work was supported by “the National Science and Technology Basic Work of China (no. 2015FY310200)”, “the State Key Program of National Natural Science Foundation of China (no. 41730109)”, “the National Natural Science Foundation of China (nos. 41404033 and 41874039)”, and “the Jiangsu Dual Creative Teams Program Project Awarded in 2017”; and IGS and iGMAS are acknowledged for providing data.