A method for optimizing selection of global ground stations for precise orbit determination of GNSS satellites

Abstract

This invention discloses an optimized selection method for global ground stations for precise GNSS satellite orbit determination, relating to the fields of precise satellite orbit determination and station selection for multiple satellite navigation systems. The method includes: dividing these stations into n clusters using a k-means clustering algorithm based on the three-dimensional coordinates of all global stations supporting four GNSS systems; performing multi-index quality assessments on the stations in each cluster over a specified time period to form a quality assessment index list for each station; and using a multi-criteria decision algorithm to rank the quality assessment results of the stations in each cluster, selecting the station ranked first in each cluster to form a network of n evenly distributed global ground stations. This invention addresses the problems existing in current GNSS precise orbit determination station selection algorithms by comprehensively using clustering and multi-criteria decision algorithms to select a uniformly distributed list of GNSS ground stations that guarantees precise orbit determination quality, possessing significant research and market value for GNSS precise orbit determination.

Description

Technical Field

[0001] This invention relates to the fields of precise satellite orbit determination and station selection for multi-satellite navigation systems. Specifically, it relates to an optimized selection method for a specified number of evenly distributed ground stations supporting multi-satellite navigation systems. This method has significant scientific research and market value for precise GNSS orbit determination and high-precision GNSS applications. Background Technology

[0002] The US GPS, Russia's GLONASS, the EU's Galileo, and China's BeiDou Navigation Satellite System (BDS) are collectively known as Global Navigation Satellite Systems (GNSS). GNSS is the most important spatiotemporal information infrastructure of our time. High-precision GNSS applications require a high-precision GNSS spatiotemporal reference. Precise GNSS satellite orbit determination generates precise satellite orbit products, providing spatial reference information for a wide range of users' multi-purpose needs such as Positioning, Navigation, and Timing (PNT). This has always been a key research focus and hot topic in the field of satellite navigation.

[0003] Precise orbit determination of GNSS satellites relies on continuous observations from globally distributed ground tracking stations. With the continuous improvement of various GNSS constellations and the implementation of the MGEX (The Multi-GNSS Experiment) project, there are now over 360 global tracking stations supporting all four systems. Theoretically, the more evenly distributed global tracking stations there are, the higher the accuracy of GNSS satellite precise orbit determination. However, in actual data processing, considering factors such as computational efficiency and hardware memory, it is usually necessary to reasonably select a certain number of evenly distributed ground tracking stations.

[0004] Scholars both domestically and internationally have conducted a series of studies on the site selection problem. Regarding site selection theory, Dvorkin's research indicates that for the GLONASS system, only 21 reasonably distributed ground monitoring stations are needed to achieve quadruple coverage of GLONASS satellites. Even if the number of stations increases by 30%, the accuracy of precise orbit determination and clock estimation can only be improved by 0.5% (Dvorkin and Karutin 2013). Wang studied the relationship between Earth rotation parameter calculation and station distribution: when the number of stations is constant, the accuracy of Earth rotation parameter calculation is highest when the ground station-Earth's center of mass vectors are pairwise orthogonal (Wang, Dang, and Xu 2013). In terms of site selection algorithms, there are currently two mainstream methods. One method is the grid method, which divides the globe into several equally sized grids and selects the stations with the best observation quality from each grid to form a station list. Another method is an algorithm that uses the DOP value (or a variant of the DOP value) as the objective function for optimization (Han Deqiang et al., 2017; Yang Wenlong, 2020). Its essence is to use the satellite orbit as the parameter to be estimated, form a precise orbit determination equation, and use the concept of DOP value in GNSS positioning to analyze the structure of the equation and select a station list with the best geometric configuration.

[0005] The grid method can achieve a uniform distribution of the final stations selected, but relying solely on the observation quality as an evaluation index for stations within the grid is not optimal for precise orbit determination. The optimization algorithm based on DOP value is theoretically rigorous, but in actual processing, it is relatively complex to calculate the partial derivatives of the observed values ​​with respect to the parameters to be estimated. Furthermore, for real-time station selection, the computational efficiency cannot meet the real-time requirements due to the need for several iterations. Summary of the Invention

[0006] To address the existing problems, this invention provides an optimized selection method for global ground stations for precise orbit determination of GNSS satellites. This method addresses the shortcomings of current GNSS precise orbit determination station selection algorithms by replacing grid division with a more efficient clustering algorithm, ensuring the uniformity of station distribution.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for optimizing the selection of global ground stations for precise orbit determination of GNSS satellites includes the following steps:

[0009] (1) Obtain all global stations that support GNSS and their three-dimensional coordinates. Based on the distance between stations, use the k-means clustering algorithm to divide these stations into n clusters, where n is the number of stations selected by the user.

[0010] (2) Perform multi-index quality assessment on the stations in each cluster within a specified time period to form a list of quality assessment indicators for each station.

[0011] (3) Using a multi-criteria decision-making method, the station quality assessment results in each cluster are sorted, and the station ranked first in each cluster is selected to form a network of n evenly distributed global ground stations, thus completing the station optimization selection.

[0012] Furthermore, the quality assessment indicators for each station include: the number of available observations within a specified time period, the proportion of available observations within a specified time period to the total number of observations, the average pseudorange multipath size of all GNSS frequencies used for precise orbit determination within a specified time period, and the average signal-to-noise ratio of all GNSS frequencies used for precise orbit determination within a specified time period.

[0013] Furthermore, step (2) includes the following processes:

[0014] Based on the raw GNSS observation data and broadcast ephemeris for each station within the corresponding time period, clock jump repair is performed on the raw observation data;

[0015] The Turboedit method is used to mark cycle slips and remove gross errors from the observations of the stations, generating a log file for each station. The log file records the number of usable observations after removing gross errors and the proportion of usable observations to the total number of observations within a specified time period.

[0016] Using the multipath linear combination observation method, the multipath size of the dual-frequency observations used for precise orbit determination at each epoch of the station within a specified time period is calculated, and the mean of the multipaths for all epochs within that time period is calculated.

[0017] Read the signal-to-noise ratio (SNR) of the dual-frequency observations used for precise orbit determination for each epoch in the station's observation data, and calculate the mean for all epochs;

[0018] The quality assessment index list for each station is formed by four indicators: the number of available observations, the proportion of available observations to the total number of observations, the average multipath value across all epochs, and the average signal-to-noise ratio across all epochs.

[0019] Furthermore, step (3) includes the following processes:

[0020] For each cluster, a multi-criteria decision-making method is used to define the weights of four quality assessment indicators. The four quality assessment indicators of each station are combined to rank them, and the station ranked first in the cluster is obtained.

[0021] The station ranked first in each cluster is selected to form a globally evenly distributed network of stations.

[0022] The beneficial effects of this invention are as follows:

[0023] 1. This invention addresses the problems existing in current GNSS precision orbit determination and station selection algorithms by replacing grid division with a more efficient clustering algorithm, thus ensuring the uniformity of station distribution.

[0024] 2. This invention analyzes multiple quality indicators of the station and introduces a multi-criteria decision-making algorithm from management science to give the best score for the station and select a list of GNSS ground stations that are evenly distributed and can guarantee the quality of precise orbit determination. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of the k-means clustering method according to an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the TOPSIS multi-criteria decision-making method according to an embodiment of the present invention. Detailed Implementation

[0028] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0029] A method for optimizing the selection of global ground stations for precise orbit determination of GNSS satellites includes the following steps:

[0030] (1) Obtain all global stations that support the four GNSS systems (GPS / GLONASS / Galileo / Beidou) and their three-dimensional coordinates. Based on the distance between the stations, use the k-means clustering algorithm to divide these stations into n clusters, where n is the number of stations selected by the user.

[0031] (2) Perform multi-index quality assessment on each station in the cluster within a specified time period to form a list of quality assessment indicators for each station.

[0032] (3) Using a multi-criteria decision-making method, the station quality assessment results in each cluster are sorted, and the station ranked first in each cluster is selected to form a network of n evenly distributed global ground stations.

[0033] The quality assessment indicators for each station include: the number of available observations within a specified time period, the proportion of available observations within a specified time period to the total number of observations, the average pseudorange multipath size of all frequencies used for precise orbit determination by the four GNSS systems (GPS / GLONASS / Galileo / Beidou) within a specified time period, and the average signal-to-noise ratio (SNR) of all frequencies used for precise orbit determination by the four GNSS systems (GPS / GLONASS / Galileo / Beidou) within a specified time period.

[0034] Step (2) includes the following processes: clock jump repair is performed on the original GNSS observation data and broadcast ephemeris for each station within the corresponding time period; cycle jump detection and gross error removal are performed on the observations of the station using the Turboedit method, and a log file for each station is generated. The log file records the number of usable observations after gross error removal and the proportion of usable observations to the total number of observations within the specified time period of the station; the multipath magnitude of the dual-frequency observations used for precise orbit determination at each epoch within the specified time period of the station is calculated using the multipath linear combination observation method, and the mean of all epochs is calculated; the signal-to-noise ratio of the dual-frequency observations used for precise orbit determination at each epoch in the observation data of the station is read, and the mean of all epochs is calculated.

[0035] Step (3) includes the following process: For each cluster, a multi-criteria decision-making method (such as TOPSIS, MEW algorithm) is used to customize the weights of four quality assessment indicators, and the four quality assessment indicators of each station are combined to sort them to obtain the station ranked first in the cluster; the station ranked first in each cluster is selected to form a globally uniformly distributed network of stations.

[0036] Here is a more specific example:

[0037] A method for optimizing the selection of global ground stations for precise orbit determination of GNSS satellites, see [link to relevant documentation]. Figure 1 The specific steps are explained below:

[0038] Step 1: Download the list of global IGS stations from the IGS data center website (https: / / files.igs.org / pub / station / general / IGSNetwork.csv). The list includes: station name, 3D coordinate information, latitude and longitude information, receiver name, supported satellite navigation systems, atomic clock type, etc. Filter out the stations that support GPS, GLONASS, Galileo, and Beidou systems, and record the names and 3D coordinate information of these stations. Here, we denote the number of stations selected as m.

[0039] Step 2: Define a custom time period and download the observation data from these stations, along with the corresponding broadcast ephemeris and station coordinate information files for that date, from the IGS data center. If the custom time period exceeds one day, download the day files for the corresponding stations and broadcast ephemeris; if the custom time period is less than one day and does not span multiple days, download the station observation data for that day and the broadcast ephemeris file for that day; if the custom time period is less than one day and spans multiple days, download the station observation data and broadcast ephemeris files for two days.

[0040] Step 3: Define the number of stations n, using the 3D coordinate information of m stations as input, and participate... Figure 2 The k-means clustering algorithm is used to divide m stations into n clusters, with each cluster containing several stations.

[0041] Step 4: Perform multi-index quality analysis for each station in each cluster. The multi-index quality analysis process for the j-th station in the i-th cluster is as follows:

[0042] 1) Clock jump repair is performed using the epoch difference of the station's observations. If a clock jump occurs at the i-th epoch, the repair method is as follows:

[0043]

[0044] In equation (1), Let L be the carrier phase observation value after repair in the i-th epoch. s (i) represents the original carrier phase observation value at the i-th epoch, c is the speed of light in vacuum, and α is a coefficient factor, which is taken as α = 10. 3 J is calculated as follows:

[0045]

[0046] In equation (2), k2 is the threshold value, and k2 = 10 is taken. -5 ~10 -7 , The candidate values ​​for clock jumps are calculated as follows:

[0047]

[0048] In equation (3), s represents the number of satellites, m represents the total number of observed satellites, and P s (i) and P s (i-1) represent the raw pseudorange observations of satellite s from the station at the i-th and (i-1)-th epochs, respectively. s (i) and L s (i-1) represent the original carrier phase observations of satellite s from the station at the i-th and (i-1)-th epochs, respectively, T s (i) is the test statistic constructed for the station and satellite s at the i-th epoch. It is true if and only if all satellites at the i-th epoch satisfy |T s (i) When |>k1≈0.001.c, it can be considered that there may be a clock jump at this epoch, where k1 represents the threshold.

[0049] 2) The Turboedit method, which combines the Melbourne-Wübbena combination with the ionospheric TEC change rate (TECR), is used to detect and label cycle slips and eliminate gross errors. The specific method is as follows:

[0050] First, the Melbourne-Wübbena combined method is used to detect large cycle slips or gross errors. Then, the wide-lane ambiguity estimate for the i-th epoch is calculated. And its variance σ(i). Its recursive formula is:

[0051]

[0052]

[0053] For the i-th epoch, if This indicates that a cycle slip is possible at this epoch. The width-lane ambiguity estimate for the current epoch is then calculated using the recursive formula. and its variance σ(i), when the (i+1)th epoch does not exceed the limit, i.e. If the condition is met, then the i-th epoch is judged to have gross error and all observations of the i-th epoch should be deleted; if the (i+1)-Δ(i)| is also out of bounds and |Δ(i+1)-Δ(i)| = 31, then the i-th epoch should also be judged to have gross error and the data should be deleted; otherwise, the i-th epoch is considered to have cycle slipped.

[0054] Then, the geometrically free combination (GF) observations are used to detect narrow aisle cycle slips. The geometrically free combination observation L at epoch i... I for:

[0055] L I =L1-L2 (6)

[0056] In equation (6), L1 and L2 represent the carrier phase observations at the first frequency f1 and the second frequency f2 used for precise orbit determination, respectively. The judgment condition is:

[0057] |[L I (i)-Q(i)]-[L I [(i-1)-Q(i-1)]|>6(λ2-λ1) (7)

[0058] |[L I (i+1)-Q(i+1)]-[L I [(i)-Q(i)]|<λ2-λ1 (8)

[0059] In equations (7) and (8), i represents the i-th epoch, Q(i-1), Q(i) and Q(i+1) represent fitting L(i-1), L(i) and L(i+1) using polynomial Q, respectively, and λ1 and λ2 represent the wavelengths corresponding to the first frequency f1 and the second frequency f2 signals, respectively.

[0060] After performing the above processing at each epoch, a log file is generated to record the ground station and satellite observations that were rejected during cycle slip and gross error detection.

[0061] 3) Calculate the pseudorange multipath magnitude for this station. Calculate the multipath magnitudes MP1 and MP2 for each epoch at the first and second frequencies (used for precise orbit determination) using a linear combination of multipath observations:

[0062]

[0063]

[0064] In equations (9) and (10), f1 and f2 are the first and second frequencies, respectively; P1 and P2 are the pseudorange observations at the first and second frequencies, respectively; and L1 and L2 are the carrier phase observations at the first and second frequencies, respectively. The average multipath size at the first and second frequencies for all epochs of the station is calculated using equations (9) and (10).

[0065] 4) Read the signal-to-noise ratio for each epoch from the observation data file of the station, and calculate the average signal-to-noise ratio of the station within the specified time period.

[0066] Step 5: Apply the method from Step 4 to all stations and compile the quality assessment indicators of each station into a table in the following format, where the names of each station are sta1, sta2, sta3, ... stam.

[0067] Table 1. List of quality assessment indicators for each station

[0068] sta1 sta2 sta3 … stam

[0069] Step 6: Define the weights for these four quality assessment indicators. If they are equally weighted, set them to [0.25, 0.25, 0.25, 0.25]. See [link to relevant documentation]. Figure 3 Using multi-criteria decision-making methods (such as TOPSIS algorithms), the station ranked first in each of the n clusters is selected to form a list of n stations, thus obtaining the optimal station network of n orbit determination stations.

[0070] In summary, this invention addresses the problems existing in current GNSS precision orbit determination and station selection algorithms by comprehensively using clustering algorithms and multi-criteria decision-making algorithms to select a uniformly distributed list of GNSS ground stations that can guarantee the quality of precision orbit determination. This invention has significant scientific research and market value for GNSS precision orbit determination.

Claims

1. A method for optimizing the selection of global ground stations for precise orbit determination of GNSS satellites, characterized in that, Includes the following steps: (1) Obtain all global stations that support GNSS and their three-dimensional coordinates. Based on the distance between stations, use the k-means clustering algorithm to divide these stations into n clusters, where n is the number of stations selected by the user. (2) Conduct multi-index quality assessments of stations in each cluster within a specified time period to form a list of quality assessment indicators for each station; The quality assessment indicators for each station include: the number of available observations within a specified time period, the proportion of available observations within a specified time period to the total number of observations, the average pseudorange multipath size of all GNSS frequencies used for precise orbit determination within a specified time period, and the average signal-to-noise ratio of all GNSS frequencies used for precise orbit determination within a specified time period. (3) Using a multi-criteria decision-making method, the quality assessment results of stations in each cluster are sorted, and the station ranked first in each cluster is selected to form a network of n evenly distributed global ground stations, thus completing the station optimization selection.

2. The method for optimizing the selection of global ground stations for precise orbit determination of GNSS satellites according to claim 1, characterized in that, Step (2) includes the following process: Based on the raw GNSS observation data and broadcast ephemeris for each station within the corresponding time period, clock jump repair is performed on the raw observation data; The Turboedit method is used to mark cycle slips and remove gross errors from the observations of the stations, generating a log file for each station. The log file records the number of usable observations after removing gross errors and the proportion of usable observations to the total number of observations within a specified time period. Using the multipath linear combination observation method, the multipath size of the dual-frequency observations used for precise orbit determination at each epoch of the station within a specified time period is calculated, and the mean of the multipaths for all epochs within that time period is calculated. Read the signal-to-noise ratio (SNR) of the dual-frequency observations used for precise orbit determination for each epoch in the station's observation data, and calculate the mean for all epochs; The quality assessment index list for each station is formed by four indicators: the number of available observations, the proportion of available observations to the total number of observations, the average multipath value across all epochs, and the average signal-to-noise ratio across all epochs.

3. The method for optimizing the selection of global ground stations for precise orbit determination of GNSS satellites according to claim 1, characterized in that, Step (3) Includes the following processes: For each cluster, a multi-criteria decision-making method is used to define the weights of four quality assessment indicators. The four quality assessment indicators of each station are combined to rank them, and the station ranked first in the cluster is obtained. The station ranked first in each cluster is selected to form a globally evenly distributed network of stations.

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