A low-orbit enhanced accelerated satellite selection method based on GDOP contribution

Abstract

This invention discloses a low-orbit enhanced accelerated satellite selection method based on GDOP contribution, belonging to the field of satellite navigation technology. The method includes: constructing a sub-satellite point screening model based on the measurement station restriction range; constructing a low-orbit satellite screening model based on the satellite spherical coverage radius; and constructing a DOP contribution star selection model. This method uses known measurement station location coordinates and LEO satellite positions to determine the orbits of medium- and high-orbit satellites, effectively improving the accuracy of medium- and high-orbit satellite orbit determination. It also achieves high-precision fitting of GNSS satellites, ensuring the accuracy of GNSS satellite orbit models.

Description

Technical Field

[0001] The present invention belongs to the field of satellite navigation technology, and in particular relates to a low-orbit enhanced accelerated satellite selection method based on GDOP contribution. Background Art

[0002] Star selection involves selecting satellites from a star catalog with the optimal geometric distribution and shortest measurement period, based on astronomical measurement specifications, to form an observation constellation with a measurement time sequence. Currently, orbit determination for high-orbit satellites primarily relies on ground-based measurement and control. However, due to limitations in ground station construction, such as high requirements for location and surrounding environment, and high construction costs, as the number of high-orbit satellites increases in the future, ground stations will struggle to provide sufficient positioning resources. Furthermore, compared to medium- and high-orbit satellites, low-orbit satellites have lower orbital altitudes, faster on-orbit speeds, and more rapid configuration changes, enabling rapid convergence of positioning parameters, achieving fast and high-precision orbit determination. Therefore, optimizing low-orbit satellites is particularly important for orbit determination of medium- and high-orbit satellites. Therefore, determining GNSS positioning and orbit using low-orbit satellites is a major challenge. Summary of the Invention

[0003] To solve the above technical problems, the present invention proposes a low-orbit enhanced accelerated satellite selection method based on GDOP contribution to solve the problems existing in the above-mentioned prior art.

[0004] To achieve the above objectives, the present invention provides a low-orbit enhanced accelerated satellite selection method based on GDOP contribution, comprising:

[0005] Calculate the station position and, based on the satellite period at the desired time, calculate the sub-satellite point coordinates;

[0006] Traversing all candidate low-orbit satellites, and screening eligible LEO satellites based on the latitude and longitude coordinate range of the measuring station location;

[0007] Calculating the spherical coverage radius of the satellite at the desired time to obtain the satellite spherical coverage radius, and screening the LEO satellites based on the satellite spherical coverage radius to obtain screened satellites;

[0008] A GDOP contribution model is constructed, and based on the GDOP contribution model, a cyclic calculation is performed on the screened satellites, and satellites with small GDOP contributions are eliminated until the remaining satellite threshold is reached, thereby completing the satellite selection.

[0009] Preferably, the expression of the sub-satellite point coordinates is:

[0010]

[0011] Where i is the orbital inclination, u is the latitude argument, Ω is the longitude of the ascending node, The longitude and latitude coordinates of the subsatellite point.

[0012] Preferably, the formula for converting the satellite space rectangular coordinate system to the geodetic coordinate system is:

[0013]

[0014] Among them, (x, y, z) are the coordinates of the spatial rectangular coordinate system, N is the radius of the zodiac circle, λ is the latitude, and e is the first eccentricity of the earth.

[0015] Preferably, the expression of the spherical coverage radius is:

[0016]

[0017] in, is the average equatorial radius of the Earth, and the orbital height of the satellite is H S The minimum elevation angle at which the ground can communicate with the satellite is E min .

[0018] Preferably, the relationship between the sub-satellite point coordinates and the spherical distance θ of any target point on the spherical surface is:

[0019]

[0020] Where θ is the spherical distance, is the latitude and longitude coordinates of the subsatellite point, is the longitude and latitude coordinates of any target point on the sphere.

[0021] Preferably, the expression of the geometric dilution of precision in the GDOP contribution model is:

[0022]

[0023] Where GDOP is the geometric dilution of precision, trace represents matrix trace, and H is the direction cosine matrix between the receiver position and the Beidou navigation star.

[0024] Preferably, the expression of the direction cosine matrix between the receiver position and the Beidou navigation star is:

[0025]

[0026] Among them, l i 、m i 、n i is the direction cosine from the approximate coordinates of the station to the position vector of the i-th satellite, i = 1, 2, ..., a, and a is the number of satellites involved in the solution of a single system.

[0027] Preferably, the process of cyclically calculating the screened satellites based on the GDOP contribution model and eliminating satellites with small GDOP contributions further includes:

[0028] Let H m To select the observation matrix for orbit determination of m navigation satellites, when the i-th satellite is removed from the m satellites, the observation matrix of the remaining m-1 satellites is: m-1 ;

[0029]

[0030] Among them, h i =[l i -m i n i 1] is the observation vector of the i-th satellite;

[0031] make Then we can get the matrix inversion formula:

[0032]

[0033] Right now

[0034] Compared with the prior art, the present invention has the following advantages and technical effects:

[0035] Based on the traditional satellite selection method, this invention designs a low-orbit enhanced Beidou / GNSS orbit determination and selection method model based on orbit phase difference and DOP contribution, taking into account the characteristics of low-Earth orbit satellites, which are lower altitude, faster on-orbit speed, and faster configuration changes. It analyzes the orbit characteristics of LEO satellites and obtains the optimal orbit determination and selection model based on the sub-satellite coordinates of the LEO satellites to be selected. This is a positioning and orbit determination and selection model that combines traditional satellite selection methods with LEO satellites. The significant technical effects brought by this invention are mainly as follows:

[0036] (1) A low-orbit enhanced BeiDou / GNSS orbit determination and selection method based on orbit phase difference and DOP contribution is proposed. Compared with the traditional star selection model, the orbit determination and positioning of GNSS satellites is carried out by combining LEO satellites and ground stations. Due to the introduction of LEO satellites and ground stations, the problem of increased star selection calculation complexity caused by uneven star selection positions caused by a single station can be eliminated.

[0037] (2) When traversing different LEO satellites, the best satellite is selected based on the DOP contribution, ensuring the accuracy of orbit determination and selection. Compared with traditional star selection methods, this paper selects the satellite based on its spherical coverage radius and the spherical distance between the LEO subsatellite point and the same measurement station, ensuring a reduced complexity of the star selection algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0039] Figure 1 Schematic diagram of the solution process of an embodiment of the present invention;

[0040] Figure 2 This is a schematic diagram of the latitude and longitude restriction range of a measuring station according to an embodiment of the present invention;

[0041] Figure 3 This is a sub-satellite point trajectory diagram according to an embodiment of the present invention;

[0042] Figure 4 A diagram defining sub-satellite points and ground coverage areas according to an embodiment of the present invention;

[0043] Figure 5 This is a schematic diagram of an embodiment of the present invention in which all sites are located within the coverage radius;

[0044] Figure 6 This is a schematic diagram of a site partially located within the coverage radius according to an embodiment of the present invention;

[0045] Figure 7 This is a schematic diagram of an embodiment of the present invention in which some sites are entirely located outside the coverage radius. DETAILED DESCRIPTION

[0046] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0047] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0048] Example 1

[0049] This embodiment provides a low-orbit enhanced accelerated satellite selection method based on GDOP contribution, including:

[0050] Step 1: Calculate the station position and calculate the sub-satellite point coordinates based on the satellite period (t0, t) at the desired time.

[0051] Step 2: Traverse all the low-orbit satellites to be selected and select the LEO satellites that meet the requirements according to the specified station longitude and latitude coordinate range.

[0052] Step 3: Calculate the spherical coverage radius of the LEO satellites in the required time period, sort them by the position relationship between the observation station and the sub-satellite point, and eliminate all LEO satellites whose observation stations are within the satellite spherical coverage radius.

[0053] Step 4: Assume that after the screening, m satellites remain. L satellites are selected from these to form the optimal observation combination (L < m). Based on the GDOP contribution model, a recursive star selection strategy is proposed, using GDOP contribution as the selection criterion. First, the satellite with the smallest GDOP contribution is removed from the m-satellite combination, resulting in an observation combination of (m - 1) stars with the optimal geometric distribution. This process is repeated, with stars with smaller GDOP contributions being removed repeatedly until L stars remain.

[0054] The method according to claim 1 is characterized in that it can solve the satellite selection problem by screening out qualified satellites based on the low orbital altitude characteristics of LEO satellites and taking into account the influence of satellite orbital altitude, eccentricity and inclination.

[0055] To further optimize the solution, in step 1, the formula for converting the satellite space rectangular coordinate system to the geodetic coordinate system is:

[0056]

[0057] Among them, (x, y, z) are the coordinates of the spatial rectangular coordinate system, N is the radius of the circle, λ is the latitude, and e is the first eccentricity of the earth.

[0058] Further optimize the solution, in step 1, the satellite point The calculation formula for the latitude and longitude coordinates is:

[0059]

[0060] Where i is the orbital inclination, u is the argument of latitude, and Ω is the longitude of the ascending node.

[0061] To further optimize the solution, in step 2, the station restriction range can be set to a square with a side length consisting of longitude and latitude lines, covering all stations, and a side length of 5° from the nearest station, and all LEO satellites located in this square are screened out.

[0062] To further optimize the solution, in step 3, since the Earth's shape is relatively regular and the satellite is far away from the ground, the impact of the Earth's shape on the satellite coverage area can generally be ignored when analyzing coverage. That is, when calculating the coverage range, the Earth is considered to be an ideal sphere with equal curvature radius at all locations.

[0063] Satellite coverage hemispherical central angle θ c , also known as the spherical coverage radius of the satellite is:

[0064]

[0065] in, is the average equatorial radius of the Earth, and the orbital height of the satellite is H S ,, the minimum elevation angle at which the ground can communicate with the satellite is E min .

[0066] To further optimize the solution, in step 2, the latitude and longitude of the satellite's sub-satellite point are The longitude and latitude of any target point on the sphere is Then the spherical distance θ between two points has the following relationship:

[0067]

[0068] Solve using inverse trigonometric functions.

[0069] To further optimize the solution, in step 4, the geometric dilution of precision (GDOP) is an important parameter used to measure the accuracy of orbit determination results during navigation and positioning. It is related to the spatial geometric distribution of navigation satellites and can be calculated as follows:

[0070]

[0071] Where, trace represents matrix trace, and H is the direction cosine matrix between the receiver position and the Beidou navigation star.

[0072]

[0073] Where: l i 、m i 、n i is the direction cosine from the approximate coordinates of the station to the position vector of the i-th satellite, i = 1, 2, ..., a, and a is the number of satellites involved in the solution of a single system.

[0074] Therefore, the positioning error is positively correlated with the GDOP value calculated by H. The star selection algorithm is to control the selection of visible stars to minimize the GDOP value.

[0075] To further optimize the solution, in step 4, let H m To select the observation matrix for orbit determination of m navigation satellites, when the i-th satellite is removed from the m satellites, the observation matrix of the remaining m-1 satellites is: m-1 , the two have the following relationship:

[0076]

[0077] Among them, h i =[l i -m i n i 1] is the observation vector of the i-th satellite.

[0078] make Then we can get the matrix inversion formula:

[0079]

[0080] Right now From this we can see that when a row is removed from the original observation matrix, GDOP 2 Add on the original basis The relevant matrix theory can prove that this term is positive. Therefore, the contribution of a single satellite i to GDOP can be written as The larger the value is, the more likely it is that after removing satellite i, The greater the increase, the worse the geometric distribution becomes, indicating that satellite i contributes more to the constellation's geometric distribution. Conversely, if ΔG is smaller, the contribution of satellite i to the constellation's geometric distribution is smaller, and the impact is smaller. Therefore, when selecting satellites based on optimal GDOP, it is best to choose low-orbit satellites with large ΔG.

[0081] Example 2

[0082] This embodiment provides a low-orbit enhanced accelerated satellite selection method based on GDOP contribution, including:

[0083] Figure 1 This is a flow chart of the method for optimizing ephemeris parameters for giant hybrid orbit constellations proposed by the present invention. Figure 1 Provide detailed explanation.

[0084] Step 1: Calculate the measuring station position. The conversion formula from the spatial rectangular coordinate system to the geodetic coordinate system is:

[0085]

[0086] Among them, (x, y, z) are the coordinates of the spatial rectangular coordinate system, N is the radius of the circle, λ is the latitude, and e is the first eccentricity of the earth.

[0087] Step 2:

[0088] According to the satellite period of the desired time, all candidate low-orbit satellites are traversed. The station restriction range can be set as a square consisting of longitude and latitude lines, covering all stations, with a side length of 5° from the nearest station, and all LEO satellites within this square are screened out. The calculation formula for the latitude and longitude coordinates is:

[0089]

[0090] Where i is the orbital inclination, u is the argument of latitude, and Ω is the longitude of the ascending node.

[0091] Step 3:

[0092] (1) Calculate the spherical coverage radius of the LEO satellite during the desired time period. Because the Earth's shape is relatively regular and the satellite is far away from the ground, the effect of the Earth's shape on the satellite's coverage area can generally be ignored when analyzing coverage. That is, when calculating coverage, the Earth is considered to be an ideal sphere with the same curvature radius at all locations.

[0093] Satellite coverage hemispherical central angle θ c , also known as the spherical coverage radius of the satellite is:

[0094]

[0095] in, is the average equatorial radius of the Earth, and the orbital height of the satellite is H S The minimum elevation angle at which the ground can communicate with the satellite is E min .

[0096] (2) The latitude and longitude of the satellite's subsatellite point are The longitude and latitude of any target point on the sphere is Then the spherical distance θ between two points has the following relationship:

[0097]

[0098] The position from the station to the sub-satellite point is solved by inverse trigonometric functions.

[0099] Step 4: Assume that there are N satellites left after screening, and select L of them to form the best observation combination (L < N). The geometric dilution of precision (GDOP) is an important parameter used to measure the accuracy of orbit determination results during navigation and positioning. It is related to the spatial geometric distribution of navigation satellites and can be calculated as follows:

[0100]

[0101] Where, trace represents matrix trace, and H is the direction cosine matrix between the receiver position and the Beidou navigation star.

[0102]

[0103] Where: l i 、m i 、n i is the direction cosine from the approximate coordinates of the station to the position vector of the i-th satellite, i = 1, 2, ..., a, and a is the number of satellites involved in the solution of a single system.

[0104] Therefore, the positioning error is positively correlated with the GDOP value calculated by H. The star selection algorithm is to control the selection of visible stars to minimize the GDOP value.

[0105] According to the GDOP contribution model, a recursive star selection strategy is proposed with GDOP contribution as the star selection decision condition. First, the star with the smallest GDOP contribution is eliminated from the m star combination to obtain the (m-1) star observation combination with the best geometric distribution. That is, let H m To select the observation matrix for orbit determination of m navigation satellites, when the i-th satellite is removed from the m satellites, the observation matrix of the remaining m-1 satellites is: m-1 , the two have the following relationship:

[0106]

[0107] Among them, h i =[l i -m i n i 1] is the observation vector of the i-th satellite.

[0108] make Then we can get the matrix inversion formula:

[0109]

[0110] Right now From this we can see that when a row is removed from the original observation matrix, GDOP 2 Add on the original basis The relevant matrix theory can prove that this term is positive. Therefore, the contribution of a single satellite i to GDOP can be written as The larger the value is, the more likely it is that after removing satellite i, The greater the increase, the worse the geometric distribution becomes, indicating that satellite i contributes more to the constellation's geometric distribution. Conversely, if ΔG is smaller, the contribution of satellite i to the constellation's geometric distribution is smaller, and the impact is smaller. Therefore, when selecting satellites based on optimal GDOP, it is best to choose low-orbit satellites with large ΔG.

[0111] And so on, the calculation is repeated and stars with smaller GDOP contributions are eliminated until L stars remain.

[0112] In the experiment, LEO screening satellites are selected by observing the positional relationship between the station and the LEO subsatellite point.

[0113] Figure 2 In the GNSS satellite positioning system, all stations are surrounded by a square-like area composed of longitude and latitude lines. If the LEO sub-satellite point is within this area, it is considered that the LEO is too close to the station, affecting the positioning effect of the GNSS satellite.

[0114] Figure 3 In the figure, it is assumed that it is the trajectory diagram of the LEO sub-satellite point. By observing the trajectory of the sub-satellite point at different time periods, the movement of the sub-satellite point can be understood.

[0115] Figure 4 The definitions of sub-satellite points and ground coverage areas are explained in detail.

[0116] Figure 5-7 In the , the location changes of the sites and the ground coverage radius are distinguished accordingly.

[0117] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A low-orbit enhanced accelerated satellite selection method based on GDOP contribution, characterized in that: The following steps are involved: Calculate the station position and, based on the satellite period at the desired time, calculate the sub-satellite point coordinates; Traversing all candidate low-orbit satellites, and screening eligible LEO satellites based on the latitude and longitude coordinate range of the measuring station location; The process of selecting the LEO satellites that meet the requirements based on the latitude and longitude coordinates of the station location is as follows: According to the satellite period of the desired time, all candidate low-orbit satellites are traversed. The station restriction range is set as a square with a side length of longitude and latitude lines, covering all stations, and a side length of 5° from the nearest station. All LEO satellites within this square are screened out. Calculating the spherical coverage radius of the satellite at the desired time to obtain the satellite spherical coverage radius, and screening the LEO satellites based on the satellite spherical coverage radius to obtain screened satellites; Constructing a GDOP contribution model, performing cyclic calculations on the screened satellites based on the GDOP contribution model and eliminating satellites with small GDOP contributions until a remaining satellite threshold is reached, thereby completing the satellite selection; The process of cyclically calculating the screened satellites based on the GDOP contribution model and eliminating satellites with small GDOP contributions further includes: According to the GDOP contribution model, a recursive star selection strategy is proposed with GDOP contribution as the star selection decision condition. First, the star with the smallest GDOP contribution is eliminated from the m star combination to obtain the m-1 star observation combination with the best geometric distribution, that is, let H m To select the observation matrix for orbit determination of m navigation satellites, when the i-th satellite is removed from the m satellites, the observation matrix of the remaining m-1 satellites is: m-1 ; Among them, h i =[l i -m i n i 1] is the observation vector of the i-th satellite; make Then we can get the matrix inversion formula: Right now When a row is removed from the original observation matrix, GDOP 2 Add on the original basis The contribution of a single satellite i to GDOP is The larger the value, the more it means that after removing satellite i, The greater the increase, that is, the worse the geometric distribution becomes, which means that satellite i contributes more to the geometric distribution of the constellation.

2. The LEO enhanced accelerated satellite selection method based on GDOP contribution according to claim 1, characterized in that: The expression of the subsatellite point coordinates is: Where i is the orbital inclination, u is the latitude argument, Ω is the longitude of the ascending node, The longitude and latitude coordinates of the subsatellite point.

3. The LEO enhanced accelerated satellite selection method based on GDOP contribution according to claim 1, characterized in that: The formula for converting the satellite space rectangular coordinate system to the geodetic coordinate system is: Among them, (x, y, z) are the coordinates of the spatial rectangular coordinate system, N is the radius of the zodiac circle, λ is the latitude, and e is the first eccentricity of the earth.

4. The method for LEO enhancement and accelerated satellite selection based on GDOP contribution according to claim 1, characterized in that: The expression of the spherical coverage radius is: in, is the average equatorial radius of the Earth, and the orbital height of the satellite is H S The minimum elevation angle between the ground and the satellite is E min .

5. The method for LEO enhancement and accelerated satellite selection based on GDOP contribution according to claim 1, characterized in that: The relationship between the sub-satellite point coordinates and the spherical distance θ of any target point on the sphere is: Where θ is the spherical distance, is the latitude and longitude coordinates of the subsatellite point, is the longitude and latitude coordinates of any target point on the sphere.

6. The method for LEO enhancement and accelerated satellite selection based on GDOP contribution according to claim 1, characterized in that: The expression of the geometric dilution of precision in the GDOP contribution model is: Where GDOP is the geometric dilution of precision, trace represents matrix trace, and H is the direction cosine matrix between the receiver position and the Beidou navigation star.

7. The method for LEO enhancement and accelerated satellite selection based on GDOP contribution according to claim 6, characterized in that: The expression of the direction cosine matrix between the receiver position and the Beidou navigation star is: Among them, l i 、m i 、n i is the direction cosine from the approximate coordinates of the station to the position vector of the i-th satellite, i = 1, 2, ..., a, and a is the number of satellites involved in the solution of a single system.

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