An optimization method for low-orbit navigation enhancement satellite constellation

Abstract

The present application discloses a method for optimizing a low-orbit navigation enhancement satellite constellation, the method comprising: determining a constellation parameter set to be optimized according to the number of sub-constellations in the low-orbit satellite constellation, and constructing constraint conditions according to preset optimization constraints; constructing a relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning PPP, and constructing a multi-objective function based on the relationship and the preset optimization goal; optimizing the parameters in the constellation parameter set to be optimized using a genetic algorithm based on the preset optimization goal, the constraint conditions and the multi-objective function to obtain an optimized constellation parameter set, and obtaining an optimized low-orbit satellite constellation based on the optimized constellation parameter set. The present application solves the technical problem that the prior art cannot reflect the convergence performance of precise point positioning PPP, and cannot perform calculations when the number of instantaneously visible satellites is less than 4.

Description

Technical Field

[0001] The present application relates to the field of satellite navigation technology, and in particular to a method for optimizing a low-orbit navigation enhancement satellite constellation. Background Art

[0002] Compared with medium and high orbit BeiDou satellites, low orbit satellites have a faster running speed relative to the ground, and the constellation geometry changes greatly in the same time, making it easy to quickly separate the carrier phase ambiguity parameters from the position parameters. As a navigation satellite to assist BeiDou, it can achieve fast initialization of Precise Point Positioning (PPP) without relying on the enhanced regional dense ground reference station network, and has become the focus of attention in the construction of the next generation satellite navigation system. The design of the low orbit satellite constellation is the primary key task for the construction and continuous evolution of the low orbit satellite navigation enhancement system.

[0003] Traditionally, Walker configuration low-orbit satellite constellations with different orbital height and inclination combinations and better performance are designed based on empirical methods or enumeration methods. However, when faced with more complex multi-objective, multi-variable, and multi-constrained optimization problems, traditional geometric analysis methods, empirical methods, and enumeration methods are not efficient or powerless, and genetic algorithms, as a robust technology that obtains global optimal solutions through random and heuristic search strategies, have also been introduced into constellation optimization design. At present, with the goal of global uniform multiple coverage, the use of genetic algorithms to find the optimal hybrid low-orbit constellation configuration under different constraints has become a common method for constructing optimized low-orbit satellite constellations. Previous simulation studies have shown that the enhancement effect of low-orbit satellite constellations on Beidou's rapid and precise positioning is related to the number of visible low-orbit satellites. The more the number, the faster the convergence speed of precise single-point positioning PPP. However, studies have shown that the positioning performance of satellite navigation systems is not only related to the number of visible satellites, but also to the spatial geometric distribution of satellites. The geometric conditions of the constellation are often characterized by the geometric dilution of precision (GDOP). Therefore, when designing the low-orbit satellite constellation, the optimal GDOP and the lowest cost were used as the optimization goals, and the low-orbit regional navigation constellation and the low-orbit global navigation constellation were designed using genetic algorithms. However, the current standard GDOP index can only reflect the instantaneous positioning accuracy of the standard navigation and positioning service, and cannot reflect the convergence performance of the precise single-point positioning PPP, and cannot be calculated when the number of instantaneously visible satellites is less than 4. Summary of the invention

[0004] The technical problem solved by this application is that the existing technology cannot reflect the convergence performance of precise single-point positioning PPP, and cannot be calculated when the number of instantaneously visible satellites is less than 4. This application provides an optimization method for a low-orbit navigation enhancement satellite constellation. In the solution provided in the embodiment of this application, on the one hand, the concept of equivalent GDOP is proposed, and a formula definition is given, which can not only comprehensively describe the continuous impact of the number of satellites, running speed, running direction and degree of geometric changes on the PPP convergence process; but also can calculate for less than four satellites.

[0005] In a first aspect, an embodiment of the present application provides an optimization method for a low-orbit navigation enhancement satellite constellation, the method comprising: determining a constellation parameter set to be optimized based on the number of sub-constellations in the low-orbit satellite constellation, and constructing constraint conditions based on preset optimization constraints; constructing a relationship between an equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning PPP, and constructing a multi-objective function based on the relationship and the preset optimization goals, wherein the equivalent GDOP characterizes the influence of the number of visible low-orbit satellites, the running speed, the running direction and the degree of change of the geometric figure on the PPP convergence process; based on the preset optimization goals, the constraints and the multi-objective function, a genetic algorithm is used to optimize the parameters in the constellation parameter set to be optimized to obtain an optimized constellation parameter set, and an optimized low-orbit satellite constellation is obtained based on the optimized constellation parameter set.

[0006] Optionally, the constellation parameter set to be optimized includes: the number of orbital planes of each sub-constellation, the number of satellites in each orbital plane, the phase factor between adjacent satellites on adjacent orbital planes in each sub-constellation, the orbital altitude and orbital inclination corresponding to each constellation, the right ascension of the ascending node of the nominal satellite, and the mean anomaly angle of the nominal satellite.

[0007] Optionally, the preset optimization constraints include ensuring double, triple and quadruple coverage availability of no less than 100%, 80% and 60% respectively on a global scale; the number of orbital planes, the number of satellites in each orbital plane, and the phase factor between adjacent satellites on adjacent orbital planes are all integers; the phase factor between adjacent satellites on adjacent orbital planes is less than the number of orbital planes.

[0008] Optionally, if the low-orbit satellite constellation includes a first sub-constellation and a second sub-constellation, a constraint condition is constructed according to a preset optimization constraint, including:

[0009] The constraints are constructed using the following formula:

[0010]

[0011] Where δ2(x) represents the availability of satellite double coverage for all sites in all epochs, δ3(x) represents the availability of satellite triple coverage for all sites in all epochs, and δ4(x) represents the availability of satellite quadruple coverage for all sites in all epochs. P 1 Indicates the orbital plane number of the first sub-constellation; S 1 Indicates the number of satellites in each orbital plane of the first sub-constellation; F 1 P represents the phase factor between adjacent satellites in the adjacent orbital plane of the first sub-constellation; 2 Indicates the orbital plane number of the second sub-constellation; S 2 Indicates the number of satellites in each orbital plane of the second sub-constellation; F 2 Represents the phase factor between adjacent satellites in the adjacent orbital plane of the second sub-constellation.

[0012] Optionally, the relationship between the equivalent geometric dilution of precision GDOP of the low-orbit satellite constellation and the probability of successful convergence of the precise point positioning PPP is constructed, including:

[0013] Construct multiple low-orbit satellite constellation models, calculate the equivalent GDOP of each low-orbit satellite constellation based on the model, and simulate and obtain observation data;

[0014] The relationship between the equivalent GDOP and the convergence time of the low-orbit enhanced Beidou PPP is calculated based on the observation data corresponding to the multiple low-orbit satellite constellation models;

[0015] Based on the calculated relationship between the equivalent GDOP index of the low-orbit satellite constellation and the convergence time of the low-orbit enhanced Beidou PPP, the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of the precise point positioning PPP is constructed.

[0016] Optionally, the LEO satellite constellation equivalent GDOP is calculated based on each LEO satellite constellation model, including:

[0017] Determine one or more trajectories of each visible satellite in the low-orbit satellite constellation over the ground station within a preset time period based on each low-orbit satellite constellation model, and sample each trajectory using a preset collection interval starting from a preset time to obtain one or more sampling points corresponding to each trajectory;

[0018] The satellite-to-ground line of the spatial geometric structure formed by the line connecting all the adopted sampling points on all the trajectories corresponding to each visible star and the ground station is calculated according to the preset standard GDOP, and the satellite-to-ground line is used as the equivalent GDOP.

[0019] Optionally, the relationship between the equivalent geometric dilution of precision GDOP of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning PPP under different convergence times is:

[0020]

[0021]

[0022]

[0023] Among them, Pr 30 Pr represents the relationship between the equivalent geometric precision factor GDOP within 30 seconds and the probability of successful convergence of precise point positioning PPP; 60 Pr represents the relationship between the equivalent geometric precision factor GDOP and the probability of successful convergence of precise point positioning PPP within 60 seconds; 120 The relationship between the equivalent geometric dilution of precision (GDOP) and the probability of successful convergence of precise point positioning (PPP) within 120 seconds; EGDOP 30|5 Indicates the equivalent geometric precision factor GDOP when the sampling time interval is 5 seconds and the sampling period is 30 seconds; EGDOP 60|5 Indicates the equivalent geometric precision factor GDOP when the sampling time interval is 5 seconds and the sampling period is 60 seconds; EGDOP 120|5 Indicates the equivalent geometric dilution of precision GDOP when the sampling interval is 5 seconds and the sampling period is 120 seconds.

[0024] Optionally, the preset optimization target includes a preset positioning performance target, a preset coverage multiplicity target and a preset construction cost target;

[0025] A multi-objective function is constructed based on the mutual relationship and the preset optimization objectives, including:

[0026] Constructing a positioning performance sub-objective function based on the mutual relationship and the preset positioning performance target;

[0027] Constructing a coverage multiplicity sub-objective function based on the preset coverage multiplicity objective;

[0028] Constructing a construction cost sub-objective function based on the constellation parameters of the low-orbit satellite constellation and the preset construction cost target;

[0029] The positioning performance sub-objective function, the coverage multiplicity sub-objective function and the construction cost sub-objective function are weighted to obtain a multi-objective function.

[0030] Optionally, the positioning performance sub-objective function is:

[0031] Q PPP (x)=|Pr T -A|

[0032] Among them, Pr T represents the probability of successful convergence of precise point positioning PPP within time T; A represents the expected probability of successful convergence of precise point positioning PPP.

[0033] Optionally, the coverage multiplicity sub-objective function is:

[0034]

[0035] Where v(x) represents the average number of visible low-orbit satellites during the entire observation period at a certain ground station; E(v(x)) represents the mean value of v(x) at all ground stations; represents the standard deviation of v(x) at all ground stations; ξ is the expected uniform coverage density.

[0036] Optionally, the construction cost sub-objective function is:

[0037]

[0038] Among them, P max Indicates the upper limit of the number of orbital surfaces; S max Indicates the upper limit of the number of satellites in each orbital plane; h max Indicates the upper limit of the orbit height; i max Indicates the upper limit of orbital inclination.

[0039] Compared with the prior art, the solution provided by the embodiment of the present application has at least the following beneficial effects:

[0040] 1. The solution provided in the embodiment of the present application, on the one hand, proposes the concept of equivalent GDOP and gives a formula definition, which can not only comprehensively describe the continuous impact of the number of satellites, operating speed, operating direction and degree of geometric change on the PPP convergence process; but also can calculate for less than four satellites.

[0041] 2. In the solution provided in the embodiment of the present application, the conversion relationship between the equivalent GDOP values ​​at different sampling intervals has the significance and advantage that the sampling interval can be appropriately enlarged in constellation optimization, reducing the sampling points required for equivalent GDOP calculation to improve the calculation efficiency of constellation optimization.

[0042] 3. In the solution provided in the embodiment of the present application, a quantitative relationship between the LEO constellation equivalent GDOP and the LEO enhanced BeiDou PPP convergence time is established, and the expected precise positioning performance of the LEO constellation can be evaluated directly by calculating the LEO constellation equivalent GDOP value, without the need for time-consuming navigation data simulation and precise positioning evaluation operations during the optimization process.

[0043] 4. In the solution provided in the embodiment of the present application, a weighted combination of expected positioning performance, expected coverage multiplicity, and minimum construction cost is used as the objective function of genetic algorithm constellation optimization. Compared with the traditional method of only using coverage multiplicity as the objective function, it better meets the design requirements of low-orbit high-precision enhanced constellations. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic diagram of a flow chart of a method for optimizing a low-orbit navigation enhancement satellite constellation provided in an embodiment of the present application;

[0045] Figure 2 A schematic diagram of an equivalent geometric dilution of precision GDOP provided in an embodiment of the present application is shown;

[0046] Figure 3A A schematic diagram showing a prior art low-orbit satellite constellation solution 1 provided in an embodiment of the present application;

[0047] Figure 3B A schematic diagram showing another prior art low-orbit satellite constellation solution 2 provided in an embodiment of the present application;

[0048] Figure 4A A schematic diagram showing the time series of positioning errors of PPP in the east direction;

[0049] Figure 4B Schematic diagram showing the time series of positioning error of PPP in the north direction;

[0050] Figure 4C Schematic diagram showing the time series of positioning error of PPP in the elevation direction;

[0051] Figure 5 A process of optimizing constellation parameters using a genetic algorithm provided in an embodiment of the present application;

[0052] Figure 6 The population and evaluation results of each generation provided by the embodiments of the present application;

[0053] Figure 7 A brief flowchart of a method for optimizing a low-orbit navigation enhancement satellite constellation provided in an embodiment of the present application. DETAILED DESCRIPTION

[0054] In the solutions provided in the embodiments of this application, the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0055] In order to better understand the above technical scheme, the technical scheme of the present application is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical scheme of the present application, rather than limitations on the technical scheme of the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0056] The following is a further detailed description of a method for optimizing a low-orbit navigation enhancement satellite constellation provided by an embodiment of the present application in conjunction with the accompanying drawings of the specification. The specific implementation of the method may include the following steps (the method flow is as follows: Figure 1 shown):

[0057] Step 101, determining a constellation parameter set to be optimized according to the number of sub-constellations in the low-orbit satellite constellation, and constructing constraint conditions according to preset optimization constraints.

[0058] Since the low-orbit satellite constellation includes one or more sub-constellations, for example, each satellite in the low-orbit satellite constellation is regarded as a sub-constellation, then each sub-constellation needs to be optimized when optimizing the low-orbit satellite constellation; and each sub-constellation corresponds to the same parameter type, for example, the parameter type includes orbital plane, orbital altitude, and orbital inclination, etc. When the parameters to be optimized for each sub-constellation are configured, the parameters to be optimized for the entire low-orbit satellite constellation include the parameters to be optimized for all sub-constellations (the "constellation parameter set to be optimized" described above or below). For example, if the number of sub-constellations in the low-orbit satellite constellation is N, and the parameters to be optimized corresponding to each sub-constellation are M, where N and M are positive integers, then the number of parameters in the constellation parameter set to be optimized corresponding to the low-orbit satellite constellation is N*M. That is to say, in the scheme provided in the embodiment of the present application, the constellation parameter set to be optimized corresponding to the low-orbit satellite constellation is related to the number of sub-constellations in the low-orbit satellite constellation.

[0059] As an example, the constellation parameter set to be optimized includes: the number of orbital planes of each sub-constellation, the number of satellites in each orbital plane, the phase factor between adjacent satellites on adjacent orbital planes in each sub-constellation, the orbital altitude and orbital inclination corresponding to each constellation, the ascending node right ascension of the nominal satellite and the mean anomaly of the nominal satellite, wherein the nominal satellite refers to a satellite in a specified orbital plane in a specific sub-constellation, such as the first satellite in the first orbital plane of the first sub-constellation is the nominal satellite. Once the ascending node right ascension and the mean anomaly of the nominal satellite are determined, since the constellation parameters determine the relative position relationship between other satellites and the satellite, the orbital parameters of all satellites in the constellation will also be determined accordingly.

[0060] In addition, in the solution provided in the embodiment of the present application, some parameters of some sub-constellations in the low-orbit satellite constellation can also be configured as specified values ​​(such as 0 or 1), and the parameters with values ​​of 0 or 1 are not optimized when optimizing the low-orbit satellite constellation, that is, the number of parameters in the constellation parameter set to be optimized is less than N*M, which is not limited here. As another example, if the low-orbit satellite constellation includes two sub-constellations, namely sub-constellation 1 and sub-constellation 2. If only the circular orbit is considered, the perigee angle of the orbital eccentricity is often set to 0, which is used as an optimization variable (or the decision variable described below); in addition, in order to prevent the overall rotation of the low-orbit satellite constellation, the ascending node right ascension and the mean anomaly of the nominal satellite of sub-constellation 1 are set to 0, and then there are 12 constellation parameters to be optimized in the low-orbit satellite constellation, which are the number of orbital planes of sub-constellation 1, the number of satellites in each orbital plane in sub-constellation 1, the phase factor between adjacent satellites on adjacent orbital planes in sub-constellation 1, the orbital altitude of each orbit in sub-constellation 1, the orbital inclination of each orbit in sub-constellation 1, the number of orbital planes of sub-constellation 2, the number of satellites in each orbital plane in sub-constellation 2, the phase factor between adjacent satellites on adjacent orbital planes in sub-constellation 2, the orbital altitude of each orbit in sub-constellation 2, the orbital inclination of each orbit in sub-constellation 2, the ascending node right ascension of the nominal satellite of sub-constellation 2, and the mean anomaly of the nominal satellite of sub-constellation 2. Based on this, the constellation parameter set x to be optimized provided in the embodiment of the present application is as follows:

[0061]

[0062] Among them, P 1 Indicates the orbital plane number of sub-constellation 1; S 1 Indicates the number of satellites in each orbital plane of sub-constellation 1; F 1 represents the phase factor between adjacent satellites in the adjacent orbital plane of sub-constellation 1; h 1 represents the orbital height of each orbit in sub-constellation 1; i 1 represents the orbital inclination of each orbit in sub-constellation 1; P 2 Indicates the orbital plane number of sub-constellation 2; S 2 Indicates the number of satellites in each orbital plane in sub-constellation 2; F 2 represents the phase factor between adjacent satellites in adjacent orbital planes in sub-constellation 2; h 2 represents the orbital height of each orbit in sub-constellation 2; i 2 represents the orbital inclination of each orbit of sub-constellation 2; Ω 2 M represents the right ascension of the ascending node of the nominal satellite of sub-constellation 2; 2 Represents the mean anomaly of the nominal satellite of sub-constellation 2.

[0063] Furthermore, when determining the constellation parameter set to be optimized corresponding to the low-orbit satellite constellation, the search range of each parameter in the constellation parameter set is also set, such as the search range when the genetic algorithm (as shown below) is used for optimization. 1 The search range is set to 6 to 12; S 1 The search range is set to 6 to 18; F 1 The search range is set to 0 to 11; h 1 The search range is set to 600km~1000km; i 1 The search range is set to 0°~110°; P 2 Set the search range to 6 to 12; S 2 Set the search range to 6 to 18; F 2 Set the search range 0~11; h 2 Set the search range to 1100km~1600km;i 2 Set the search range 0°~110°;Ω 2 Set the search range to 0°~30°; M 2 The search range is set to 0° to 60°. It should be understood that the search range set for each parameter should not only include the global optimal solution, but also should not be too large to prevent increasing the search burden. The specific setting and corresponding adjustment can be made according to the needs, and no limitation is made here.

[0064] In the solution provided in the embodiment of the present application, in order to achieve the optimization of the low-orbit satellite constellation, it is also necessary to pre-set the optimization goal and the preset optimization constraints, that is, to clarify the constellation design goal (see below), design constraints and decision variables (corresponding to the above "optimization variables"), and transform the optimization problem of the low-orbit satellite constellation into an optimization solution; wherein, the design goal refers to the core indicator used to evaluate the quality of the optimization results during the optimization process; the design constraint is the limiting condition in the optimization process. As an example, the preset optimization constraints include ensuring double, triple and quadruple coverage availability of not less than 100%, 80% and 60% respectively on a global scale; the number of orbital planes, the number of satellites in each orbital plane, and the phase factor between adjacent satellites on adjacent orbital planes are all integers; the phase factor between adjacent satellites on adjacent orbital planes is less than the number of orbital planes.

[0065] As an example, taking the above-mentioned low-orbit satellite constellation including two sub-constellations, sub-constellation 1 and sub-constellation 2, the constraint conditions are constructed according to the preset optimization constraints, including:

[0066] The constraints are constructed using the following formula:

[0067]

[0068] Among them, δ2(x) represents the availability of double coverage of satellites at all sites in all epochs, δ3(x) represents the availability of triple coverage of satellites at all sites in all epochs, and δ4(x) represents the availability of quadruple coverage of satellites at all sites in all epochs.

[0069] Step 102, constructing the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning PPP, and constructing a multi-objective function based on the relationship and the preset optimization goal, wherein the equivalent GDOP characterizes the impact of the number of visible low-orbit satellites, the running speed, the running direction and the degree of geometric change on the PPP convergence process.

[0070] As mentioned in the previous background section, the standard GDOP can only reflect the instantaneous positioning accuracy of the standard navigation positioning service, and cannot reflect the convergence performance of the precise point positioning PPP. In the solution provided in the embodiment of the present application, in order to reflect the convergence performance of the precise point positioning PPP, the concept of equivalent geometric precision factor GDOP is proposed. For ease of understanding, the concept of equivalent geometric precision factor GDOP is briefly introduced below.

[0071] Figure 2 A schematic diagram of an equivalent geometric dilution of precision GDOP provided in an embodiment of the present application is shown.

[0072] For example, determine one or more tracks of each visible satellite in the low-orbit satellite constellation running over the ground station within a preset time, and sample each track using a preset collection interval from a preset time to obtain one or more sampling points corresponding to each track; calculate the satellite-to-ground line of the spatial geometric structure formed by the line connecting all the adopted sampling points on all tracks corresponding to each visible star and the ground station according to the preset standard GDOP, and use the satellite-to-ground line as the equivalent GDOP. For example, Figure 2 As shown in the figure, within a period of time S, the satellite draws several tracks above the ground station. From time t = 0, a sampling point is taken at intervals of time τ on each track. Each track can have at most Points, Indicates rounding up, and then according to the standard GDOP form, calculate the spatial geometric structure formed by the connection lines of all sampling points on all trajectories and ground stations (that is, all solid and dotted lines in the figure represent the satellite-ground connection lines, while the traditional standard GDOP only involves the solid lines representing the satellite-ground connection lines), and define this value as the equivalent GDOP, recorded as EGDOP S|τ , where S and τ are both in seconds.

[0073] Furthermore, it should be noted that the selection of the sampling interval τ directly affects the number of virtual observations of the satellite-ground connection and thus affects the EGDOP S|τFor a shorter sampling time interval τ, the encrypted points formed by a shorter sampling time interval τ / n can be considered as "parallel address points", where n is a positive integer; that is, it is assumed that the satellite-to-ground connection between the same sampling point on the same trajectory and the ground station has not changed in a very short period of time, then the relationship between the equivalent GDOPs corresponding to different sampling time intervals, that is, EGDOP S|τ With EGDOP S|(τ / n) The mutual relationships are as follows.

[0074] Assuming that the number of satellites visible at a certain epoch k on a ground station is q, for the coefficient matrix H of the observation equation when solving the pseudo-range single-point positioning, the first three columns of the matrix reflect the projection of the lines connecting each satellite and the station in the east-west direction, north-south direction and elevation direction at the same epoch, which is related to the number of satellites and the azimuth and altitude angle of the satellite relative to the station. Since there is only one receiver clock error parameter for the receiver at a certain station, the elements in the fourth column are all 1; that is, the matrix H k It consists of the direction cosine matrix corresponding to the location parameters and the column vector corresponding to the receiver clock error parameters, all of which are 1:

[0075]

[0076] Among them, l, m and p are the direction cosine parameters corresponding to the east, north and elevation components respectively.

[0077] Under the premise of q≥4, the standard GDOP is defined as:

[0078]

[0079] For the sampling process with duration S and sampling interval τ, the observation equation design matrix is:

[0080]

[0081] In the formula, the superscript and subscript of H represent the epoch number and time, respectively.

[0082]

[0083] If the sampling interval becomes τ / n, then:

[0084]

[0085] Finally, the equivalent GDOP (EGDOP) corresponding to the sampling time interval τ S|τ ) and the equivalent GDOP (EGDOP) corresponding to the sampling time interval τ / n S|(τ / n) ) are as follows:

[0086]

[0087] In the solution provided in the embodiment of the present application, the conversion relationship between equivalent GDOP values ​​at different sampling intervals has the significance and advantage that the sampling interval can be appropriately enlarged in constellation optimization, and the sampling points required for equivalent GDOP calculation can be reduced to improve the calculation efficiency of constellation optimization.

[0088] Furthermore, in order to illustrate that the actual impact of PPP is not only coverage, but also satellite speed, direction, distribution, etc., and the parameters that can reflect the combined effect of these factors, the following uses two low-orbit satellite constellation solutions obtained by existing technologies as an example to illustrate.

[0089] Here, both low-orbit solution 1 and low-orbit solution 2 are solutions obtained by the prior art, not solutions optimized by the present invention. The purpose is simply to illustrate that the two solutions have obvious differences in PPP convergence performance when the coverage (number of visible satellites) is the same, indicating that the actual factors affecting PPP are not only coverage, but also satellite speed, direction, distribution, etc. The parameter that can reflect the comprehensive effect of these factors is the equivalent GDOP mentioned in the present invention. It is precisely because the equivalent GDOP of the two is different that the difference in PPP convergence performance is caused.

[0090] For example, see Figure 3A , Figure 3B , Figure 4A , Figure 4B as well as Figure 4C ,in, Figure 3A A schematic diagram showing a prior art low-orbit satellite constellation solution 1 provided in an embodiment of the present application; Figure 3B A schematic diagram showing another prior art low-orbit satellite constellation solution 2 provided in an embodiment of the present application; Figure 4A A schematic diagram showing the time series of positioning errors of PPP in the east direction; Figure 4B Schematic diagram showing the time series of positioning error of PPP in the north direction; Figure 4C Schematic diagram showing the time series of positioning error of PPP in the elevation direction.

[0091] Specifically, the coverage (number of visible satellites) of low-orbit scheme 1 and low-orbit scheme 2 are the same, and the average number of visible low-orbit satellites is 7.4 and 7.5 respectively. However, the convergence time after enhancing Beidou PPP is 0.5min and 1.3min respectively. The reasons are analyzed as follows: the orbit height of the low-orbit constellation in scheme 1 is low, the satellite runs faster relative to the ground, the sky track passed per unit time is longer, and the degree of change of the constellation geometry is greater; the distribution of low-orbit satellites in scheme 1 is better relative to the observation station. It can be seen from Figure 3 that there are low-orbit satellites distributed in basically all directions. In terms of altitude angle, there are both high-elevation angle observations above 75° and low-elevation angle observations of about 15°; in addition, the running directions of low-orbit satellites in scheme 1 are staggered, with both movement from southwest to northeast and movement from northwest to southeast, which is beneficial to the improvement of the geometry in all directions, while scheme 2 is basically movement from southeast to northwest, which is relatively simple. In order to describe the combined impact of multiple factors, the equivalent GDOP of the LEO constellation of Scheme 1 and Scheme 2 for 1 minute cumulative duration (sampling interval 5s) was calculated, and the results were 0.51 and 0.68 respectively. The smaller equivalent GDOP value of Scheme 1 indicates that its cumulative geometric figure changes more significantly in the corresponding period, and the gain of convergence enhancement is also greater, which matches the actual situation. It can be seen that Figure 3A , Figure 3B , Figure 4A , Figure 4B as well as Figure 4C It is verified that the convergence time of low-orbit enhanced Beidou PPP is not simply related to the number of visible low-orbit satellites.

[0092] further, Figure 3A , Figure 3B , Figure 4A , Figure 4B as well as Figure 4C For the low-orbit constellations in Scheme 1 and Scheme 2, the equivalent GDOP of 1 minute cumulative duration at a 5 second sampling interval is used The calculated results are 0.51 and 0.68 respectively. At a sampling interval of 1s, the equivalent GDOP of 1min cumulative time is The calculated results are 0.23 and 0.30 respectively. It can be found that The calculation result is exactly of times, verifying the correctness of the conversion formula derivation in the technical solution.

[0093] Furthermore, in the solution provided in the embodiment of the present application, in order to enable the equivalent geometric precision factor GDOP to characterize the precise point positioning PPP convergence performance, it is also necessary to construct the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the precise point positioning PPP convergence time. As an example, in the solution provided in the embodiment of the present application, the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence in different convergence time periods is constructed.

[0094] As an example, constructing the relationship between the equivalent geometric precision factor GDOP of a low-orbit satellite constellation and the probability of successful convergence of a precise single-point positioning PPP includes: constructing multiple low-orbit satellite constellation models, calculating the equivalent GDOP of its low-orbit satellite constellation based on each low-orbit satellite constellation model and simulating and obtaining observation data; calculating the relationship between the equivalent GDOP and the low-orbit enhanced Beidou PPP convergence time based on the observation data corresponding to the multiple low-orbit satellite constellation models; constructing the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of a precise single-point positioning PPP based on the relationship between the calculated equivalent GDOP index of the low-orbit satellite constellation and the probability of successful convergence of a low-orbit enhanced Beidou PPP. That is, in the solution provided in the embodiment of the present application, multiple simulated low-orbit constellations and their observation data are used to establish the relationship between the equivalent GDOP of the low-orbit constellation and the probability of successful convergence of the low-orbit enhanced Beidou PPP.

[0095] As another example, the relationship between the equivalent GDOP of the low-orbit constellation and the probability of successful PPP convergence within 30 seconds, 60 seconds, and 120 seconds is constructed. The specific formula is as follows:

[0096] When the sampling interval is 5 seconds, the probability of PPP converging successfully in 30 seconds is Pr 30 Equivalent GDOP (EGDOP 30|5 ) is:

[0097]

[0098] When the sampling interval is 5 seconds, the probability of PPP converging successfully in 60 seconds is Pr 60 Equivalent GDOP (EGDOP 60|5 ) is:

[0099]

[0100] When the sampling interval is 5 seconds, the probability of PPP converging successfully in 120 seconds is Pr 120 Equivalent GDOP (EGDOP 120|5 ) is:

[0101]

[0102] According to the above relationship, the sampling genetic algorithm in the embodiment of the present application can directly convert the equivalent GDOP of the low-orbit constellation into the probability of successful PPP convergence. For example, when the equivalent GDOP of the low-orbit constellation with a cumulative duration of 1 minute is less than 0.29, 0.30 and 0.51, it means that fast PPP convergence within 1 minute can be achieved with probabilities of 100%, 95% and 65%, respectively. By comparing the calculated probability with the expected convergence probability, the adaptability of the individual can be evaluated. In the genetic algorithm, each constellation parameter set to be optimized is regarded as an individual.

[0103] In the solution provided in the embodiment of the present application, a quantitative relationship between the LEO constellation equivalent GDOP and the LEO enhanced BeiDou PPP convergence time is established, and the expected precise positioning performance of the LEO constellation can be evaluated directly by calculating the LEO constellation equivalent GDOP value, without the need for time-consuming navigation data simulation and precise positioning evaluation operations during the optimization process.

[0104] Step 103: Based on the preset optimization goal, the constraint conditions and the multi-objective function, a genetic algorithm is used to optimize the parameters in the constellation parameter set to obtain an optimized constellation parameter set, and an optimized low-orbit satellite constellation is obtained based on the optimized constellation parameter set.

[0105] As mentioned above, in order to achieve the optimization of the low-orbit satellite constellation, it is also necessary to pre-set optimization goals and preset optimization constraints. Normally, the ideal constellation (optimized constellation) should be close to the expected precise positioning convergence performance requirements. As an example, the preset optimization goals include preset positioning performance goals, preset coverage multiplicity goals, and preset construction cost goals. For example, the preset positioning performance goals include a probability of 80% to achieve a horizontal positioning accuracy of 10 cm and an elevation of 20 cm within 1 minute globally; the preset coverage multiplicity goal is that 8 satellites are evenly visible under a 7° cutoff satellite elevation angle globally; the preset construction cost goal is to reduce the construction cost as much as possible. That is, in the solution provided in the embodiment of the present application, the optimization of the low-orbit satellite constellation is a multi-objective optimization process that includes positioning performance, coverage multiplicity, and construction cost, so it is necessary to construct a multi-objective function. As an example, a positioning performance sub-objective function is constructed based on the mutual relationship and the preset positioning performance target; a coverage multiplicity sub-objective function is constructed based on the preset coverage multiplicity target; a construction cost sub-objective function is constructed based on the constellation parameters of the low-orbit satellite constellation and the preset construction cost target; and the positioning performance sub-objective function, the coverage multiplicity sub-objective function and the construction cost sub-objective function are weighted to obtain a multi-objective function.

[0106] As another example, based on the mutual relationship and the preset positioning performance target, a positioning performance sub-objective function Q is constructed. PPP (x) is as follows:

[0107] Q PPP (x)=|Pr T -A| ⑾

[0108] Among them, Pr T represents the probability of successful convergence of precise point positioning PPP within time T; A represents the expected probability of successful convergence of precise point positioning PPP.

[0109] For example, the closer the probability of the precise point positioning PPP successfully achieving rapid convergence within 1 minute is to the expected 80%, the better the individual is. Specifically, the objective function Q PPP (x) is as follows:

[0110] Q PPP (x)=|Pr 60 -80% |

[0111] Among them, Pr 60 It can be obtained by the above formula (9).

[0112] From the above formula, we can see that the closer the probability of PPP successfully achieving rapid convergence within 1 minute is to the expected 80%, the better the individual is. This probability value can be calculated by the equivalent GDOP value, where the actual sampling time interval used to calculate the equivalent GDOP value is τ * As an example, in order to improve the optimization efficiency, the actual sampling time interval τ * = 15s, so the convergence probability and EGDOP should be used 60|5 The relationship between EGDOP 60|15 Convert to EGDOP 60|5 , while EGDOP 60|15 The calculated value is the average value of the equivalent GDOP calculated values ​​of all ground stations on the ground. The details are as follows:

[0113]

[0114] As another example, a coverage multiplicity sub-objective function is constructed based on the preset coverage multiplicity objective. Specifically, the coverage multiplicity sub-objective function Q Ncov The expression (x) is as follows:

[0115]

[0116] Where v(x) represents the average number of visible low-orbit satellites during the entire observation period at a certain ground station; E(v(x)) represents the mean value of v(x) at all ground stations; represents the standard deviation of v(x) at all ground stations; ξ is the expected uniform coverage multiplicity, for example, ξ=8.

[0117] From the above formula, we can see that Q NCov (x) is described as the mean E(v(x)) and standard deviation of v(x) at all ground stations Take a compromise function.

[0118] As another example, a construction cost sub-objective function Q is constructed based on the constellation parameters of the low-orbit satellite constellation and the preset construction cost target. Cost (x). Specifically, the coverage multiplicity sub-objective function Q Cost The expression (x) is as follows:

[0119]

[0120] Among them, P max Indicates the upper limit of the number of orbital surfaces; S max Indicates the upper limit of the number of satellites in each orbital plane; h max Indicates the upper limit of the orbit height; i max Indicates the upper limit of orbital inclination.

[0121] Generally speaking, the fewer orbital planes and the fewer satellites in each orbital plane, the lower the satellite launch cost and manufacturing cost. The lower the orbital altitude and the lower the orbital inclination, the lower the satellite launch cost. Therefore, Q Cost (x) can reflect the goal of minimizing the cost of constellation construction. max , S max 、h max 、i max The values ​​are as follows

[0122]

[0123] Based on this, the multi-objective function constructed based on the positioning performance sub-objective function, the coverage multiplicity sub-objective function and the construction cost sub-objective function is as follows:

[0124] f(x)=min{w1·Q PPP (x)+w2·Q NCov (x)+w3·Q Cost (x)} ⒃

[0125] Among them, w1 represents the weight corresponding to the positioning performance, w2 represents the weight corresponding to the coverage multiplicity, and w3 represents the weight corresponding to the construction cost. For example, w1, w2 and w3 can be set to 0.5, 0.3 and 0.2 respectively.

[0126] In the solution provided in the embodiment of the present application, a weighted combination of expected positioning performance, expected coverage multiplicity, and minimum construction cost is used as the objective function of genetic algorithm constellation optimization. Compared with the traditional method of only using coverage multiplicity as the objective function, it better meets the design requirements of low-orbit high-precision enhanced constellations.

[0127] As an example, the solution provided in the embodiment of the present application uses a genetic algorithm to optimize the parameters of the constellation parameter set to be optimized for the low-orbit satellite constellation as an individual. Before optimization, the genetic algorithm toolbox parameters are first configured to set the decision variables and search range, constraints, objective function, encoding method, decoding method, initial population generation method, population size, selection operator, crossover operator, mutation operator, crossover probability, mutation probability, number of elite individuals, and algorithm termination conditions.

[0128] As another example, the genetic algorithm toolbox in the Matlab 2018b software package is used for data processing (other software platforms such as Python also integrate genetic algorithm toolboxes for development and use), and the input parameters are set as follows: decision variables and search ranges, constraints and objective functions, binary encoding, decimal decoding, and the initial population uses a uniform generation operator with a population size of 200. The selection operator uses a competitive selection operator, the crossover operator uses the Laplace operator, and the mutation operator uses a power function mutation operator. At the same time, integer truncation technology and constraint processing technology are introduced. The crossover probability is 0.8, the mutation probability is 0.2, the number of elite individuals is 4, and the algorithm termination condition is 20 generations of inheritance. Next, the genetic algorithm toolbox is used to optimize the constellation parameters. Specifically, the process of genetic algorithm for optimizing constellation parameters is as follows: Figure 5 The population and evaluation results of each generation are shown in Figure 6 shown.

[0129] Furthermore, the above Figure 6 This is the result of the process of using the method of the present invention to perform genetic algorithm constellation optimization design. It can be seen that with the advancement of reproduction and evolution, the corresponding penalty value gradually decreases, the fitness of the population gradually becomes stronger, and the optimal individual of the last generation (the termination condition in the example is set to 20 generations of inheritance) can obtain the optimal low-orbit high-precision enhanced constellation configuration after decoding.

[0130] Finally, the optimized constellation parameter set is output. After decoding, the optimal individual of the last generation can obtain the optimal low-orbit high-precision enhanced constellation configuration. As an example, the optimized constellation parameter set results are as follows:

[0131]

[0132] In addition, for ease of understanding, a brief flowchart of a method for optimizing a low-orbit navigation enhancement satellite constellation provided in an embodiment of the present application is given below. Figure 7 .exist Figure 7 In the flowchart shown, the scheme includes the following steps: Step ①: Input the optimization problem of low-orbit high-precision satellite constellation. Step ②: Determine the decision variables and their search range based on the number of sub-constellations of the hybrid low-orbit constellation. Step ③: Determine the constraints based on the requirements such as N-layer coverage availability, partial parameter integer constraints and inequality constraints. Step ④: Reasonably weight the target factors such as expected positioning performance, expected coverage multiplicity, and minimum construction cost to construct a multi-objective function. Step ⑤: Configure the genetic algorithm toolbox parameters, set the decision variables and search range, constraints, objective function, encoding method, decoding method, initial population generation method, population size, selection operator, crossover operator, mutation operator, crossover probability, mutation probability, number of elite individuals, and algorithm termination conditions. Step ⑥: Use the genetic algorithm toolbox to optimize the constellation parameters. Step ⑦: Output the optimal configuration parameter set of the low-orbit constellation.

[0133] The solution provided in the embodiment of the present application, on the one hand, proposes the concept of equivalent GDOP and provides a formula definition, which can not only comprehensively describe the continuous impact of the number of satellites, operating speed, operating direction and degree of geometric change on the PPP convergence process; but also can calculate for less than four satellites.

[0134] In the solution provided in the embodiment of the present application, a quantitative relationship between the LEO constellation equivalent GDOP and the LEO enhanced BeiDou PPP convergence time is established, and the expected precise positioning performance of the LEO constellation can be evaluated directly by calculating the LEO constellation equivalent GDOP value, without the need for time-consuming navigation data simulation and precise positioning evaluation operations during the optimization process.

[0135] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for optimizing a low-orbit navigation enhancement satellite constellation, characterized in that: include: Determining a constellation parameter set to be optimized according to the number of sub-constellations in the low-orbit satellite constellation, and constructing constraint conditions according to preset optimization constraints; Constructing the relationship between the equivalent geometric dilution of precision (GDOP) of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning (PPP), and constructing a multi-objective function based on the relationship and the preset optimization goal, wherein the equivalent geometric dilution of precision (GDOP) characterizes the influence of the number of visible low-orbit satellites, the running speed, the running direction and the degree of geometric figure change on the PPP convergence process; Based on the preset optimization goal, the constraint condition and the multi-objective function, a genetic algorithm is used to optimize the parameters in the constellation parameter set to be optimized to obtain an optimized constellation parameter set, and based on the optimized constellation parameter set, an optimized low-orbit satellite constellation is obtained; Construct the relationship between the equivalent geometric dilution of precision (GDOP) of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning (PPP), including: Construct multiple low-orbit satellite constellation models, calculate the equivalent geometric dilution of precision (GDOP) of each low-orbit satellite constellation based on each low-orbit satellite constellation model, and obtain observation data through simulation; Based on the observation data corresponding to the multiple low-orbit satellite constellation models, the relationship between the equivalent geometric precision factor GDOP index and the low-orbit enhanced Beidou PPP convergence time is calculated; Based on the calculated relationship between the equivalent geometric precision factor GDOP index of the low-orbit satellite constellation and the convergence time of the low-orbit enhanced Beidou PPP, the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of the precise point positioning PPP is established; Calculate the equivalent geometric dilution of precision (GDOP) of each LEO satellite constellation based on its LEO satellite constellation model, including: Determine one or more trajectories of each visible satellite in the low-orbit satellite constellation over the ground station within a preset time period based on each low-orbit satellite constellation model, and sample each trajectory using a preset collection interval starting from a preset time to obtain one or more sampling points corresponding to each trajectory; According to the preset standard GDOP, the satellite-to-ground line of the spatial geometric structure formed by the line connecting all the adopted sampling points on all the trajectories corresponding to each visible star and the ground station is calculated, and the satellite-to-ground line is used as the equivalent geometric dilution of precision GDOP; The preset optimization objectives include a preset positioning performance objective, a preset coverage multiplicity objective, and a preset construction cost objective; A multi-objective function is constructed based on the mutual relationship and the preset optimization objectives, including: Constructing a positioning performance sub-objective function based on the mutual relationship and the preset positioning performance target; Constructing a coverage multiplicity sub-objective function based on the preset coverage multiplicity objective; Constructing a construction cost sub-objective function based on the constellation parameters of the low-orbit satellite constellation and the preset construction cost target; The positioning performance sub-objective function, the coverage multiplicity sub-objective function and the construction cost sub-objective function are weighted to obtain a multi-objective function.

2. The method according to claim 1, characterized in that The constellation parameter set to be optimized includes: the number of orbital planes of each sub-constellation, the number of satellites in each orbital plane, the phase factor between adjacent satellites on adjacent orbital planes in each sub-constellation, the orbital altitude and orbital inclination corresponding to each constellation, the right ascension of the ascending node of the nominal satellite, and the mean anomaly angle of the nominal satellite.

3. The method according to claim 2, characterized in that in, The preset optimization constraints include ensuring double, triple and quadruple coverage availability of no less than 100%, 80% and 60% respectively on a global scale; the number of orbital planes, the number of satellites in each orbital plane, and the phase factor between adjacent satellites on adjacent orbital planes are all integers; the phase factor between adjacent satellites on adjacent orbital planes is less than the number of orbital planes.

4. The method according to claim 3, characterized in that If the low-orbit satellite constellation includes a first sub-constellation and a second sub-constellation, a constraint condition is constructed according to a preset optimization constraint, including: The constraints are constructed using the following formula: Where δ2(x) represents the availability of satellite double coverage for all sites in all epochs, δ3(x) represents the availability of satellite triple coverage for all sites in all epochs, and δ4(x) represents the availability of satellite quadruple coverage for all sites in all epochs. P 1 Indicates the orbital plane number of the first sub-constellation; S 1 Indicates the number of satellites in each orbital plane of the first sub-constellation; F 1 P represents the phase factor between adjacent satellites in the adjacent orbital plane of the first sub-constellation; 2 Indicates the orbital plane number of the second sub-constellation; S 2 Indicates the number of satellites in each orbital plane of the second sub-constellation; F 2 Represents the phase factor between adjacent satellites in the adjacent orbital plane of the second sub-constellation.

5. The method according to any one of claims 1 to 4, characterized in that: in, Under different convergence times, the relationship between the equivalent geometric precision factor GDOP of the low-orbit satellite constellation and the probability of successful convergence of precise point positioning PPP is: Among them, Pr 30 Pr represents the relationship between the equivalent geometric precision factor GDOP and the probability of successful convergence of precise point positioning PPP within 30 seconds; 60 Pr represents the relationship between the equivalent geometric precision factor GDOP and the probability of successful convergence of precise point positioning PPP within 60 seconds; 120 The relationship between the equivalent geometric dilution of precision (GDOP) and the probability of successful convergence of precise point positioning (PPP) within 120 seconds; EGDOP 30|5 Indicates the equivalent geometric precision factor GDOP when the sampling time interval is 5 seconds and the sampling period is 30 seconds; EGDOP 60|5 Indicates the equivalent geometric precision factor GDOP when the sampling time interval is 5 seconds and the sampling period is 60 seconds; EGDOP 120|5 Indicates the equivalent geometric dilution of precision GDOP when the sampling interval is 5 seconds and the sampling period is 120 seconds.

6. The method according to claim 1, characterized in that The positioning performance sub-objective function is: Q PPP (x)=Pr T -A Among them, Pr T represents the probability of successful convergence of precise point positioning PPP within time T; A represents the expected probability of successful convergence of precise point positioning PPP.

7. The method according to claim 6, characterized in that The coverage multiplicity sub-objective function is: Where v(x) represents the average number of visible low-orbit satellites during the entire observation period at a certain ground station; E(v(x)) represents the mean value of v(x) at all ground stations; represents the standard deviation of v(x) at all ground stations; ξ is the expected uniform coverage density.

8. The method according to claim 6, characterized in that The construction cost sub-objective function is: Among them, P max Indicates the upper limit of the number of orbital surfaces; S max Indicates the upper limit of the number of satellites in each orbital plane; h max Indicates the upper limit of the orbit height; i max Indicates the upper limit of orbital inclination.

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