Fast optimization method of regional navigation constellation based on revisit characteristics

Abstract

The application discloses a regional navigation constellation fast optimization method based on revisit characteristics, and belongs to the field of orbit perturbation and satellite constellation configuration. The application is realized by the following method: initial values of a regression orbit are calculated based on a J2 average orbit dynamics model, an iterative correction method is used to correct the ascending node drift, and high-precision revisit coverage of satellites on a target coverage area is realized according to a strict regression orbit design result. Through a constellation configuration parameter selection method, the range of constellation configuration parameters required by a navigation task is determined, an initial solution is obtained by using a genetic algorithm based on an initial population, a local search algorithm is used to optimize the initial solution obtained by the genetic algorithm, and the optimal result under the constellation configuration parameters is obtained. A plurality of sets of constellation configuration parameters in the range of constellation configuration parameters required by the navigation coverage task are optimized and solved one by one, a plurality of constellation configuration optimization results are obtained, multi-index comprehensive evaluation is carried out based on the navigation positioning task requirement, and the optimal navigation constellation configuration is screened.

Description

Technical Field

[0001] The present invention relates to a method for rapid optimization of a regional navigation constellation based on revisit characteristics, which is particularly suitable for constructing a low-orbit satellite navigation system that accurately covers a target area with a minimum number of satellites, and belongs to the field of orbital perturbation and satellite constellation configuration. Background Art

[0002] In recent years, the global satellite navigation system has continued to improve. The four major global navigation systems, represented by the US GPS, Russia's GLONASS, Europe's Galileo, and China's BeiDou system, collectively provide high-precision positioning, navigation, and timing services to users worldwide. However, for many navigation missions focused solely on regional coverage, the global, all-weather coverage capabilities of existing navigation systems are redundant. Therefore, considering building a low-orbit regional navigation satellite system could significantly reduce the launch, construction, and maintenance costs of the navigation system.

[0003] Currently, most navigation satellites are deployed in medium- and high-orbit orbits. Compared to traditional medium- and high-orbit satellites, low-orbit satellites offer numerous advantages. First, low-orbit satellites are closer to the ground, shortening the signal propagation path and directly reducing atmospheric latency and signal attenuation. This is crucial for applications requiring extremely high positioning accuracy, such as self-driving cars, drone delivery, precision agriculture, and disaster response. Second, low-orbit satellites offer shorter signal transmission latency, as electromagnetic waves require less time to propagate over shorter distances. This not only improves the real-time nature of navigation services, but is also particularly crucial for rapid positioning updates in dynamic environments, ensuring users receive the latest location information instantly, enhancing user experience and safety. Furthermore, if navigation coverage is only required for a specific area, the constellation size of low-orbit satellites can be much smaller than that of medium- and high-orbit systems. This significantly reduces construction and maintenance costs, providing a more economically viable option for developing countries to establish autonomous navigation systems or navigation augmentation systems.

[0004] The existing design methods for navigation constellations are mainly based on providing navigation and positioning services on a global scale, and the design theory for navigation constellations in specific regions is still imperfect. Focusing on the design of navigation constellations in specific regions, domestic and foreign scholars have proposed a variety of constellation optimization methods, including genetic algorithms. Genetic algorithms are a method for optimizing problems based on modern genetics, Darwin's theory of evolution, and biological simulation technology. During the optimization process, it is necessary to calculate the navigation and positioning performance of the constellation within the coverage time period. During the constellation optimization process, it is necessary to perform orbit recursion and calculate the GDOP value for each integral step. The amount of calculation is too large, resulting in low optimization efficiency. Therefore, it is necessary to find a more efficient optimization model to improve the optimization efficiency. The present invention introduces a virtual ground station and introduces a new constellation optimization model based on the virtual ground station to solve the problem of too large GDOP value calculation. Summary of the Invention

[0005] The present invention aims to provide a rapid optimization method for regional navigation constellations based on revisit characteristics. The method uses the J2 average orbit dynamics model to determine the initial value of the regression orbit. It then uses an iterative correction method to correct the ascending node drift caused by high-order Earth gravitational perturbations, resulting in a strict regression orbit design. High-precision revisit coverage of the target coverage area by the satellite is achieved based on the strict regression orbit design. A constellation configuration parameter selection method is used to determine the range of constellation configuration parameters required for the navigation mission. For the given constellation configuration parameters, an initial solution is obtained using a genetic algorithm based on an initial population. This initial solution obtained by the genetic algorithm is optimized using a local search algorithm to obtain the optimal result under the constellation configuration parameters. A hybrid genetic and local search algorithm based on the initial population is used to optimize and solve multiple sets of constellation configuration parameters within the constellation configuration parameter range required for the navigation coverage mission, obtaining multiple constellation configuration optimization results. A multi-index comprehensive evaluation of the multiple constellation configuration optimization results is then performed based on the navigation and positioning mission requirements to screen out the optimal navigation constellation configuration. Constellation satellites are deployed based on the optimal navigation constellation configuration obtained by the present invention, meeting the high-precision and high-frequency navigation requirements for the target coverage area under given multiple performance index constraints.

[0006] The purpose of the present invention is achieved through the following technical solutions.

[0007] The method for rapid optimization of regional navigation constellations based on revisit characteristics disclosed in the present invention comprises the following steps:

[0008] Step 1: Based on the mission requirements of the navigation coverage area and combined with the J2 average orbit dynamics model, solve the initial value of the regression orbit that meets the revisit characteristics.

[0009] The regression parameters of the selected regression track and the longitude and latitude coordinates of the center point of the target coverage area are used as the initial values ​​of the regression track optimization input. The regression parameters and the longitude and latitude coordinates of the center point are given in the form of number pairs. Among them, the regression parameters are defined as

[0010] {j,k} RGT (1) In the formula, j and k correspond to the orbit number and regression period of the regression orbit respectively, and RGT represents the regression orbit. The coordinates of the center point of the target coverage area are expressed in the form of longitude and latitude, and are defined as

[0011] [ψ0,φ0](2) In the formula, ψ0,φ0 correspond to the longitude and latitude of the center point respectively. Given the number of orbital elements, the average orbital semi-major axis is and orbital eccentricity The initial value is

[0012]

[0013] According to the Gaussian perturbation equation under J2 perturbation, the differential equations are continuously iterated after substituting the initial values ​​until the mean orbital semi-major axis is and the average satellite angular velocity convergence

[0014]

[0015] Where, is the rate of change of the mean ascending node right ascension, J2 is the second-order harmonic perturbation coefficient of the Earth's non-spherical gravity, μ is the Earth's central gravitational constant, R e is the radius of the Earth, is the mean orbital inclination, is the average latitude argument change rate, ω e is the Earth's rotation rate.

[0016] Average orbital inclination As the variable to be solved, the following constraints need to be satisfied in the iterative solution

[0017]

[0018] Solve equations (3)(4)(5) together to obtain the initial value of the periodic revisit orbit As shown in formula (6)

[0019]

[0020] Step 2: Based on the initial value of the regression orbit obtained in step 1, the ascending node drift under the high-order gravitational perturbations of the Earth is corrected using an iterative correction algorithm to obtain a strict regression orbit design result that meets the revisit characteristics.

[0021] At the beginning of the correction, the initial value of the regression orbit shown in formula (6) is substituted into the differential equation shown in formula (7) as input

[0022]

[0023] Where T is a regression period, is the mean anomaly of the satellite.

[0024] According to formula (7), the state transfer matrix Φ of the correction process is obtained as follows:

[0025]

[0026] According to formula (8), the difference of orbital elements that need to be corrected in each iteration is determined as

[0027]

[0028] Where Δψ SAT , Δφ SATare the latitude and longitude coordinate differences of the ground projection of the ascending node after the satellite runs a strict regression cycle compared to the initial moment. Keeping other orbital elements unchanged, the iterative process only corrects the orbit semi-major axis and orbital inclination. According to formula (9), the ascending node drift under the high-order gravitational perturbation of the earth is corrected to obtain the strict regression orbit design result. The correction result is shown in formula (10)

[0029]

[0030] Where, is the initial value of the orbit after iterative correction. The physical quantities with * represent the corrected results.

[0031] By making each member satellite in the subsequently optimized constellation share the orbital semi-major axis, orbital eccentricity, and orbital inclination of the regression orbit, each member satellite also has the periodic revisit characteristic.

[0032] Step 3: Determine the objective function of the satellite positioning optimization model based on the navigation and positioning requirements of the constellation. Based on the objective function of the satellite positioning optimization model, use the three configuration parameters that control the final navigation performance of the constellation as inputs to the constellation configuration optimization method. The three configuration parameters for the final navigation performance of the constellation are the number of constellation satellites, the number of virtual ground stations required by the constellation, and the expected low elevation angle value of the constellation, which are abbreviated as [N S ,N P ,ε f ].

[0033] The virtual ground stations are a set of multiple sub-satellite points evenly distributed at the same latitude as the center point of the target coverage area. The number of virtual ground stations is equal to the number of regression orbits within a regression period of the strict regression orbit determined in step 2. By introducing virtual ground stations, solving the geometric positioning dilution of precision factor (GDOP) values ​​of the constellation relative to the target area at multiple coverage moments is simplified to solving the GDOP values ​​of the constellation relative to multiple virtual ground stations at one moment, thereby simplifying the objective function of the satellite positioning optimization model.

[0034] According to the objective function of the simplified satellite positioning optimization model, the constellation configuration parameter selection method is combined to determine the value range of the constellation configuration parameter, and the value range of the constellation configuration parameter is used as the value range of the input quantity of the constellation configuration optimization method in the subsequent step 5. The constellation configuration parameter selection method includes the number of virtual ground stations N required for the constellation. P Selection method, number of constellation satellites N S Screening iterative method, constellation expected low elevation angle value ε f Selection method. Among them, the number of constellation satellites N S The screening iterative method is based on the number of virtual ground stations N required by the constellation. P The selection method is carried out. For each constellation, the number of virtual ground stations required to cover NP , can be obtained by the minimum constellation satellite number N S . P The corresponding minimum constellation satellite number N S .

[0035] The number of virtual ground stations required by the constellation N P The specific implementation method of the selection method is that the number of virtual ground stations required by the constellation N P , corresponding to the number of coverage moments of the satellites in a regression period, according to the selection of the navigation coverage task requirement, the number of virtual ground stations needs to meet

[0036] 1≤N P ≤j RGT (11) wherein j RGT is the number of orbits in a regression period.

[0037] The minimum constellation satellite number N S The screening iteration method is as follows: the number of virtual ground stations N P The corresponding minimum constellation satellite number N S is realized by screening iteration. Given a satellite number N S,try , as the minimum satellite number N S , the input of the screening iteration method. The minimum satellite number screening iteration method optimizes the phase parameters of each member satellite of the constellation using a genetic algorithm to obtain an initial constellation configuration. In the iteration process of the minimum satellite number screening iteration method, for different satellite numbers, the phase parameters of each member satellite of the constellation are optimized using a genetic algorithm to obtain a temporary constellation configuration. The positioning accuracy of the initial constellation configuration corresponding to the given N S,try The initial value exceeds the preset accuracy condition at the coverage moment, then the number of satellites is reduced until the temporary constellation configuration cannot meet the preset accuracy condition, and the result of the second last time is taken as the minimum satellite number N S When the initial constellation configuration corresponding to the given N S,try The initial value cannot meet the preset accuracy condition at the coverage moment, then the number of satellites is increased until the temporary constellation configuration can meet the preset condition, and the result of the last time is taken as the minimum satellite number N S . The coverage moment refers to the moment when a satellite in the constellation passes above the target area. According to the minimum constellation satellite number N S The screening iteration method pre-screens the minimum number of satellites required for coverage to ensure that the constellation configuration of the minimum number of satellites obtained by pre-screening accurately covers the target area.

[0038] The expected low-elevation value of the constellation ε f The selection method is as follows: the expected low-elevation value of the constellation ε fSelect according to the navigation and positioning task requirements to meet

[0039] ε f ≥5° (12)

[0040] Furthermore, the objective function of the simplified constellation positioning accuracy comprehensive optimization model is:

[0041]

[0042] Where J is the objective function, the geometric positioning precision dilution factor GDOP is the performance indicator for evaluating the positioning accuracy of the navigation and positioning system, m, l are counting variables, W1, W2, W3 are weight coefficients, {ε m}3 refers to a subset of the three minimum pitch angle values ​​in the pitch angle set of all satellites relative to the ground station, expressed in vector form.

[0043] Through the objective function of the simplified constellation positioning accuracy comprehensive optimization model, it is ensured that the optimized constellation configuration can achieve navigation positioning that meets the preset accuracy in the target area within the time period of covering the target area.

[0044] Step 4: Divide the value range of the constellation configuration parameters determined in Step 3 into multiple different constellation configuration parameter combinations. For each parameter combination, the constellation configuration parameters are used as input to a constellation optimization method. During each iteration of the constellation optimization method, the input configuration parameters are optimized using the constellation optimization method. The optimization process uses the phase parameters of each constellation member satellite as the variables to be optimized, and minimizing the objective function value is the optimization objective. The constellation optimization method includes a genetic algorithm based on an initial population and a local search algorithm.

[0045] The specific implementation method of the constellation optimization method is as follows: for each set of constellation configuration parameters, based on the preset initial population, a genetic algorithm is used to find the global optimal initial feasible solution, and then the Nelder-Mead algorithm or other suitable local search algorithm is used to optimize the initial feasible solution obtained by the genetic algorithm to obtain the optimal result under the constellation configuration parameters.

[0046] Multiple groups of constellation configuration parameters within the constellation configuration parameter range determined in step 3 are optimized and solved one by one to obtain constellation configuration optimization results under multiple corresponding constellation configuration parameters as candidate navigation constellation configuration optimization results.

[0047] Step 5: Based on the target coverage area, conduct a comprehensive multi-index evaluation of the candidate navigation constellation solutions to screen out the optimal navigation constellation configuration that meets the coverage performance requirements.

[0048] Based on the candidate navigation constellation configurations generated by the constellation optimization method in Step 4, a comprehensive performance evaluation method for regional coverage is constructed to evaluate each of their core performance indicators, such as total coverage duration, revisit period, and navigation positioning accuracy. Based on this, a constellation configuration optimization result that meets the preset requirements on all these performance indicators and achieves the best overall performance is selected, thus becoming the optimal navigation constellation configuration.

[0049] Based on the optimal navigation constellation configuration obtained in step five, constellation satellite deployment is performed to meet the high-precision and high-frequency navigation requirements for the target coverage area under the given multi-performance indicator constraints.

[0050] Beneficial effects:

[0051] 1. The present invention discloses a rapid optimization method for regional navigation constellations based on revisit characteristics. The method obtains the initial solution of the regression orbit through J2 average orbit dynamics theory calculations, and corrects the orbit ascending node drift under high-order Earth gravitational perturbations to obtain a strict regression orbit design result. Compared with the uncorrected initial solution of the regression orbit, the strict regression orbit design result achieves high-precision revisit coverage of the satellite in the target coverage area.

[0052] 2. The present invention discloses a rapid regional navigation constellation optimization method based on revisit characteristics. Based on the objective function of a satellite positioning optimization model, three configuration parameters that control the constellation's ultimate navigation performance are used as inputs to the constellation configuration optimization method. A constellation configuration parameter selection method is used to determine the range of constellation configuration parameters required for the navigation mission. For given constellation configuration parameters, an initial solution is obtained using an initial population-based genetic algorithm based on the objective function of a simplified comprehensive constellation positioning accuracy optimization model. This initial solution is then optimized using a local search algorithm to achieve the optimal result for the constellation configuration parameters. Compared to an unsimplified comprehensive constellation positioning accuracy optimization model, this method offers improved computational efficiency and faster optimization.

[0053] 3. The disclosed method for rapid regional navigation constellation optimization based on revisit characteristics employs a hybrid genetic and local search algorithm based on an initial population to optimize multiple constellation configuration parameters within the range required for navigation coverage. This method then performs a multi-metric comprehensive evaluation of these constellation configuration optimization results based on the navigation and positioning mission requirements to identify the optimal navigation constellation configuration. Compared to direct optimization under the constraints of multiple performance metrics, this comprehensive performance evaluation method for regional coverage avoids optimization failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The figure is a flow chart of the method for rapid optimization of regional navigation constellations based on revisit characteristics of the present invention.

[0055] Figure 2 This is the trajectory diagram of the subsatellite point of the strict regression orbit designed in steps 1 and 2 of the embodiment.

[0056] Figure 3 : This is the relationship between the positioning accuracy index and the total coverage time of each constellation solution in the embodiment.

[0057] Figure 4 This is the relationship between the revisit time and the total coverage time of each constellation solution in the embodiment.

[0058] Figure 5 This is a trend chart of the change in the ascending node offset of the strict regression orbit before and after correction.

[0059] Figure 6 This is the initial time distribution diagram of the constellation satellites for the final optimization result. DETAILED DESCRIPTION

[0060] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0061] Example 1:

[0062] The target coverage area is selected as Beijing, and the longitude and latitude coordinates are [ψ0, φ0] = [39.9°N, 116.4°E]. The regression orbit parameters are {j, k} RGT ={14,1} RGT The DE421 ephemeris is used to obtain the gravitational field data, where the Earth's gravitational constant μ e =398600.436233km 3 / s 2 , the second-order harmonic coefficient of the earth's gravity is J2 = 0.00108262668355, and the radius of the earth is R e =6378.1363km. The constellation expects a low elevation angle value ε f The range is selected as ε f ∈[5°,20°]. The regional navigation satellite system needs to meet the following requirements:

[0063] (1) Within one regression cycle, the target coverage area should be covered as many times as possible;

[0064] (2) The total coverage time of the constellation within one regression cycle shall not be less than 5 hours;

[0065] (3) The constellation revisits the target coverage area at least once every hour;

[0066] (4) During the coverage period, the average value of the navigation positioning accuracy indicator GDOP shall not be greater than 4.

[0067] like Figure 1As shown, the method for rapid optimization of regional navigation constellations based on revisit characteristics disclosed in this embodiment is specifically implemented in the following steps:

[0068] Step 1: Based on the mission requirements of the navigation coverage area and combined with the J2 average orbit dynamics model, solve the initial value of the regression orbit that meets the revisit characteristics.

[0069] The regression parameters of the regression track and the longitude and latitude coordinates of the center point of the target coverage area are selected as the initial values ​​of the regression track optimization input. The regression parameters and the longitude and latitude coordinates of the center point are given in the form of number pairs. According to the simulation embodiment, the regression parameters are selected as

[0070] {j,k} RGT ={14,1} RGT (14) In formula, j and k correspond to the orbit number and regression period of the regression orbit respectively, and RGT represents the regression orbit. The coordinates of the center point of the target coverage area are expressed in the form of longitude and latitude, and are defined as

[0071] [ψ0,φ0]=[39.9°N, 116.4°E] (15) where ψ0 and φ0 correspond to the longitude and latitude of the center point, respectively. Given the number of orbital elements, the average orbital semi-major axis is and orbital eccentricity The initial value is

[0072]

[0073] According to the Gaussian perturbation equation under J2 perturbation, the differential equations are continuously iterated after substituting the initial values ​​until the mean orbital semi-major axis is and the average satellite angular velocity convergence

[0074]

[0075] Where, is the rate of change of the mean ascending node right ascension, J2 is the second-order harmonic perturbation coefficient of the Earth's non-spherical gravity, μ is the Earth's central gravitational constant, R e is the radius of the Earth, is the mean orbital inclination, is the average latitude argument change rate, ω e is the Earth's rotation rate.

[0076] Average orbital inclination As the variable to be solved, the following constraints need to be satisfied in the iterative solution

[0077]

[0078] Solve equations (16)(17)(18) together to obtain the initial value of the periodic revisit orbit As shown in formula (19)

[0079]

[0080] Step 2: Based on the initial value of the regression orbit obtained in step 1, the ascending node drift under the high-order gravitational perturbations of the Earth is corrected using an iterative correction algorithm to obtain a strict regression orbit design result that meets the revisit characteristics.

[0081] At the beginning of the correction, the initial value of the regression orbit shown in formula (19) is substituted into the differential equation group shown in formula (20) as input

[0082]

[0083] Where T is a regression period, is the mean anomaly of the satellite.

[0084] According to formula (20), the state transfer matrix Φ of the correction process is obtained as follows:

[0085]

[0086] According to formula (21), the difference of orbital elements that need to be corrected in each iteration is determined as

[0087]

[0088] Where Δψ SAT , Δφ SAT are the latitude and longitude coordinate differences of the ground projection of the ascending node after the satellite runs a strict regression cycle compared to the initial moment. Keeping other orbital elements unchanged, the iterative process only corrects the orbit semi-major axis and orbital inclination. According to formula (22), the ascending node drift under the high-order gravitational perturbation of the earth is corrected to obtain the strict regression orbit design result. The correction result is shown in formula (23)

[0089]

[0090] Where, is the initial value of the orbit after iterative correction. The physical quantities with * represent the corrected results.

[0091] According to formula (20)(21)(22), the number of orbital elements in the iterative process can be calculated as The maximum angular deviation allowed for the projection of the subsatellite point of the ascending node within a regression cycle is set to 10 -8 °. Then the total corrections for the orbital semi-major axis and orbital inclination are

[0092] The final strict regression orbit correction result is

[0093]

[0094] like Figure 2 As shown in Figure 3, after running a strict regression cycle under the J2 perturbation, the sub-satellite point can be accurately coincided.

[0095] By making each member satellite in the subsequently optimized constellation share the orbital semi-major axis, orbital eccentricity, and orbital inclination of the regression orbit, each member satellite also has the periodic revisit characteristic.

[0096] Step 3: Determine the objective function of the satellite positioning optimization model based on the navigation and positioning requirements of the constellation. Based on the objective function of the satellite positioning optimization model, use the three configuration parameters that control the final navigation performance of the constellation as inputs to the constellation configuration optimization method. The three configuration parameters for the final navigation performance of the constellation are the number of constellation satellites, the number of virtual ground stations required by the constellation, and the expected low elevation angle value of the constellation, which are abbreviated as [N S ,N P ,ε f ].

[0097] The virtual ground stations are a set of multiple sub-satellite points evenly distributed at the same latitude as the center point of the target coverage area. The number of virtual ground stations is equal to the number of regression orbits within a regression period of the strict regression orbit determined in step 2. By introducing virtual ground stations, solving the geometric positioning dilution of precision factor (GDOP) values ​​of the constellation relative to the target area at multiple coverage moments is simplified to solving the GDOP values ​​of the constellation relative to multiple virtual ground stations at one moment, thereby simplifying the objective function of the satellite positioning optimization model.

[0098] According to the objective function of the simplified satellite positioning optimization model, the constellation configuration parameter selection method is combined to determine the value range of the constellation configuration parameter, and the value range of the constellation configuration parameter is used as the value range of the input quantity of the constellation configuration optimization method in the subsequent step 5. The constellation configuration parameter selection method includes the number of virtual ground stations N required for the constellation. P Selection method, number of constellation satellites N S Screening iterative method, constellation expected low elevation angle value ε f Selection method. Among them, the number of constellation satellites N S The screening iterative method is based on the number of virtual ground stations N required by the constellation. P The selection method is carried out. For each constellation, the number of virtual ground stations required to cover N P , can be achieved through the minimum number of constellation satellites N S The screening iterative method obtains the same P The corresponding minimum number of constellation satellites N S .

[0099] The number of virtual ground stations N required for the constellationP The specific implementation method of the selection method is: the number of virtual ground stations N required for the constellation P , corresponding to the number of satellite coverage moments in a regression cycle, is selected according to the navigation coverage mission requirements. The number of virtual ground stations needs to meet

[0100] 1≤N P ≤j RGT (25) Among them, j RGT is the number of orbits in one regression period.

[0101] Minimum number of constellation satellites N S The screening iteration method is as follows: with the number of virtual ground stations N P The corresponding minimum number of constellation satellites N S It is achieved by screening iteration. Given a number of satellites N S,try , as the minimum number of satellites N S The input of the screening iterative method. The minimum number of satellites screening iterative method uses a genetic algorithm to optimize the phase parameters of each constellation member satellite to obtain an initial constellation configuration. During the iterative process of the minimum number of satellites screening iterative method, for different numbers of satellites, the genetic algorithm is used to optimize the phase parameters of each constellation member satellite to obtain a temporary constellation configuration. Given N S,try If the positioning accuracy of the initial constellation configuration corresponding to the initial value exceeds the preset accuracy condition at the coverage moment, the number of satellites is reduced by one until the number is reduced to a point where the temporary constellation configuration cannot meet the preset accuracy condition. The second-to-last result is taken as the minimum number of satellites N. S When the given N S,try If the positioning accuracy of the initial constellation configuration corresponding to the initial value cannot meet the preset accuracy conditions at the coverage time, the number of satellites is increased until the number increases to the temporary constellation configuration that can meet the preset conditions. The last result is taken as the minimum number of satellites N. S The coverage time refers to the time when a satellite in the constellation passes over the target area. S The screening iterative method pre-screens the minimum number of satellites required for coverage to ensure that the constellation configuration with the minimum number of satellites obtained in pre-screening accurately covers the target area.

[0102] Constellation expected low elevation angle value ε f The selection method is as follows: constellation expected low elevation angle value ε f Select according to the navigation and positioning task requirements to meet

[0103] ε f ≥5° (26)

[0104] Furthermore, the objective function of the simplified constellation positioning accuracy comprehensive optimization model is:

[0105]

[0106] Where J is the objective function, the geometric positioning precision dilution factor GDOP is the performance indicator for evaluating the positioning accuracy of the navigation and positioning system, m, l are counting variables, W1, W2, W3 are weight coefficients, It refers to the subset of the three minimum pitch angle values ​​in the pitch angle set of all satellites relative to the ground station, expressed in vector form.

[0107] Through the objective function of the simplified constellation positioning accuracy comprehensive optimization model, it is ensured that the optimized constellation configuration can achieve navigation positioning that meets the preset accuracy in the target area within the time period of covering the target area.

[0108] According to the task constraints of the embodiment, the number of virtual ground stations N required for the selected constellation is P The value range is N P ∈[1,14], the constellation expects a low elevation angle value ε f The value range is ε f ∈[5°,20°]. The minimum number of constellation satellites N required to meet mission coverage requirements S By the minimum number of constellation satellites N S The number of virtual ground stations N required by the constellation to meet the navigation coverage mission requirements in the embodiment is calculated using the screening iterative method. P The minimum number of constellation satellites N required to meet the coverage mission requirements S The corresponding relationship is

[0109] Table 1 Minimum number of constellation satellites to meet navigation coverage mission requirements

[0110]

[0111] Step 4: Divide the value range of the constellation configuration parameters determined in Step 3 into multiple different constellation configuration parameter combinations. For each parameter combination, the constellation configuration parameters are used as input to a constellation optimization method. During each iteration of the constellation optimization method, the input configuration parameters are optimized using the constellation optimization method. The optimization process uses the phase parameters of each constellation member satellite as the variables to be optimized, and minimizing the objective function value is the optimization objective. The constellation optimization method includes a genetic algorithm based on an initial population and a local search algorithm.

[0112] The specific implementation method of the constellation optimization method is as follows: for each set of constellation configuration parameters, based on the preset initial population, a genetic algorithm is used to find the global optimal initial feasible solution, and then the Nelder-Mead algorithm or other suitable local search algorithm is used to optimize the initial feasible solution obtained by the genetic algorithm to obtain the optimal result under the constellation configuration parameters.

[0113] Multiple groups of constellation configuration parameters within the constellation configuration parameter range determined in step 3 are optimized and solved one by one to obtain constellation configuration optimization results under multiple corresponding constellation configuration parameters as candidate navigation constellation configuration optimization results.

[0114] The constellation configuration parameter N P ∈[1,14], ε f ∈[5°,20°], permutations and combinations were performed to form a total of 224 sets of configuration parameters. The optimization algorithm was used to obtain 268 constellation solutions that minimized the objective function. (Since the optimization algorithm has multiple solutions, a set of configuration parameters may correspond to multiple constellation solutions.) For the constellation optimization method, the genetic algorithm was selected as the global optimal algorithm, and the Nelder-Mead algorithm was selected as the local optimization method.

[0115] Step 5: Based on the target coverage area, conduct a comprehensive multi-index evaluation of the candidate navigation constellation solutions to screen out the optimal navigation constellation configuration that meets the coverage performance requirements.

[0116] Based on the candidate navigation constellation configurations generated by the constellation optimization method in Step 4, a comprehensive performance evaluation method for regional coverage is constructed to evaluate each of their core performance indicators, such as total coverage duration, revisit period, and navigation positioning accuracy. Based on this, a constellation configuration optimization result that meets the preset requirements on all these performance indicators and achieves the best overall performance is selected, thus becoming the optimal navigation constellation configuration.

[0117] Figure 3 、 Figure 4 The distribution relationship between the average value of navigation positioning accuracy index GDOP and total coverage time, and the distribution relationship between revisit time and total coverage time of the optimized constellation relative to the target coverage area within a regression cycle are given respectively. Figure 3 、 Figure 4 The constellation solutions in can satisfy:

[0118] (1) Within one regression cycle, the target coverage area can be covered multiple times;

[0119] (2) The total coverage time of the constellation within one regression cycle shall not be less than 5 hours;

[0120] (3) The constellation revisits the target coverage area at least once every hour;

[0121] (4) During the coverage period, the average value of the navigation positioning accuracy indicator GDOP shall not be greater than 4.

[0122] etc. Figure 3 、 4The intersection of the two black dashed boxes in the constellation solution set is also the constellation solution set that meets the navigation mission requirements. Based on the mission constraints, the constellation with the best performance indicators and the least number of satellites is selected as the optimization result of this embodiment. Its configuration parameters are:

[0123] [N S , N P , ε f ]=[27, 13, 10°] (28)

[0124] Figure 5 The trend diagram of the ascending node offset change of the strict regression orbit obtained by steps one and two before and after correction is given. Figure 5 As can be seen in Figure 2, when no correction is made, the cumulative drift of the ascending node's spherical surface distance difference within ten regression cycles is 3.214 km. After correction using step 2, the cumulative drift of the ascending node's spherical surface distance difference within ten regression cycles is only 0.479 km, which is only 14% of the drift before correction. In addition, Figure 6 The initial time distribution diagram of the constellation satellites of the final optimization result is given. At this initial time, the satellites can just cover the target coverage area in the embodiment and can achieve:

[0125] (1) Within one regression cycle, the target coverage area can be covered 13 times;

[0126] (2) In one regression cycle, the total coverage time of the constellation is 312 minutes, or 5 hours and 12 minutes;

[0127] (3) The constellation revisits the target coverage area every 0.472 hours;

[0128] (4) During the coverage period, the average value of the navigation positioning accuracy indicator GDOP was 3.6.

[0129] The simulation results show that by traversing and solving different combinations of configuration parameters, it is possible to more efficiently optimize the regional navigation constellation that meets multiple performance index constraints. Figure 5 and Figure 6 The results shown effectively verify the feasibility of the present invention. The optimized constellation has both revisit characteristics and can meet the multiple performance index constraints required by the navigation mission.

[0130] Based on the optimal navigation constellation configuration obtained in step five, constellation satellite deployment is performed to meet the high-precision and high-frequency navigation requirements for the target coverage area under the given multi-performance indicator constraints.

[0131] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A fast optimization method for regional navigation constellations based on revisit characteristics, characterized by: The following steps are included: Step 1: Based on the mission requirements of the navigation coverage area and the J2 average orbit dynamics model, solve the initial value of the regression orbit that meets the revisit characteristics; Step 2: Based on the initial value of the regression orbit obtained in step 1, an iterative correction algorithm is used to correct the ascending node drift under the high-order gravitational perturbations of the Earth, and a strict regression orbit design result that meets the revisit characteristics is obtained; Step 3: Determine the objective function of the satellite positioning optimization model according to the navigation and positioning requirements of the constellation. Based on the objective function of the satellite positioning optimization model, the three configuration parameters for regulating the final navigation performance of the constellation are used as inputs of the constellation configuration optimization method. The three configuration parameters for the final navigation performance of the constellation are the number of constellation satellites, the number of virtual ground stations required by the constellation, and the expected low elevation angle value of the constellation, which are abbreviated as Step 4: Divide the value range of the constellation configuration parameters determined in step 3 into multiple groups of different constellation configuration parameter combinations; for each group of parameter combinations, use the constellation configuration parameters as input to the constellation optimization method; in each optimization process of the constellation optimization method, use the constellation optimization method to optimize the input configuration parameters; the optimization process uses the phase parameters of each member satellite of the constellation as the variable to be optimized, and minimizes the objective function value as the optimization goal; Step 5: Based on the target coverage area, conduct a comprehensive multi-index evaluation of the candidate navigation constellation solutions to screen out the optimal navigation constellation configuration that meets the coverage performance requirements.

2. The method for rapid optimization of regional navigation constellations based on revisit characteristics according to claim 1, wherein: The implementation method of step one is: The regression parameters of the selected regression track and the longitude and latitude coordinates of the center point of the target coverage area are used as the initial values ​​of the regression track optimization input; the regression parameters and the longitude and latitude coordinates of the center point are given in the form of number pairs; the regression parameters are defined as {j, k} RGT (1) Where j and k correspond to the orbit number and regression period of the regression orbit, respectively, and RGT represents the regression orbit. The coordinates of the center point of the target coverage area are expressed in the form of longitude and latitude, defined as [ψ0, φ0] (2) Where ψ0 and φ0 correspond to the longitude and latitude of the center point, respectively. Given the number of orbital elements, the average orbital semi-major axis is and orbital eccentricity The initial value is According to the Gaussian perturbation equation under J2 perturbation, the differential equations are continuously iterated after substituting the initial values ​​until the mean orbital semi-major axis is and the average satellite angular velocity convergence Where, is the rate of change of the right ascension of the mean ascending node, J2 is the second-order harmonic perturbation coefficient of the Earth's non-spherical gravity, μ is the Earth's central gravitational constant, R e is the radius of the Earth, is the mean orbital inclination, is the average latitude argument change rate, ω e is the Earth's rotation rate; Average orbital inclination As the variable to be solved, the following constraints need to be satisfied in the iterative solution Solve equations (3)(4)(5) together to obtain the initial value of the periodic revisit orbit As shown in formula (6) 3. The method for rapid optimization of regional navigation constellations based on revisit characteristics according to claim 2, wherein: The implementation method of step 2 is: At the beginning of the correction, the initial value of the regression orbit shown in formula (6) is substituted into the differential equation shown in formula (6) as input Where T is a regression period, is the satellite's mean anomaly; According to formula (7), the state transfer matrix Φ of the correction process is obtained as follows: According to formula (8), the difference of orbital elements that need to be corrected in each iteration is determined as Where Δψ SAT , Δφ SAT They are the difference in latitude and longitude coordinates of the ground projection of the ascending node after the satellite runs a strict regression cycle compared to the initial moment; keeping other orbital elements unchanged, the iterative process only corrects the orbital semi-major axis and orbital inclination; according to formula (9), the ascending node drift under the high-order gravitational perturbation of the earth is corrected to obtain the strict regression orbit design result, and the correction result is shown in formula (10) Where, is the initial value of the orbit after iterative correction; the physical quantity with * represents the corrected result; By making each member satellite in the subsequently optimized constellation share the orbital semi-major axis, orbital eccentricity, and orbital inclination of the regression orbit, each member satellite also has the periodic revisit characteristic.

4. The method for rapid optimization of regional navigation constellations based on revisit characteristics according to claim 3, wherein: The implementation method of step three is: The virtual ground stations are a set of multiple sub-satellite points evenly distributed at the same latitude as the center point of the target coverage area. The number of virtual ground stations is equal to the number of regression orbits within a regression period of the strict regression orbit determined in step 2. By introducing virtual ground stations, solving the geometric positioning dilution of precision factor (GDOP) values ​​of the constellation relative to the target area at multiple coverage moments is simplified to solving the GDOP values ​​of the constellation relative to multiple virtual ground stations at one moment, thereby simplifying the objective function of the satellite positioning optimization model. According to the objective function of the simplified satellite positioning optimization model, the value range of the constellation configuration parameters is determined in combination with the constellation configuration parameter selection method, and the value range of the constellation configuration parameters is used as the value range of the input quantity of the constellation configuration optimization method in the subsequent step 5; the constellation configuration parameter selection method includes the number of virtual ground stations N required for the constellation P Selection method, number of constellation satellites N S Screening iterative method, constellation expected low elevation angle value ε f Selection method; Among them, the number of constellation satellites N S The screening iterative method is based on the number of virtual ground stations N required by the constellation. P The selection method is carried out; for each constellation, the number of virtual ground stations N required to cover P , through the minimum number of constellation satellites N S The screening iterative method obtains the same P The corresponding minimum number of constellation satellites N S ; The number of virtual ground stations N required for the constellation P The specific implementation method of the selection method is: the number of virtual ground stations N required for the constellation P , corresponding to the number of satellite coverage moments in a regression cycle, is selected according to the navigation coverage mission requirements. The number of virtual ground stations needs to meet 1≤N P ≤j RGT (11) Among them, j RGT is the number of orbits in one regression period; Minimum number of constellation satellites N S The screening iteration method is as follows: with the number of virtual ground stations N P The corresponding minimum number of constellation satellites N S It is achieved by screening iteration; given a number of satellites N S,try , as the minimum number of satellites N S The input of the screening iterative method; The minimum number of satellites screening iterative method uses genetic algorithms to optimize the phase parameters of each member satellite of the constellation to obtain an initial constellation configuration; During the iterative process of the minimum number of satellites screening iterative method, for different numbers of satellites, the genetic algorithm is used to optimize the phase parameters of each member satellite of the constellation to obtain a temporary constellation configuration; Given N S,try If the positioning accuracy of the initial constellation configuration corresponding to the initial value exceeds the preset accuracy condition at the coverage moment, the number of satellites is reduced by one until the number is reduced to a point where the temporary constellation configuration cannot meet the preset accuracy condition. The second-to-last result is taken as the minimum number of satellites N. S ; When the given N S,try If the positioning accuracy of the initial constellation configuration corresponding to the initial value cannot meet the preset accuracy conditions at the coverage time, the number of satellites is increased until the number increases to the temporary constellation configuration that can meet the preset conditions. The last result is taken as the minimum number of satellites N. S The coverage time refers to the time when a satellite in the constellation passes over the target area; according to the minimum number of constellation satellites N S The iterative screening method pre-screens the minimum number of satellites required for coverage, ensuring that the constellation configuration with the minimum number of satellites obtained in the pre-screening accurately covers the target area; Constellation expected low elevation angle value ε f The selection method is as follows: constellation expected low elevation angle value ε f Select according to the navigation and positioning task requirements to meet e f ≥5° (12) The objective function of the simplified comprehensive optimization model of constellation positioning accuracy is: Where, is the objective function, the geometric positioning precision dilution factor GDOP is the performance index for evaluating the positioning accuracy of the navigation and positioning system, m, l are counting variables, W1, W2, W3 are weight coefficients, It refers to the subset of the three smallest pitch angles in the set of all satellite pitch angles relative to the ground station, expressed in vector form; Through the objective function of the simplified constellation positioning accuracy comprehensive optimization model, it is ensured that the optimized constellation configuration can achieve navigation positioning that meets the preset accuracy in the target area within the time period of covering the target area.

5. The method for rapid optimization of regional navigation constellations based on revisit characteristics according to claim 4, wherein: The constellation optimization method includes a genetic algorithm based on an initial population and a local search algorithm.

6. The method for rapid optimization of regional navigation constellations based on revisit characteristics according to claim 4, wherein: The specific implementation method of the constellation optimization method is as follows: for each set of constellation configuration parameters, based on the preset initial population, a genetic algorithm is used to find the global optimal initial feasible solution. The initial feasible solution obtained by the Nelder-Mead algorithm is then optimized to obtain the optimal result under the constellation configuration parameters; Multiple groups of constellation configuration parameters within the constellation configuration parameter range determined in step 3 are optimized and solved one by one to obtain constellation configuration optimization results under multiple corresponding constellation configuration parameters as candidate navigation constellation configuration optimization results.

7. The method for rapid optimization of regional navigation constellations based on revisit characteristics according to claim 6, wherein: The implementation method of step six is: Based on the candidate navigation constellation configuration optimization results generated by the constellation optimization method in step 4, a comprehensive performance evaluation method for regional coverage is constructed to evaluate their total coverage duration, revisit period, and core performance indicators of navigation positioning accuracy one by one. On this basis, a constellation configuration optimization result that meets the preset requirements on all these performance indicators and has the best overall performance is selected, which is the optimal navigation constellation configuration; Based on the optimal navigation constellation configuration obtained in step five, constellation satellite deployment is performed to meet the high-precision and high-frequency navigation requirements for the target coverage area under the given multi-performance indicator constraints.

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