Intelligent Optimization Algorithm of NSGA-III for the Configuration of InSAR Satellite Cluster

Abstract

The present invention discloses an NSGA-III intelligent optimization algorithm for the configuration of an InSAR satellite constellation. The relative motion of the InSAR satellite constellation is modeled using the description method of the E / I vector. According to the baseline length constraints of height measurement imaging with long and short baselines in the InSAR satellite system, the optimization variables and their optimization ranges of the "concentric ring" configuration are determined. The inter-satellite distance objective function, configuration stability objective function, and altimetry performance objective function are constructed from three perspectives: the safety, stability, and usefulness of the constellation configuration. Finally, the above three objective functions are optimized and solved by the multi-objective NSGA-III optimization algorithm to obtain the optimal InSAR satellite constellation configuration that meets the requirements of inter-satellite collision avoidance, configuration stability, and altimetry accuracy. The multi-objective intelligent optimization algorithm provided by the present invention effectively solves the problem of solving multi-objective and multi-constraint in the optimization design of the InSAR satellite constellation, realizes the intelligent optimization design of the "concentric ring" configuration of the satellite constellation, and provides a technical basis for the task of the InSAR satellite constellation system to obtain high-precision DEM products.

Description

Technical Field

[0001] The present invention relates to the configuration design of satellite clusters, and specifically, to a method for optimizing the configuration of an InSAR satellite cluster based on the NSGA-III algorithm. Background Art

[0002] Cluster satellites have received extensive attention and applications at home and abroad due to their high flexibility, short development cycle, and low launch cost. The InSAR satellite cluster system can utilize the relative orbital characteristics of member satellites to achieve functions such as interferometric altimetry, high-resolution mapping imaging, and ground moving target indication (GMTI), expanding the application scope of traditional SAR satellites.

[0003] The configuration design of the InSAR cluster system needs to coordinate the conflicting indicators among various factors on the basis of fully considering factors such as configuration stability, long and short baseline matching, altimetry accuracy, and inter-satellite safety distance, and obtain a practical and optimal solution, which is an engineering optimization problem involving multiple objectives and multiple constraints. At present, a large number of studies have been carried out on the application scenarios of InSAR satellite system altitude measurement at home and abroad, and various configuration design methods have been proposed. For example, "A Method for Forming a Distributed Satellite Synthetic Aperture Radar" (Patent No. CN 101520511 B) takes the constraint conditions of the optimal combination of multiple groups of baselines as the design input and proposes a "concentric ring" InSAR formation configuration design method, which realizes the design requirement that the formation system satisfies the optimal baseline combination at any time; in 2009, Li Yang, Zhang Running, etc. in "Formation Orbit Configuration Design Based on InSAR Mission Performance Requirements", aiming at the requirements of the altitude measurement accuracy of the InSAR dual-satellite formation for the orbit configuration, proposed four configuration design schemes and analyzed the advantages and disadvantages of the four schemes; in 2013, Wu Shengang, Qian Shan, etc. in "Research on the Design and Control Method of the Flying Angle of Distributed InSAR Satellites", proposed an InSAR satellite formation flying configuration design method with a specific flying angle based on the Hill equation and gave the constraint conditions to ensure the stability of the flying angle. However, most of the existing results only consider the two-satellite formation and mostly carry out configuration design with the goal of configuration stability or baseline altimetry accuracy, and do not start from the engineering application of the InSAR satellite system and comprehensively consider the requirements of system safety, stability, and usefulness for system design. Summary of the Invention

[0004] Aiming at the deficiencies of the above background art, the present invention provides an NSGA-III intelligent optimization algorithm for the configuration of an InSAR satellite cluster, which successfully solves the difficult multi-objective and multi-constraint optimization problem in the configuration design of the InSAR cluster; designs a "concentric ring" cluster configuration in which two slave satellites move relative to one master satellite, and this configuration works in a way of combining long and short baselines, and can simultaneously meet the design requirements in aspects such as inter-satellite collision avoidance, configuration stability, and altimetry performance.

[0005] The present invention adopts the following technical solutions to achieve the above-mentioned invention objectives:

[0006] Step 1, InSAR constellation satellite relative kinematic modeling based on relative E / I vectors:

[0007] When using relative E / I vectors to describe the constellation configuration, an intuitive configuration geometric relationship can be obtained with fewer orbital elements, which is convenient for the configuration design of satellite constellations. The constellation relative kinematic model established based on relative E / I vectors is:

[0008]

[0009] where p = a|Δe| is the in-plane configuration size; s = a|Δi| is the out-of-plane configuration size; l x = Δa is the offset amount of the radial fly-around center; l y = a(Δω0 + ΔM0 + ΔΩ0cosi) is the offset amount along the track direction around the fly-around center; is the phase angle of the in-plane vibration; θ is the phase angle of the out-of-plane vibration.

[0010] Step 2, Combining the actual engineering requirements of InSAR satellite constellation long and short baseline collocation interference imaging, clarify the "concentric ring" configuration optimization variables and variable value ranges based on the constellation relative kinematic model.

[0011] Step 3, Based on the constellation relative kinematic model, establish three objective functions with inter-satellite safety, configuration stability, and measurement performance as optimization indicators.

[0012] Specifically: Construct objective functions from three perspectives of inter-satellite safety, configuration stability, and measurement performance, which are respectively:

[0013] G1 = -min{d1, d2}

[0014]

[0015]

[0016] G1, G2, and G3 are respectively the configuration safety evaluation function, configuration stability evaluation function, and measurement performance evaluation function; d1 is the minimum value of the distance between the master satellite and the slave satellite; d2 is the minimum value of the distance between the slave satellites; v d is the drift velocity of the constellation configuration along the track direction; σ Δh is the height measurement error, P T is the time coverage rate to meet a certain accuracy requirement, α and β are weighting coefficients, and N is the number of slave satellites.

[0017] Step 4, construct an intelligent optimization design algorithm for the InSAR satellite constellation configuration based on the NSGA-III algorithm:

[0018] The NSGA-III multi-objective optimization algorithm maintains the diversity of the population based on well-distributed reference points and can efficiently solve high-dimensional multi-objective optimization problems. For the configuration design problem in the present invention, the process of using the NSGA-III algorithm for optimization and solution is as follows:

[0019] Step 4.1, initialize the population in the NSGA-III algorithm and set the algorithm parameters. The algorithm parameters include population size, number of iterations, crossover probability, mutation probability, etc.;

[0020] Step 4.2, set the optimization variable parameters related to the objective function. In the present invention, the optimization variables are set as the configuration size p and the phase angle in the orbital plane of two slave satellites Each individual in the population is denoted as a 4D vector The objective function vector is denoted as [G1, G2, G3];

[0021] Step 4.3, randomly generate an initial parent population P with a population size of S t and generate an offspring population Q through genetic operations such as crossover and mutation t ;

[0022] Step 4.4, merge the parent population and the offspring population to obtain a new population R with a population size of 2S t and calculate the fitness values of the individuals in R t , that is, the objective function values;

[0023] Step 4.5, perform a fast non-dominated sorting on the new population R t to obtain several non-dominated levels, and then select S better individuals based on the reference points as the parent population for the next generation;

[0024] Step 4.6, repeat Steps 4.3 to 4.5 until the algorithm reaches the optimal or maximum number of iterations, and then end the evolution process.

[0025] Step 5, after the optimization is completed, calculate the orbital element parameters of the slave satellites in the InSAR satellite constellation according to the orbital elements of the master satellite and the numerical values of the configuration optimization variables to complete the configuration optimization design.

[0026] Determine the target configuration parameters according to the Pareto optimal solution Combine the orbital element parameters [a, e, i, ω, Ω, M] of the master satellite and the target configuration parameters to calculate the orbital element parameters of the slave satellites. Among them, a is the semi-major axis, e is the eccentricity, i is the orbital inclination, ω is the argument of perigee, M is the mean anomaly, and Ω is the right ascension of the ascending node of the satellite.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] Considering the design requirements of the InSAR satellite constellation configuration from three aspects of safety, stability and usefulness, taking the inter-satellite distance evaluation function, configuration stability evaluation function and measurement performance evaluation function as multi-objective optimization objects, and using the NSGA-III algorithm to optimize and solve the three objective functions, the intelligent optimization design of the InSAR satellite constellation configuration is realized, and the multi-objective and multi-constraint problem difficult to solve in engineering practice is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flowchart of the optimization design of the InSAR satellite constellation configuration based on NSGA-III;

[0030] Figure 2 is the Pareto optimal solution obtained by using the NSGA-III algorithm to optimize the constellation configuration;

[0031] Figure 3 is a schematic three-dimensional trajectory diagram of the "concentric ring" configuration of the satellite constellation in the relative coordinate system;

[0032] Figure 4 is a schematic diagram of the change curve of the inter-satellite distance within one orbital period;

[0033] Figure 5 is a schematic diagram of the change curve of the measurement accuracy of the long and short baselines within one orbital period;

[0034] Figure 6 is a schematic diagram of the change curve of the length of the vertical effective baseline within one orbital period. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0036] As shown in the Figure 1 accompanying drawings, the present invention provides an NSGA-III intelligent optimization algorithm for the InSAR satellite constellation configuration, which includes the following steps:

[0037] Step 1: Based on the relative E / I vector, establish a relative kinematic model of the constellation.

[0038] Describing the cluster configuration using relative E / I vectors can directly show the geometric relationship of the cluster configuration, facilitating the configuration design of satellite clusters. To describe the relative motion of the slave satellite with respect to the master satellite, the relative inclination vector Δi and the relative eccentricity vector Δe are defined as follows:

[0039]

[0040]

[0041] where θ is the phase angle of the relative inclination vector, and ΔΩ is the difference in the right ascension of the ascending node between the two satellites. is the argument of perigee. Δi X and Δi Y are the two components of the relative inclination vector, and Δe X and Δe Y are the two components of the relative eccentricity vector.

[0042] Let the argument of perigee of the master satellite be ω and the mean anomaly be M. Define the mean latitude argument u = ω + M, then the linearized relative motion equation can be obtained as:

[0043]

[0044] where v is the orbital velocity of the satellite, and Δa represents the difference in the semi-major axis. Considering that SAR satellites generally use low-earth and near-circular orbits, the distance between satellites is small, and Δu is a small quantity. Therefore, the relative motion equation represented by the relative E / I vector can be further simplified as:

[0045]

[0046] where p = a|Δe| is the configuration size in the plane, s = a|Δi| is the configuration size out of the plane, l x = Δa is the offset amount of the radial fly-around center, and l y = a(Δω0 + ΔM0 + ΔΩ0cosi) is the offset amount of the along-track fly-around center. is the phase angle of the vibration in the plane, and θ is the phase angle of the vibration out of the plane. At this time, the cluster configuration can be represented by six configuration parameters: p, l x ,l y ,s, and θ.

[0047] Step 2: Combining the actual engineering requirements of the InSAR satellite cluster for long and short baseline collocated interferometric imaging, based on the cluster relative kinematic model, clarify the optimization variables and their value ranges of the "concentric ring" configuration. In the "concentric ring" configuration, two slave satellites and the master satellite form two baselines with different lengths. According to the available length constraints of the long and short baselines, determine the optimization range of the optimization variable in the optimization algorithm.

[0048] Step 3: Based on the relative kinematic model of the cluster, establish three objective functions with inter-satellite safety, configuration stability, and high measurement performance as the optimization indicators.

[0049] Step 3.1: Description of the configuration safety performance index of the InSAR satellite cluster system:

[0050] When the inter-satellite distance is relatively close, collisions are likely to occur. Therefore, it is necessary to establish a configuration safety index to ensure that there is no collision between the master satellite and the slave satellites, and there is also a sufficient safety distance between the slave satellites.

[0051] Take the minimum value of the distance between the master satellite and the slave satellites, defined as:

[0052] d1 = min{r1, r2, …, r N} (5)

[0053] Where, i represents the slave satellite, satisfying i = 1, 2, …, N, and N is the number of slave satellites.

[0054] Take the minimum value of the distances between the slave satellites, defined as:

[0055]

[0056] Where, i, j ∈ (1, N), satisfying i ≠ j.

[0057] To ensure the configuration safety of the InSAR satellite cluster, when designing the configuration, the values of d1 and d2 should be large enough. Therefore, construct the configuration safety performance index shown in formula (7):

[0058] G1 = -min{d1, d2} (7)

[0059] The smaller the value of G1, the larger the values of d1 and d2. Therefore, optimizing the performance index G1 can ensure that the InSAR cluster satellites do not collide and meet the safety of the cluster system.

[0060] Step 3.2: Description of the configuration stability performance index of the InSAR satellite cluster system:

[0061] The J2 perturbation will cause the cluster configuration and the cluster center to drift or rotate, which is the main factor damaging the cluster configuration. According to the first-order theory, when considering the long-term perturbation of the J2 term, the average change rate of the orbital elements is:

[0062]

[0063] Where, n is the average orbital angular velocity; R e is the radius of the Earth; J2 = 1082.63×10-6 is the perturbation term coefficient. Considering that the orbital element difference between the primary satellite and the secondary satellite is a small quantity, the average change rate of the orbital element difference is:

[0064]

[0065] where

[0066] The "concentric ring" configuration designed in the present invention satisfies z = 0, and the cluster configuration is the most unstable in the y direction. According to the concept of the generalized J2 invariant configuration, the condition for stability in the y direction is:

[0067]

[0068] The drift velocity of the cluster configuration along the track direction is To ensure the stability of the InSAR satellite cluster configuration, the design configuration should satisfy v d →0. Combining the above configuration stability conditions, the following configuration stability performance index is constructed:

[0069]

[0070] The smaller the value of G2, the smaller the drift velocity. Therefore, optimizing the performance index G2 can ensure that the InSAR cluster system will not drift in the y direction and meet the stability of the cluster system.

[0071] Step 3.3: Description of the altimetry mission performance index of the InSAR satellite cluster system

[0072] The vertical effective baseline B for the digital elevation model (DEM) ECT , which is the projection of the relative position between satellites in the radial plane of the radar beam and then projected again onto the vertical direction of the beam radial. Its expression is:

[0073] B ECT = |xsinφ + zcosφ| (12)

[0074] where φ is the nadir angle. Ignoring the influence of the earth's curvature, the height measurement error is:

[0075]

[0076] where R0 is the slant range from the primary satellite to the target; θ0 is the central viewing angle; λ is the radar signal wavelength; N L is the number of independent looks of the complex image; γ is the image interference decorrelation coefficient, which can be expressed as the product of decorrelation factors. If the influence of volume scattering is ignored, the spaceborne SAR interference decorrelation coefficient γ can be simplified to geometric decorrelation γ g , and its expression is:

[0077]

[0078] Among them, is the terrain slope angle; R res is the radar range resolution, which can be obtained through R res = c / 2B e where c is the speed of light and B e is the effective bandwidth.

[0079] Through the above equations, the relationship between the altimetry error and the configuration parameters can be obtained. On this basis, considering the altimetry performance indicators of the InSAR satellite constellation system include two parts:

[0080] 1) Altimetry accuracy index, that is, the altimetry error σ Δh The smaller the value, the higher the altimetry accuracy of the InSAR constellation system;

[0081] 2) Time coverage index, that is, the proportion P T of the orbital period time that meets the altimetry accuracy requirements. The larger this value, the higher the usefulness of the constellation. The specific definition of the proportion P T is:

[0082] P T = sum{t: σ Δh (t) < σ ΔhT , t ∈ T} / T (15)

[0083] where σ ΔhT is the target altimetry error; T is an orbital period; sum{·} represents the time set within an orbital period where the altimetry error is less than σ ΔhT .

[0084] Based on the above content, the optimization performance objective function of the altimetry mission of the InSAR satellite constellation system can be established as:

[0085]

[0086] where α and β are weighting coefficients, satisfying α > 0 and β > 0.

[0087] The smaller the value of G3, the smaller the value of σ Δh or the larger the value of P T . Therefore, optimizing the performance indicator G3 can ensure that the InSAR satellite constellation system has very good altimetry performance and meets the usefulness of the constellation system.

[0088] Step 4: Use the NSGA-III algorithm to optimize and solve the three objective functions, obtain the Pareto optimal solution set, and determine the target configuration parameters and satellite orbit element parameters according to the optimal solution to realize the intelligent optimal design of the InSAR satellite constellation configuration.

[0089] Specifically, the following optimization process is adopted to perform intelligent optimization design on the InSAR satellite constellation configuration based on the NSGA-III algorithm.

[0090] (1) Initialize the population in the NSGA-III algorithm and set the algorithm parameters. The algorithm parameters include population size, number of iterations, crossover probability, mutation probability, etc.;

[0091] (2) Set the optimization variable parameters related to the objective function. In the present invention, the optimization variables are set as the configuration size p and phase angle in the orbital plane of two slave satellites Each individual in the population is denoted as a 4D vector The objective function vector is denoted as [G1, G2, G3];

[0092] (3) Randomly generate an initial parent population P with a population size of S t and generate an offspring population Q through genetic operations such as crossover and mutation t ;

[0093] (4) Combine the parent population and the offspring population to obtain a new population R with a population size of 2S t , calculate the fitness values of the individuals in R t , that is, the objective function values;

[0094] (5) Perform fast non-dominated sorting on the new population R t to obtain several non-dominated levels, and then select S better individuals based on the reference point as the parent population for the next generation;

[0095] (6) Repeat steps (3) to (5) until the algorithm reaches the optimal or maximum number of iterations, and then end the evolutionary process.

[0096] In step 5, after the optimization is completed, combine the main satellite orbit elements and the numerical values of the optimization variables corresponding to the Pareto optimal solution to calculate the InSAR satellite constellation configuration and the slave satellite orbit parameters.

[0097] Embodiment

[0098] Given that the reference orbit of the constellation is a near-circular orbit with an orbital altitude of 550 km and σ ΔhT is taken as 3 m. According to the "concentric ring" configuration characteristics, the constraint condition z = 0 is obtained. To ensure the configuration stability and the main satellite is located at the center of the configuration, set the constraints l x = 0, l y = 0. Set the available length constraint of the short baseline B1 to be 250 m to 550 m, and the available length constraint of the long baseline B2 to be 700 m to 1050 m, then the optimization variables The optimization range can be set as: p1 ∈ [0, 800m], p2 ∈ [0, 1500m], In addition, the baseline also needs to meet certain accuracy requirements. Therefore, the constraints that the available baseline should satisfy are:

[0099] 250m ≤ B1 ≤ 550m && σ Δh (B1) ≤ σ ΔhT

[0100] 700m ≤ B2 ≤ 1050m && σ Δh (B2) ≤ σ ΔhT

[0101] Among them, σ Δh (B1) and σ Δh (B2) are the height measurement errors of the baseline. The main satellite orbit parameters and simulation input parameters are shown in Table 1 and Table 2.

[0102] Table 1 Main satellite orbit parameters

[0103]

[0104]

[0105] Table 2 Simulation input parameters

[0106] Based on the above configuration parameters and constraints, the three objective functions are optimized and solved. The Figure 2 convergence of the Pareto front solutions of the three objective functions during the optimization process is shown. It can be seen that the more iterations, the better the solution set; when the maximum number of iterations is reached, the algorithm has found the optimal solution (as shown by the arrow in the figure), and the optimization variables corresponding to the optimal solution are p1 = 777.69m, p2 = 1397.07m,

[0107] According to the above optimization variables and the main satellite orbit elements, the optimized design results of the InSAR satellite constellation are shown in Table 3 and Table 4.

[0108] Table 3 Orbit elements and configuration parameters of Slave Satellite 1

[0109]

[0110] Table 4 Orbit elements and configuration parameters of Slave Satellite 2

[0111]

[0112]

[0113] Appendix Figure 3 The three-dimensional configuration of the satellite cluster is given, and this configuration meets the design requirements of the "concentric ring" configuration.

[0114] Appendix Figure 4 The variation of the inter-satellite distance within one orbital period is given, where R1 and R2 are the distances between two slave satellites and the master satellite, and R 12 is the distance between the two slave satellites. It can be seen from the figure that the inter-satellite distances are all above 500m, and the satellites will not collide, so the safety of the configuration can be guaranteed.

[0115] Appendix Figure 5 The variation of the ranging accuracy of short and long baselines within one orbital period is given, where the percentages P T of the time when the short baseline and the long baseline meet the 3m accuracy requirement within one orbital period are 69.44% and 83.33% respectively.

[0116] Appendix Figure 6 The vertical effective baseline length within one orbital period is given. The symbol "*" in the figure represents the available baselines that meet the length constraint and the accuracy constraint.

[0117] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. The NSGA-III intelligent optimization algorithm for the InSAR satellite constellation configuration, characterized in that , including: Step 1: Based on the relative eccentricity / inclination vector, establish the relative kinematic model of the InSAR satellite cluster, and design the "concentric ring" cluster configuration in which two slave satellites move relative to one master satellite; Step 2: Based on the relative kinematic model, combine the long and short baselines of the InSAR satellite cluster to determine the optimization variables and their optimization ranges of the "concentric ring" configuration; Step 3: Based on the relative kinematic model of the cluster, establish objective functions with inter-satellite safety, configuration stability, and high measurement performance as optimization indicators, namely: inter-satellite distance objective function, configuration stability objective function, and high measurement performance objective function; Specifically, in Step 3.1, establish the inter-satellite distance objective function G1 of the InSAR satellite cluster system: G1 = -min{d1, d2}, where d1 is the minimum value of the distance between the master satellite and the slave satellite, and d2 is the minimum value of the distance between each slave satellite; Step 3.2, establish the configuration stability objective function G2 of the InSAR satellite cluster system: Using the concept of a generalized invariant configuration, the y-direction drift velocity of the configuration center is made zero, ensuring the stability of the configuration along the track direction. The stability condition is Δa, and the drift velocity of the cluster configuration along the track direction is v d , where n is the average orbital angular velocity and v d →0, Step 3.3, establish the high-performance objective function G3 of the InSAR satellite cluster system: It includes two parts, namely the height measurement accuracy index and the time coverage rate index. Among them, the height measurement accuracy index is the height measurement error σ Δh , and the time coverage rate index is the proportion P of the orbital period time that meets the height measurement accuracy requirement T , where N is the number of slave satellites, and α and β are weighting coefficients, satisfying α > 0 and β > 0; Step 4: Use the NSGA-III algorithm to optimize and solve the objective function to obtain the Pareto optimal solution set. Specifically, Step 4.1, initialize the population in the NSGA-III algorithm, and set the algorithm parameters, including population size, number of iterations, crossover probability, and mutation probability; Step 4.2: Set the optimization variable parameters related to the objective function. The optimization variables are the configuration size p and the phase angle within the orbital planes of the two slave satellites. Each individual in the population is denoted as a 4D vector. The objective function vector is denoted as [G1, G2, G3]. Step 4.3, randomly generate an initial parental population P with a population size of S t , and generate an offspring population Q through genetic operations such as crossover and mutation t ; Step 4.4, merge the parental population and the offspring population to obtain a new population R with a population size of 2S t , and calculate the fitness values of the individuals in R t , i.e., the objective function values; Step 4.5, perform fast non-dominated sorting on the new population R t to obtain several non-dominated levels, and then select the better S individuals based on the reference point as the parental population for the next generation; Step 4.6, repeat Step 4.3 to Step 4.5 until the algorithm reaches the optimal or maximum number of iterations, then end the evolution process to obtain the Pareto optimal solution; Step 5: Determine the target configuration parameters and satellite orbit element parameters according to the Pareto optimal solution to realize the intelligent optimization design of the cluster configuration.

2. The NSGA-III intelligent optimization algorithm for the InSAR satellite constellation configuration according to claim 1, characterized in that Step 1 specifically includes: Step 1.1, describe the cluster configuration using the relative eccentricity / inclination vector. The relative inclination vector is Δi, and the relative eccentricity vector is Δe. Then the linearized relative motion equation is: Among them, Δi X and Δi Y are two components of the relative inclination vector; Δe X and Δe Y are two components of the relative eccentricity vector; v is the orbital velocity of the satellite, a is the semi-major axis, and Δa is the difference in semi-major axis; Δr and are the relative motion states, and the subscripts R, T, and N represent the radial, along-track, and normal directions respectively, and u is the mean argument of latitude; Step 1.2, simplify the relative motion equation in Step 1.1 to: where p and s are the configuration dimensions in and out of the plane respectively, and l x is the offset from the radial flying-around center, and l y is the offset along the track towards the flying-around center, and θ are the phase angles of the motion in and out of the xoy plane respectively.

3. The NSGA-III intelligent optimization algorithm for the InSAR satellite constellation configuration according to claim 2, characterized in that In the said step 2, two slave satellites and the master satellite in the "concentric ring" cluster configuration form two baselines with different lengths. According to the available length constraints of the long and short baselines, the optimization variables in the optimization algorithm, namely the in-plane configuration size and the in-plane phase angle of the two slave satellites, are determined. The optimization range.

4. The NSGA-III intelligent optimization algorithm for the InSAR satellite constellation configuration according to claim 1, characterized in that In step 3.2, Δa is the difference in semi-major axes. In the formula a, e, and i are the semi-major axis, eccentricity, and orbital inclination of the primary star respectively; Δe and Δi are the differences in eccentricity and orbital inclination between the secondary star and the primary star; n is the mean orbital angular velocity, R e is the radius of the Earth, and J2 = 1082.63 × 10 -6 is the perturbation term coefficient.

5. The NSGA-III intelligent optimization algorithm for the InSAR satellite constellation configuration according to claim 4, characterized in that The height measurement error in Step 3.3 is: Among them, R0 is the slant range from the main star to the target; θ0 is the central viewing angle; λ is the radar signal wavelength; N L is the number of independent looks of the complex image; γ is the image interference decorrelation coefficient, B ECT is the vertical effective baseline; The orbital period time ratio P T is as follows: P T = sum{t:σ Δh (t) < σ ΔhT , t ∈ T} / T Among them, σ ΔhT is the target altimetry error; T is an orbital period; sum{·} represents the time set in an orbital period when the altimetry error is less than σ ΔhT .

6. The NSGA-III intelligent optimization algorithm for the InSAR satellite cluster configuration according to claim 1, characterized in that Specifically in the step 5: Determine the target configuration parameters according to the Pareto optimal solution Calculate the slave satellite orbital element parameters by combining the master satellite orbital element parameters [a, e, i, ω, Ω, M] and the target configuration parameters, where a is the semi-major axis, e is the eccentricity, i is the orbital inclination, ω is the argument of perigee, M is the mean anomaly, and Ω is the right ascension of the ascending node of the satellite.

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