Star group cooperative area positioning method based on communication ranging

Abstract

The invention relates to a satellite group cooperative area positioning method based on communication ranging, and belongs to the technical field of spacecraft navigation. Three reference satellites are selected in a satellite group space area, and a positioning reference is constructed; determining an initial relative motion state Xim0 of any member satellite m in the LVLH system based on a positioning reference; a triangular vector closed loop is formed by the relative positions of the satellite i, the satellite j and the satellite k; according to the triangular vector closed loop, establishing a relative orbit state consistency constraint model; introducing the consistency constraint model into a filtering algorithm, establishing a distributed Kalman filtering algorithm, and obtaining a measurement updating equation, namely star group distributed state estimation; according to the invention, cluster dynamic ad hoc network relative navigation is realized on the premise of limited satellite-borne measurement and control resources and complex space optical environment, the global positioning navigation problem under limited information interaction is solved, and the method has the capability of fast and accurate area positioning of an in-and-out satellite group system and global state sensing under limited resources.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft navigation, and relates to a method for cooperative regional positioning of a satellite swarm based on communication ranging. Background Technique

[0002] Swarm formation flight is a highly pioneering emerging space technology field. Due to the great application potential and advantages of swarm flight, more and more foreign space missions adopt swarm flight technology to achieve. Each satellite maintains contact and jointly undertakes tasks such as signal processing, communication, and payload. The task functions are jointly completed by the entire satellite swarm. Small satellites, with their ability to quickly and flexibly adapt to tasks and the characteristics of low cost and rapid access to space, are increasingly becoming an important part of various space equipment and space application systems and are a necessary supplement to large satellites. The technical characteristics of small satellites such as light weight, low cost, and short development cycle are the material basis and necessary conditions for adopting a satellite swarm system. Therefore, micro-nano satellite swarms have great advantages and broad application prospects.

[0003] Precise relative navigation between swarm members and then determining the position of each member satellite within the swarm is a prerequisite for tasks such as maintaining and changing the relative orbit configuration of micro-nano satellite swarms. Micro-nano satellite swarm member relative navigation faces problems such as strong miniaturization constraints, numerous moving objects within the region, high-dynamic time-varying coupling of motion and topology, and discontinuous and incomplete information. Traditional differential GPS relative navigation cannot adapt to the micro-nano satellite load and limited link channels, and the field of view pointing of means such as vision / microwave / laser is limited or remote ranging cannot be achieved.

[0004] Current research on inter-satellite relative measurement mainly focuses on formation flight tasks with a small number of satellites, and can only achieve relative navigation between two satellites. When the number of satellites in the swarm is large, the number and range of relative measurement channels are limited, the amount of information interaction increases sharply, the communication channel is easily blocked, and the computing power is limited. Therefore, how to achieve autonomous cooperative regional positioning of the satellite swarm has become a difficult problem, and a new positioning means needs to be sought that can both adapt to miniaturization constraints and have the ability of wide-range, multi-channel, and long-distance positioning. Summary of the Invention

[0005] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, and proposing a method for cooperative regional positioning of a satellite swarm based on communication ranging, to achieve cluster dynamic self-organizing network relative navigation under the premise of limited on-board TT&C resources and complex space optical environment, solve the global positioning and navigation problem under limited information interaction, and have the ability of fast and accurate regional positioning for satellites entering and leaving the satellite swarm system at will and global state perception under resource constraints.

[0006] The solution of the present invention to solve the technology is:

[0007] A method for cooperative regional positioning of a satellite swarm based on communication ranging, comprising:

[0008] Select 3 reference stars, namely satellite i, satellite j, and satellite k, within the spatial region of the satellite constellation; construct a positioning reference.

[0009] Based on the positioning reference, determine the initial relative orbits of the other member satellites in the satellite constellation with respect to the 3 reference stars, that is, the initial relative motion state X of any member satellite m in the LVLH system. im0 ;

[0010] Form a triangular vector closed loop from the relative positions among satellite i, satellite j, and satellite k; establish a relative orbit state consistency constraint model according to the triangular vector closed loop; and introduce the consistency constraint model into the filtering algorithm to establish a distributed Kalman filtering algorithm under geometric topology consistency constraints, obtain the measurement update equation, that is, the constellation distributed state estimation, and complete the regional positioning of each satellite.

[0011] In the above method for constellation cooperative regional positioning based on communication ranging, the specific construction of the positioning reference is as follows:

[0012] According to the geometric configuration among all members of the constellation, select 3 satellites with an acute triangle configuration as the reference; use angle measurement and ranging, nonlinear dynamics, orbit maneuvering, and introduce geometric topology consistency constraint means to achieve fast and high-precision relative navigation among the reference stars. The 3 reference stars that complete high-precision relative navigation serve as the spatial reference, and other satellite members in the group use the ranging information with the reference stars to achieve relative navigation; at the same time, since the combined configuration among constellations is dynamically changing, when the triangle configuration among the 3 selected references is not conducive to establishing a high-precision spatial reference, the reference stars will be reselected according to the star selection rules.

[0013] The method for constructing the positioning reference includes:

[0014] S11. Optimally select reference stars;

[0015] S12. Determine the relative measurement scheme of angle measurement and ranging among the 3 reference stars;

[0016] S13. Determine the algorithm for the initial relative orbits among the reference stars.

[0017] In the above method for constellation cooperative regional positioning based on communication ranging, it is characterized in that: in the above S11, the method for optimally selecting reference stars is as follows:

[0018] First, establish an optimization model for reference star selection; the configuration of the reference stars should preferably be an equilateral triangle, and the ratio of the distance of the satellite corresponding to the shortest side in the triangle to the maximum distance among all satellites should be as large as possible.

[0019] Suppose there are N satellites in total. In a unified coordinate system, let pos i =[x i , y i , z i T represent the spatial coordinates of the i-th satellite. Then the distance ρ ij between satellite i and satellite j is:

[0020]

[0021] For the triangle configuration formed by satellites i, j, and k, the side lengths are the distances between the corresponding satellites. Define α i,ijk as the angle corresponding to satellite i in this triangle, that is:

[0022]

[0023] Two objective functions J1 and J2 are established and are respectively expressed as:

[0024] maxJ1 = min(α i,ijk , α j,ijk , α k,ijk ) i, j, k ∈ {1, 2, …, N}

[0025]

[0026] Among them, and J2 ≤ 1;

[0027] Considering the influence of the two objective functions comprehensively, the optimization model for selecting the reference stars is constructed as follows:

[0028] find i, j, k ∈ {1, 2, …, N}

[0029] max J = λ1J1 + λ2J2

[0030] Among them, J is the value of the optimization function;

[0031] λ1 and λ2 are the weights of the two objectives.

[0032] In the above method for collaborative regional positioning of satellite clusters based on communication ranging, in S12, determine the relative measurement scheme of angle measurement and distance measurement between three reference stars:

[0033] Select the line-of-sight measurement star from the reference stars according to the optical conditions; define the incident solar angle α as the angle formed by the straight line from the target to the sun and the straight line from the target to the satellite; when α is large, the target is difficult to measure due to light saturation; according to the positions of the sun, the target, and the satellite, with the help of the cosine theorem, calculate the angle α through the following formula:

[0034] ​

[0035] In the formula, D ts is the distance from the target to the sun;

[0036] D tm is the distance from the target to the observed star;

[0037] D ms is the distance from the observed star to the sun;

[0038] When the incident solar angle affects the observation accuracy, select the reference star with a smaller solar incident angle among the three reference stars as the line-of-sight measurement star, that is, determine the relative measurement scheme of angle measurement and distance measurement between the three reference stars.

[0039] In the above method for positioning a star cluster collaboration area based on communication ranging, in S13, the determination method of the initial relative orbit algorithm between reference stars is as follows:

[0040] Establish a measurement model y:

[0041]

[0042] In the formula, α ij , β ij are respectively the azimuth angle and elevation angle of satellite j relative to satellite i;

[0043] ρ ij is the relative distance of satellite j relative to satellite i;

[0044] ρ ik is the relative distance of satellite k relative to satellite i;

[0045] ρ jk is the relative distance of satellite k relative to satellite j;

[0046] ε α , ε β are respectively the measurement error of the azimuth angle and the measurement error of the elevation angle; and ε α and ε β both follow a zero-mean Gaussian distribution;

[0047] and are respectively the ranging errors between any two satellites; and and follow a zero-mean Gaussian distribution;

[0048] Set the unit line-of-sight vector l ij of satellite j relative to satellite i as:

[0049]

[0050] Each set of unit line-of-sight vectors of satellite j relative to satellite i satisfies:

[0051]

[0052] where t is any moment;

[0053] is the relative motion state of satellite j relative to satellite i;

[0054] n is the end time;

[0055] Therefore, the initial relative orbit determination problem between satellite j and satellite i is transformed into the following optimization problem:

[0056]

[0057] where Φ r (t t , t0) is the state transition submatrix;

[0058] t t is the current moment;

[0059] t0 is the initial moment;

[0060] X ij0 is the initial relative motion state of satellite j relative to satellite i;

[0061] Set matrix A as:

[0062]

[0063] According to the definition of singular value decomposition and its connection with the constrained optimization of linear functions, perform singular value decomposition on matrix A, and take the right eigenvector corresponding to the smallest singular value to obtain the unit vector of X ij0 in the least squares sense

[0064] According to the angle measurement information [α ij0 β ij0 T and the range measurement information ρ ij0 at the initial moment, calculate the initial relative position r ij0 of satellite j in the LVLH system at the initial moment;

[0065] Therefore, according to and r ij0 obtain the initial relative motion state X ij0 of satellite j relative to satellite i;

[0066] For the initial relative motion state X ik0 ​, which is solved from three groups of relative distance measurements and the relative position vectors of three groups of satellites;

[0067] Based on the angle measurement and ranging information of satellite i with respect to satellite j, the relative position of satellite j in the LVLH system is calculated in real time Then, based on the ranging information between satellites in real time Calculate and The included angle θ between t ;

[0068] Set the initial relative motion state of satellite k in the LVLH system as The relative motion state of satellite k at any time Is:

[0069]

[0070] In the formula, Φ(t t , t0) is the state transition matrix of satellite i in the LVLH system;

[0071] Since the relative motion states of satellite k at times t1, t2, and t3 Are all time functions of X ik0 , a set of simultaneous equations are established based on the ranging information and the calculated angles:

[0072]

[0073] In the formula, Is the relative position of satellite j in the LVLH system;

[0074] Solve the above equation to obtain the initial relative motion state X of satellite k in the LVLH system ik0 ; Thus, the initial relative motion states X ij0 , X ik0 Of satellite i with respect to satellite j in the LVLH system are obtained respectively; Based on X ij0 And X ik0 Determine the relative orbit situation of the three satellites of satellite i, satellite j, and satellite k, and realize the determination of the initial relative orbit of the three-satellite formation.

[0075] In the above method for star cluster collaborative regional positioning based on communication ranging, the initial relative position r of satellite j in the LVLH system at the initial moment ij0 Is:

[0076]

[0077] In the above method for star cluster collaborative regional positioning based on communication ranging, the initial relative motion state X of satellite j relative to satellite i ij0 Is:

[0078]

[0079] In the above method for collaborative regional positioning of a satellite cluster based on communication ranging, and the included angle θ t is:

[0080]

[0081] In the above method for collaborative regional positioning of a satellite cluster based on communication ranging, it is characterized in that: the initial relative motion state X of the satellite m in the LVLH system im0 is determined as follows:

[0082] After the positioning reference is constructed by 3 reference satellites, the other member satellites determine the initial relative orbit by measuring the distance to the reference satellites; establish the measurement equation y for the member satellite m to measure the distance to the satellites i, j, and k m is:

[0083]

[0084] In the formula, ρ im is the distance between the member satellite m and the satellite i;

[0085] ρ mj is the distance between the member satellite m and the satellite j;

[0086] ρ mk is the distance between the member satellite m and the satellite k;

[0087] is the distance measurement error between the member satellite m and the satellite i;

[0088] is the distance measurement error between the member satellite m and the satellite j;

[0089] is the distance measurement error between the member satellite m and the satellite k;

[0090] Assume that the initial relative motion state of the member satellite m in the LVLH system is:

[0091] It is known from the properties of the state transition matrix that the relative motion state of the satellite m at any time is obtained according to the state transition matrix of the satellite i in the LVLH system and the initial relative motion state of the satellite k

[0092]

[0093] In the formula, Φ(t t,t0) is the state transfer matrix of satellite i in the LVLH system; Φ(t t ,t0) only with the average angular velocity of the orbit of satellite i and the time interval Δt=t t -t0 related;

[0094] Due to the relative motion state of satellite m at t1 and t2 Yes X im0 The time function of , therefore, according to the ranging information, the simultaneous equations are:

[0095]

[0096] In the formula, is the relative position of satellite j in the LVLH system, which is calculated in real time as a known quantity;

[0097] is the relative position of satellite k in the LVLH system, which is calculated in real time as a known quantity;

[0098] Solving the nonlinear equations in the above formula, we can obtain the initial relative motion state X of satellite m in the LVLH system: im0 .

[0099] In the above-mentioned satellite cluster coordinated regional positioning method based on communication ranging, the method for estimating the distributed state of the satellite cluster is:

[0100] Establish a geometric topological consistency constraint model for relative orbits; set satellite k to measure satellite i, and let the relative orbit state of satellite i in the LVLH coordinate system of satellite k be Then, the triangular vector closed loop formed by the relative positions of satellites i, j, and k satisfies:

[0101]

[0102] In the formula, is the transformation matrix from the LVLH coordinate system of satellite k to the LVLH coordinate system of satellite i;

[0103] The consistency constraint equation of the relative velocity is obtained by derivation with respect to time. After being combined with the consistency constraint equation of the relative position, the consistency constraint model of the relative orbit state is established as shown below:

[0104]

[0105] In the formula, is the generalized rotation matrix:

[0106]

[0107] The consistency constraint model is introduced into the filtering algorithm, a distributed Kalman filtering algorithm under the geometric topology consistency constraint is established, and the calculation process is designed. The corresponding measurement update process is as follows:

[0108]

[0109] In the formula, γ represents the consistency coefficient, represents a priori estimate.

[0110] The beneficial effects of the present invention compared with the prior art are:

[0111] (1) The present invention realizes relative navigation of cluster dynamic self-organizing network under the premise of limited onboard measurement and control resources and complex space optical environment;

[0112] (2) The present invention solves the problem of global positioning and navigation under limited information interaction, and has the capability of fast and accurate regional positioning of the constellation system that can enter and exit at will, and global state perception under resource constraints;

[0113] (3) The present invention first establishes a triangular vector closed loop composed of the relative positions of three satellites; based on the triangular vector closed loop, a relative orbit state consistency constraint model is established; and the consistency constraint model is introduced into the filtering algorithm to establish a distributed Kalman filtering algorithm under the geometric topology consistency constraint condition, thereby obtaining a measurement update equation, i.e., a distributed state estimation of the star cluster, and completing the regional positioning of each satellite; the positioning is accurate and can be updated in real time. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 This is a flow chart of the satellite cluster collaborative regional positioning of the present invention. DETAILED DESCRIPTION

[0115] The present invention will be further described below in conjunction with the embodiments.

[0116] The present invention provides a cluster collaborative regional positioning method based on communication ranging, which realizes cluster dynamic self-organizing network relative navigation under the premise of limited satellite-borne measurement and control resources and complex space optical environment, solves the global positioning and navigation problem under limited information interaction, and has the ability of fast and accurate regional positioning of the star cluster system that can enter and exit at any time and global state perception under resource constraints.

[0117] The satellite cluster collaborative regional positioning method based on communication ranging, such as Figure 1 As shown, the specific steps include:

[0118] Select three reference satellites, satellite i, satellite j, and satellite k, in the satellite constellation space area to build a positioning reference. The specific steps of building a positioning reference are:

[0119] According to the geometric configuration among all the members of the satellite constellation, three satellites in an acute triangle configuration are selected as the benchmarks; by means of angle measurement and ranging, nonlinear dynamics, orbital maneuver, and introducing geometric topology consistency constraints, fast and high-precision relative navigation among the benchmark satellites is achieved. The three benchmark satellites that complete high-precision relative navigation serve as the space benchmark, and other satellite members in the constellation use the ranging information with the benchmark satellites to achieve relative navigation under this space benchmark; at the same time, since the combined configuration among the satellite constellations is dynamically changing, when the triangle configuration among the three selected benchmarks is not conducive to establishing a high-precision space benchmark, the benchmark satellites will be reselected according to the satellite selection rules.

[0120] The methods for constructing the positioning benchmark include:

[0121] S11. Optimally select the benchmark satellites.

[0122] The method for optimally selecting the benchmark satellites is as follows:

[0123] First, establish an optimization model for selecting the benchmark satellites; the configuration of the benchmark satellites should preferably be an equilateral triangle, and the ratio of the distance of the satellite corresponding to the shortest side in the triangle to the maximum distance among all satellites should be as large as possible.

[0124] Suppose there are a total of N satellites. In a unified coordinate system, let pos i =[x i ,y i ,z i T represent the spatial coordinates of the i-th satellite. Then the distance ρ ij between satellite i and satellite j is:

[0125]

[0126] For the triangle configuration composed of satellites i, j, and k, its side lengths are the distances between the corresponding satellites. Define α i,ijk as the angle corresponding to satellite i in this triangle, that is:

[0127]

[0128] Two objective functions J1 and J2 are established, which are respectively expressed as:

[0129] maxJ1=min(α i,ijk ,α j,ijk ,α k,ijk )i,j,k∈{1,2,…,N}

[0130]

[0131] where, and J2≤1. ​

[0132] Taking into account the influence of the two objective functions, the optimization model for selecting the benchmark satellite is constructed as follows:

[0133] find i,j,k∈{1,2,…,N}

[0134] max J=λ1J1+λ2J2

[0135] Among them, J is the optimization function value.

[0136] λ1 and λ2 are the weights of the two objectives.

[0137] S12. Determine the relative measurement scheme for angle and distance measurement among the three reference stars.

[0138] In addition to measuring the distance between the reference stars, the line-of-sight measurement stars are selected from the reference stars according to the optical conditions. The performance of the optical camera is affected by the sunlight conditions, including the intensity, direction, wavelength and other aspects of the light. Under high-quality sunlight conditions, the sensor can obtain more information, thereby improving the brightness and contrast of the image. For example, changes in the wavelength of sunlight may also cause refraction, scattering and other problems in the optical system, thereby affecting the measurement and detection performance of the sensor. Poor incident angles, such as strong sunlight or backlight conditions, may cause strong reflections on the lens surface, produce halos or shadows, cause light spots and glare, and reduce the clarity and color reproduction of the image.

[0139] Determine the relative measurement scheme for angle measurement and distance measurement between the three reference stars:

[0140] Select the line-of-sight measurement star from the reference stars according to the optical conditions; define the incident solar angle α as the angle formed by the straight line from the target to the sun and the straight line from the target to the satellite; when α is large, the target is difficult to measure due to light saturation; according to the positions of the sun, target and satellite, with the help of the cosine theorem, calculate the angle α by the following formula:

[0141]

[0142] Where D ts is the distance from the target to the sun;

[0143] D tm is the distance from the target to the observed star;

[0144] D ms To observe the distance from the star to the sun;

[0145] When the incident solar angle has an impact on the observation accuracy, the reference star with a smaller solar incident angle is selected from the three reference stars as the line of sight measurement star, that is, the relative measurement scheme of angle measurement and distance measurement among the three reference stars is determined.

[0146] S13. Algorithm for determining the initial relative orbit between reference satellites.

[0147] The method for determining the algorithm of the initial relative orbit between reference satellites is as follows:

[0148] Establish a measurement model y:

[0149]

[0150] where α ij , β ij are respectively the azimuth angle and elevation angle of satellite j relative to satellite i.

[0151] ρ ij is the relative distance between satellite j and satellite i.

[0152] ρ ik is the relative distance between satellite k and satellite i.

[0153] ρ jk is the relative distance between satellite k and satellite j.

[0154] ε α , ε β are respectively the measurement error of the azimuth angle and the measurement error of the elevation angle; and ε α and ε β both follow a zero-mean Gaussian distribution.

[0155] and are respectively the ranging errors between any two satellites; and and follow a zero-mean Gaussian distribution.

[0156] Set the unit line-of-sight vector l ij of satellite j relative to satellite i as:

[0157]

[0158] Each group of unit line-of-sight vectors of satellite j relative to satellite i satisfies:

[0159]

[0160] where t is any moment.

[0161] is the relative motion state of satellite j relative to satellite i.

[0162] n is the end time.

[0163] Therefore, the problem of initial relative orbit determination between satellite j and satellite i is transformed into the following optimization problem:

[0164]

[0165] In the formula, Φ r (t t , t0) is the state transition sub - matrix.

[0166] t t is the current time.

[0167] t0 is the initial time.

[0168] X ij0 is the initial relative motion state of satellite j relative to satellite i.

[0169] Set the matrix A as:

[0170]

[0171] According to the definition of singular - value decomposition and its connection with the constrained optimization of linear functions, perform singular - value decomposition on matrix A, take the right eigenvector corresponding to the smallest singular value, and obtain the unit vector of X ij0 in the least - squares sense

[0172] According to the angle - measurement information [α ij0 β ij0 T and the range - measurement information ρ ij0 , calculate the initial relative position r ij0 of satellite j in the LVLH system at the initial time.

[0173] The initial relative position r ij0 of satellite j in the LVLH system at the initial time is:

[0174]

[0175] Therefore, according to and r ij0 obtain the initial relative motion state X ij0 of satellite j relative to satellite i.

[0176] The initial relative motion state X ij0 of satellite j relative to satellite i is:

[0177]

[0178] For the initial relative motion state X ik0 of satellite k relative to satellite i, it is solved from three groups of relative - distance measurements and three groups of relative - position vectors of the satellites.

[0179] From the angle - measurement and range - measurement information of satellite i to satellite j, the relative position of satellite j in the LVLH system is calculated in real time Then the real-time satellite ranging information Calculate and The angle θ t .

[0180] and The angle θ t for:

[0181]

[0182] Assume that the initial relative motion state of satellite k in the LVLH system is The relative motion state of satellite k at any time for:

[0183]

[0184] In the formula, Φ(t t ,t0) is the state transfer matrix of satellite i in the LVLH system.

[0185] Due to the relative motion state of satellite k at t1, t2 and t3 All X ik0 The time function, therefore, according to the distance measurement information and the angle obtained, the simultaneous equations are:

[0186]

[0187] In the formula, is the relative position of satellite j in the LVLH system.

[0188] Solving the above equation, we can obtain the initial relative motion state X of satellite k in the LVLH system: ik0 ; Thus, the initial relative motion state X of satellite i to satellite j in the LVLH system is obtained respectively ij0 , X ik0 According to X ij0 and X ik0 Determine the relative orbits of satellite i, satellite j, and satellite k, and determine the initial relative orbits of the three-star formation.

[0189] Based on the positioning benchmark, the initial relative orbits of other member satellites of the satellite constellation relative to the three benchmark satellites are determined, that is, the initial relative motion state X of any member satellite m in the LVLH system is im0 .

[0190] The initial relative motion state of satellite m in the LVLH system is X im0 The method for determining is:

[0191] After the three reference satellites complete the construction of the positioning benchmark, the other member satellites achieve initial relative orbit determination by measuring the distance between them and the reference satellites; establish the measurement equation y for distance measurement between member satellite m and satellite i, satellite j, and satellite k m for:

[0192]

[0193] In the formula, ρ im is the distance between member star m and satellite i;

[0194] ρ mj is the distance between member star m and satellite j;

[0195] ρ mk is the distance between member star m and satellite k;

[0196] is the distance measurement error between member star m and satellite i;

[0197] is the distance measurement error between member star m and satellite j;

[0198] is the distance measurement error between member star m and satellite k;

[0199] Obviously, the three equations shown above alone are not enough to solve the relative orbital parameters in six dimensions. At least two measurements are needed to establish the equations for the solution.

[0200] Assume that the initial relative motion state of member star m in the LVLH system is:

[0201] According to the properties of the state transfer matrix, the relative motion state of satellite m at any time can be obtained according to the state transfer matrix of satellite i in the LVLH system and the initial relative motion state of satellite k.

[0202]

[0203] In the formula, Φ(t t ,t0) is the state transfer matrix of satellite i in the LVLH system; Φ(t t ,t0) only with the average angular velocity of the orbit of satellite i and the time interval Δt=t t -t0 related;

[0204] Due to the relative motion state of satellite m at t1 and t2 Yes X im0 The time function of , therefore, according to the ranging information, the simultaneous equations are:

[0205]

[0206] In the formula, is the relative position of satellite j in the LVLH system, which is calculated in real time and is a known quantity.

[0207] is the relative position of satellite k in the LVLH system, which is calculated in real time and is a known quantity.

[0208] Solve the non-linear equation system above to obtain the initial relative motion state X of satellite m in the LVLH system im0 .

[0209] A triangular vector closed loop is formed by the relative positions among satellite i, satellite j, and satellite k; according to the triangular vector closed loop, a relative orbit state consistency constraint model is established; and the consistency constraint model is introduced into the filtering algorithm to establish a distributed Kalman filtering algorithm under geometric topology consistency constraint conditions, obtain the measurement update equation, that is, the constellation distributed state estimation, and complete the regional positioning of each satellite.

[0210] The method of constellation distributed state estimation is as follows:

[0211] Establish a geometric topology consistency constraint model for the relative orbit; assume that satellite k realizes the measurement of satellite i, and let the relative orbit state of satellite i in the LVLH coordinate system of satellite k be Then, the triangular vector closed loop formed by the relative positions among satellite i, satellite j, and satellite k satisfies:

[0212]

[0213] In the formula, is the transformation matrix from the LVLH coordinate system of satellite k to the LVLH coordinate system of satellite i;

[0214] Derive the consistency constraint equation of the relative velocity with respect to time, and after combining it with the relative position consistency constraint equation, realize the establishment of the relative orbit state consistency constraint model as follows:

[0215]

[0216] In the formula, is the generalized rotation matrix:

[0217]

[0218] Introduce the consistency constraint model into the filtering algorithm to establish a distributed Kalman filtering algorithm under geometric topology consistency constraint conditions, design the calculation process, and the corresponding measurement update process is as follows:

[0219]

[0220] In the formula, γ represents the consistency coefficient, represents the prior estimate.

[0221] The present invention realizes relative navigation of cluster dynamic self-organizing network under the premise of limited spaceborne TT&C resources and complex space optical environment; solves the global positioning and navigation problem under limited information interaction, and has the capabilities of fast and accurate regional positioning of the on-off satellite swarm system and global state perception under resource constraints;

[0222] The present invention first establishes a triangular vector closed loop formed by the relative positions of three satellites; according to the triangular vector closed loop, a relative orbit state consistency constraint model is established; and the consistency constraint model is introduced into the filtering algorithm to establish a distributed Kalman filtering algorithm under geometric topology consistency constraint conditions, obtain a measurement update equation, that is, satellite swarm distributed state estimation, and complete the regional positioning of each satellite; the positioning is accurate and can be updated in real time.

[0223] Although the present invention has been disclosed above with preferred embodiments, it is not used to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the technical solution of the present invention all belong to the protection scope of the technical solution of the present invention.

Claims

1. A satellite cluster collaborative regional positioning method based on communication ranging, characterized in that: include: Select three reference satellites in the satellite constellation space area, namely, satellite i, satellite j, and satellite k; Build positioning benchmarks; Based on the positioning reference, the initial relative orbits of other member satellites of the satellite constellation relative to the three reference satellites are determined, that is, the initial relative motion state X of any member satellite m in the LVLH system is im0 ; The relative positions of satellites i, j and k constitute a triangular vector closed loop. Based on the triangular vector closed loop, a relative orbit state consistency constraint model is established. The consistency constraint model is introduced into the filtering algorithm, and a distributed Kalman filtering algorithm under the condition of geometric topological consistency constraints is established to obtain the measurement update equation, that is, the distributed state estimation of the star cluster, and complete the regional positioning of each satellite.

2. The method for coordinated regional positioning of a constellation based on communication ranging according to claim 1, characterized in that: The construction positioning benchmark is specifically: According to the geometric configuration between the members of the entire star cluster, three satellites with acute triangle configuration are selected as the benchmark; the fast and high-precision relative navigation between the benchmark satellites is realized by using angle measurement and ranging, nonlinear dynamics, orbital maneuvers, and the introduction of geometric topological consistency constraints. The three benchmark satellites with high-precision relative navigation are used as the space benchmark. The other satellite members in the group use the ranging information with the benchmark satellite to realize relative navigation under this space benchmark; at the same time, because the combined configuration between the star clusters is dynamically changing, when the triangle configuration between the three selected benchmarks is not conducive to the establishment of a high-precision space benchmark, the benchmark satellite will be reselected according to the star selection rules; Methods for constructing positioning benchmarks include: S11. Optimize and select the reference star; S12, determining a relative measurement scheme for angle and distance measurement among the three reference stars; S13. An algorithm for determining the initial relative orbits between reference stars.

3. The method for coordinated regional positioning of a constellation based on communication ranging according to claim 2, characterized in that: In S11, the method for optimizing the selection of the reference star is: First, an optimization model for selecting reference satellites is established; the configuration of the reference satellite is as equilateral as possible, and the ratio of the satellite distance corresponding to the shortest side of the triangle to the maximum distance between all satellites is as large as possible; Assume there are N satellites in total, in a unified coordinate system, with pos i =[x i ,y i ,z i ] T represents the spatial coordinates of the i-th satellite, then the distance ρ between satellite i and satellite j ij for: For the triangle configuration formed by satellites i, j, and k, the side length is the distance between the corresponding satellites, and α is defined i,ijk is the angle of the corresponding angle of satellite i in the triangle, that is: The two objective functions J1 and J2 established are expressed as: maxJ1=min(a i,ijk ,a j,ijk ,a k,ijk )i,j,k∈{1,2,…,N} in, And J2≤1; Taking into account the influence of the two objective functions, the optimization model for selecting the benchmark satellite is constructed as follows: find i,j,k∈{1,2,…,N} max J=λ1J1+λ2J2 Where J is the optimization function value; λ1 and λ2 are the weights of the two objectives.

4. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 2, characterized in that: In S12, a relative measurement scheme for angle measurement and distance measurement between the three reference stars is determined: Select the line-of-sight measurement star from the reference stars according to the optical conditions; define the incident solar angle α as the angle formed by the straight line from the target to the sun and the straight line from the target to the satellite; when α is large, the target is difficult to measure due to light saturation; according to the positions of the sun, target and satellite, with the help of the cosine theorem, calculate the angle α by the following formula: Where D ts is the distance from the target to the sun; D tm is the distance from the target to the observed star; D ms To observe the distance from the star to the sun; When the incident solar angle has an impact on the observation accuracy, the reference star with a smaller solar incident angle is selected from the three reference stars as the line of sight measurement star, that is, the relative measurement scheme of angle measurement and distance measurement among the three reference stars is determined.

5. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 2, characterized in that: In S13, the method for determining the initial relative orbit algorithm between the reference stars is: Establish the measurement model y: In the formula, α ij , β ij are the azimuth and elevation angles of satellite j relative to satellite i, respectively; ρ ij is the relative distance of satellite j to satellite i; ρ ik is the relative distance of satellite k to satellite i; ρ jk is the relative distance of satellite k to satellite j; ε α , ε β are the measurement errors of azimuth and elevation respectively; and ε α and ε β All obey zero-mean Gaussian distribution; and are the ranging errors between any two satellites respectively; and and It follows a zero-mean Gaussian distribution; Set the unit line of sight vector l of satellite j relative to satellite i ij for: Each set of unit sight vectors of satellite j relative to satellite i satisfies: Where t is any time; is the relative motion state of satellite j relative to satellite i; n is the end time; Therefore, the initial relative orbit determination problem between satellite j and satellite i is transformed into the following optimization problem: In the formula, Φ r (t t ,t0) is the state transition sub-matrix; t t for the current moment; t0 is the initial time; X ij0 is the initial relative motion state of satellite j relative to satellite i; Assume the matrix A is: According to the definition of singular value decomposition and its connection with constrained optimization of linear functions, the matrix A is decomposed into singular values, and the right eigenvector with the smallest singular value is taken to obtain X in the least squares sense. ij0 The unit vector According to the angle measurement information [α ij0 β ij0 ] T and ranging information ρ ij0 , calculate the initial relative position r of satellite j in the LVLH system at the initial time ij0 ; Therefore, according to and r ij0 Get the initial relative motion state X of satellite j relative to satellite i ij0 ; For the initial relative motion state X of satellite k relative to satellite i ik0 , solved by three sets of relative distance measurements and three sets of satellite relative position vectors; Based on the angle and distance measurement information of satellite i to satellite j, the relative position of satellite j in the LVLH system is calculated in real time. Then the real-time satellite ranging information Calculate and The angle θ t ; Assume that the initial relative motion state of satellite k in the LVLH system is The relative motion state of satellite k at any time for: In the formula, Φ(t t ,t0) is the state transfer matrix of satellite i in the LVLH system; Due to the relative motion state of satellite k at t1, t2 and t3 All X ik0 The time function, therefore, according to the distance measurement information and the angle obtained, the simultaneous equations are: In the formula, is the relative position of satellite j in the LVLH system; Solving the above equation, we can obtain the initial relative motion state X of satellite k in the LVLH system: ik0 ; Thus, the initial relative motion state X of satellite i to satellite j in the LVLH system is obtained respectively ij0 , X ik0 According to X ij0 and X ik0 Determine the relative orbits of satellite i, satellite j, and satellite k, and determine the initial relative orbits of the three-star formation.

6. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 5, characterized in that: The initial relative position r of satellite j in the LVLH system at the initial time ij0 for:

7. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 5, characterized in that: The initial relative motion state of satellite j relative to satellite i is X ij0 for:

8. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 5, characterized in that: and The angle θ t for:

9. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 1, characterized in that: The initial relative motion state of the satellite m in the LVLH system is X im0 The method to determine is: After the three reference satellites complete the construction of the positioning benchmark, the other member satellites achieve initial relative orbit determination by measuring the distance between them and the reference satellites; establish the measurement equation y for distance measurement between member satellite m and satellite i, satellite j, and satellite k m for: In the formula, ρ im is the distance between member star m and satellite i; ρ mj is the distance between member star m and satellite j; ρ mk is the distance between member star m and satellite k; is the distance measurement error between member star m and satellite i; is the distance measurement error between member star m and satellite j; is the distance measurement error between member star m and satellite k; Assume that the initial relative motion state of member star m in the LVLH system is: According to the properties of the state transfer matrix, the relative motion state of satellite m at any time can be obtained according to the state transfer matrix of satellite i in the LVLH system and the initial relative motion state of satellite k. In the formula, Φ(t t ,t0) is the state transfer matrix of satellite i in the LVLH system; Φ(t t ,t0) only with the average angular velocity of the orbit of satellite i and the time interval Δt=t t -t0 related; Due to the relative motion state of satellite m at t1 and t2 Yes X im0 The time function of , therefore, according to the ranging information, the simultaneous equations are: In the formula, is the relative position of satellite j in the LVLH system, which is calculated in real time as a known quantity; is the relative position of satellite k in the LVLH system, which is calculated in real time as a known quantity; Solving the nonlinear equations in the above formula, we can obtain the initial relative motion state X of satellite m in the LVLH system: im0 .

10. The method for satellite cluster coordinated regional positioning based on communication ranging according to claim 1, characterized in that: The method for estimating the distributed state of the star cluster is: Establish a geometric topological consistency constraint model for relative orbits; Assume that satellite k measures satellite i, and let the relative orbit state of satellite i in the LVLH coordinate system of satellite k be Then, the triangular vector closed loop formed by the relative positions of satellites i, j, and k satisfies: In the formula, is the transformation matrix from the LVLH coordinate system of satellite k to the LVLH coordinate system of satellite i; The consistency constraint equation of the relative velocity is obtained by derivation with respect to time. After being combined with the consistency constraint equation of the relative position, the consistency constraint model of the relative orbit state is established as shown below: In the formula, is the generalized rotation matrix: The consistency constraint model is introduced into the filtering algorithm, a distributed Kalman filtering algorithm under the geometric topology consistency constraint is established, and the calculation process is designed. The corresponding measurement update process is as follows: In the formula, γ is the consistency coefficient; represents a priori estimate.

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