Cluster aircraft cooperative positioning method suitable for singular configuration

Abstract

The invention discloses a cluster aircraft cooperative positioning method suitable for a singular configuration, and aims to solve the problem that the positioning precision is sharply reduced when a to-be-positioned aircraft and a reference aircraft are in a poor configuration similar to a plane or a straight line in a cluster positioning process. In the cooperative positioning data preparation part, an appropriate virtual offset vector is added to the position of a reference aircraft to optimize the overall configuration, and then the optimized information is used for positioning calculation to obtain the accurate position and speed coordinates of the to-be-positioned aircraft. Compared with a cluster aircraft which does not adopt an optimized positioning algorithm based on the arrival frequency difference, the method provided by the invention can obtain better positioning precision in an aircraft cluster with a singular configuration, and is suitable for practical application.

Description

Technical Field

[0001] The present invention relates to the field of positioning and navigation technology, and in particular to a collaborative positioning method for clustered aircraft with strange configurations. Background Art

[0002] In recent years, aircraft swarm collaboration technology has attracted increasing attention at home and abroad. Aircraft swarms have the advantages of large working range, high reliability, simultaneous execution of multiple tasks, and high overall efficiency, and can be used in disaster survey and rescue. Aircraft swarm technology, that is, a certain formation arrangement and task allocation of multiple aircraft to meet mission requirements, includes the formation generation, maintenance and change of swarm flight, as well as the planning and organization of swarm flight missions. It is an important trend in the development of future aircraft flight technology.

[0003] The performance of traditional aircraft cluster collaborative positioning methods is greatly affected by the cluster configuration. Only when the aircraft configuration in the cluster meets certain requirements can good positioning accuracy be achieved. In the case of singular configurations such as quasi-straight-line and quasi-plane configurations, the positioning accuracy is greatly affected. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a collaborative positioning method for clustered aircraft with strange configurations in view of the defects involved in the background technology.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A collaborative positioning method for clustered aircraft of a singular configuration includes the following steps:

[0007] Step 1), obtaining measurement data required for collaborative positioning of an aircraft cluster; the aircraft cluster includes m+n aircraft, wherein m aircraft are aircraft to be positioned, and n aircraft are reference aircraft, the reference aircraft can be positioned autonomously through satellite signals, and the aircraft to be positioned cannot receive satellite signals for autonomous positioning, and the relative distance and speed information between the aircraft can be obtained through sensors;

[0008] Step 1.1), the reference aircraft measures the latitude, longitude, and altitude of its location through its own navigation system to obtain the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system:

[0009]

[0010] Wherein, (x, y, z) is the position coordinate of the reference aircraft in the Earth-centered Earth-fixed coordinate system; lat, lon, alt are the latitude, longitude, and altitude position coordinates of the reference aircraft, respectively; a is the major radius of the reference ellipsoid, b is the minor radius of the reference ellipsoid, e is the eccentricity of the reference ellipsoid, and N is the curvature radius of the reference ellipsoid, where the reference ellipsoid is the ellipsoid model specified by the WGS-84 global coordinate system;

[0011] Step 1.2), the reference aircraft measures the velocity of the aircraft system through its own navigation system and converts it to the Earth-centered Earth-fixed coordinate system, which is expressed as:

[0012] v e =R be v b ;

[0013]

[0014] Among them, φ, θ, ψ are the roll angle, pitch angle, and yaw angle of the aircraft respectively; v e is the speed of the aircraft in the Earth-centered Earth-fixed coordinate system, v b is the speed of the aircraft in the aircraft system, R be is the transformation matrix between the aircraft system and the Earth-centered Earth-fixed coordinate system;

[0015] Step 1.3), the aircraft measures the relative distance between the aircraft through the sensor, and its expression is:

[0016]

[0017] Among them, (x i ,y i ,z i ), (x j ,y j ,z j ) are the position coordinates of aircraft i and aircraft j in the Earth-centered Earth-fixed coordinate system respectively; d r is the ranging error, d i,j is the measured relative distance between aircraft i and aircraft j;

[0018] Step 1.4), the aircraft measures the relative speed v between the aircraft through sensors i,j , whose expression is:

[0019] v i,j =v i -v j +v r ;

[0020] Among them, v r is the speed measurement error vector, v i , vj are the velocity vectors of aircraft i and aircraft j, respectively, v i,j is the measured relative speed between aircraft i and aircraft j;

[0021] Step 2), according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, determine the configuration type of the aircraft formation, the configuration type includes a straight line configuration, a plane configuration, and a configuration other than a straight line configuration and a plane configuration, let the straight line configuration and the plane configuration be singular configurations, and the configuration other than the straight line configuration and the plane configuration be non-singular configurations:

[0022] P=[p1,...,p n ],p i =[x i ,y i ,z i ] T ;

[0023]

[0024] [e,~]=PCA(A T );

[0025]

[0026] Among them, (x i ,y i ,z i ) is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system, denoted by p i ; P is the reference aircraft position matrix, n is the number of reference aircraft, A is the reference aircraft position matrix after standardization, PCA is the principal component analysis algorithm; e is the column vector of the percentage of explained variance in the total variance, result is the judgment result, is_line, is_plane, is_randn are the mark values ​​of linear configuration, plane configuration, and non-singular configuration, th_line, th_plane are the thresholds of linear configuration proportion and plane configuration proportion, e(1) is the proportion of principal component variance, and e(2) is the proportion of secondary component variance;

[0027] Step 3), if the formation is a straight line configuration or a plane configuration, calculate its characteristic vector and the offset vector of each reference aircraft therein respectively;

[0028] Step 3.1), if the formation is a straight line configuration or a plane configuration, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the relative distance between the aircraft, and the relative speed between the aircraft are arranged as follows:

[0029] DR=(d 1,j ,d 2,j ...dn,j ,v 1,j ,v 2,j ...v n,j );

[0030] sor_ind = argsort(DR(1:n));

[0031] sor_DR=(DR(sor_ind),DR(sor_ind+n);

[0032] sor_P = P(sor_ind);

[0033] Where DR is the relative measurement information matrix, d i,j is the distance between the i-th reference aircraft and the j-th aircraft to be positioned, v i,j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, n is the number of reference aircraft; argsort is an ascending sort operation, sor_ind is a sorting index, P is the reference aircraft position matrix, sor_DR is the sorted relative measurement information matrix, sor_P is the sorted reference aircraft position matrix;

[0034] Step 3.2), if the formation is a straight line configuration, calculate the characteristic vector of the straight line configuration and the offset vector of each reference aircraft in the straight line configuration according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after sorting and the relative distance between the reference aircraft and the aircraft to be positioned:

[0035] Step 3.2.1), calculate the centralized reference aircraft position data:

[0036]

[0037] c i =p i -Centroid;

[0038] Among them, Centroid is the average value of all reference aircraft positions, p i is the position of reference aircraft i, c i is the position of the reference aircraft i after centralization;

[0039] Step 3.2.2), calculate the direction vector of the fitted line:

[0040] A=[c1,c2...c n ];

[0041] (~,V) = svd(A);

[0042] v=V(:,1);

[0043] Among them, A is the position matrix of the centralized reference aircraft, c i is the position of the reference aircraft i after centralization, svd is the singular value decomposition algorithm, V is the right singular vector obtained by svd decomposition, v is the main direction vector, that is, the direction vector of the fitting line, that is, the eigenvector of the straight line configuration;

[0044] Step 3.2.3), according to the direction vector of the fitted straight line and the relative distance between the sorted reference aircraft and the aircraft to be positioned, calculate the offset vector of each reference aircraft in the straight line configuration:

[0045]

[0046] where r i is a random vector, v is the reference aircraft fitting straight line direction vector, n i is a random vector perpendicular to the direction vector of the fitting line, r_line is the empirical multiple, sor_DR(n+1-i) is the distance between the n+1-ith reference aircraft and the jth aircraft to be located after sorting, n is the number of reference aircraft, N i,j is the offset vector of the i-th reference aircraft used when calculating the position of the j-th aircraft to be located;

[0047] Step 3.3), if the formation is a plane configuration, calculate the characteristic vector of the plane configuration and the offset vector of each reference aircraft in the plane configuration according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after sorting and the relative distance between the reference aircraft and the aircraft to be positioned:

[0048] Step 3.3.1), let the fitting plane equation be:

[0049] z=ax+by+c;

[0050] The coefficients of the plane equation are obtained by least squares solution:

[0051] ax+by-z+c=0;

[0052]

[0053] Step 3.3.2), according to the fitted reference aircraft plane expression, obtain the unit normal vector of the fitted reference aircraft plane:

[0054]

[0055] Among them, a, b, c are the coefficients of the fitting plane, x i ,y i ,z i is the position of each dimension of the reference aircraft i, V nThe unit normal vector of the plane fitted to the reference aircraft, i.e., the eigenvector of the plane configuration;

[0056] Step 3.3.3), based on the unit normal vector of the fitted plane and the relative distance between the sorted reference aircraft and the aircraft to be positioned, calculate the offset vector of each reference aircraft in the plane configuration:

[0057]

[0058] Where V n is the reference aircraft fitting straight line direction vector, r_plane is the empirical multiple, sor_DR(n+1-i) is the distance between the n+1-ith reference aircraft and the jth aircraft to be positioned after sorting, N i,j is the offset vector of the i-th reference aircraft used when calculating the position of the j-th aircraft to be located;

[0059] Step 4), if the formation is a linear configuration or a planar configuration, the position coordinates of the reference aircraft after the offset in the earth-centered earth-fixed coordinate system are calculated according to the offset vectors of each reference aircraft and the position coordinates of the reference aircraft after the sorting in the earth-centered earth-fixed coordinate system, and the expression is:

[0060] p′ i =sor_P(:,i)+N i,j ;

[0061] where sor_P(:,i) is the position of the i-th reference aircraft after sorting, N i,j is the offset vector of the i-th reference aircraft used to calculate the position of the j-th aircraft to be located, p i ′ is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system after the offset;

[0062] Step 5), if the formation is a straight line configuration or a plane configuration, obtain the relative distance information between the offset aircraft to be positioned and the reference aircraft:

[0063] According to the offset vector of each reference aircraft and the relative distance between the reference aircraft and the aircraft to be positioned after sorting, the relative distance information between the aircraft to be positioned and the reference aircraft after offset is calculated, and its expression is:

[0064]

[0065] where sor_DR(i) is the distance between the i-th reference aircraft and the j-th aircraft to be located after sorting, sor_DR(n+1-i) is the distance between the n+1-i-th reference aircraft and the j-th aircraft to be located after sorting, and N i,jis the offset vector of the i-th reference aircraft used to calculate the position of the j-th aircraft to be located, rate is the empirical multiple, r_line and r_plane are the empirical multiples of the straight line configuration and plane configuration respectively, is_line and is_plane are the flag values ​​of the straight line configuration and plane configuration respectively, d i,j ′ is the distance between the i-th reference aircraft and the j-th aircraft to be positioned after the offset;

[0066] Step 6), calculate the position and speed of the aircraft to be located;

[0067] Step 6.1), if the formation is a non-singular configuration:

[0068] Step 6.1.1), calculate the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft according to the relative distance and relative speed between the reference aircraft and the aircraft to be positioned, and the expression is:

[0069] TR j =[d i,2 -d i,1 d i,3 -d i,1 …d i,j -d i,1 ];

[0070] FR j =[v i,2 -v i,1 v i,3 -v i,1 …v i,j -v i,1 ];

[0071] where d i,j is the distance between the i-th reference aircraft and the j-th aircraft to be positioned, v i,j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, TR j is the pseudo-range difference between the aircraft j to be positioned and each reference aircraft, FR j is the pseudo-range rate difference between the aircraft j to be positioned and each reference aircraft;

[0072] Step 6.1.2), according to the pseudo-range difference between the aircraft to be positioned and each reference aircraft, the pseudo-range rate difference between the aircraft to be positioned and each reference aircraft, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, and the velocity of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the velocity and position information of the aircraft to be positioned are calculated;

[0073] Step 6.2), if the formation is a straight line configuration or a plane configuration:

[0074] Step 6.2.1), according to the relative distance and relative speed between the reference aircraft and the aircraft to be positioned after the offset, the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft after the offset are calculated, and the expression is:

[0075] TR j ′=[d i,2 ′-d i,1 ′ d i,3 ′-d i,1 ′ … d i,j ′-d i,1 ′];

[0076] FR j ′=[v i,2 -v i,1 v i,3 -v i,1 … v i,j -v i,1 ];

[0077] where d i,j ′ is the distance between the aircraft j to be positioned and the reference aircraft i after the offset, v i,j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, TR j ′ is the pseudo-range difference between the aircraft j to be positioned and each reference aircraft after offset, FR j ′ is the pseudo-range rate difference between the aircraft j to be positioned and each reference aircraft after the offset;

[0078] Step 6.2.2), based on the pseudorange difference between the aircraft to be located and each reference aircraft after the offset, the pseudorange rate difference between the aircraft to be located and each reference aircraft after the offset, the position coordinates of the reference aircraft in the geocentric Earth-fixed coordinate system after the offset, and the speed of the reference aircraft in the geocentric Earth-fixed coordinate system, the speed and position information of the aircraft to be located are calculated.

[0079] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0080] The present invention discloses a collaborative positioning method for clustered aircrafts with singular configurations, which optimizes the configurations between reference aircrafts and aircrafts to be positioned, so that the geometric configuration used for clustered aircraft positioning is more reasonable. Compared with clustered aircraft positioning algorithms that do not use optimization, the present invention can also achieve better positioning accuracy when the aircraft cluster configuration is singular, and is suitable for practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a schematic diagram of the principle flow of the method of the present invention;

[0082] Figure 2A schematic diagram of the configuration distribution and offset vector of a straight-line-configured aircraft formation at a specific moment;

[0083] Figure 3 The error curve of cooperative position solution for the aircraft formation in a straight line configuration;

[0084] Figure 4 The error curve of cooperative speed solution for a straight-line-configured aircraft formation;

[0085] Figure 5 The schematic diagram of the configuration distribution and offset vector of the plane-configured aircraft formation at a specific moment;

[0086] Figure 6 The error curve of cooperative position solution for the aircraft formation in a planar configuration;

[0087] Figure 7 This is the error curve of the coordinated velocity solution for a plane-configured aircraft formation. DETAILED DESCRIPTION

[0088] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0089] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete, and will fully express the scope of the present invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0090] The method of the present invention optimizes the cluster aircraft configuration by adding a virtual offset vector, so that the formation configuration in cluster positioning is more reasonable, thereby improving the positioning accuracy and enhancing the adaptability of the cluster aircraft positioning algorithm to poor configuration conditions.

[0091] like Figure 1 As shown, a collaborative positioning method for clustered aircraft of a singular configuration includes the following steps:

[0092] Step 1), obtaining measurement data required for collaborative positioning of an aircraft cluster; the aircraft cluster includes m+n aircraft, wherein m aircraft are aircraft to be positioned, and n aircraft are reference aircraft, the reference aircraft can be positioned autonomously through satellite signals, and the aircraft to be positioned cannot receive satellite signals for autonomous positioning, and the relative distance and speed information between the aircraft can be obtained through sensors;

[0093] Step 1.1), the reference aircraft measures the latitude, longitude, and altitude of its location through its own navigation system to obtain the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system:

[0094]

[0095] Wherein, (x, y, z) is the position coordinate of the reference aircraft in the Earth-centered Earth-fixed coordinate system; lat, lon, alt are the latitude, longitude, and altitude position coordinates of the reference aircraft, respectively; a is the major radius of the reference ellipsoid, b is the minor radius of the reference ellipsoid, e is the eccentricity of the reference ellipsoid, and N is the curvature radius of the reference ellipsoid, where the reference ellipsoid is the ellipsoid model specified by the WGS-84 global coordinate system;

[0096] Step 1.2), the reference aircraft measures the velocity of the aircraft system through its own navigation system and converts it to the Earth-centered Earth-fixed coordinate system, which is expressed as:

[0097] v e =R be v b ;

[0098]

[0099] Among them, φ, θ, ψ are the roll angle, pitch angle, and yaw angle of the aircraft respectively; v e is the speed of the aircraft in the Earth-centered Earth-fixed coordinate system, v b is the speed of the aircraft in the aircraft system, R be is the transformation matrix between the aircraft system and the Earth-centered Earth-fixed coordinate system;

[0100] Step 1.3), the aircraft measures the relative distance between the aircraft through the sensor, and its expression is:

[0101]

[0102] Among them, (x i ,y i ,z i ), (x j ,y j ,z j ) are the position coordinates of aircraft i and aircraft j in the Earth-centered Earth-fixed coordinate system respectively; d r is the ranging error, d i,j is the measured relative distance between aircraft i and aircraft j;

[0103] Step 1.4), the aircraft measures the relative speed v between the aircraft through sensors i,j , whose expression is:

[0104] v i,j =v i -v j +v r ;

[0105] Among them, v r is the speed measurement error vector, vi , v j are the velocity vectors of aircraft i and aircraft j, respectively, v i,j is the measured relative speed between aircraft i and aircraft j;

[0106] Step 2), since there is a linear relationship between the plane configuration and the straight line configuration, which is a configuration of the reference aircraft position, it will cause serious geometric accuracy attenuation problems during positioning, so here the formation configuration must be distinguished and optimized for these two configurations respectively. According to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the configuration type of the aircraft formation is judged, and the configuration types include straight line configuration, plane configuration, and configurations other than straight line configuration and plane configuration. Let the straight line configuration and plane configuration be singular configurations, and the configurations other than the straight line configuration and plane configuration be non-singular configurations:

[0107] P=[p1,...,p n ],p i =[x i ,y i ,z i ] T ;

[0108]

[0109] [e,~]=PCA(A T );

[0110]

[0111] Among them, (x i ,y i ,z i ) is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system, expressed as p i ; P is the reference aircraft position matrix, n is the number of reference aircraft, A is the reference aircraft position matrix after standardization, PCA is the principal component analysis algorithm; e is the column vector of the percentage of explained variance in the total variance, result is the judgment result, is_line, is_plane, is_randn are the mark values ​​of straight line configuration, plane configuration, straight line configuration and non-singular configuration respectively, th_line, th_plane are the threshold of straight line configuration proportion and plane configuration proportion respectively, e(1) is the proportion of principal component variance, e(2) is the proportion of subordinate component variance;

[0112] The purpose of standardizing the position of the reference aircraft in the Earth-centered Earth-fixed coordinate system is to obtain smaller position difference information from larger values ​​of Earth-centered Earth-fixed coordinate values ​​in a smaller array, so as to make the formation judgment more accurate. The principal component analysis algorithm can analyze the linear relationship of the 3D information in the position matrix of the reference aircraft in the Earth-centered Earth-fixed coordinate system, and obtain the variance proportion of each component. Since the variance proportion of the principal component accounts for the vast majority in the linear configuration, and the variance proportion of the principal component and the secondary component accounts for the vast majority in the planar configuration, the configuration type can be determined by setting a certain threshold and then judging the principal and secondary components.

[0113] Step 3), if the formation is a straight line configuration or a plane configuration, calculate its characteristic vector and the offset vector of each reference aircraft therein respectively;

[0114] Step 3.1), if the formation is a straight line configuration or a plane configuration, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the relative distance between the reference aircraft and the aircraft to be positioned, and the relative speed between the reference aircraft and the aircraft to be positioned are arranged as follows:

[0115] DR=(d 1,j ,d 2,j ...d n,j ,v 1,j ,v 2,j ...v n,j );

[0116] sor_ind = argsort(DR(1:n));

[0117] sor_DR=(DR(sor_ind),DR(sor_ind-n);

[0118] sor_P = P(sor_ind);

[0119] Where DR is the relative measurement information matrix, d i,j is the distance between the i-th reference aircraft and the j-th aircraft to be positioned, v i,j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, n is the number of reference aircraft; argsort is an ascending sort operation, sor_ind is a sorting index, P is the reference aircraft position matrix, sor_DR is the sorted relative measurement information matrix, sor_P is the sorted reference aircraft position matrix;

[0120] The ordering here and the reverse selection numbering of the offset vector size below are to make the offset vector of the reference aircraft closer to the aircraft to be positioned larger and the offset vector of the reference aircraft farther from the aircraft to be positioned smaller, so that the offset reference aircraft forms a better ellipsoidal configuration. At this time, the configuration in which the aircraft to be positioned are distributed in the center of the ellipsoidal configuration is more ideal, which not only improves the positioning accuracy of the aircraft to be positioned in the center of the formation, but also improves the positioning accuracy of the aircraft to be positioned distributed at the edge of the formation.

[0121] Step 3.2), if the formation is a straight line configuration, calculate the characteristic vector of the straight line configuration and the offset vector of each reference aircraft in the straight line configuration according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after sorting and the relative distance between the reference aircraft and the aircraft to be positioned:

[0122] Step 3.2.1), calculate the centralized reference aircraft position data:

[0123]

[0124] c i =p i -Centroid;

[0125] Among them, Centroid is the average value of all reference aircraft positions, p i is the position of reference aircraft i, c i is the position of the reference aircraft i after centralization;

[0126] Step 3.2.2), calculate the direction vector of the fitted line:

[0127] A=[c1,c2...c n ];

[0128] (~,V) = svd(A);

[0129] v=V(:,1);

[0130] Among them, A is the position matrix of the centralized reference aircraft, c i is the position of the reference aircraft i after centralization, svd is the singular value decomposition algorithm, V is the right singular vector obtained by svd decomposition, v is the main direction vector, that is, the direction vector of the fitting line, that is, the eigenvector of the straight line configuration;

[0131] The centralization process is performed here to obtain smaller position difference information from the larger value of the Earth-centered Earth-fixed coordinate value, so as to fit the straight line direction vector more accurately.

[0132] Step 3.2.3), according to the direction vector of the fitted straight line and the relative distance between the sorted reference aircraft and the aircraft to be positioned, calculate the offset vector of each reference aircraft in the straight line configuration:

[0133]

[0134] where r i is a random vector, v is the reference aircraft fitting straight line direction vector, n i is a random vector perpendicular to the direction vector of the fitting line, r_line is the empirical multiple, sor_DR(n+1-i) is the distance between the n+1-ith reference aircraft and the jth aircraft to be located after sorting, n is the number of reference aircraft, N i,j is the offset vector of the i-th reference aircraft used when calculating the position of the j-th aircraft to be located;

[0135] Here, the direction of the offset vector is a random direction perpendicular to the direction vector of the fitted line. In use, the directions of each vector can be restricted so that they are randomly distributed within different angle ranges. In this way, the problem of poor post-offset configuration caused by similar post-offset vector directions, which rarely occurs in the original algorithm, can be avoided while retaining randomness.

[0136] Step 3.3), if the formation is a plane configuration, calculate the characteristic vector of the plane configuration and the offset vector of each reference aircraft in the plane configuration according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after sorting and the relative distance between the reference aircraft and the aircraft to be positioned:

[0137] Step 3.3.1), let the fitting plane equation be:

[0138] z=ax+by+c;

[0139] The coefficients of the plane equation are obtained by least squares solution:

[0140] ax+by-z+c=0;

[0141]

[0142] Step 3.3.2), according to the fitted reference aircraft plane expression, obtain the unit normal vector of the fitted reference aircraft plane:

[0143]

[0144] Among them, a, b, c are the coefficients of the fitting plane, x i ,y i ,z i is the position of each dimension of the reference aircraft i, V nThe unit normal vector of the plane fitted to the reference aircraft, i.e., the eigenvector of the plane configuration;

[0145] Step 3.3.3), based on the unit normal vector of the fitted plane and the relative distance between the sorted reference aircraft and the aircraft to be positioned, calculate the offset vector of each reference aircraft in the plane configuration:

[0146]

[0147] Where V n is the reference aircraft fitting straight line direction vector, r_plane is the empirical multiple, sor_DR(n+1-i) is the distance between the n+1-ith reference aircraft and the jth aircraft to be positioned after sorting, N i,j is the offset vector of the i-th reference aircraft used when calculating the position of the j-th aircraft to be located;

[0148] Here, the offset vector is parallel to the plane normal vector and has two directions. Evenly distributing all offset vectors in these two directions can enable the offset reference aircraft to obtain a better configuration.

[0149] Step 4), if the formation is a linear configuration or a planar configuration, the position coordinates of the reference aircraft after the offset in the earth-centered earth-fixed coordinate system are calculated according to the offset vectors of each reference aircraft and the position coordinates of the reference aircraft after the sorting in the earth-centered earth-fixed coordinate system, and the expression is:

[0150] p′ i =sor_P(:,i)+N i,j ;

[0151] where sor_P(:,i) is the position of the i-th reference aircraft after sorting, N i,j is the offset vector of the i-th reference aircraft used to calculate the position of the j-th aircraft to be located, p i ′ is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system after the offset;

[0152] Step 5), if the formation is a straight line configuration or a plane configuration, obtain the relative distance information between the offset aircraft to be positioned and the reference aircraft:

[0153] According to the offset vector of each reference aircraft and the relative distance between the reference aircraft and the aircraft to be positioned after sorting, the relative distance information between the aircraft to be positioned and the reference aircraft after offset is calculated, and its expression is:

[0154]

[0155] where sor_DR(i) is the distance between the i-th reference aircraft and the j-th aircraft to be located after sorting, sor_DR(n+1-i) is the distance between the n+1-i-th reference aircraft and the j-th aircraft to be located after sorting, and N i,j is the offset vector of the i-th reference aircraft used to calculate the position of the j-th aircraft to be located, rate is the empirical multiple, r_line and r_plane are the empirical multiples of the straight line configuration and plane configuration respectively, is_line and is_plane are the flag values ​​of the straight line configuration and plane configuration respectively, d i,j ′ is the distance between the i-th reference aircraft and the j-th aircraft to be positioned after the offset;

[0156] Here, multiplying the distance by a certain empirical multiple can prevent the situation where multiple reference aircraft are at the same distance from the aircraft to be located after the offset, making the algorithm more stable. Here is a recommended value for the empirical multiple: rate∈[0.7,0.9].

[0157] Step 6), calculate the position and speed of the aircraft to be located;

[0158] Step 6.1), if the formation is a non-singular configuration:

[0159] Step 6.1.1), according to the relative distance and relative speed between the reference aircraft and the aircraft to be positioned, calculate the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft, and the expression is:

[0160] TR j =[d i,2 -d i,1 d i,3 -d i,1 …d i,j -d i,1 ];

[0161] FR j =[v i,2 -v i,1 v i,3 -v i,1 …v i,j -v i,1 ];

[0162] where d i,j is the distance between the i-th reference aircraft and the j-th aircraft to be positioned, v i,j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, TR j is the pseudo-range difference between the aircraft j to be positioned and each reference aircraft, FR j is the pseudo-range rate difference between the aircraft j to be positioned and each reference aircraft;

[0163] Step 6.1.2), according to the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, and the velocity of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the velocity and position information of the aircraft to be positioned are calculated;

[0164] Step 6.2), if the formation is a straight line configuration or a plane configuration:

[0165] Step 6.2.1), according to the relative distance between the reference aircraft and the aircraft to be positioned after the offset, and the relative speed between the reference aircraft and the aircraft to be positioned after the offset, the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft after the offset are calculated, and the expression is:

[0166] TR j ′=[d i,2 ′-d i,1 ′ d i,3 ′-d i,1 ′ … d i,j ′-d i,1 ′];

[0167] FR j ′=[v i,2 -v i,1 v i,3 -v i,1 … v i,j -v i,1 ];

[0168] where d i,j ′ is the distance between the aircraft j to be positioned and the reference aircraft i after the offset, v i,j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, TR j ′ is the pseudo-range difference between the aircraft j to be positioned and each reference aircraft after offset, FR j ′ is the pseudo-range rate difference between the aircraft j to be positioned and each reference aircraft after the offset;

[0169] Since this algorithm is essentially a translation of the reference aircraft, it only affects the position-related information in the relative information, such as the pseudorange difference, but has no effect on the velocity. Therefore, the pseudorange rate difference is the same as that in the non-singular configuration.

[0170] Step 6.2.2), based on the pseudorange difference between the aircraft to be located and each reference aircraft after the offset, the pseudorange rate difference between the aircraft to be located and each reference aircraft after the offset, the position coordinates of the reference aircraft in the geocentric earth-fixed coordinate system after the offset, and the speed of the reference aircraft in the geocentric earth-fixed coordinate system, the speed and position information of the aircraft to be located are calculated.

[0171] In order to verify the effectiveness of the virtual vector offset optimization method proposed in the present invention for collaborative positioning of clustered aircraft with singular configurations, a digital simulation analysis was performed.

[0172] A cluster collaborative positioning simulation is carried out when the aircraft formation is in a straight configuration. There are 10 aircraft to be positioned in the cluster and 10 reference aircraft. Figure 2 Schematic diagram of the configuration distribution and offset vector of the reference aircraft when positioning the No. 6 aircraft to be positioned. Figure 3 , Figure 4 The coordinate positioning position and velocity error curves of the aircraft formation in a straight line configuration with and without the use of this method are shown respectively. It can be seen that the direct coordinate solution error result in a straight line configuration is very large, while the error result is significantly reduced after using this method, indicating that the present invention has greatly improved the positioning result of the straight line configuration.

[0173] A cluster collaborative positioning simulation is carried out when the aircraft formation is in a planar configuration. There are 7 aircraft to be positioned in the cluster and 13 reference aircraft. Figure 5 Schematic diagram of the configuration distribution and offset vector of the reference aircraft when locating the No. 18 aircraft to be located. Figure 6 , Figure 7 The coordinate positioning position and velocity error curves of the aircraft formation in a straight line configuration with and without the use of this method are shown respectively. It can be seen that the direct coordinate solution error result in a straight line configuration is very large, while the error result is significantly reduced after using this method, indicating that the present invention has greatly improved the positioning result of the straight line configuration.

[0174] Combining the two sets of simulations, it can be found that this algorithm improves the formation configuration under singular configuration by adding a virtual vector offset to the position of the reference aircraft, which greatly reduces the collaborative solution error.

[0175] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0176] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit 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 collaborative positioning method for clustered aircraft of a singular configuration, characterized in that: The following steps are involved: Step 1), obtaining measurement data required for collaborative positioning of an aircraft cluster; the aircraft cluster includes m+n aircraft, wherein m aircraft are aircraft to be positioned, and n aircraft are reference aircraft, the reference aircraft can be positioned autonomously through satellite signals, and the aircraft to be positioned cannot receive satellite signals for autonomous positioning, and the relative distance and speed information between the aircraft can be obtained through sensors; Step 1.1), the reference aircraft measures the latitude, longitude, and altitude of its location through its own navigation system to obtain the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system: Wherein, (x, y, z) is the position coordinate of the reference aircraft in the Earth-centered Earth-fixed coordinate system; lat, lon, alt are the latitude, longitude, and altitude position coordinates of the reference aircraft, respectively; a is the major radius of the reference ellipsoid, b is the minor radius of the reference ellipsoid, e is the eccentricity of the reference ellipsoid, and N is the curvature radius of the reference ellipsoid, where the reference ellipsoid is the ellipsoid model specified by the WGS-84 global coordinate system; Step 1.2), the reference aircraft measures the velocity of the aircraft system through its own navigation system and converts it to the Earth-centered Earth-fixed coordinate system, which is expressed as: v e =R be v b ; Among them, φ, θ, ψ are the roll angle, pitch angle, and yaw angle of the aircraft respectively; v e is the speed of the aircraft in the Earth-centered Earth-fixed coordinate system, v b is the speed of the aircraft in the aircraft system, R be is the transformation matrix between the aircraft system and the Earth-centered Earth-fixed coordinate system; Step 1.3), the aircraft measures the relative distance between the aircraft through the sensor, and its expression is: Among them, (x i ,y i ,z i ), (x j ,y j ,z j ) are the position coordinates of aircraft i and aircraft j in the Earth-centered Earth-fixed coordinate system respectively; d r is the ranging error, d i,j is the measured relative distance between aircraft i and aircraft j; Step 1.4), the aircraft measures the relative speed v between the aircraft through sensors i,j , whose expression is: v i，j =v i -v j +v r ; Among them, v r is the speed measurement error vector, v i , v j are the velocity vectors of aircraft i and aircraft j, respectively, v i，j is the measured relative speed between aircraft i and aircraft j; Step 2), according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, determine the configuration type of the aircraft formation, the configuration type includes a straight line configuration, a plane configuration, and a configuration other than a straight line configuration and a plane configuration, let the straight line configuration and the plane configuration be singular configurations, and the configuration other than the straight line configuration and the plane configuration be non-singular configurations: P=[p1,...,p n ],p i =[x i ,y i ,z i ] T ; [and,~]=PCA(A T ); Among them, (x i ,y i , z i ) is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system, denoted by p i ; P is the reference aircraft position matrix, n is the number of reference aircraft, A is the reference aircraft position matrix after standardization, PCA is the principal component analysis algorithm; e is the column vector of the percentage of explained variance in the total variance, result is the judgment result, is_line, is_plane, is_randn are the mark values ​​of linear configuration, plane configuration, and non-singular configuration, th_line, th_plane are the thresholds of linear configuration proportion and plane configuration proportion, e(1) is the proportion of principal component variance, and e(2) is the proportion of secondary component variance; Step 3), if the formation is a straight line configuration or a plane configuration, calculate its characteristic vector and the offset vector of each reference aircraft therein respectively; Step 3.1), if the formation is a straight line configuration or a plane configuration, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the relative distance between the aircraft, and the relative speed between the aircraft are arranged as follows: DR=(d 1，j ,d 2，j …d n，j ,v 1，j ,v 2，j …v n，j ); sor_ind=argsort(DR(1:n)); sor_DR=(DR(sor_ind), DR(sor_ind+n); sor_P = P(sor_ind); Where DR is the relative measurement information matrix, d i，j is the distance between the i-th reference aircraft and the j-th aircraft to be positioned, v i，j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, n is the number of reference aircraft; argsort is an ascending sort operation, sor_ind is a sorting index, P is the reference aircraft position matrix, sor_DR is the sorted relative measurement information matrix, sor_P is the sorted reference aircraft position matrix; Step 3.2), if the formation is a straight line configuration, calculate the characteristic vector of the straight line configuration and the offset vector of each reference aircraft in the straight line configuration according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after sorting and the relative distance between the reference aircraft and the aircraft to be positioned: Step 3.2.1), calculate the centralized reference aircraft position data: c i =p i -Centroid; Among them, Centroid is the average value of all reference aircraft positions, p i is the position of reference aircraft i, c i is the position of the reference aircraft i after centralization; Step 3.2.2), calculate the direction vector of the fitted line: A=[c1,c2...c n ]; (~,V) = svd(A); v=V(:,1); Among them, A is the position matrix of the centralized reference aircraft, c i is the position of the reference aircraft i after centralization, svd is the singular value decomposition algorithm, V is the right singular vector obtained by svd decomposition, v is the main direction vector, that is, the direction vector of the fitting line, that is, the eigenvector of the straight line configuration; Step 3.2.3), according to the direction vector of the fitted straight line and the relative distance between the sorted reference aircraft and the aircraft to be positioned, calculate the offset vector of each reference aircraft in the straight line configuration: where r i is a random vector, v is the reference aircraft fitting straight line direction vector, n i is a random vector perpendicular to the direction vector of the fitting line, r_line is the empirical multiple, sor_DR(n+1-i) is the distance between the n+1-ith reference aircraft and the jth aircraft to be located after sorting, n is the number of reference aircraft, N i,j is the offset vector of the i-th reference aircraft used when calculating the position of the j-th aircraft to be located; Step 3.3), if the formation is a plane configuration, calculate the characteristic vector of the plane configuration and the offset vector of each reference aircraft in the plane configuration according to the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after sorting and the relative distance between the reference aircraft and the aircraft to be positioned: Step 3.3.1), let the fitting plane equation be: z=ax+by+c; The coefficients of the plane equation are obtained by least squares solution: ax+by-z+c=0; Step 3.3.2), according to the fitted reference aircraft plane expression, obtain the unit normal vector of the fitted reference aircraft plane: Among them, a, b, c are the coefficients of the fitting plane, x i ,y i ,z i is the position of each dimension of the reference aircraft i, V n The unit normal vector of the plane fitted to the reference aircraft, i.e., the eigenvector of the plane configuration; Step 3.3.3), based on the unit normal vector of the fitted plane and the relative distance between the sorted reference aircraft and the aircraft to be positioned, calculate the offset vector of each reference aircraft in the plane configuration: Where V n is the reference aircraft fitting straight line direction vector, r_plane is the empirical multiple, sor_DR(n+1-i) is the distance between the n+1-ith reference aircraft and the jth aircraft to be positioned after sorting, N i,j is the offset vector of the i-th reference aircraft used when calculating the position of the j-th aircraft to be located; Step 4), if the formation is a linear configuration or a planar configuration, the position coordinates of the reference aircraft after the offset in the earth-centered earth-fixed coordinate system are calculated according to the offset vectors of each reference aircraft and the position coordinates of the reference aircraft after the sorting in the earth-centered earth-fixed coordinate system, and the expression is: p′ i =sor_P(:,i)+N i,j ; where sor_P(:,i) is the position of the i-th reference aircraft after sorting, N i,j is the offset vector of the i-th reference aircraft used to calculate the position of the j-th aircraft to be located, p i ′ is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system after the offset; Step 5), if the formation is a straight line configuration or a plane configuration, obtain the relative distance information between the offset aircraft to be positioned and the reference aircraft: According to the offset vector of each reference aircraft and the relative distance between the reference aircraft and the aircraft to be positioned after sorting, the relative distance information between the aircraft to be positioned and the reference aircraft after offset is calculated, and its expression is: where sor_DR(i) is the distance between the i-th reference aircraft and the j-th aircraft to be located after sorting, sor_DR(n+1-i) is the distance between the n+1-i-th reference aircraft and the j-th aircraft to be located after sorting, and N i，j is the offset vector of the i-th reference aircraft used to calculate the position of the j-th aircraft to be located, rate is the empirical multiple, r_line and r_plane are the empirical multiples of the straight line configuration and plane configuration respectively, is_line and is_plane are the flag values ​​of the straight line configuration and plane configuration respectively, d i，j ′ is the distance between the i-th reference aircraft and the j-th aircraft to be positioned after the offset; Step 6), calculate the position and speed of the aircraft to be located; Step 6.1), if the formation is a non-singular configuration: Step 6.1.1), calculate the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft according to the relative distance and relative speed between the reference aircraft and the aircraft to be positioned, and the expression is: TR j =[d i，2 -d i，1 d i，3 -d i，1 … d i，j -d i，1 ]; FR j =[v i，2 -v i，1 v i，3 -v i，1 … v i，j -v i，1 ]; where d i，j is the distance between the i-th reference aircraft and the j-th aircraft to be positioned, v i，j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, TR j is the pseudo-range difference between the aircraft j to be positioned and each reference aircraft, FR j is the pseudo-range rate difference between the aircraft j to be positioned and each reference aircraft; Step 6.1.2), according to the pseudo-range difference between the aircraft to be positioned and each reference aircraft, the pseudo-range rate difference between the aircraft to be positioned and each reference aircraft, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, and the velocity of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the velocity and position information of the aircraft to be positioned are calculated; Step 6.2), if the formation is a straight line configuration or a plane configuration: Step 6.2.1), according to the relative distance and relative speed between the reference aircraft and the aircraft to be positioned after the offset, the pseudo-range difference and pseudo-range rate difference between the aircraft to be positioned and each reference aircraft after the offset are calculated, and the expression is: TR j ′=|d i，2 ′-d i，1 ′ d i，3 ′-d i，1 ′ … d i，j ′-d i，1 ′|; FR j ′=[v i，2 -v i，1 v i，3 -v i，1 … v i，j -v i，1 ]; where d i，j ′ is the distance between the aircraft j to be positioned and the reference aircraft i after the offset, v i，j is the relative speed between the i-th reference aircraft and the j-th aircraft to be positioned, TR j ′ is the pseudo-range difference between the aircraft j to be positioned and each reference aircraft after offset, FR j ′ is the pseudo-range rate difference between the aircraft j to be positioned and each reference aircraft after the offset; Step 6.2.2), based on the pseudorange difference between the aircraft to be located and each reference aircraft after the offset, the pseudorange rate difference between the aircraft to be located and each reference aircraft after the offset, the position coordinates of the reference aircraft in the geocentric Earth-fixed coordinate system after the offset, and the speed of the reference aircraft in the geocentric Earth-fixed coordinate system, the speed and position information of the aircraft to be located are calculated.

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