A collaborative positioning method for clustered aircraft with unique configurations

Abstract

This invention discloses a collaborative positioning method for swarming aircraft with unusual configurations. This method addresses the problem of a sharp drop in positioning accuracy when the target aircraft and the reference aircraft are positioned in a poorly aligned plane or straight line during cluster positioning. During collaborative positioning data preparation, a suitable virtual offset vector is added to the reference aircraft's position to optimize the overall configuration. This optimized information is then used for positioning calculations, resulting in more accurate position and velocity coordinates for the target aircraft. Compared to unoptimized swarm positioning algorithms based on arrival frequency difference, this method achieves superior positioning accuracy even in swarms of aircraft with unusual configurations, making it suitable for practical applications.

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 unusual configurations. Background Art

[0002] In recent years, collaborative aircraft swarm technology has garnered increasing attention both domestically and internationally. Aircraft swarms offer advantages such as a large operating range, high reliability, the ability to perform multiple tasks simultaneously, and high overall efficiency, making them suitable for applications in disaster recovery and rescue. Swarm technology, which involves the formation and task allocation of multiple aircraft to meet mission requirements, encompasses the creation, maintenance, and modification of swarm flight formations, as well as the planning and organization of swarm flight missions. It represents a key trend in the future development of aircraft technology.

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

[0004] The technical problem to be solved by the present invention is to provide a collaborative positioning method for cluster aircraft with strange configurations in order to address 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 unusual configurations, comprising the following steps:

[0007] Step 1) Acquire measurement data required for collaborative positioning of an aircraft cluster; the aircraft cluster comprises m+n aircraft, where m are aircraft to be positioned and n are reference aircraft. The reference aircraft can autonomously locate themselves using satellite signals, while the aircraft to be positioned cannot autonomously locate themselves by receiving satellite signals. Relative distance and speed information between the aircraft can be obtained through sensors;

[0008] In step 1.1), the reference aircraft measures its latitude, longitude, and altitude using its own navigation system to obtain the reference aircraft's position coordinates in the Earth-centered Earth-fixed coordinate system:

[0009]

[0010] Where (x, y, z) are the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system; lat, lon, and alt are the latitude, longitude, and altitude 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 radius of curvature of the reference ellipsoid. The reference ellipsoid is the ellipsoid model specified in the WGS-84 global coordinate system.

[0011] In 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. The expression is:

[0012] v e =R be v b ;

[0013]

[0014] Among them, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle of the aircraft respectively; v e is the velocity 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] In step 1.3), the aircraft measure the relative distance between the aircraft through sensors, which is expressed as:

[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; 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 the sensor 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, v i,j is the measured relative velocity between aircraft i and aircraft j;

[0021] Step 2) Determine the configuration type of the aircraft formation based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system. The configuration types include linear configuration, planar configuration, and configurations other than linear and planar configurations. Let linear configuration and planar configuration be singular configurations, and configurations other than linear and planar configurations 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, 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 flag values ​​of linear configuration, plane configuration, and non-singular configuration respectively, th_line and th_plane are the thresholds of linear configuration proportion and plane configuration proportion respectively, e(1) is the proportion of principal component variance, and e(2) is the proportion of subordinate component variance;

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

[0028] In step 3.1), if the formation is a straight line or planar configuration, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the relative distance between aircraft, and the relative speed between 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 the sort index, P is the reference aircraft position matrix, sor_DR is the sorted relative measurement information matrix, and 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 based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system 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 the reference aircraft i, c i is the position of the reference aircraft i after centering;

[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 reference aircraft after centralization, c i is the position of the reference aircraft i after centering, 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] In step 3.2.3), the offset vectors of the reference aircraft in the straight line configuration are calculated based on the direction vector of the fitted line and the relative distance between the reference aircraft and the aircraft to be positioned after sorting:

[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 positioned 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 planar configuration, calculate the eigenvector of the planar configuration and the offset vector of each reference aircraft in the planar configuration based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system 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 solving the least squares method:

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

[0052]

[0053] Step 3.3.2) According to the fitted reference aircraft plane expression, the unit normal vector of the fitted reference aircraft plane is obtained:

[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] In step 3.3.3), the offset vectors of each reference aircraft in the plane configuration are calculated based on the unit normal vector of the fitted plane and the relative distance between the adjusted reference aircraft and the aircraft to be positioned:

[0057]

[0058] Where V n is the direction vector of the fitted straight line of the reference aircraft, 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 or planar configuration, the position coordinates of the offset reference aircraft in the Earth-centered Earth-fixed coordinate system are calculated based on the offset vectors of each reference aircraft and the position coordinates of the adjusted reference aircraft in the Earth-centered Earth-fixed coordinate system. 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 positioned, 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 vectors 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 positioned 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 positioned 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 the plane configuration respectively, is_line and is_plane are the flag values ​​of the straight line configuration and the 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 velocity of the aircraft to be located;

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

[0068] In step 6.1.1), the pseudorange difference and pseudorange rate difference between the aircraft to be positioned and each reference aircraft are calculated based on the relative distance and relative velocity between the reference aircraft and the aircraft to be positioned. The expressions are:

[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) Calculate the velocity and position information of the aircraft to be positioned based on the obtained pseudorange differences between the aircraft to be positioned and each reference aircraft, the pseudorange rate differences 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;

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

[0074] In step 6.2.1), based on the relative distance and relative velocity between the reference aircraft and the aircraft to be positioned after the offset, the pseudorange difference and pseudorange rate difference between the aircraft to be positioned and each reference aircraft after the offset are calculated. The expressions are:

[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] In step 6.2.2), the velocity and position information of the aircraft to be positioned are calculated based on the pseudorange difference between the aircraft to be positioned and each reference aircraft after the offset, the pseudorange rate difference between the aircraft to be positioned and each reference aircraft after the offset, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after the offset, and the velocity of the reference aircraft in the Earth-centered Earth-fixed coordinate system.

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

[0080] This invention discloses a collaborative positioning method for swarm aircraft with unusual configurations. By optimizing the configurations between reference aircraft and the aircraft to be positioned, the proposed method optimizes the geometric configuration used for swarm positioning. Compared to unoptimized swarm positioning algorithms, this method achieves superior positioning accuracy even in swarms with unusual configurations, making it suitable for practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 Schematic diagram of the principle flow of the method of the present invention;

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

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

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

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

[0086] Figure 6 The error curve of cooperative position solution for a plane-configured aircraft formation;

[0087] Figure 7 The error curve of cooperative velocity solution for a plane-configured aircraft formation. DETAILED DESCRIPTION

[0088] The technical solution of the present invention is further described in detail below with reference to 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 convey the scope of the 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 configuration of cluster aircraft by adding a virtual offset vector, making the formation configuration in cluster positioning more reasonable, thereby improving 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) Acquire measurement data required for collaborative positioning of an aircraft cluster; the aircraft cluster comprises m+n aircraft, where m are aircraft to be positioned and n are reference aircraft. The reference aircraft can autonomously locate themselves using satellite signals, while the aircraft to be positioned cannot autonomously locate themselves by receiving satellite signals. Relative distance and speed information between the aircraft can be obtained through sensors;

[0093] In step 1.1), the reference aircraft measures its latitude, longitude, and altitude using its own navigation system to obtain the reference aircraft's position coordinates in the Earth-centered Earth-fixed coordinate system:

[0094]

[0095] Where (x, y, z) are the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system; lat, lon, and alt are the latitude, longitude, and altitude 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 radius of curvature of the reference ellipsoid. The reference ellipsoid is the ellipsoid model specified in the WGS-84 global coordinate system.

[0096] In 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. The expression is:

[0097] v e =R be v b ;

[0098]

[0099] Among them, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle of the aircraft respectively; v e is the velocity 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] In step 1.3), the aircraft measure the relative distance between the aircraft through sensors, which is expressed as:

[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; 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 the sensor 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, v i,j is the measured relative velocity between aircraft i and aircraft j;

[0106] Step 2) Since the linear relationship between the reference aircraft positions, such as the planar configuration and the linear configuration, can lead to serious geometric accuracy degradation during positioning, the formation configuration must be distinguished and optimized for each of these two configurations. Based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the configuration type of the aircraft formation is determined. The configuration types include linear configuration, planar configuration, and configurations other than linear and planar configurations. Linear and planar configurations are defined as singular configurations, and configurations other than linear and planar configurations are defined as 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 flag values ​​of linear configuration, plane configuration, linear configuration and non-singular configuration respectively, th_line, th_plane are the threshold of linear 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 normalizing the reference aircraft's position in the Earth-centered, Earth-fixed coordinate system is to minimize positional discrepancies in smaller arrays from larger Earth-centered, Earth-fixed coordinate values, thereby enhancing formation determination. The principal component analysis algorithm analyzes the linear relationships in the three-dimensional position matrix of the reference aircraft in the Earth-centered, Earth-fixed coordinate system and determines the variance contribution of each component. Since the principal component accounts for the majority of the variance in linear configurations, and the sum of the principal and secondary components accounts for the majority of the variance in planar configurations, the configuration type can be determined by setting a threshold and then evaluating the principal and secondary components.

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

[0114] In step 3.1), if the formation is a straight line or planar 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 the sort index, P is the reference aircraft position matrix, sor_DR is the sorted relative measurement information matrix, and sor_P is the sorted reference aircraft position matrix;

[0120] The ordering here and the reverse order of offset vector size selection described below are designed to ensure that the offset vectors of reference aircraft closer to the target aircraft are larger, while those farther from the target aircraft are smaller, thereby forming an optimal ellipsoidal configuration for the offset reference aircraft. This ideal configuration, with the target aircraft positioned in the center of the ellipsoidal configuration, improves the positioning accuracy not only for the target aircraft in the center of the formation but also for those at the edges.

[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 based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system 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 the reference aircraft i, c i is the position of the reference aircraft i after centering;

[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 reference aircraft after centralization, c i is the position of the reference aircraft i after centering, 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] In step 3.2.3), the offset vectors of the reference aircraft in the straight line configuration are calculated based on the direction vector of the fitted line and the relative distance between the reference aircraft and the aircraft to be positioned after sorting:

[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 positioned 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] The offset vectors are random directions perpendicular to the fitted line direction vector. During use, the directions of the individual vectors can be constrained to distribute them randomly within different angle ranges. This preserves randomness while avoiding the rare issue in the original algorithm where similar offset vector directions lead to poor post-offset configurations.

[0136] Step 3.3) If the formation is a planar configuration, calculate the eigenvector of the planar configuration and the offset vector of each reference aircraft in the planar configuration based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system 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 solving the least squares method:

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

[0141]

[0142] Step 3.3.2) According to the fitted reference aircraft plane expression, the unit normal vector of the fitted reference aircraft plane is obtained:

[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] In step 3.3.3), the offset vectors of each reference aircraft in the plane configuration are calculated based on the unit normal vector of the fitted plane and the relative distance between the adjusted reference aircraft and the aircraft to be positioned:

[0146]

[0147] Where V n is the direction vector of the fitted straight line of the reference aircraft, 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 or planar configuration, the position coordinates of the offset reference aircraft in the Earth-centered Earth-fixed coordinate system are calculated based on the offset vectors of each reference aircraft and the position coordinates of the adjusted reference aircraft in the Earth-centered Earth-fixed coordinate system. 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 positioned, 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 vectors 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 positioned 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 positioned 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 the plane configuration respectively, is_line and is_plane are the flag values ​​of the straight line configuration and the 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] Multiplying the distance by a certain empirical multiple here can prevent the situation where multiple reference aircraft are at the same distance as the aircraft to be located after the offset, making the algorithm more stable. The recommended value of the empirical multiple is given here: rate∈[0.7,0.9].

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

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

[0159] In step 6.1.1), based on the relative distance and relative velocity between the reference aircraft and the aircraft to be positioned, calculate the pseudorange difference and pseudorange rate difference between the aircraft to be positioned and each reference aircraft. 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) Calculate the velocity and position information of the aircraft to be positioned based on the obtained pseudorange difference and pseudorange 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;

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

[0165] In step 6.2.1), based on the relative distance between the reference aircraft and the aircraft to be positioned after the offset, and the relative velocity between the reference aircraft and the aircraft to be positioned after the offset, the pseudorange difference and pseudorange rate difference between the aircraft to be positioned and each reference aircraft after the offset are calculated. The expressions are:

[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 essentially translates 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) Calculate the velocity and position information of the aircraft to be located 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 Earth-centered Earth-fixed coordinate system after the offset, and the velocity of the reference aircraft in the Earth-centered Earth-fixed coordinate system.

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

[0172] A cluster collaborative positioning simulation is performed when the aircraft formation is in a straight line 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 locating the No. 6 aircraft to be located. Figure 3 、 Figure 4 The following plots show the position and velocity error curves for collaborative positioning of a formation of aircraft in a straight-line configuration, with and without the use of this method. It can be seen that the direct collaborative solution in a straight-line configuration results in a large error, while the use of this method significantly reduces the error, demonstrating that the present invention significantly improves positioning results in a 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 following plots show the position and velocity error curves for collaborative positioning of a formation of aircraft in a straight-line configuration, with and without the use of this method. It can be seen that the direct collaborative solution in a straight-line configuration results in a large error, while the use of this method significantly reduces the error, demonstrating that the present invention significantly improves positioning results in a straight-line configuration.

[0174] Combining the two sets of simulations, it can be found that the 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 commonly 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 their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense.

[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 unusual configurations, characterized in that: The following steps are involved: Step 1) Acquire measurement data required for collaborative positioning of an aircraft cluster; the aircraft cluster comprises m+n aircraft, where m are aircraft to be positioned and n are reference aircraft. The reference aircraft can autonomously locate themselves using satellite signals, while the aircraft to be positioned cannot autonomously locate themselves by receiving satellite signals. Relative distance and speed information between the aircraft can be obtained through sensors; In step 1.1), the reference aircraft measures its latitude, longitude, and altitude using its own navigation system to obtain the reference aircraft's position coordinates in the Earth-centered Earth-fixed coordinate system: Among them, x, y, z are the X-axis, Y-axis, and Z-axis coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system; lat, lon, and alt are the latitude, longitude, and altitude position coordinates of the reference aircraft respectively; a e is the major radius of the reference ellipsoid, e is the eccentricity of the reference ellipsoid, and N is the radius of curvature of the reference ellipsoid, where the reference ellipsoid is the ellipsoid model specified by the WGS-84 global coordinate system; In 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. The expression is: v e =R be v b ; Among them, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle of the aircraft respectively; v e is the velocity 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; In step 1.3), the aircraft measure the relative distance between the aircraft through sensors, which is expressed as: Among them, x i 、y i 、z i are the X-axis, Y-axis, and Z-axis coordinates of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system, respectively. j 、y j 、z j are the X-axis, Y-axis, and Z-axis coordinates of the j-th aircraft to be positioned in the Earth-centered Earth-fixed coordinate system; d r is the ranging error, d i,j is the measured relative distance between the i-th reference aircraft and the j-th aircraft to be positioned; Step 1.4), the aircraft measures the relative speed v between the aircraft through the sensor 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 the i-th reference aircraft and the j-th aircraft to be positioned, v i,j is the measured relative velocity between the i-th reference aircraft and the j-th aircraft to be positioned; Step 2) Determine the configuration type of the aircraft formation based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system. The configuration types include linear configuration, planar configuration, and configurations other than linear and planar configurations. Let linear configuration and planar configuration be singular configurations, and configurations other than linear and planar configurations be non-singular configurations: P=[p1,…,p n ],p i =[x i ,y i ,z i ] T ; [t,~]=PCA(P′ T ); Among them, p i is the position of the i-th reference aircraft in the Earth-centered Earth-fixed coordinate system; P is the reference aircraft position matrix, n is the number of reference aircraft, P′ is the reference aircraft position matrix after standardization, PCA is the principal component analysis algorithm; t 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 flag values ​​of linear configuration, plane configuration, and non-singular configuration respectively, th_line, th_plane are the thresholds of linear configuration proportion and plane configuration proportion respectively, t(1) is the proportion of principal component variance, t(2) is the proportion of subordinate component variance; Step 3) If the formation is a straight line configuration or a planar configuration, calculate its characteristic vector and the offset vector of each reference aircraft therein respectively; In step 3.1), if the formation is a straight line or planar configuration, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system, the relative distance between aircraft, and the relative speed between 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 the sort index, P is the reference aircraft position matrix, sor_DR is the sorted relative measurement information matrix, and 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 based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system 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 the reference aircraft i, c i is the position of the reference aircraft i after centering; 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 reference aircraft after centralization, c i is the position of the reference aircraft i after centering, svd is the singular value decomposition algorithm, V is the right singular vector obtained by svd decomposition, and v is the direction vector of the fitting line; In step 3.2.3), the offset vectors of the reference aircraft in the straight line configuration are calculated based on the direction vector of the fitted line and the relative distance between the reference aircraft and the aircraft to be positioned after sorting: 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 fitted line, r_line is the empirical multiple of the straight line configuration, 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 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 planar configuration, calculate the eigenvector of the planar configuration and the offset vector of each reference aircraft in the planar configuration based on the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system 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 solving the least squares method: ax+by-z+c=0; Step 3.3.2) According to the fitted reference aircraft plane expression, the unit normal vector of the fitted reference aircraft plane is obtained: 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; In step 3.3.3), the offset vectors of each reference aircraft in the plane configuration are calculated based on the unit normal vector of the fitted plane and the relative distance between the adjusted reference aircraft and the aircraft to be positioned: Among them, r_plane is the experience 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 or planar configuration, the position coordinates of the offset reference aircraft in the Earth-centered Earth-fixed coordinate system are calculated based on the offset vectors of each reference aircraft and the position coordinates of the adjusted reference aircraft in the Earth-centered Earth-fixed coordinate system. 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 vectors 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 positioned 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 positioned 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 the plane configuration respectively, is_line and is_plane are the flag values ​​of the straight line configuration and the 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 velocity of the aircraft to be located; Step 6.1), if the formation is a non-singular configuration: In step 6.1.1), the pseudorange difference and pseudorange rate difference between the aircraft to be positioned and each reference aircraft are calculated based on the relative distance and relative velocity between the reference aircraft and the aircraft to be positioned. The expressions are: 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) Calculate the velocity and position information of the aircraft to be positioned based on the obtained pseudorange differences between the aircraft to be positioned and each reference aircraft, the pseudorange rate differences 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; Step 6.2), if the formation is a straight line or a flat plane: In step 6.2.1), based on the relative distance and relative velocity between the reference aircraft and the aircraft to be positioned after the offset, the pseudorange difference and pseudorange rate difference between the aircraft to be positioned and each reference aircraft after the offset are calculated. The expressions are: 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 velocity 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 pseudorange rate difference between the aircraft j to be positioned and each reference aircraft after offset; In step 6.2.2), the velocity and position information of the aircraft to be positioned are calculated based on the pseudorange difference between the aircraft to be positioned and each reference aircraft after the offset, the pseudorange rate difference between the aircraft to be positioned and each reference aircraft after the offset, the position coordinates of the reference aircraft in the Earth-centered Earth-fixed coordinate system after the offset, and the velocity of the reference aircraft in the Earth-centered Earth-fixed coordinate system.

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