A passive multi-point fusion positioning method based on UAV cooperative formation

Abstract

The present invention discloses a passive multi-point fusion positioning method based on cooperative formation of unmanned aerial vehicles. A nonlinear equation group is constructed by generalized cross-correlation algorithm and analytical expression of hyperbolic equation, and then the passive multi-point positioning formula of unmanned aerial vehicles is derived based on matrix partitioning and elementary row transformation to obtain the analytical solution of target position, and the analytical solution error is analyzed based on the error multidimensional normal distribution function and the maximum eigenvalue of the analytical solution matrix; then the unmanned aerial vehicle formation space rectangular coordinate reference system is constructed, and the DOA and TDOA three-station passive multi-point positioning method is combined with the least squares fitting method to obtain the positioning expected coordinates and error distribution formula, and finally a simulated annealing algorithm is designed to search for the optimal fusion positioning formation configuration of unmanned aerial vehicles. Through a large number of simulation experiments and comparisons, the basic characteristics of the unmanned aerial vehicle spatial configuration that can achieve high-precision target positioning are obtained by the present invention, and it can achieve real-time collaborative high-precision positioning of multiple unmanned aerial vehicles under three-dimensional dynamic conditions.

Description

Technical Field

[0001] The present invention relates to the field of multi-source fusion positioning of unmanned aerial vehicle (UAV) formations, and in particular to a passive multi-point fusion positioning method based on cooperative UAV formations. Background Art

[0002] Passive multi-point fusion positioning for unmanned aerial vehicles (UAVs) is widely used in coordinated command and control operations such as military reconnaissance, raids, and manhunts, as well as in general aviation applications such as civil air show performances, emergency rescue, and terrain exploration. Due to the limited payload capacity of individual UAVs, the limited variety of sensors they carry, and their limited range, the coordinated operation of multiple UAVs can effectively expand the temporal and spatial coverage of surveillance and detection, improve the real-time performance of target detection, leverage the advantages of multi-sensor collaboration, enhance target recognition accuracy, strengthen the system's anti-interference performance, and improve system reliability and fault tolerance. Therefore, multi-UAV formation flight and passive multi-point fusion positioning technologies have gradually become a research hotspot in the UAV field. However, research on multi-UAV coordination in my country started relatively late, and current research primarily focuses on setting specific scenarios and the tasks to be completed by the UAV swarm, and then developing related work based on this. Furthermore, existing UAV passive multi-point positioning technologies still suffer from large errors and imperfect error analysis methods. Summary of the Invention

[0003] In response to the problems of the existing technology, the present invention provides a passive multi-point fusion positioning method based on UAV cooperative formation, which can reduce positioning errors and improve the high-precision collaborative positioning capability of UAVs.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A passive multi-point fusion positioning method based on UAV cooperative formation includes the following steps:

[0006] Step S1, constructing a nonlinear equation system using a generalized cross-correlation algorithm and an analytical expression of a hyperbolic equation; then deriving a passive multi-point positioning formula for the UAV based on matrix partitioning and elementary row transformation to obtain an analytical solution for the target position; finally, performing an analytical solution error analysis based on an error multidimensional normal distribution function and the maximum eigenvalue of the analytical solution matrix;

[0007] Step S2: Construct a spatial rectangular coordinate reference system for the UAV formation, use the DOA and TDOA three-station passive multi-point positioning method combined with the least squares fitting method to obtain the positioning expected coordinates and error distribution formula, and then design a simulated annealing algorithm to search for the optimal fusion positioning formation configuration of the UAVs.

[0008] Furthermore, the final expression of the target position analytical solution in step S1 is as follows:

[0009]

[0010] in:

[0011]

[0012]

[0013]

[0014] i=1,2,3,x i1 =x i -x1,y i1 =y i -y1,i=2,3;(x i ,y i ), i=1,2,3 means no

[0015] Human-machine position coordinates; P1 is the reference drone position, P1 = [x1, y1]; P2, P3 are the other two drone positions, P2 = [x2, y2], P3 = [x3, y3]; x ij Represents x i -x j ,y ij represents y i -y j ; that is, the coordinate representation of UAV i in the coordinate system of UAV j; r1 represents the Euclidean distance of the target position measured from the reference UAV P1; r ij represents the distance difference between the target and the i-th UAV and the j-th UAV; ||P i ,P j ||2 means from position P i To position P j The 2-norm of .

[0016] Furthermore, the step S2 specifically includes:

[0017] Step S21: constructing a rectangular coordinate system for the UAV formation space based on the UAV position vectors; and obtaining a standard orthogonal basis by Schmidt orthogonalization;

[0018] Step S22: Based on the DOA and TDOA three-station collaborative detection technology, the target position is determined by the spatial geometric relationship between the UAV and the target. First, UAV 1 is used as the reference UAV, and UAVs 1, 2, and 3 are divided into two groups: 1, 2 and 1, 3. Then, dual-station passive positioning analysis is performed on each group to obtain the expected positioning coordinate analytical solution and error probability distribution characteristics.

[0019] Step S23: Fit the solution space of the analytical solution using a linear least squares fitting method to obtain the estimated position of the target point and the error distribution formula;

[0020] Step S24: Design a simulated annealing algorithm to search for different UAV spatial position configurations, and then obtain the optimal fusion positioning formation configuration of the UAVs with the minimum mean square error of the optimized Euclidean distance positioning.

[0021] Furthermore, the optimal fusion positioning formation configuration of UAVs finally obtained has the following characteristics:

[0022] (1) The spatial configuration of the three drones forms a spatial obtuse triangle with an angle of 90-120 degrees;

[0023] (2) Two of the UAVs are initially at the same or similar flight altitude, and the other UAV has a certain flight altitude difference from the other two UAVs;

[0024] (3) The ratio of the side lengths of the spatial triangle formed by the three drones is close to the shortest side: the second shortest side: the longest side = 1:1.33:1.76.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. Compared with traditional methods, the 95% confidence interval of the target lateral positioning error in the UAV fusion positioning formation configuration of the present invention does not exceed 25 meters, and the 95% confidence interval of the direction-finding positioning error does not exceed 27 meters. It has the advantages of small positioning error and high collaborative positioning accuracy.

[0027] 2. The passive multi-point fusion positioning method based on UAV cooperative formation proposed in the present invention has good real-time positioning performance and can solve the problems of low accuracy of single-station passive positioning detection and easy interception of active positioning detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is the overall technical roadmap of the passive multi-point fusion positioning method based on UAV formation of the present invention;

[0029] Figure 2 Schematic diagram of a passive multi-point positioning method based on cooperative formation of UAVs in the present invention

[0030] Figure 3 It is a dual-station passive positioning analysis model based on DOA and TDOA;

[0031] Figure 4 This is the flow chart of the optimal passive positioning configuration search algorithm for UAVs based on simulated annealing;

[0032] Figure 5The optimal passive multi-point positioning configuration for UAVs that can achieve high-precision target positioning1;

[0033] Figure 6 Optimal passive multi-point positioning configuration for UAVs that can achieve high-precision target positioning 2;

[0034] Figure 7 is the positioning error distribution under the optimal configuration of the UAV. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0036] like Figure 1 and Figure 2 As shown, the present invention discloses a passive multi-point fusion positioning method based on cooperative formation of UAVs. First, the least squares method is used to calculate the analytical solution for target positioning under the influence of various Gaussian white noises, and the target's three-dimensional position estimate is obtained. Then, a UAV spatial configuration optimization model based on the simulated annealing algorithm is constructed to solve the UAV spatial configuration with the minimum mean square error of target positioning. Subsequently, through a large number of simulation experiments and comparisons, the basic characteristics of the UAV spatial configuration that can achieve high-precision target positioning are obtained. The specific steps are as follows:

[0037] Step 1: Derivation of the UAV passive multi-point positioning formula

[0038] Step 1.1 Construct analytical solution equation

[0039] Assume that three drones in a two-dimensional plane receive signals transmitted by the same target signal source, such as Figure 3 As shown, the coordinates of the drone positions are (x i ,y i ),i=1,2,3, the target position coordinates are T:[x,y].

[0040] Assume that the received signal of the i-th UAV is:

[0041] u i (t) = s(td i )+v i (t),i=1,2,3

[0042] Among them, s(t) is the source signal emitted by the target, d i is the delay of the source signal propagating to the i-th UAV, v i (t) is a time-delayed Gaussian white noise, and the noise and signal are independent of each other.

[0043] First, taking the time delay of the first UAV as the reference benchmark, the generalized cross-correlation (GCC) algorithm is used to estimate the time difference between the source signal arriving at the i-th UAV and the first reference UAV:

[0044] d i1 =d i -d1,i=2,3

[0045] Then, using the time difference d i1 and the speed of light c. Based on the geometric relationship between the drone and the target, the equations are set to solve the target position, and the distance difference r between the target and the i-th drone and the first drone can be obtained. i1 for:

[0046] r i1 =cd i1 =r i -r1,i=2,3

[0047] Among them, r i is the distance from the target to the i-th UAV, satisfying

[0048] The hyperbola equation is constructed based on the path difference between the electromagnetic wave reaching the i-th UAV and the first UAV:

[0049]

[0050] Then r i Squaring both sides gives:

[0051] r i 2 =(x i -x) 2 +(y i -y) 2 =K i -2x i x-2y i y+x 2 +y 2 ,i=1,2,3

[0052] in,

[0053] Using the hyperbolic equation to construct a nonlinear system of equations can solve the target position, but it is very difficult to solve the nonlinear system of equations. Therefore, consider converting the system of equations formed by the above formula into a pseudo-linear system of equations and substituting it into:

[0054] (r i1 +r1) 2 =K i -2x ix-2y i y+x 2 +y 2

[0055]

[0056] To eliminate x 2 and y 2 , then subtract r1 from both sides of the above equation 2 =K1-2x1x-2y1y+x 2 +y 2 We can get:

[0057]

[0058]

[0059]

[0060] Right now:

[0061]

[0062] Among them, x i1 =x i -x1,y i1 =y i -y1,i=2,3.

[0063] Now we have a nonlinear system of equations. To solve this system of equations, we first consider r1 as a known quantity, so we can get the following matrix expression:

[0064] AX=F

[0065] in,

[0066] With rank(A) = 2, the number of unknowns in the system equals the number of equations, and there is a unique solution. Solving the equation using the pseudo-inverse method yields:

[0067]

[0068] Thus, the system of equations is transformed into a pseudo-linear system of equations about the unknowns x, y and r1. The following problem is to solve this pseudo-linear system of equations.

[0069] Step 1.2 Derivation of analytical solution

[0070] By combining the two hyperbolic equations and deriving the formula to solve the pseudo-linear equation, we can obtain the least squares estimates of x and y:

[0071]

[0072] in,

[0073] make

[0074] but

[0075] Again

[0076] but

[0077] In this way, x and y can be converted into an expression related to q1, q2, p1, and p2:

[0078]

[0079] At this point, there is only one unknown variable in the system of equations, which is r1. The following equation can be obtained:

[0080]

[0081] At this time, the equation is equivalent to is a quadratic equation in r1, where:

[0082]

[0083] By solving the quadratic equation, We can get two solutions for r1. Based on the prior information, we discard an invalid solution and bring the valid solution into the above equations to obtain the analytical solution of the target T:

[0084]

[0085] in:

[0086]

[0087] i=1,2,3,x i1 =x i -x1,y i1 =y i -y1,i=2,3.

[0088] Step 1.3 Analytical solution error analysis

[0089] The analytical solution formula based on the target position T can be further simplified as:

[0090]

[0091] Among them, P1 is the reference drone position, P1 = [x1, y1]; P2, P3 are the positions of the other two drones, P2 = [x2, y2], P3 = [x3, y3]; xij Represents x i -x j , which is the coordinate representation of UAV i in the coordinate system of UAV j; r1 represents the Euclidean distance of the target position measured from the reference UAV P1; P i ,P j2 Indicates that from position P i To position P j 2-norm of ;

[0092] According to the model assumptions, we have:

[0093] x k1 '~N(x k1 ,σ1 2 ),x k1 '=x k1 +N(0,σ1 2 )

[0094] y k1 '~N(y k1 ,σ2 2 ),y k1 '=y k1 +N(0,σ2 2 )

[0095] r'~N(r,δ 2 ),r'=r+N(0,δ 2 )

[0096] Among them, x k1 ' represents the x-axis position of the k-th UAV with white noise relative to the reference UAV, k1 ' represents the y-axis position of the kth UAV with white noise relative to the reference UAV; x k1 and y k1 denote the x-axis position and y-axis position of the k-th UAV relative to the reference UAV without white noise, N(u,σ 2 ) indicates that it obeys the normal distribution with mean u and mean square deviation σ.

[0097] According to the formula for summing variance of independent probability distributions:

[0098] D(X+Y)=D(X)+D(Y)

[0099] Where X and Y represent random variables that obey a certain probability distribution.

[0100] The formula for the product variance of two independent normally distributed random variables is:

[0101]

[0102] The product characteristics of two identical normally distributed random variables are:

[0103]

[0104] Among them, χ 2 (1) represents the chi-square distribution with 1 degree of freedom, and D(χ 2 (n))=2n, where n is the degree of freedom. Therefore, we have:

[0105]

[0106] It is deduced that:

[0107]

[0108] At this time, the change of A is:

[0109]

[0110]

[0111]

[0112]

[0113] Among them, t x ' represents the horizontal x-axis coordinate of the target obtained under white noise interference, t y ' represents the vertical y-axis coordinate of the target obtained under white noise interference; σ1 represents the horizontal standard deviation of the relative positioning of the UAV, and σ2 represents the vertical standard deviation of the relative positioning of the UAV; π tx Represents the probability distribution of the target position in the horizontal direction, π ty Represents the probability distribution of the target position in the vertical direction.

[0114] Step 2: Design of optimal UAV spatial configuration search algorithm based on simulated annealing algorithm

[0115] Step 2.1 Construct the UAV formation space rectangular coordinate system

[0116] Arbitrarily select a UAV as the reference UAV. The coordinates of the reference UAV are always (0,0,0). The vector from UAV 2 to the reference UAV is p2: (x2, y2, z2), and the vector from UAV 3 to the reference UAV is p3: (x3, y3, z3). When the three UAVs are not collinear, the vector space S formed by these three UAVs is p =span(p2,p3), using Gram-schmidt orthogonalization to construct a standard orthogonal basis:

[0117]

[0118] in,<p2,γ1> It means finding the cosine of the angle between vector p2 and vector γ1.

[0119] There is a vector space span(p2,p3)=span(γ1,γ2).

[0120] Assume that the ship and the reference drone form a vector p4:(x4,y4,z4). p4 is not coplanar with p2 and p3. Therefore, there is a basis vector γ3 orthogonal to γ1 and γ2:

[0121] γ3=p3-λ

[0122] λ=<p3,γ1> γ1+<p3,γ2> γ2

[0123] At this point, the three drones and the ship form a rectangular coordinate system with a standard orthogonal basis: [γ1, γ2, γ3]. The coordinates of the reference drone as the origin are (0, 0, 0). In this space, the relative position of the drone and the ship remains invariant under linear changes, that is:

[0124]

[0125] Where ψ is the space S p = any linear transformation in span(γ1,γ2).

[0126] Step 2.2 Three-station passive positioning based on DOA and TDOA

[0127] In order to solve the problem that the single-station passive positioning detection accuracy is low and the active positioning detection is easy to be intercepted, this section will focus on the three-station collaborative detection technology based on DOA and TDOA. The target position is determined by the spatial geometric relationship between the UAV and the target. First, UAV 1 is used as the reference UAV, and UAVs 1, 2, and 3 are divided into two groups, 1, 2 and 1, 3. Then, dual-station passive positioning analysis is performed on one of the groups respectively. The specific positioning model is shown in the attached figure. Figure 1 shown.

[0128] For passive positioning in three-dimensional space, a three-dimensional coordinate system is constructed with drone 1 as the coordinate origin, so that the three drones 1, 2, and 3 are in the same plane. Let drone 1 be the reference drone and target T be the radiation source. The coordinates of drones 1, 2, and 3 are: s1: (x1, y1, z1), s2: (x2, y2, z2), s3: (x3, y3, z3), the coordinates of target T are T: (x, y, z), the target azimuth and pitch angles of the radiation source to drone 1 are α and β respectively, and the time required for the electromagnetic wave emitted by the radiation source to reach drone i is d i , then the time difference between arriving at drone i and arriving at drone 1 is di1 , then according to the geometric relationship:

[0129]

[0130] Where c is the speed of light. The first equation in the system is based on the TDOA equation, which uses the path difference between the electromagnetic wave reaching UAV i and UAV 1 to generate a hyperboloid. The second equation is the equation of the spatial line defined by UAV 1 and the direction of arrival of the signal. Based on spatial geometry, the TDOA hyperboloid and the DOA spatial line intersect at two points, one of which is the location of the desired radiation source, target T.

[0131] Definition n=[cosβcosα,cosβsinα,sinβ] T ,get:

[0132] cd i1 +||s1-ng||=||s i -ng||

[0133] Squaring both sides yields:

[0134] 2cd i1 ||s1-ng||=2(s1-s i ) T ng+||s i || 2 -||s1|| 2 -c 2 (d i1 ) 2

[0135] Let h = || s i || 2 -||s1|| 2 -c 2 (d i1 ) 2 , and then square both ends of the above equation, we can get a quadratic equation about g: a0g 2 +b0g+c0=0, where:

[0136]

[0137] At this time, you can obtain Substituting the obtained g into the above equations, the coordinate position of the target T can be obtained:

[0138] X=ng

[0139] At this time, the coordinates are two positioning results about UAV 1 obtained by measuring the path difference between UAV 1 and UAV 2 and the lateral angle information of the electromagnetic wave received by UAV 1. It is necessary to use the direction-finding angle information of UAV 2 and use the DOA space line and the TDOA hyperboloid to intersect at two points again. The two sets of results are combined to finally determine that one of the points is the final radiation source, that is, the target T position.

[0140] Subsequently, using the same method, for UAV 1 and UAV 3, the final position of the radiation source, i.e., point T, is obtained by taking the path difference between the radiation source and UAV 3 and the path difference between the radiation source and UAV 1, as well as the lateral angle information of the radiation source reaching UAV 1 and UAV 3. Due to the existence of path difference error and angle error, the T points obtained by the two sets of models do not necessarily intersect at one point, but are within a certain error space range.

[0141] Step 2.3 Least Squares Fitting

[0142] The reference values X1X2 of the two sets of target positions are obtained by two sets of passive positioning methods based on the combination of DOA-TDOA.

[0143] The ideal DOA reference value is a straight line, but in actual measurement, due to the inevitable measurement error of the direction-finding base station (i.e., drone), the result is a ray distributed within a certain spatial error range (azimuth, pitch angle), resulting in positioning error. According to the model assumptions, there are:

[0144]

[0145]

[0146] Among them, α i ' represents the deflection angle of the i-th UAV to the target with white noise, β i ' represents the pitch angle of the i-th UAV to the target under white noise interference.

[0147] The ideal TDOA reference value is a portion of a hyperbolic surface, but due to the inevitable errors in electromagnetic wave transmission signals, the result is a surface distributed within a certain spatial error range.

[0148]

[0149] Among them, s i ' represents the equation of the spatial line with white noise between the i-th UAV and the target position direction.

[0150] According to the combination of DOA and TDOA, the reference UAV and the two auxiliary UAVs perform dual-station positioning respectively, and obtain the observation values of the target position respectively:

[0151] X1k =N 1k g,k=2,3

[0152] Among them, X 1k represents the feasible solution vector space for dual-station positioning of the reference UAV 1 and UAV k (k = 2, 3), N 1k Represents the angle measurement coefficient matrix, N 1k =[n1 n2 n3…] T , g is the intermediate variable of the analytical solution.

[0153] Because the unknown parameter s in g i is related to the target position, so the result is about s i The function is not a linear equation about the target position, but a pseudo-linear form. Since these linear equations do not necessarily have exact solutions, the least squares estimation method is used to fit the solution space to obtain the estimated position of the target point T.

[0154] Step 2.4 Design of optimal unmanned machine type search method

[0155] Based on the assumption that each positioning error is independent and the analytical solution form in step 1, it can be obtained that when the following relationship is satisfied between the UAV and the target position, the UAV's in-plane positioning error for the target is minimized:

[0156]

[0157]

[0158] like Figure 4 The figure below shows a flowchart for the simulated annealing-based algorithm for searching for the optimal passive positioning configuration for UAVs. Assuming that the horizontal positioning error and the direction-finding angle error are independent of each other—that is, the direction-finding angle error is unaffected by the UAV's spatial configuration—then the relative position coordinates between the UAVs need to be optimized to minimize the vector modulus. However, directly optimizing a dual-objective nonlinear function is extremely difficult. Therefore, a more intuitive and simple approach is to use a simulated annealing algorithm to search for different UAV spatial configurations and then determine the optimized configuration that minimizes the mean squared error of the Euclidean distance.

[0159] The pseudo code of the mean square error optimization algorithm for positioning using the simulated annealing algorithm is as follows:

[0160] Mean square error optimization algorithm for UAV positioning model based on simulated annealing algorithm

[0161]

[0162]

[0163] Finally, the UAV cooperative formation that is more suitable for UAV fusion positioning is obtained, as shown in the attached figure. Figure 5 、 6 As shown, the UAV formation has the following characteristics:

[0164] (1) The spatial configuration of the three drones forms a spatial obtuse triangle with an angle of 90-120 degrees.

[0165] (2) The two UAVs are initially at the same or similar flight altitude, and the other UAV has a certain flight altitude difference from the other two UAVs.

[0166] (3) The ratio of the side lengths of the spatial triangle formed by the three drones is close to the shortest side: the second shortest side: the longest side = 1:1.33:1.76.

[0167] Finally, we can get Figure 7 The positioning error distribution under the optimal configuration of the UAV shown in the figure achieves high-precision target positioning.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A passive multi-point fusion positioning method based on UAV cooperative formation, characterized in that: The method comprises the following steps: Step S1: Construct a nonlinear system of equations using the generalized cross-correlation algorithm and the analytical expression of the hyperbolic equation. Then, derive the passive multi-point positioning formula for the UAV based on matrix partitioning and elementary row transformation to obtain the analytical solution of the target position. Finally, perform analytical solution error analysis based on the error multidimensional normal distribution function and the maximum eigenvalue of the analytical solution matrix. The final expression of the analytical solution of the target position is as follows: in: x i1 =x i -x1,y i1 =y i -y1,i=2,3;(x i ,y i ), i=1,2,3 represent the coordinates of the drone positions; P1 is the reference drone position, P1=[x1,y1]; P2, P3 are the positions of the other two drones, P2=[x2,y2], P3=[x3,y3]; x ij Represents x i -x j ,y ij represents y i -y j ; that is, the coordinate representation of UAV i in the coordinate system of UAV j; r1 represents the Euclidean distance of the target position measured from the reference UAV P1; r ij represents the distance difference between the target and the i-th UAV and the j-th UAV; ||P i ,P j ||2 means from position P i To position P j 2-norm of ; Step S2: Construct a spatial rectangular coordinate reference system for the UAV formation, adopt the DOA and TDOA three-station passive multi-point positioning method, and combine it with the least squares fitting method to obtain the positioning expected coordinates and error distribution formula, and then design a simulated annealing algorithm to search for the optimal fusion positioning formation configuration of the UAVs.

2. The passive multi-point fusion positioning method based on UAV cooperative formation according to claim 1 is characterized in that: The step S2 specifically includes: Step S21: constructing a rectangular coordinate system for the UAV formation space based on the UAV position vectors; and obtaining a standard orthogonal basis by Schmidt orthogonalization; Step S22: Based on the DOA and TDOA three-station collaborative detection technology, the target position is determined by the spatial geometric relationship between the UAV and the target. First, UAV 1 is used as the reference UAV, and UAVs 1, 2, and 3 are divided into two groups: 1, 2 and 1, 3. Then, dual-station passive positioning analysis is performed on each group to obtain the expected positioning coordinate analytical solution and error probability distribution characteristics. Step S23: Using a linear least squares fitting method to fit the solution space of the analytical solution to obtain the estimated position of the target point and the error distribution formula; Step S24: Design a simulated annealing algorithm to search for different UAV spatial position configurations to obtain the optimal fusion positioning formation configuration of UAVs with the minimum mean square error of the optimized Euclidean distance positioning.

3. The passive multi-point fusion positioning method based on UAV cooperative formation according to claim 1 is characterized in that: The final optimal fusion positioning formation configuration of UAVs has the following characteristics: (1) The spatial configuration of the three drones forms a spatial obtuse triangle with an angle of 90-120 degrees; (2) Two of the UAVs are initially at the same or similar flight altitude, and the other UAV has a certain flight altitude difference from the other two UAVs; (3) The ratio of the side lengths of the spatial triangle formed by the three drones is close to the shortest side: the second shortest side: the longest side = 1:1.33:1.76.

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