Single anchor point observable unmanned aerial vehicle self-positioning method and system

Abstract

The invention provides a single-anchor-point observable unmanned aerial vehicle self-positioning method and system. The method comprises the following steps that firstly, a single-anchor-point unmanned aerial vehicle self-positioning system based on the AOA positioning principle is built, and an expression of a positioning measurement true value about a self-positioning parameter is deduced; secondly, defining a positioning function of the built single-anchor unmanned aerial vehicle self-positioning system according to the self-positioning parameters and a self-positioning measurement true value, and proving the observability of the single-anchor unmanned aerial vehicle self-positioning system on the basis; establishing a self-positioning problem of an original single-anchor unmanned aerial vehicle self-positioning system according to the self-positioning measurement value probability density function expression, and establishing an equivalent self-positioning problem of the single-anchor unmanned aerial vehicle self-positioning system according to the monotonicity of the self-positioning measurement value probability density function expression about a cost function; and finally, solving the self-positioning problem of the equivalent single-anchor unmanned aerial vehicle self-positioning system based on a modified maximum likelihood iterative algorithm, obtaining an optimal self-positioning parameter value, and realizing unmanned aerial vehicle self-positioning.

Description

Technical Field

[0001] The present invention belongs to the technical field of UAV self - positioning, and particularly relates to a UAV self - positioning method and system observable with a single anchor point. Background Technique

[0002] Unmanned aerial vehicles (UAVs) have the advantages of low cost, high mobility, and high reliability. The line - of - sight links of the air - to - ground and air - to - air links between UAVs and ground nodes and air nodes have higher channel quality than those of ground cellular networks, which makes UAVs show great development prospects in wireless communication applications such as data collection, communication relay, and vehicle - to - everything (V2X). The flexibility of UAVs brings a new dimension to network design, and the network performance can be effectively improved by reasonably planning UAV communication systems.

[0003] However, compared with ground networks, the system design of UAV communication networks depends on the accurate perception of the UAV's own position and the alignment and calibration of the local coordinate system, that is, the self - positioning of UAVs. In urban high - occlusion environments, UAV self - positioning mainly uses anchor - point signals for positioning. P. Sinha et al. studied the influence of three - dimensional antennas on the positioning accuracy of the time of arrival (TOA) and time difference of arrival (TDOA) of UAVs, thus revealing the basic limitations of current UAV three - dimensional positioning. In order to make full use of the advantages of both angle - of - arrival (AOA) positioning and ranging positioning, X. Kang et al. studied the self - positioning of UAVs with hybrid AOA and TDOA, significantly improving the self - positioning accuracy of UAVs. To meet the observability requirements of the positioning system, the above - mentioned work all requires at least four anchor points with large differences in position distribution. The self - positioning has high requirements for the number of anchor points and the spatial distribution of anchor points, and is extremely vulnerable to external noise and interference, so the positioning accuracy cannot be guaranteed. In complex environments, how to achieve observable UAV self - positioning based on a small number of anchor points or even a single anchor point is still an open proposition in the academic community. Summary of the Invention

[0004] Aiming at the current situation that there is a lack of a UAV self - positioning method observable with a single anchor point in the current UAV communication network, the present invention proposes a UAV self - positioning method and system observable with a single anchor point to improve the UAV self - positioning performance with the support of a small number of anchor points.

[0005] To solve the above - mentioned technical problems, the present invention provides the following technical solutions: A UAV self - positioning method observable with a single anchor point, comprising the following steps: Step 1: Build a single-anchor UAV self-localization system based on the AOA positioning principle, set the self-localization parameters, deduce the expression of the true value of the self-localization measurement with respect to the self-localization parameters, and obtain the true value of the self-localization measurement; Step 2: Set the positioning function of the built single-anchor UAV self-localization system based on the true value of the self-localization measurement, and prove that the built single-anchor UAV self-localization system is observable; Step 3: Obtain the expression of the self-localization measurement value based on the true value of the self-localization measurement, then obtain the probability density function expression of the self-localization measurement value according to the measurement noise distribution, and then establish the self-localization problem of the original single-anchor UAV self-localization system; and construct the self-localization problem of the equivalent single-anchor UAV self-localization system; Step 4: Solve the self-localization problem of the equivalent single-anchor UAV self-localization system to obtain the optimal self-localization parameter value and achieve UAV self-localization.

[0006] Furthermore, the single-anchor UAV self-localization system in Step 1 includes one anchor and one UAV that needs self-localization.

[0007] Furthermore, the self-localization parameters in Step 1 are:

[0008] where is the alignment angle of the UAV local coordinate system, and the initial position of the UAV is , where respectively represent the initial position coordinates of the UAV on the axis.

[0009] Furthermore, the expression of the true value of the self-localization measurement with respect to the self-localization parameters in Step 1 is:

[0010] where represents the true value of the azimuth angle between the UAV and the anchor at the th moment, represents the true value of the pitch angle between the UAV and the anchor at the th moment; respectively represent the components of the UAV displacement on the axis at the th moment; represents the coordinate rotation matrix related to the alignment angle of the UAV local coordinate system; represents the UAV displacement at the th moment, represents the total number of moments; represents the modulus of the first two elements of the vector, Indicates matrix transpose.

[0011] Furthermore, the positioning function of the single-anchor UAV self-positioning system established in step 2 is:

[0012] where and represent the positioning functions of the single-anchor UAV self-positioning system with respect to the azimuth angle and pitch angle respectively, and their independent variables are respectively, and the dependent variables are and ; The symbol represents a -dimensional vector, represents the set of true azimuth angle values between the UAV and the anchor point at moments, represents

[0013] the set of true pitch angle values between the UAV and the anchor point at Furthermore, in step 2, the method to prove that the established single-anchor UAV self-positioning system is observable is as follows: Prove that the positioning function of the azimuth angle is an injective function with respect to Prove that the positioning function of the pitch angle is an injective function with respect to ; Prove that and are surjective functions, then the positioning function is a bijective function with respect to the self-positioning parameters, that is, the established single-anchor UAV self-positioning system is observable.

[0014] Furthermore, the expression of the self-positioning measurement value in step 3 is:

[0015] where represents the measured azimuth angle between the UAV and the anchor point, represents the measured pitch angle between the UAV and the anchor point, represents the azimuth angle measurement noise; represents the pitch angle measurement noise.

[0016] Furthermore, the expression of the probability density function of the self-positioning measurement value in step 3 is:

[0017] where is the expression of the probability density function of the self-positioning measurement value, represents the cost function, represents the covariance set matrix of the azimuth measurement noise and the pitch measurement noise; represents the covariance matrix of the azimuth measurement noise, represents the covariance of the azimuth measurement noise at the first moment, represents the covariance of the azimuth measurement noise at the represents the covariance matrix of the pitch measurement noise, represents the covariance of the pitch measurement noise at the first moment, represents the covariance of the pitch measurement noise at the The self - localization problem of the original single - anchor UAV self - localization system described in step 3 is:

[0018] The self - localization problem of the original single - anchor UAV self - localization system is equivalent to:

[0019] where, making maximized, the corresponding , is the self - localization parameter sought for self - localization.

[0020] Furthermore, in the said step 4, solving the self - localization problem of the equivalent single - anchor UAV self - localization system includes the following sub - steps: Step 4.1. Initialize the UAV self - localization parameter value , set the iteration threshold , and the number of iterations , and take the initialized UAV self - localization parameter value as the local point of iteration; Step 4.2: In the th iteration, first let the initial position of the UAV be the value corresponding to the local point of this iteration, that is , the self - localization problem of the equivalent single - anchor UAV self - localization system is transformed into the form of , and solved by maximum likelihood estimation to obtain the optimized value of the UAV local coordinate system alignment angle; Step 4.3: In the th iteration, let the UAV local coordinate system alignment angle be the optimized value of this iteration, that is , then the self - localization problem of the equivalent single - anchor UAV self - localization system is transformed into the form of , and for the cost function Perform convex approximation to convert it into an upper-bound convex form , and solve the convex approximation problem through a convex optimization algorithm to obtain the optimized value of the initial position of the UAV ; Step 4.4: If the relative decrease in the objective function in this iteration compared to the previous iteration is less than the iteration threshold , then stop the iteration, and the optimized value of this iteration is the value of the UAV self-positioning parameter; otherwise, it will be used as the local point for the next iteration, and return to Step 4.2

[0021] On the other hand, the present invention provides a UAV self-positioning system observable by a single anchor point, including: True value acquisition module: It is used to build a single-anchor-point UAV self-positioning system based on the AOA positioning principle, set self-positioning parameters, deduce the expression of the true value of the self-positioning measurement with respect to the self-positioning parameters, and obtain the true value of the self-positioning measurement; Positioning function construction module: It is used to set the positioning function of the built single-anchor-point UAV self-positioning system based on the true value of the self-positioning measurement, and prove that the built single-anchor-point UAV self-positioning system is observable; Self-positioning problem construction module: It is used to obtain the expression of the self-positioning measurement value based on the true value of the self-positioning measurement, then obtain the expression of the probability density function of the self-positioning measurement value according to the measurement noise distribution, and then establish the self-positioning problem of the original single-anchor-point UAV self-positioning system according to the expression of the probability density function of the self-positioning measurement value; and construct the self-positioning problem of the equivalent single-anchor-point UAV self-positioning system; Solution module: It is used to solve the self-positioning problem of the equivalent single-anchor-point UAV self-positioning system to obtain the optimal self-positioning parameter value and achieve UAV self-positioning

[0022] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a single-anchor-point observable UAV self-positioning method and system, which can significantly reduce the requirement for the number of external anchor points for UAV self-positioning while ensuring the observability requirements of the positioning system. On this basis, a modified maximum likelihood iterative algorithm is proposed to efficiently solve the self-positioning problem. The proposed single-anchor-point observable UAV self-positioning method and system can be widely applied to the self-positioning scenarios of UAV clusters in urban environments where global positioning signals are blocked Description of the Drawings

[0023] To more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0024] Figure 1 Schematic diagram of a single-anchor-point observable UAV self-positioning system according to an embodiment of the present invention; Figure 2 Flowchart of the method implemented by the present invention; Figure 3 Schematic diagram comparing the RMSE and CRLB of the proposed self-positioning scheme in an embodiment of the present invention. Detailed implementation manners

[0025] To make the purpose, technical solutions and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention in conjunction with the drawings in the present invention. Obviously, the described embodiments are some embodiments of the present invention, rather than all embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0026] Embodiment 1 As Figure 1 shown, this embodiment provides a single-anchor-point observable UAV self-positioning system and method, specifically as follows: Figure 1 A single-anchor-point UAV self-positioning system considering the AOA positioning principle in a specific embodiment of the present invention. The system includes an anchor point and a UAV that needs to self-position. The anchor point sends a positioning signal to the UAV, and the UAV self-positioning is realized by adopting the AOA positioning principle for the received signal. The self-positioning parameters are the initial position of the UAV and the alignment angle of the local coordinate system.

[0027] As Figure 2 shown is the flowchart of the method of the present invention. The implementation process includes the following steps: Step 1: Build a single-anchor-point UAV self-positioning system based on the AOA positioning principle, set the self-positioning parameters, deduce the expression of the true value of the self-positioning measurement with respect to the self-positioning parameters, and obtain the true value of the self-positioning measurement; First, build a single-anchor UAV self-positioning system based on the AOA positioning principle. The system consists of an anchor and a UAV that needs to self-position. The self-positioning system realizes the self-positioning of the UAV through the AOA positioning principle, and the self-positioning parameters are the initial position of the UAV and the alignment angle of the local coordinate system. Then, combining the anchor position, the displacement of the UAV in the local coordinate system at each moment, and the self-positioning parameters, the expression of the true value of the self-positioning measurement with respect to the self-positioning parameters is derived.

[0028] The anchor position described in step 1 is ; the initial position of the UAV is , where respectively represent the -th moment's initial position coordinates of the UAV on the axis; the alignment angle of the UAV's local coordinate system is , then the self-positioning parameters of the UAV self-positioning system are .

[0029] The displacement of the UAV at each moment described in step 1 is , where represents the number of moments, represents the displacement of the UAV at the -th moment, respectively represent the components of the displacement of the UAV at the -th moment on the axis, represents the total number of moments, where is required to meet the observability requirements of the subsequent self-positioning system, represents matrix transpose.

[0030] For the AOA self-positioning system, the self-positioning measurement is the azimuth angle and elevation angle between the UAV and the anchor. Then, the expression of the true value of the self-positioning measurement with respect to the self-positioning parameters described in step 1 is:

[0031] where, where represents the true value of the azimuth angle between the UAV and the anchor at the -th moment, represents the true value of the elevation angle between the UAV and the anchor at the -th moment; respectively represent the components of the displacement of the UAV at the -th moment on the axis; represents the displacement of the UAV at the -th moment, represents the total number of moments; represents the modulus of the first two elements of the vector, represents matrix transpose, and its expression is:

[0032] Step 2: Set the positioning function of the built single-anchor UAV self-positioning system based on the true value of the self-positioning measurement, and prove that the built single-anchor UAV self-positioning system is observable; First, define the positioning function of the built single-anchor UAV self-positioning system according to the self-positioning parameters and the true value of the self-positioning measurement. Then, prove that the positioning function is an injective function with respect to the self-positioning parameters respectively. Finally, combining the surjective characteristics of the function, it is obtained that the positioning function is a bijective function with respect to the self-positioning parameters, that is, the built single-anchor UAV self-positioning system is observable.

[0033] The positioning function of the single-anchor UAV self-positioning system described in Step 2 is:

[0034] where and represent the positioning functions of the single-anchor UAV self-positioning system with respect to the azimuth angle and the pitch angle respectively, and their independent variables are , and the dependent variables are and ; The symbol represents a -dimensional vector, and represents the set of true values of the azimuth angle between the UAV and the anchor point at moments, and represents

[0035] the set of true values of the pitch angle between the UAV and the anchor point at moments. The process of the positioning function described in Step 2 being an injective function with respect to the self-positioning parameters is as follows: First, prove that is an injective function with respect to . For , assume that there exists a set of independent variables such that , that is, at time , the function values corresponding to

[0036] are all equal to the function value of

[0037] where represents the multiplier corresponding to the th moment. Then, simplifying the above formula gives:

[0038] Since is an independent arbitrary value, the condition for the above equation to hold is , , and hold simultaneously. According to the first sub-condition , that is the condition for is , Regarding is an injective function.

[0039] Then prove that Regarding is an injective function. Similarly, assume that there exists a drone position coordinate such that , then the following equation holds:

[0040] where , using multipliers to add the squares of the function values over time gives:

[0041] Since is an independent arbitrary value, the above equation is equal to , always holds, that is , Regarding is an injective function.

[0042] Finally, according to what is described in Step 1 , then and are surjective functions, then the positioning function is a bijective function with respect to the self-positioning parameters, that is, the single-anchor drone self-positioning system built is observable.

[0043] Step 3: Obtain the expression of the measured value of the self-positioning measurement based on the true value of the self-positioning measurement, then obtain the expression of the probability density function of the measured value of the self-positioning measurement according to the measurement noise distribution, and then establish the self-positioning problem of the original single-anchor drone self-positioning system based on the expression of the probability density function of the measured value of the self-positioning measurement; and construct the self-positioning problem of the equivalent single-anchor drone self-positioning system; The expression of the measured value of the self-positioning measurement described in Step 3 is:

[0044] where represents the measured value of the azimuth angle between the drone and the anchor point, Represents the pitch angle measurement value between the representative drone and the anchor point. Represents the azimuth measurement noise, whose covariance matrix is , Represents the covariance of the azimuth measurement noise at the first moment, Represents the Covariance of the azimuth measurement noise at the th moment; Represents the pitch angle measurement noise, whose covariance matrix is , Represents the covariance of the pitch angle measurement noise at the first moment, Represents the Covariance of the pitch angle measurement noise at the th moment.

[0045] The expression of the probability density function of the self - localization measurement value described in Step 3 is:

[0046] Where Represents the cost function, Represents the covariance set matrix of the azimuth measurement noise and the pitch angle measurement noise.

[0047] The self - localization problem of the original single - anchor - point UAV self - localization system described in Step 3 is:

[0048] Its meaning is: make Maximize the corresponding , which is the self - localization parameter sought for self - localization. Since Is monotonically decreasing with respect to the cost function , the self - localization problem of the original single - anchor - point UAV self - localization system can be equivalently:

[0049] Step 4: Solve the self - localization problem of the above - mentioned equivalent single - anchor - point UAV self - localization system based on the modified maximum - likelihood iterative algorithm to obtain the optimal self - localization parameter value and achieve UAV self - localization.

[0050] The specific steps of the modified maximum - likelihood iterative algorithm described in Step 4 are as follows: Step 4.1: Initialize the UAV self - localization parameter value , set the iteration threshold , and the number of iterations . And use the initialized UAV self - localization parameter value as the local point of the iteration; Step 4.2: In the th iteration, first let the initial position of the UAV Be the value corresponding to the local point of this iteration, that is For this iteration local point corresponding value, that is , the self - localization problem of the equivalent single - anchor UAV self - localization system can be transformed into a form, and this problem can be efficiently solved by maximum likelihood estimation to obtain the optimized value of the alignment angle of the UAV local coordinate system ; Step 4.3: In the th iteration, let the alignment angle of the UAV local coordinate system be the optimized value of this iteration, that is , then the self - localization problem of the equivalent single - anchor UAV self - localization system can be transformed into a form. Perform a convex approximation on the cost function to transform it into an upper - bound convex form , and solve the convex approximation problem through a convex optimization algorithm to obtain the optimized value of the initial position of the UAV ; Step 4.4: If the relative decrease of the objective function in this iteration compared to the previous objective function is less than the iteration threshold , stop the iteration, and the optimized value of this iteration is the value of the UAV self - localization parameter; otherwise, use it as the local point for the next iteration and return to Step 4.2.

[0051] Figure 3 The comparison of the Root Mean Square Error (RMSE) and the Cramer - Rao Lower Bound (CRLB) of the proposed self - localization scheme for different UAV displacements in the embodiments of the present invention is given. It can be seen that the RMSE of the proposed UAV self - localization scheme is extremely close to the CRLB theoretical performance, indicating good self - localization performance.

[0052] Embodiment 2 This embodiment provides a single - anchor observable UAV self - localization system, including: True value acquisition module: It is used to build a single - anchor UAV self - localization system based on the AOA positioning principle, set the self - localization parameters of the UAV self - localization system, deduce the expression of the true value of the self - localization measurement with respect to the self - localization parameters, and obtain the true value of the self - localization measurement; Positioning function construction module: It is used to set the positioning function of the built single - anchor UAV self - localization system based on the true value of the self - localization measurement, and prove that the built single - anchor UAV self - localization system is observable; Self - positioning problem construction module: It is used to obtain the expression of the measured value of the self - positioning measurement based on the true value of the self - positioning measurement, then obtain the expression of the probability density function of the self - positioning measurement value according to the measurement noise distribution, and further establish the self - positioning problem of the original single - anchor UAV self - positioning system based on the expression of the probability density function of the self - positioning measurement value; and construct the self - positioning problem of the equivalent single - anchor UAV self - positioning system. Solution module: It is used to solve the self - positioning problem of the equivalent single - anchor UAV self - positioning system, obtain the optimal self - positioning parameter value, and realize UAV self - positioning.

[0053] It should be understood that the parts not elaborated in detail in this specification all belong to the prior art.

[0054] It should be understood that the above description of the preferred embodiment is relatively detailed, and it should not be considered as a limitation to the protection scope of the invention patent. It is not necessary and impossible to enumerate all implementation manners here. Under the inspiration of the present invention, without departing from the scope protected by the claims of the present invention, those of ordinary skill in the art can also make substitutions or deformations, which all fall within the protection scope of the present invention. The scope of protection requested by the present invention shall be subject to the appended claims.

Claims

1. A self - positioning method for an unmanned aerial vehicle with a single anchor point observable, characterized in that, It includes the following steps: Step 1: Build a single-anchor UAV self-localization system based on the AOA localization principle, set self-localization parameters, derive the expression of the true value of self-localization measurement with respect to self-localization parameters, and obtain the true value of self-localization measurement; Step 2: Set the localization function of the built single-anchor UAV self-localization system based on the true value of the self-localization measurement, and prove that the built single-anchor UAV self-localization system is observable; Step 3: Obtain the expression of the self-localization measurement value based on the true value of the self-localization measurement, then obtain the probability density function expression of the self-localization measurement value according to the measurement noise distribution, and then establish the self-localization problem of the original single-anchor UAV self-localization system according to the probability density function expression of the self-localization measurement value; and construct the self-localization problem of the equivalent single-anchor UAV self-localization system; Step 4: Solve the self-localization problem of the equivalent single-anchor UAV self-localization system to obtain the optimal self-localization parameter value and achieve UAV self-localization.

2. The single-anchor-point observable UAV self-positioning method according to claim 1, characterized in that: In Step 1, the single-anchor UAV self-localization system includes an anchor point and a UAV that needs self-localization.

3. A single-anchor-point observable UAV self-localization method according to claim 1, characterized in that: The self-positioning parameters in step 1 are as follows: Among them, is the alignment angle of the UAV local coordinate system, and the initial position of the UAV is , where respectively represent the initial position coordinates of the UAV on the axis.

4. A method for self-positioning of an unmanned aerial vehicle with a single anchor point observable according to claim 3, characterized in that: The expression of the true value of the self-localization measurement with respect to the self-localization parameters in Step 1 is: Among them, among them represents the true value of the azimuth angle between the drone and the anchor point at the moment, represents the true value of the pitch angle between the drone and the anchor point at the moment; respectively represent the components of the drone displacement on the axis at the moment; represents the coordinate rotation matrix related to the alignment angle of the drone local coordinate system; represents the drone displacement at the moment, represents the total number of moments; represents the modulus of the first two elements of the vector, represents the matrix transpose.

5. The single-anchor-point observable UAV self-localization method according to claim 4, characterized in that: The localization function of the built single-anchor UAV self-localization system in Step 2 is: in, and Respectively represent the positioning functions of the single anchor UAV self-positioning system with respect to azimuth and pitch angle, and their independent variables are , the dependent variables are and ; The symbol represents a A vector of dimension, express The set of true values ​​of the azimuth angle between the drone and the anchor point at each moment, express The true value set of the pitch angle between the drone and the anchor point at each moment.

6. The single-anchor-point observable UAV self-positioning method according to claim 5, characterized in that: In Step 2, the method for proving that the built single-anchor UAV self-localization system is observable is as follows: Prove the orientation angle positioning function is a one-to-one function with respect to ; Prove the positioning function of the pitch angle is a mono-injective function; Proof and are surjective functions, then the positioning function is a bijective function with respect to the self-positioning parameters, that is, the built single-anchor UAV self-positioning system is observable.

7. A method for self - positioning of an unmanned aerial vehicle with a single anchor point observable according to claim 5, characterized in that: The expression of the self-localization measurement value in Step 3 is: wherein represents the azimuth measurement value between the UAV and the anchor point, represents the pitch angle measurement value between the UAV and the anchor point, represents the azimuth measurement noise; represents the pitch angle measurement noise.

8. A method for self-positioning of an unmanned aerial vehicle with a single anchor point observable according to claim 7, characterized in that: The probability density function expression of the self-localization measurement value in Step 3 is: Among them, is the expression of the probability density function of the self-positioning measurement value, represents the cost function, represents the covariance set matrix of the azimuth measurement noise and the pitch measurement noise; represents the covariance matrix of the azimuth measurement noise, represents the covariance of the azimuth measurement noise at the first moment, represents the covariance of the azimuth measurement noise at the represents the covariance matrix of the pitch measurement noise, represents the covariance of the pitch measurement noise at the first moment, represents the covariance of the pitch measurement noise at the The self-localization problem of the original single-anchor UAV self-localization system in Step 3 is: The self-localization problem of the original single-anchor UAV self-localization system is equivalent to: Among them, the corresponding to the maximization of is the self-positioning parameter sought by self-positioning.

9. A method for self - positioning of an unmanned aerial vehicle with a single anchor point observable according to claim 7, characterized in that: In Step 4, solving the self-localization problem of the equivalent single-anchor UAV self-localization system includes the following sub-steps: Step 4.

1. Initialize the UAV self-localization parameter values , set the iteration threshold , and the number of iterations , and use the initialized UAV self-localization parameter values as the local point of iteration; Step 4.2: In the th iteration, first set the initial position of the UAV to the value corresponding to the local point of this iteration, that is , and the self-positioning problem of the equivalent single-anchor UAV self-positioning system is transformed into in the form of, and solved by maximum likelihood estimation to obtain the optimized value of the alignment angle of the UAV local coordinate system; Step 4.3: In the th iteration, let the alignment angle of the UAV local coordinate system be the optimized value for this iteration, that is, , then the self-positioning problem of the equivalent single-anchor UAV self-positioning system is transformed into in the form of. For the cost function , perform a convex approximation to transform it into an upper-bound convex form . Solve the convex approximation problem through a convex optimization algorithm to obtain the optimized value of the initial position of the UAV; Step 4.4: If the relative decrease in the objective function in this iteration compared to the previous objective function is less than the iteration threshold , stop the iteration, and the optimized value of this iteration is the value of the UAV self-localization parameter; otherwise, it will be used as the local point for the next iteration and return to Step 4.

2.

10. A single-anchor-point observable UAV self-positioning system, characterized in that, It includes: True value acquisition module: It is used to build a single-anchor UAV self-localization system based on the AOA localization principle, set self-localization parameters, derive the expression of the true value of self-localization measurement with respect to self-localization parameters, and obtain the true value of self-localization measurement; Localization function construction module: It is used to set the localization function of the built single-anchor UAV self-localization system based on the true value of the self-localization measurement, and prove that the built single-anchor UAV self-localization system is observable; Self-localization problem construction module: It is used to obtain the expression of the self-localization measurement value based on the true value of the self-localization measurement, then obtain the probability density function expression of the self-localization measurement value according to the measurement noise distribution, and then establish the self-localization problem of the original single-anchor UAV self-localization system according to the probability density function expression of the self-localization measurement value; and construct the self-localization problem of the equivalent single-anchor UAV self-localization system; Solution module: It is used to solve the self-localization problem of the equivalent single-anchor UAV self-localization system to obtain the optimal self-localization parameter value and achieve UAV self-localization; The single-anchor observable UAV self-localization system is used to execute the steps in the single-anchor observable UAV self-localization method according to any one of claims 1-9.

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