Optimal geometric configuration method and its application in RSS source localization of UAV clusters

Abstract

The present invention discloses an optimal geometric configuration method for RSS source positioning of a drone cluster and its application. The method comprises the following steps: performing RSS measurement on a drone cluster under flight domain constraints to establish an optimal geometric configuration problem; in a hovering state, without considering flight altitude and horizontal distance, decomposing the optimal geometric configuration problem into conventional and unconventional cases according to framework theory, respectively establishing the optimal sensor-target geometry; then, considering domain constraints, determining the optimal geometric configuration scheme for the drone cluster in the hovering state through geometric and algebraic analysis; in low-speed and high-speed flight states, based on the optimal geometric configuration scheme in the hovering state, applying the sensor equivalence placement criterion and considering domain constraints, determining the optimal geometric configuration scheme for the drone cluster in low-speed and high-speed flight states. The method can be used to refine prior estimation results. The present invention greatly improves the accuracy of estimation results for RSS source positioning of drone clusters.

Description

Technical Field

[0001] The present invention relates to the fields of source positioning technology and unmanned aerial vehicle (UAV) positioning technology, and in particular to an optimal geometric configuration method for UAV cluster RSS source positioning and its application. Background Art

[0002] With the advancement of wireless communication and robotics technologies, the use of drone swarms for source positioning is playing an increasingly important role in ground-based mobile user positioning, disaster relief, wildlife tracking, and electronic warfare. Compared to traditional base station positioning and satellite positioning, drone positioning offers advantages such as ease of deployment and flexible deployment. Based on the specific drone positioning sensors, positioning technologies can be generally categorized as AOA positioning, TOA positioning, TDOA positioning, and RSS (Received Signal Strength) positioning. In practical applications, RSS positioning has the lowest requirements for hardware and wireless propagation environments, making it widely used.

[0003] For RSS source localization based on drone swarms, the optimal unbiased estimation error is determined by the Cramer-Rao bound (CRLB). The CRLB consists of two components: measurement conditions and intrinsic settings. Measurement conditions are related to the wireless propagation environment and the drone's sampling state, while intrinsic settings refer to the drone-target geometry. Therefore, finding the optimal measurement location for a drone swarm is of great significance.

[0004] Under unrestricted conditions, research on optimal RSS sensor placement in wireless sensor network localization has yielded promising results. In the paper "Optimal Sensor Placement for Target Localization and Tracking in 2D and 3D," the authors derive the optimal relative geometry between sensors and targets based on tight frame theory and propose an analytical method for finding the optimal sensor position, denoted as Algorithm 1. However, given the unique characteristics of UAV positioning, additional constraints must be considered, such as terrain restrictions and the safe distance between the UAV and the target. Furthermore, UAVs have the capability to measure while flying. Unlike straightforward sensor placement, the flight state of the UAV must also be considered. Given these considerations, optimizing the geometric configuration of UAV swarms for RSS source localization, within the flight domain constraints and under varying flight states, is crucial. Summary of the Invention

[0005] The purpose of the present invention is to provide an optimal geometric configuration method and its application in RSS source positioning of drone clusters, to find the optimal geometric configuration of drone clusters in RSS source positioning under domain constraints, and to re-evaluate the target position based on this configuration, thereby improving the accuracy of the estimation result.

[0006] The technical solution to achieve the purpose of the present invention is: an optimal geometric configuration method for UAV cluster RSS source positioning, including:

[0007] Step S1: perform RSS measurement on a UAV cluster under flight domain restrictions and establish an optimal geometric configuration problem to optimize the UAV measurement geometry settings;

[0008] Step S2: In the hovering state, without considering the flight altitude and horizontal distance, the optimal geometric configuration problem is decomposed into conventional and unconventional cases according to the framework theory, and the optimal sensor-target geometry is determined respectively. Then, considering the domain constraints, the optimal geometric configuration scheme of the UAV cluster in the hovering state is determined through geometric and algebraic analysis;

[0009] Step S3: In the low-speed flight state, based on the optimal geometric configuration scheme in the hovering state, the sensor equivalent placement criterion is applied, and domain restrictions are considered to determine the optimal geometric configuration scheme for the UAV cluster in the low-speed flight state;

[0010] Step S4: In the high-speed flight state, based on the optimal geometric configuration scheme in the hovering state, the sensor equivalence placement criterion is applied, and domain restrictions are considered to determine the optimal geometric configuration scheme for the UAV cluster in the high-speed flight state.

[0011] A method for locating RSS sources of a drone cluster includes the following steps:

[0012] Step 1: Based on the prior estimation, the target position of the initial evaluation is obtained and it is assumed that the target is located at this position;

[0013] Step 2: Based on the optimal geometric configuration method for UAV cluster RSS source positioning according to any one of claims 1 to 5, perform optimal geometric configuration of the UAV cluster;

[0014] Step 3: Perform RSS measurement and refine the prior evaluation based on the measurement results.

[0015] Compared with the existing technology, the present invention has the following significant advantages: (1) The optimal geometric configuration scheme for UAV cluster RSS measurement proposed follows the D-optimization criterion, that is, maximizing the determinant of the Fisher information matrix, and comprehensively considers the flight domain restrictions and flight status of the UAV, making the application scenarios of the scheme more extensive; (2) A variety of optimal UAV cluster geometric configuration schemes are proposed, which greatly improves the accuracy of the estimation results of UAV cluster RSS source positioning and can be used to refine the prior estimation results.

[0016] Additional aspects and advantages of the present invention will be set forth in part in the following description, will become apparent from the following description, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a specific implementation flow chart of the geometric configuration method of the present invention for refining prior estimates.

[0018] Figure 2 This is a schematic diagram of the optimal geometric setting scheme of the drone cluster of the present invention.

[0019] Figure 3 This is a performance result diagram of the optimal UAV cluster geometric setting solution of the present invention. DETAILED DESCRIPTION

[0020] This paper provides multiple optimal geometric configuration schemes for drone swarm RSS source positioning and their applications. In drone swarm positioning systems, the measured position of drones relative to the target significantly influences the final assessment accuracy. To this end, following the D-optimization criterion (maximizing the determinant of the Fisher information matrix), and considering flight area restrictions and the different flight states of drones, we propose multiple optimal drone swarm geometric configuration schemes.

[0021] The optimal geometric configuration method for UAV cluster RSS source positioning of the present invention includes:

[0022] Step S1: perform RSS measurement on a UAV cluster under flight domain restrictions and establish an optimal geometric configuration problem to optimize the UAV measurement geometry settings;

[0023] Step S2: In the hovering state, without considering the flight altitude and horizontal distance, the optimal geometric configuration problem is decomposed into conventional and unconventional cases according to the framework theory, and the optimal sensor-target geometry is determined respectively. Then, considering the domain constraints, the optimal geometric configuration scheme of the UAV cluster in the hovering state is determined through geometric and algebraic analysis;

[0024] Step S3: In the low-speed flight state, based on the optimal geometric configuration scheme in the hovering state, the sensor equivalent placement criterion is applied, and domain restrictions are considered to determine the optimal geometric configuration scheme for the UAV cluster in the low-speed flight state;

[0025] Step S4: In the high-speed flight state, based on the optimal geometric configuration scheme in the hovering state, the sensor equivalence placement criterion is applied, and domain restrictions are considered to determine the optimal geometric configuration scheme for the UAV cluster in the high-speed flight state.

[0026] Furthermore, the step S1 is specifically as follows:

[0027] The UAV cluster consists of N UAVs, which measure the RF signal strength emitted by the target radiation source on the ground; the total number of measurements of UAV i is recorded as M i , the position of UAV i in the jth measurement is U i,j =(x i,j ,y i,j ,z i,j ); the target’s position is unknown, recorded as s = (x, y, 0);

[0028] According to the electromagnetic wave propagation path loss model, the RSS value of drone i measured at the jth time is R i,j =p0-10γlg(d i,j )+η i,j ,d i,j =||sU i,j ||, where ||.|| represents the 2-norm, p0 is the target's transmit power, γ is the path loss factor of the signal propagation environment, and η i,j The mean is 0 and the variance is σ i Gaussian noise; it is assumed that the measurement noise between each UAV is independent of each other;

[0029] The Fisher information matrix characterizes the effective information content of the measurement. The Fisher information matrix, or FIM, is written as follows:

[0030]

[0031] in,

[0032]

[0033] Among them, β i,j The horizontal angle between the i-th UAV and the target is measured for the j-th time, that is,

[0034] In order to maximize the amount of effective information, the D-optimization criterion is adopted, that is, the UAV position U is set to maximize the determinant of F. i,j ; UAV position U i,jBy r i,j , β i,j and flight altitude h i,j The only certainty;

[0035] At the same time, the UAV cluster has the minimum flight height h0 and the minimum horizontal distance r0 conditions during the measurement process, that is, r i,j ≥r0,z i,j =h i,j ≥h0;

[0036] In summary, the problem of optimizing the geometry setup of UAV measurement is formulated as

[0037]

[0038] str i,j ≥r0,z i,j =h i,j ≥h0

[0039] Among them, r represents r i,j The set of β represents β i,j The set of h represents h i,j A collection of .

[0040] Furthermore, the step S2 is specifically as follows:

[0041] Assume that the UAV is in a hovering state during the positioning task, that is, the maximum speed of the UAV is c max = 0, for drone i, we get x i,j =x i ,y i,j =y i , j=1…M i ;

[0042] The FIM is simplified to:

[0043]

[0044] in,

[0045]

[0046] Among them, β i is the horizontal angle between the i-th UAV and the target during the measurement process, that is,

[0047] G is a 2-dimensional symmetric matrix, so

[0048]

[0049] Therefore, the objective of problem P is replaced by minimizing According to the tight frame theory, the relative geometry of the optimal UAV and the target is obtained; let It can be summarized into the following two theorems:

[0050] Theorem 1: If In normal circumstances, we get If and only if

[0051] Theorem 2: If This is an unusual situation, and we get If and only if i=1…N,i≠k;

[0052] At the same time, the optimal FIM determinant |F| in both conventional and unconventional cases is obtained. * regular 、|F| * irregular :

[0053]

[0054]

[0055] Based on the above theorem and the optimal FIM determinant, through geometric and algebraic analysis, the optimal solution to problem P is obtained, that is, the optimal geometric setting of the drone cluster;

[0056]

[0057] 1) When In the hovering state, the optimal geometric setting of the drone cluster satisfies

[0058]

[0059]

[0060] 2) When In the hovering state, the optimal geometric setting of the drone cluster satisfies

[0061] r i =max{r0,h0},h i =h0

[0062]

[0063] Where β0 is a constant.

[0064] Furthermore, the step S3 is specifically as follows:

[0065] The UAV is in a low-speed flight state and cannot complete the entire horizontal circle flight relative to the target, that is, Mi c max t0<2πr * , where c max is the maximum speed of the UAV, t0 is the time interval between two valid measurement intervals, and consider a normal case:

[0066] FIM is written

[0067]

[0068] Decompose the problem P into the optimal geometric setting of the UAV cluster at each measurement, that is, G j The geometric setting with the largest eigenvalue; G j For G in M i = 1, according to the optimal geometric setting under hovering, a set of analytical horizontal angles between the UAV cluster and the target are obtained, denoted as [β 1,0 ,β 2,0 ,…β N,0 ];

[0069] Assuming the drone is flying at speed c, combined with the global rotation equivalence theorem for optimal placement, we obtain the following optimal geometric setup:

[0070] r i,j =max{r0,h0},h i,j =h0

[0071]

[0072] The above setting is the optimal solution to problem P.

[0073] Furthermore, the step S4 is specifically as follows:

[0074] The UAV can complete the entire horizontal circle flight relative to the target, that is, M i c max t0≥2πr * , M i >2, FIM is written as

[0075]

[0076] The problem P is decomposed into the optimal geometric setting problem for each UAV when multiple measurements are taken, namely G i The problem of setting the maximum eigenvalue; for each UAV, uniform circular flight is the optimal geometry; let β 0,i is the starting horizontal angle of the i-th UAV; combined with the domain constraints, the optimal geometric setting scheme of the UAV cluster is:

[0077] r i,j=max{r0,h0},h i,j =h0

[0078]

[0079] The above construction is the optimal solution to problem P. Under this geometric setting, each UAV flies a full circle;

[0080] At the same time, according to the flip equivalence theorem of optimal placement, the flipped structure is equivalent when any number of sensor positions are flipped about the target; the geometric setting obtained by flipping some measurement points of the consistent circular flight is also optimal; based on this, another optimal geometric setting scheme is proposed, let K i To satisfy For any integer, the optimal geometric setting of the UAV cluster is:

[0081] r i,j =max{r0,h0},h i,j =h0,

[0082]

[0083]

[0084] Under the above settings, each drone performed a super-semicircle flight, but not a full circle flight.

[0085] The present invention proposes a method for locating the RSS source of a UAV cluster, comprising the following steps:

[0086] Step 1: Based on the prior estimation, the target position of the initial evaluation is obtained and it is assumed that the target is located at this position;

[0087] Step 2: Based on the optimal geometric configuration method in the RSS source positioning of the drone cluster, perform the optimal geometric configuration of the drone cluster;

[0088] Step 3: Perform RSS measurement and refine the prior evaluation based on the measurement results.

[0089] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0090] Example

[0091] 1. Model and parameters

[0092] The UAV cluster consists of N UAVs, which measure the RF signal strength emitted by the target radiation source on the ground. The total number of measurements of UAV i is M i The position of UAV i at the jth measurement is U i,j =(x i,j ,y i,j ,z i,j ). The target’s position is unknown and is recorded as s = (x, y, 0). According to the electromagnetic wave propagation path loss model, the RSS value of drone i in the jth measurement is R i,j =p0-10γlg(d i,j )+η i,j ,d i,j =||su i,j ||, ||.|| represents the 2-norm, p0 is the target transmission power, γ is the path loss factor of the signal propagation environment, η i,j The mean is 0 and the variance is σ i Gaussian noise. Change the coordinates of the drone's position and introduce r i,j ,h i,j ,β i,j ,in,

[0093]

[0094] At the same time, due to terrain and safety factors, the UAV cluster has a minimum flight altitude and a minimum horizontal distance, that is, r i,j ≥r0,z i,j =h i,j ≥h0. 2. Specific implementation methods

[0096] Assuming that the estimated target position is obtained through a priori evaluation, the drone cluster implements the optimal geometric configuration plan based on this evaluation. Figure 1 The specific implementation process is described.

[0097] First, the flight state of the UAV in the positioning task is judged, which is divided into hovering, low-speed flight, and high-speed flight, where hovering means the maximum speed of the UAV c max ≈0, low-speed flight means M i c max t0<2πmax{r0,h0}, high-speed flight indicates M i c max t0≥2πmax{r 0, h0}. For three different flight states, the corresponding optimal geometric setting solutions are assigned.

[0098] Figure 2 The following optimal UAV swarm geometry setup is described, Figure 2 Different grayscales represent different drones.

[0099] ①Hover, such as Figure 2 As shown in a:

[0100] make judge and The size relationship with

[0101] when The optimal measurement position of the drone cluster is: r i =max{r 0, h0}, Among them, β i The analytical expression can be directly obtained from the frame theory.

[0102] when The optimal measurement position of the drone cluster is:

[0103] ② Low-speed flight, such as Figure 2 As shown in b:

[0104] Satisfied by framework theory A set of analytical solutions for i = 1…N. The optimal UAV swarm geometry is set as: Among them, 0 <c≤c max .

[0105] ③ High-speed flight:

[0106] There are two equivalent optimal UAV cluster geometry settings. The first option is super semicircular flight, such as Figure 2 As shown in c; Option 2 is full circle flight, such as Figure 2 As shown in d. Let β 0,i is the starting relative horizontal angle of the i-th UAV to the target.

[0107] The super semicircle flight plan is: where K i Can be satisfied Any integer.

[0108] The full circle flight plan is:

[0109] In order to verify the practical effect of the present invention, the inventors carried out a simulation experiment in a real scenario. Figure 3The performance of these configurations varies with the magnitude of the prior estimation error. Assuming a preliminary estimate of the target position is obtained through the prior estimation, the drone swarm then re-evaluates the target using the optimal geometric configuration proposed by the inventors. A swarm of 15 drones performs RSS source localization of a ground target; each drone samples 16 samples, the horizontal distance between the drone and the preliminary estimated target is limited to 60 meters, and the drone flight altitude is limited to 100 meters. The measurement error variance for 10 drones is 12 dB, and the measurement error variance for 5 drones is 16 dB. As can be seen from the figure, the robustness of these optimal drone configurations for different flight states is ranked as follows: high-speed flight (full circle) > high-speed flight (super-semicircle) > low-speed flight > hovering. Furthermore, even in the presence of large prior estimation errors, the re-estimation performance of the drone swarm remains good under these configurations.

[0110] The present invention takes into account domain restrictions and the flight status of the drone, making the solution applicable to a series of practical scenarios, such as terrain restrictions and drone safety issues.

Claims

1. An optimal geometric configuration method for UAV cluster RSS source positioning, characterized by: include: Step S1: perform RSS measurement on a UAV cluster under flight domain restrictions and establish an optimal geometric configuration problem to optimize the UAV measurement geometry settings; Step S2: In the hovering state, without considering the flight altitude and horizontal distance, the optimal geometric configuration problem is decomposed into conventional and unconventional cases according to the framework theory, and the optimal sensor-target geometry is determined respectively. Then, considering the domain constraints, the optimal geometric configuration scheme of the UAV cluster in the hovering state is determined through geometric and algebraic analysis; Step S3: In the low-speed flight state, based on the optimal geometric configuration scheme in the hovering state, the sensor equivalent placement criterion is applied, and domain restrictions are considered to determine the optimal geometric configuration scheme for the UAV cluster in the low-speed flight state; Step S4: In the high-speed flight state, based on the optimal geometric configuration scheme in the hovering state, the sensor equivalence placement criterion is applied, and domain restrictions are considered to determine the optimal geometric configuration scheme for the UAV cluster in the high-speed flight state.

2. The optimal geometric configuration method for UAV cluster RSS source positioning according to claim 1 is characterized in that: The step S1 is specifically as follows: The UAV cluster consists of N UAVs, which measure the RF signal strength emitted by the target radiation source on the ground; the total number of measurements of UAV i is recorded as M i , the position of UAV i in the jth measurement is U i,j =(x i,j ,y i,j ,z i,j ); the target’s position is unknown, recorded as s = (x, y, 0); According to the electromagnetic wave propagation path loss model, the RSS value of drone i measured at the jth time is R i,j =p0-10γlg(d i,j )+η i,j ,d i,j =||sU i,j ||, where ||.|| represents the 2-norm, p0 is the target's transmit power, γ is the path loss factor of the signal propagation environment, and η i,j The mean is 0 and the variance is σ i Gaussian noise; it is assumed that the measurement noise between each UAV is independent of each other; The Fisher information matrix characterizes the effective information content of the measurement. The Fisher information matrix, or FIM, is written as follows: in, Among them, β i,j The horizontal angle between the i-th UAV and the target is measured for the j-th time, that is, In order to maximize the amount of effective information, the D-optimization criterion is adopted, that is, the UAV position U is set to maximize the determinant of F. i,j ; UAV position U i,j By r i,j , β i,j and flight altitude h i,j The only certainty; At the same time, the UAV cluster has the minimum flight height h0 and the minimum horizontal distance r0 conditions during the measurement process, that is, r i,j ≥r0,z i,j =h i,j ≥h0; In summary, the problem of optimizing the geometry setup of UAV measurement is formulated as s.t.r i,j ≥r0,z i,j =h i,j ≥h0 Among them, r represents r i,j The set of β represents β i,j The set of h represents h i,j A collection of .

3. The optimal geometric configuration method for UAV cluster RSS source positioning according to claim 2 is characterized in that: The step S2 is specifically as follows: Assume that the UAV is in a hovering state during the positioning task, that is, the maximum speed of the UAV is c max = 0, for drone i, we get x i,j =x i ,y i,j =y i , j=1…M i ; The FIM is simplified to: in, Among them, β i is the horizontal angle between the i-th UAV and the target during the measurement process, that is, G is a 2-dimensional symmetric matrix, so Therefore, the objective of problem P is replaced by minimizing According to the tight frame theory, the relative geometry of the optimal UAV and the target is obtained; let It can be summarized into the following two theorems: Theorem 1: If In normal circumstances, we get If and only if Theorem 2: If This is an unusual situation, and we get If and only if At the same time, the optimal FIM determinant |F| in both conventional and unconventional cases is obtained. * regular 、|F| * irregular : Based on the above theorem and the optimal FIM determinant, through geometric and algebraic analysis, the optimal solution to problem P is obtained, that is, the optimal geometric setting of the drone cluster; make 1) When In the hovering state, the optimal geometric setting of the drone cluster satisfies 2) When In the hovering state, the optimal geometric setting of the drone cluster satisfies r i =max{r0,h0},h i =h0 i=1…N,i≠k Where β0 is a constant.

4. The optimal geometric configuration method for UAV cluster RSS source positioning according to claim 3 is characterized in that: The step S3 is specifically as follows: The UAV is in a low-speed flight state and cannot complete the entire horizontal circle flight relative to the target, that is, M i c max t0<2πr * , where c max is the maximum speed of the UAV, t0 is the time interval between two valid measurement intervals, and consider a normal case: FIM is written Decompose the problem P into the optimal geometric setting of the UAV cluster at each measurement, that is, G j The geometric setting with the largest eigenvalue; G j For G in M i = 1, according to the optimal geometric setting under hovering, a set of analytical horizontal angles between the UAV cluster and the target are obtained, denoted as [β 1,0 ,β 2,0 ,…β N,0 ]; Assuming the drone is flying at speed c, combined with the global rotation equivalence theorem for optimal placement, we obtain the following optimal geometric setup: r i,j =max{r 0, h0},h i,j =h0 The above setting is the optimal solution to problem P.

5. The optimal geometric configuration method for UAV cluster RSS source positioning according to claim 4 is characterized in that: The step S4 is specifically as follows: The UAV can complete the entire horizontal circle flight relative to the target, that is, M i c max t0≥2πr * , M i >2, FIM is written as The problem P is decomposed into the optimal geometric setting problem for each UAV when multiple measurements are taken, namely G i The problem of setting the maximum eigenvalue; for each UAV, uniform circular flight is the optimal geometry; let β 0,i is the starting horizontal angle of the i-th UAV; Combined with domain restrictions, the optimal geometric setting scheme for drone clusters is: r i,j =max{r 0, h0},h i,j =h0 The above construction is the optimal solution to problem P. Under this geometric setting, each UAV flies a full circle; At the same time, according to the flip equivalence theorem of optimal placement, the flipped structure is equivalent when any number of sensor positions are flipped about the target; the geometric setting obtained by flipping some measurement points of the consistent circular flight is also optimal; based on this, another optimal geometric setting scheme is proposed, let K i To satisfy For any integer, the optimal geometric setting of the UAV cluster is: r i,j =max{r 0, h0},h i,j =h0, Under the above settings, each drone performed a super-semicircle flight, but not a full circle flight.

6. A method for locating RSS sources of drone clusters, characterized in that: The following steps are involved: Step 1: Based on the prior estimation, the target position of the initial evaluation is obtained and it is assumed that the target is located at this position; Step 2: Based on the optimal geometric configuration method for UAV cluster RSS source positioning according to any one of claims 1 to 5, perform optimal geometric configuration of the UAV cluster; Step 3: Perform RSS measurement and refine the prior evaluation based on the measurement results.

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