A method and system for bearing-only passive positioning of unmanned aerial vehicles during formation flight

Abstract

The present invention provides a pure bearing passive positioning method and system for unmanned aerial vehicles performing formation flight, the method comprising: passively receiving a signal transmitted by a signal transmitting unmanned aerial vehicle for the unmanned aerial vehicle to be positioned; wherein, when each unmanned aerial vehicle in a circular formation has a fixed number, the unmanned aerial vehicle at the center of the circle and any two unmanned aerial vehicles on the circumference of the circle in the circular formation are used as signal transmitting unmanned aerial vehicles, and the unmanned aerial vehicles at other positions passively receive signals; based on the received signal and a pre-constructed passive signal receiving unmanned aerial vehicle positioning model, the position of the signal receiving unmanned aerial vehicle is obtained; wherein, the passive signal receiving unmanned aerial vehicle positioning model is specifically as follows: a first auxiliary circle and a second auxiliary circle are respectively constructed with a line connecting the unmanned aerial vehicle at the center of the circle to two other selected unmanned aerial vehicles as a chord; based on the fixed-length and fixed-angle hidden circle principle, standardized equations of the first auxiliary circle and the second auxiliary circle are respectively constructed, and the passive signal receiving unmanned aerial vehicle positioning model is obtained by combining the equations.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative control of unmanned aerial vehicles, and in particular, relates to a method and system for pure bearing passive positioning of unmanned aerial vehicles in formation flight. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] The coordinated formation of drones is the main force of future intelligent military operations and one of the most important new combat technologies emerging on the intelligent battlefield. Its characteristics of zero flexibility, maneuverability, easy adjustment, and low energy consumption play a vital role in information warfare, especially in the coordinated reconnaissance, tracking, rounding up, attacking, and intercepting of drone groups. With the development of high-tech means such as wireless communication technology and radar equipment, the realization of drone formation flight through passive positioning technology is a key technology with scientific significance and challenges.

[0004] Passive positioning technology can quickly locate the radar position through reconnaissance warfare distributed in different locations, so as to obtain detailed information, which is particularly important for modern electronic warfare in the era of informatization, intelligence and networking; on the other hand, small drones with low flying altitude and slow speed are no longer suitable for high-density complex electromagnetic environments. Although traditional active positioning uses radar, laser, sonar and other equipment to locate the target in real time with high stability and high accuracy, such high-frequency transmission and reception of signals are not conducive to the concealment of combat, and it is easy to expose one's own position, so that it can be detected by the opponent's passive detection system, take electronic defense measures, and be interfered with. The inventor found that most of the existing positioning technologies are based on active positioning, that is, the user terminal needs to send a radio positioning application signal to the navigation satellite, and the navigation satellite then forwards this signal to the ground control center, which sends a ranging signal, and performs positioning settlement at the ground control center according to the time of signal transmission, and then sends the positioning information to the user terminal. Passive positioning technology is a high-precision technology that uses equipment to locate targets without emitting electromagnetic waves but receiving radio signals. Compared with active positioning, passive positioning technology is more accurate and has a larger coverage range. It is a key technology for winning future weaponized and informationized wars. However, the existing passive positioning technology is only in the research stage and no specific implementation plan has been given yet. Summary of the invention

[0005] In order to solve the above-mentioned problems, the present disclosure provides a method and system for pure bearing source positioning in formation flight of unmanned aerial vehicles. The scheme adopts a pure bearing passive positioning method to adjust the positions of unmanned aerial vehicles in a formation of unmanned aerial vehicles, that is, some unmanned aerial vehicles in the formation transmit signals, and the remaining unmanned aerial vehicles passively receive signals, and the bearing information is extracted therefrom for positioning, so as to adjust the positions of the unmanned aerial vehicles. The scheme ensures the coordinated stability of the unmanned aerial vehicle formation while avoiding the problem of position exposure due to high-frequency transmission and reception of signals.

[0006] According to a first aspect of an embodiment of the present disclosure, a method for bearing-only passive positioning in formation flight of unmanned aerial vehicles is provided, which is applied to a circular formation formed by a plurality of unmanned aerial vehicles, wherein the circular formation is composed of a central unmanned aerial vehicle and unmanned aerial vehicles evenly distributed on the circumference, and the method comprises:

[0007] The UAV to be located passively receives the signal transmitted by the UAV that transmits the signal; wherein, when each UAV in the circular formation has a fixed number, the UAV that transmits the signal needs to meet the following constraints: the UAV at the center of the circular formation and any two UAVs on the circumference are used as the UAV that transmits the signal, and the UAVs at other positions passively receive the signal;

[0008] Based on the received signal and the pre-built passive signal receiving drone positioning model, the position of the receiving signal drone is obtained;

[0009] Among them, the passive signal receiving drone positioning model is specifically:

[0010] The first auxiliary circle and the second auxiliary circle are respectively constructed with the line from the drone at the center of the circle to the other two selected drones as the chord;

[0011] Based on the principle of fixed-length and fixed-angle hidden circle, the standardized equations of the first auxiliary circle and the second auxiliary circle are constructed respectively, and the passive reception signal UAV positioning model is obtained by combining the equations.

[0012] Furthermore, the first auxiliary circle and the second auxiliary circle are respectively constructed with the lines from the drone at the center of the circle to the other two selected drones as chords, wherein only two circles exist such that the intersection of the first auxiliary circle and the second auxiliary circle is located at the position of the drone to be located.

[0013] Furthermore, when only the drone at the center of the circle and one drone on the circumference have numbers and serve as signal transmitting drones, no less than two additional drones with unknown numbers are required to serve as signal transmitting drones.

[0014] Furthermore, the passive signal receiving drone positioning model is specifically expressed as follows:

[0015]

[0016] Among them, R is the radius of the UAV circular formation; α 1 is the circular angle subtended by the chord corresponding to the first auxiliary circle; α 2 is the circular angle subtended by the chord corresponding to the second auxiliary circle; θ 2 is the angle between the chord corresponding to the first auxiliary circle and the positive direction of the x-axis; θ 2 ' is the angle formed by the chord corresponding to the second auxiliary circle and the positive direction of the x-axis.

[0017] According to a second aspect of an embodiment of the present disclosure, a bearing-only passive positioning system for drones performing formation flight is provided, which is applied to a circular formation formed by a number of drones, wherein the circular formation is composed of a central drone and drones evenly distributed on the circumference, and the method comprises:

[0018] A signal receiving unit, which is used to passively receive the signal transmitted by the signal transmitting drone for the drone to be located; wherein, when each drone in the circular formation has a fixed number, the signal transmitting drone must meet the following constraints: the drone at the center of the circular formation and any two drones on the circumference are used as signal transmitting drones, and the drones at other positions passively receive signals;

[0019] A positioning unit, which is used to obtain the position of the receiving signal drone based on the received signal and a pre-built passive receiving signal drone positioning model;

[0020] Among them, the passive signal reception UAV positioning model is specifically as follows: the first auxiliary circle and the second auxiliary circle are respectively constructed with the line connecting the UAV at the center of the circle to the other two selected UAVs as the chord; based on the fixed-length and fixed-angle implicit circle principle, the standardized equations of the first auxiliary circle and the second auxiliary circle are respectively constructed, and the passive signal reception UAV positioning model is obtained by combining the equations.

[0021] According to a third aspect of an embodiment of the present disclosure, there is provided an electronic device comprising a memory, a processor and a computer program stored and running on the memory, wherein when the processor executes the program, the method for pure bearing passive positioning of unmanned aerial vehicles performing formation flight is implemented.

[0022] According to a fourth aspect of an embodiment of the present disclosure, a non-transitory computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the method for pure bearing passive positioning of unmanned aerial vehicles performing formation flight is implemented.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] (1) The present disclosure provides a method and system for pure bearing source positioning of drones in formation flight. The scheme adopts a pure bearing passive positioning method to adjust the positions of drones in a drone formation, that is, some drones in the formation transmit signals, and the remaining drones passively receive signals, and extract bearing information from them for positioning, so as to adjust the positions of the drones. The scheme ensures the coordinated stability of the drone formation while avoiding the problem of position exposure due to high-frequency transmission and reception of signals.

[0025] (2) The pure azimuth source positioning method disclosed in the present invention does not require real-time acquisition of the accurate positions of the drone itself and surrounding drones. By acquiring the relative positions of surrounding drones and applying the fixed-length fixed-angle implicit circle principle (i.e., a fixed-size circle is implied when an angle of a fixed degree is facing a line segment of a fixed length), the drone's position can be accurately calculated. At the same time, when the drone deviates from the predetermined track, the error index can be constrained and adjusted to adjust the drone to the precise expected location.

[0026] Advantages of additional aspects of the present disclosure will be given in part in the following description and in part will become apparent from the following description or will be learned through practice of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0028] Figure 1 This is a schematic diagram of direction information received by the drone described in the embodiment of the present disclosure;

[0029] Figure 2 A schematic diagram of a circular UAV formation described in an embodiment of the present disclosure;

[0030] Figure 3 It is a flow chart of the bearing-only passive positioning method for UAVs performing formation flight described in the embodiment of the present disclosure;

[0031] Figure 4 It is a schematic diagram of a positioning model of a UAV that passively receives signals as described in an embodiment of the present disclosure;

[0032] Figure 5 A schematic diagram for determining the position of the center of a circle in an embodiment of the present disclosure;

[0033] Figure 6 A schematic diagram for determining the radius of a circle described in an embodiment of the present disclosure;

[0034] Figure 7 is the angle θ described in the embodiment of the present disclosure 1 Schematic diagram of determination;

[0035] Figure 8 is the center coordinate (x) of circle 1 (i.e., the first auxiliary circle) described in the embodiment of the present disclosure. 1 ,y 1 ) is determined schematically;

[0036] Fig. 9 Schematic diagram of solving circle 2 (i.e., the second auxiliary circle) described in the embodiment of the present disclosure;

[0037] Fig.10 This is an interface display diagram of the theoretical values ​​of max x, min x, max y and min y obtained by running LINGO described in the embodiments of the present disclosure;

[0038] Fig.11 It is a polar coordinate schematic diagram of the drone formation described in the embodiment of the present disclosure;

[0039] Fig.12 It is a schematic diagram of a trajectory with a deviation angle described in an embodiment of the present disclosure;

[0040] FIG. 13( a ) is a diagram of the Q 1 To Q n Position coordinates LINGO operation result interface display diagram;

[0041] FIG. 13( b ) is a diagram of the Q 1 To Q n Schematic diagram of position coordinate running trajectory results;

[0042] Fig.14 It is a schematic diagram of positioning five angles in scenario 1 in the embodiment of the present disclosure. DETAILED DESCRIPTION

[0043] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0044] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0045] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0046] In the absence of conflict, the embodiments in the present disclosure and the features in the embodiments may be combined with each other.

[0047] Embodiment 1:

[0048] The purpose of this embodiment is to provide a pure bearing passive positioning method for UAVs performing formation flight.

[0049] A method for pure bearing passive positioning in formation flight of unmanned aerial vehicles is applied to a circular formation formed by a number of unmanned aerial vehicles, wherein the circular formation is composed of a central unmanned aerial vehicle and unmanned aerial vehicles evenly distributed on the circumference, and the method comprises:

[0050] The UAV to be located passively receives the signal transmitted by the UAV that transmits the signal; wherein, when each UAV in the circular formation has a fixed number, the UAV that transmits the signal needs to meet the following constraints: the UAV at the center of the circular formation and any two UAVs on the circumference are used as the UAV that transmits the signal, and the UAVs at other positions passively receive the signal;

[0051] Based on the received signal and the pre-built passive signal receiving drone positioning model, the position of the receiving signal drone is obtained;

[0052] Among them, the passive signal receiving drone positioning model is specifically:

[0053] The first auxiliary circle and the second auxiliary circle are respectively constructed with the line from the drone at the center of the circle to the other two selected drones as the chord;

[0054] Based on the principle of fixed-length and fixed-angle implicit circle (that is, when an angle of fixed degree faces a line segment of fixed length, a circle of fixed size is implied), the standardized equations of the first auxiliary circle and the second auxiliary circle are constructed, and the passive reception signal UAV positioning model is obtained by combining the equations.

[0055] Furthermore, the first auxiliary circle and the second auxiliary circle are respectively constructed with the lines from the drone at the center of the circle to the other two selected drones as chords, wherein only two circles exist such that the intersection of the first auxiliary circle and the second auxiliary circle is located at the position of the drone to be located.

[0056] Furthermore, when only the drone at the center of the circle and one drone on the circumference have numbers and serve as signal transmitting drones, no less than two additional drones with unknown numbers are required to serve as signal transmitting drones.

[0057] Furthermore, the passive signal receiving drone positioning model is specifically expressed as follows:

[0058]

[0059] Among them, R is the radius of the UAV circular formation; α1 is the circular angle subtended by the chord corresponding to the first auxiliary circle; α 2 is the circular angle subtended by the chord corresponding to the second auxiliary circle; θ 2 is the angle between the chord corresponding to the first auxiliary circle and the positive direction of the x-axis; θ 2 ' is the angle formed by the chord corresponding to the second auxiliary circle and the positive direction of the x-axis.

[0060] Specifically, the solution described in this embodiment is described in detail below with reference to the accompanying drawings:

[0061] In order to maintain the formation of the drone formation, the solution described in this embodiment adjusts the position of the drone by adopting a pure azimuth passive positioning method, that is, a few drones in the formation transmit signals, and the remaining drones passively receive signals, from which azimuth information is extracted for positioning, so as to adjust the position of the drone.

[0062] For convenience, the solution described in this embodiment needs to meet the following assumptions:

[0063] (1) The relative position relationship with other UAVs in the formation remains unchanged;

[0064] (2) Eliminate low-probability events, such as the impact of bad weather on the flight location;

[0065] (3) There are no interference factors that may cause errors in the numerical values ​​during the transmission and reception of directional information;

[0066] (4) The deviation of the drone with a slight deviation in position is negligible;

[0067] (5) The transmitter transmits signals in the order from smallest to largest numbers.

[0068] Further, for the convenience of description, the following are the definitions of relevant symbols;

[0069]

[0070]

[0071] In the scheme described in this embodiment, Figure 1 As shown, first assume that each drone in the formation has a fixed number, and the relative position relationship with other drones in the formation remains unchanged; the direction information received by the drone receiving the signal is agreed to be: the angle between the drone and the line connecting any two drones transmitting the signal. For example: drones numbered FY01, FY02 and FY03 transmit signals, and the direction information received by the drone numbered FY04 is α1, α2, α3. Below, the scheme described in this embodiment is explained separately based on different drone formation situations:

[0072] Scenario 1: Pure bearing passive positioning method for UAV circular formation (taking a circular formation of ten UAVs as an example)

[0073] like Figure 2 As shown in the figure, let the FY00 drone be located at the center of the circle, among which 9 drones (numbered FY01-FY09) are evenly distributed on a certain circumference. When the drone (FY00) located at the center of the circle and the other two drones in the formation transmit signals, the remaining drones with slightly deviated positions passively receive signals. When the position of the drone transmitting the signal is not deviated and the number is known, a passive signal receiving drone positioning model can be established to determine the position of the drone receiving the signal. Specifically:

[0074] First, establish an XY-axis plane rectangular coordinate system to simplify the model; three drones are needed to transmit information, of which one FY00 located at the center of the circle is used. Therefore, it is necessary to select two more drones on the circumference to transmit signals. The solution described in this embodiment selects FY03 and FY09; then, a positioning model for the drone that passively receives signals is established based on the signals transmitted by the three determined drones; assuming that the drone to be determined is numbered FY02, use the fixed-length and fixed-angle implicit circle principle in geometric problems to establish a mathematical model of the circle where the signal receiver FY02 is located. By solving the geometric expressions of circle 1 and circle 2 together, their coordinates in the rectangular coordinate system are obtained, and finally a positioning model is established. Figure 3 As shown, the solution ideas are as follows:

[0075] Step 1: In order to simplify the model in the scheme described in this example, first establish a plane rectangular coordinate system with FY00 as the origin (O), FY01 as the X-axis, and the direction perpendicular to X as the Y-axis.

[0076] The plane rectangular coordinate system is based on the number axis, which is composed of two mutually perpendicular number axes with the same origin. It can simplify complex mathematical models, embody the mutual transformation between modern mathematical problems and geometric problems, and make the analysis and solution process of geometric problems more intuitive and visual.

[0077] Step 2: Use drones FY00, FY03 and FY09 to build a positioning model for drone FY02 that passively receives signals. Figure 4 As shown, specifically:

[0078] The steps to establish a positioning model for a passive signal receiving drone are as follows:

[0079] ① Connect the center of the circle and FY03 and FY09 to form two line segments L1 and L2.

[0080] ② Use L1 and L2 as chords to draw circles 1 and 2 respectively. There are countless circles passing through the chords, but there are only two circles that satisfy the condition that the intersection of the two circles is in FY02.

[0081] ③ Establish the geometric expressions of circle 1 and circle 2 to form a system of equations, and solve the system of equations to obtain the coordinates of the intersection, which is the FY02 positioning point required in the question. At this point, the positioning model of the passive signal receiving drone is completed.

[0082] Step 3: Solving the Geometry Model

[0083] In the process of solving the model, it is necessary to find the geometric expressions of circle 1 and circle 2 based on the relationship between the perpendicular bisector and the internal angle of the triangle, the sine and cosine theorems and other knowledge, and then solve the equations together to obtain the coordinates of FY02.

[0084] (I) Establishment of the standardized equations of circles 1 and 2

[0085] First, take circle 1 as an example, the establishment process is as follows:

[0086] ① Find the center of the circle (C 1 )

[0087] like Figure 5 As shown, because in the same circle, the circumferential angle subtended by the same arc is equal to half of the central angle, so let the circumferential angle subtended by arc L1 be α 1 (α 1 It is known that is the direction information received by the drone), draw the perpendicular bisector of the chord segment L1, and find a point on the perpendicular bisector such that the angle between it and the arc L1 is equal to 2α 1 , then this point is the center point C of circle 1 1 , the opposite angle is the central angle of the circle.

[0088] ②Determination of the radius of the circle (r1)

[0089] like Figure 6 As shown, let the radius of the circle where the drones are evenly distributed in the rectangular coordinate system be R, the radius of circle 1 be r1, the intersection point of the perpendicular line of chord L1 and the chord be P, and in the triangle ΔOPC 1 , ∠OPC 1 is the angle between the perpendicular bisector and the chord L1, so the triangle is a right triangle, ∠PC 1 O is α 1 , OP and OC 1 Satisfies the law of sines:

[0090]

[0091] From this we can find:

[0092]

[0093] ③OC 1 The angle θ formed with the positive direction of the x-axis 1Determination

[0094] like Figure 7 As shown in the question, we know that the circular angle is α 1 , through the relationship between the central angle and the circumference angle twice, we can get:

[0095] ∠OC 1 P=α 1 (3)

[0096] Since the sum of the interior angles of a right triangle is 180°, we can obtain:

[0097]

[0098] Below is the OC 1 The angle θ formed with the positive direction of the x-axis 1 , the angle between line segment L1 and the positive direction of the x-axis is θ 2 , the following formula is obtained from the angle relationship:

[0099]

[0100] ④ Coordinates of the center of the circle (x 1 ,y 1 )

[0101] like Figure 8 As shown, let the center of the circle (C 1 ) is (x 1 ,y 1 ), draw a perpendicular line from the center of the circle to the negative direction of the Y axis to obtain a right triangle. From the sine and cosine formulas of a right triangle, we get:

[0102] x 1 = r1cosθ 1 (6)

[0103] y 1 =r1sinθ 1 (7)

[0104] ⑤ Combine the equations to get the normalized equation of a circle

[0105]

[0106] ⑥ Similarly, we get the standardized equation of circle 2

[0107] like Fig. 9 As shown, let the circular angle subtended by arc L2 be α 2 , let the center of the circle be (C 2 ), the angle between the center of the circle and the coordinate axis is θ 2 ', the remaining conditions are the same as those of circle 1, and the standardized equation of circle 2 is as follows:

[0108]

[0109] Step 4: Solve the equations of circles 1 and 2 simultaneously:

[0110] Combining the equations of circle 1 and 2, the formula is as follows:

[0111]

[0112] The quadratic nonlinear equation generally has multiple solutions. In order to obtain a unique solution that meets the conditions (the coordinate position of FY02), the range of the solution needs to be constrained. Draw a circle with radius , the actual position of FY01 is (x0, y0), and the ideal position of FY01 is (R, 0). As can be seen from the question, there is a slight deviation between the actual position of the drone and the ideal position, so the distance between the two points is required to be less than the radius of the circle. That is, the solution satisfies the following neighborhood 1 conditions:

[0113]

[0114] The solution obtained by numerical simulation software is: the coordinates of FY01 are (0.8585, 0.7517).

[0115] Scenario 2: Bearing-only passive positioning method for a circular formation of drones with unknown numbers

[0116] A drone with a slightly deviated position receives signals from drones numbered FY00 and FY01, and also receives signals from several drones with unknown numbers in the formation. If the position of the drone transmitting the signal is not deviated, in addition to FY00 and FY01, it is determined that several more drones need to transmit signals to achieve effective positioning of the drone.

[0117] Step 1: Model building

[0118] ① Establishment of constraints

[0119] Code Notes:

[0120] Assume that the number of the located drone is q, and the number of the signal transmitting drone is n i , α i For q and n i The angle of To determine the pitch angle of the signal transmitting drone, To send a signal to a drone i The radius of the circle, To send a signal to a drone i The horizontal axis of To send a signal to a drone iThe ordinate of the object, (x, y) is the coordinate of q, R is the center of the flying circle, i = 1, 2, 3, β ij n i , n j The angle with q, d ij n i , n j The distance between.

[0121] Because the essential method of establishing different circles is the same, this embodiment is based on Figure 4 The example solves a circle.

[0122] First, make n i The perpendicular bisector of the chord, and then according to the relevant knowledge of the circle, half of the central angle on the same chord is equal to the circumference angle on this chord, so according to the sine and cosine relationship of right triangles, we can get:

[0123]

[0124] From the positional relationship of the argument (i.e. the difference between a certain angle and 360°), we can get the value of n i The slope of the equation of the straight line at the center of the circle is:

[0125]

[0126] The slope obtained from equation (13) can be used to calculate the equation of the straight line locating the center of the circle:

[0127]

[0128] If you want to determine the center of the circle where the positioning circle is located, you need to add another condition, that is, the distance from the center to the origin is equal to the square of the radius:

[0129]

[0130] According to formula (14) (15), the standard equation of the circle can be determined:

[0131]

[0132] Since q is the intersection of several circles, the coordinates of q satisfy equation (16):

[0133]

[0134] To determine the specific location of the located drone, the condition of slight position deviation must be met first:

[0135] (xx q ) 2 +(yy q ) 2 <ε (18)

[0136] The cosine value of the UAV that transmits information and the UAV that receives information:

[0137]

[0138] It should be noted that: i ∈{2, 3, 4, 5, 6, 7, 8, 9},

[0139] ②Establishment of objective function

[0140] 1.maxx 2.minx (21)

[0141] 3.max y 4.min y

[0142] If 1=2 and 3=4, then the intersection point determined by several circles is not only unique but also within the neighborhood of the theoretical value, and the number of required drones can also be determined.

[0143] Step 2: LINGO program running results of the model

[0144] The program first solves the feasible solution and verifies the existence of the solution. Then, two different objective functions are added to the LINGO program to respectively find the minimum and maximum values ​​of the horizontal coordinate of the positioning. The running results show that the minimum and maximum values ​​are equal, and the same result can be obtained for the vertical coordinate, thus verifying the uniqueness of the solution. Therefore, the final conclusion is to select two other drones to locate a certain drone.

[0145] Input three groups of data into the LINGO program respectively, taking 2, 6, and 8 as examples. After running, input the code of the located UAV in the input box. By solving the final result according to the LINGO program, it can be found that the codes of the auxiliary positioning UAVs 1 and 2 can be obtained, and they are consistent with the codes of the auxiliary positioning UAVs in the three groups of data randomly generated by the numerical simulation software, proving that at least two more UAVs need to transmit signals to achieve effective positioning of the UAV.

[0146] Depend on Fig.10 It can be seen that max x=min x=0.174633, max y=min y=-0.984634, which means that the intersection point determined by several circles is not only unique but also within the neighborhood of the theoretical value, and the number of required drones can also be determined.

[0147] Scenario 3: Drone Position Adjustment Strategy

[0148] The goal of the drone position adjustment strategy is: according to the formation requirements, one drone is located at the center of the circle, and the other 9 drones are evenly distributed on the circumference of a preset radius (the scheme described in this embodiment is set to 100m). When the position of the drone is slightly deviated at the initial moment, a reasonable drone position adjustment scheme needs to be given, that is, through multiple adjustments, each time the drone numbered FY00 and a maximum of 3 drones on the circumference are selected to transmit signals, and the remaining drones are adjusted to the ideal position according to the received direction information so that the 9 drones are finally evenly distributed on a certain circumference.

[0149] Table 1 Initial position of the UAV

[0150] Drone Number Polar coordinates (m,°) 0 (0，0) 1 (100，0) 2 (98，40.10) 3 (112，80.21) 4 (105，119.75) 5 (98，159.86) 6 (112，199.96) 7 (105，240.07) 8 (98，280.17) 9 (112，320.28)

[0151] As shown in Table 1, according to the pre-set, the UAV transmitting the information selects FY00 and determines Fig.11 As shown in the polar coordinate diagram, another UAV transmitting information is FY01 because it is at the correct position on the circumference. The determination of the last UAV is arbitrary. This embodiment assumes that the determined one is UAV FY06.

[0152] Step 1: Determination of trajectory with deviation angle

[0153] Because during the flight of the drone, the drone must be repositioned after a continuous period of time Δt, because during the flight, as time goes by, there is a certain deviation δ between the actual navigation track and the ideal navigation track. In order to calculate a more accurate numerical solution, this embodiment sets the deviation δ, and the numerical simulation software can depict the trajectory of each deviation δ. The specific steps are as follows:

[0154] ① The line segment connecting the initial point and the end point of the located drone Q is first divided into 10 equal parts, and then a circular neighborhood with a radius of 0.01 is made. Then a point is randomly selected in the circular neighborhood as the next located drone Q after Δt time 1 location;

[0155] ②Connect Q 1 The line segment with the end point is divided into 9 equal parts, and then a circular neighborhood with a radius of 0.01 is made. Then a point is randomly selected in the circular neighborhood as the next located drone Q after 2Δt time. 2 location;

[0156] ③ Continue to divide according to this rule until you reach a turning point, which is when the original uniform speed changes to deceleration motion, and record it as Q m , each time divided into 2 equal parts, until the position becomes Q n And the next Δt finally flies to the end point.

[0157] Its specific trajectory is as follows Fig.12 As shown, the final arrival position is 0.0284 meters away from the expected position.

[0158] Step 2: Q 1 To Q n Establishment of location coordinates

[0159] Q 1 To Q n The establishment of the position coordinates can refer to the scheme of situation 1 (the method of pure bearing passive positioning of a circular formation of unknown numbered UAVs). The results of running in the numerical simulation software are shown in Figures 13(a) and 13(b).

[0160] Simplified idea for scenario 3:

[0161] Step 1: Substitute the degrees of the five known angles (α 1 ,α 2 ,α 3 ,β 1 ,β 2 )like Fig.14 ;

[0162] Step 2: Establish the equation and intersection point of the circle based on the chord;

[0163] Step 3: Substitute the intersection point into the preset error constraint conditions to see if they meet the requirements, thereby determining the specific location of the drone.

[0164] Figure 13(b) shows the actual motion trajectory (dark color) and positioning trajectory (light color) of the UAV. As shown in Figure 13(b), the overall deviation between the two is not large, which can be regarded as effective positioning.

[0165] Embodiment 2:

[0166] The purpose of this embodiment is to provide a pure bearing passive positioning system for unmanned aerial vehicles performing formation flight.

[0167] A pure bearing passive positioning system for UAVs performing formation flight is applied to a circular formation formed by a number of UAVs, wherein the circular formation is composed of a central UAV and UAVs evenly distributed on the circumference. The method comprises:

[0168] A signal receiving unit, which is used to passively receive the signal transmitted by the signal transmitting drone for the drone to be located; wherein, when each drone in the circular formation has a fixed number, the signal transmitting drone must meet the following constraints: the drone at the center of the circular formation and any two drones on the circumference are used as signal transmitting drones, and the drones at other positions passively receive signals;

[0169] A positioning unit, which is used to obtain the position of the receiving signal drone based on the received signal and a pre-built passive receiving signal drone positioning model;

[0170] Among them, the passive signal reception UAV positioning model is specifically as follows: the first auxiliary circle and the second auxiliary circle are respectively constructed with the line connecting the UAV at the center of the circle to the other two selected UAVs as the chord; based on the fixed-length and fixed-angle implicit circle principle, the standardized equations of the first auxiliary circle and the second auxiliary circle are respectively constructed, and the passive signal reception UAV positioning model is obtained by combining the equations.

[0171] Furthermore, the system described in this embodiment corresponds to the method described in Embodiment 1, and its technical details have been described in detail in Embodiment 1, so they will not be repeated here.

[0172] In further embodiments, there is also provided:

[0173] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in Embodiment 1 is performed. For the sake of brevity, no further description is given here.

[0174] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0175] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0176] A computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method described in embodiment 1 is completed.

[0177] The method in the first embodiment can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0178] Those skilled in the art will appreciate that the units, i.e., algorithm steps, of the various examples described in the present embodiment can be implemented in electronic hardware or in a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this disclosure.

[0179] The above-mentioned embodiment provides a method and system for bearing-only passive positioning of unmanned aerial vehicles during formation flight, which can be realized and has broad application prospects.

[0180] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A pure bearing passive positioning method for UAVs performing formation flight. It is characterized in that The method is applied to a circular formation formed by a plurality of drones, wherein the circular formation is composed of a central drone and drones evenly distributed on the circumference. The method comprises: The UAV to be located passively receives the signal transmitted by the UAV that transmits the signal; wherein, when each UAV in the circular formation has a fixed number, the UAV that transmits the signal needs to meet the following constraints: the UAV at the center of the circular formation and any two UAVs on the circumference are used as the UAV that transmits the signal, and the UAVs at other positions passively receive the signal; Based on the received signal and the pre-built passive signal receiving drone positioning model, the position of the receiving signal drone is obtained; The passive signal receiving drone positioning model is specifically as follows: the first auxiliary circle and the second auxiliary circle are respectively constructed with the line connecting the drone at the center of the circle to the other two selected drones as the chord; based on the fixed-length and fixed-angle hidden circle principle, the standardized equations of the first auxiliary circle and the second auxiliary circle are respectively constructed, and the passive signal receiving drone positioning model is obtained by combining the equations; Among them, the passive signal receiving drone positioning model is specifically expressed as follows: in, R is the radius of the UAV circular formation; is the circular angle subtended by the chord corresponding to the first auxiliary circle; is the circular angle subtended by the chord corresponding to the second auxiliary circle; is the chord corresponding to the first auxiliary circle and The angle formed by the positive direction of the axis; is the chord corresponding to the second auxiliary circle and The angle formed by the positive direction of the axis.

2. A method for purely bearing-free passive positioning of unmanned aerial vehicles in formation flight as claimed in claim 1, It is characterized in that The first auxiliary circle and the second auxiliary circle are respectively constructed with the lines from the drone at the center of the circle to the other two selected drones as chords, wherein only two circles exist that satisfy the intersection of the first auxiliary circle and the second auxiliary circle at the position of the drone to be located.

3. The method for purely bearing-free passive positioning of unmanned aerial vehicles in formation flight according to claim 1, It is characterized in that When only the UAV at the center of the circle and one UAV on the circumference have numbers and serve as signal transmitting UAVs, no less than two additional UAVs with unknown numbers are required to serve as signal transmitting UAVs.

4. A pure bearing passive positioning system for UAVs performing formation flight. It is characterized in that The system is applied to a circular formation formed by a number of drones, wherein the circular formation is composed of a central drone and drones evenly distributed around the circumference. The system includes: A signal receiving unit, which is used to passively receive the signal transmitted by the signal transmitting drone for the drone to be located; wherein, when each drone in the circular formation has a fixed number, the signal transmitting drone must meet the following constraints: the drone at the center of the circular formation and any two drones on the circumference are used as signal transmitting drones, and the drones at other positions passively receive signals; A positioning unit, which is used to obtain the position of the receiving signal drone based on the received signal and a pre-built passive receiving signal drone positioning model; The passive signal receiving drone positioning model is specifically as follows: the first auxiliary circle and the second auxiliary circle are respectively constructed with the line connecting the drone at the center of the circle to the other two selected drones as the chord; based on the fixed-length and fixed-angle hidden circle principle, the standardized equations of the first auxiliary circle and the second auxiliary circle are respectively constructed, and the passive signal receiving drone positioning model is obtained by combining the equations; Among them, the passive signal receiving drone positioning model is specifically expressed as follows: in, R is the radius of the UAV circular formation; is the circular angle subtended by the chord corresponding to the first auxiliary circle; is the circular angle subtended by the chord corresponding to the second auxiliary circle; is the chord corresponding to the first auxiliary circle and The angle formed by the positive direction of the axis; is the chord corresponding to the second auxiliary circle and The angle formed by the positive direction of the axis.

5. A bearing-only passive positioning system for unmanned aerial vehicles performing formation flight as claimed in claim 4, It is characterized in that The first auxiliary circle and the second auxiliary circle are respectively constructed with the lines from the drone at the center of the circle to the other two selected drones as chords, wherein only two circles exist that satisfy the intersection of the first auxiliary circle and the second auxiliary circle at the position of the drone to be located.

6. A pure bearing passive positioning system for unmanned aerial vehicles performing formation flight as claimed in claim 4, It is characterized in that When only the UAV at the center of the circle and one UAV on the circumference have numbers and serve as signal transmitting UAVs, no less than two additional UAVs with unknown numbers are required to serve as signal transmitting UAVs.

7. An electronic device, comprising a memory, a processor and a computer program stored and running on the memory, wherein when the processor executes the program, it implements the pure bearing passive positioning method for unmanned aerial vehicles performing formation flight as described in any one of claims 1 to 3.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the pure bearing passive positioning method for unmanned aerial vehicles performing formation flight as described in any one of claims 1 to 3.

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