Blind user positioning method based on jammer cluster

Abstract

The application provides a blind user positioning method based on a jammer cluster, and relates to the field of positioning, and the method comprises the following steps: the jammer cluster acquires low-orbit satellite signals at different time points; for the same time point, the MUSIC algorithm is used to calculate and predict the low-orbit satellite signals; a space cone is constructed, with the jammer as the cone top, the satellite-jammer direction as the axis, and a preset half-cone angle; a projection prediction circle of the space cone and the ground plane is obtained; the intersection area of the projection prediction circles at different time points is determined as the area where the ground target is located, and the positioning result of the ground target is obtained by calculating the centroid. In the above method, the low-orbit satellite signals received by the jammer cluster are calculated and predicted, a prediction area is formed on the ground, then the centroid is calculated by using the Monte Carlo algorithm, and the prediction position of the ground target is obtained, so that the non-cooperative positioning under special conditions such as limited network conditions and remote areas is realized, and the positioning effect and instantaneity are good.

Description

Technical Field

[0001] This invention relates to the field of positioning, and is a technology applicable to ground target positioning, particularly a blind user positioning method based on jamming machine clusters. Background Technology

[0002] With the rapid development of low-Earth orbit (LEO) satellites, their role in communication and jamming is becoming increasingly prominent. LEO satellite users do not have internet access, giving them stronger anti-jamming capabilities and environmental adaptability compared to traditional communication methods that rely on terrestrial internet infrastructure. At the same time, LEO satellite signals are characterized by narrow beams and high ground power, significantly reducing the effectiveness of other traditional jamming methods. This leads to numerous technical challenges for suppression and deception jamming, including incomplete spatial and frequency domain coverage, ease of monitoring and identification, and directional filtering. These challenges have become a major hurdle in positioning and jamming, making the location of ground targets conducting communication urgently needed.

[0003] Most existing positioning methods rely on the Internet or communication links to obtain auxiliary information, such as differential positioning (DGPS) and RTK positioning (network RTK). Once network conditions are limited or interrupted, their positioning performance will be significantly reduced, or they may even fail to work properly. This defect is particularly prominent in remote areas, emergency scenarios, and highly dynamic platforms.

[0004] Cooperative positioning, such as PPP / PPP-RTK, can significantly improve positioning accuracy and robustness through multi-node information sharing. However, its dependence on communication networks, system complexity, and real-time performance limits its application in weak networks and highly dynamic scenarios. Against this backdrop, non-cooperative positioning has emerged and is gradually gaining a certain position in the positioning field. Summary of the Invention

[0005] To address the technical challenge of insufficient positioning accuracy and timeliness when locating ground targets under special conditions, this invention proposes a blind user positioning method based on a cluster of jamming machines. The method includes:

[0006] Step S1: The jamming machine cluster acquires low-Earth orbit satellite signals at different times, wherein the low-Earth orbit satellite signals are signals transmitted by low-Earth orbit satellites to ground targets;

[0007] Step S2: For the same moment, the MUSIC algorithm is used to predict the acquired low-orbit satellite signal and calculate the three-dimensional coordinates of the low-orbit satellite. Then, a spatial cone with the jammer as the cone apex, the satellite-jammer direction as the axis, and a preset half-cone angle is constructed. Then, the projection prediction circle of the spatial cone and the ground plane is obtained.

[0008] Step S3: Determine the intersection area of ​​the projection prediction circles at different times as the area where the ground target is located, and calculate the centroid to obtain the positioning result of the ground target.

[0009] Optionally, step S3 includes:

[0010] Determine the intersection region of the projected prediction circles at different times;

[0011] Determine the smallest rectangular region that encompasses the intersecting areas;

[0012] The centroid of the intersection region is calculated using the Monte Carlo algorithm according to the following formula to obtain the localization result of the ground target:

[0013] ,

[0014] Where C represents the centroid coordinates, The coordinates of the i-th throw point that lands in the intersection area are represented by , and n represents the number of throw points that land in the intersection area. This represents the weight coefficient corresponding to the i-th throwing point. , This represents the minimum distance from the i-th throwing point to the vertex of the region. This represents the distance from the i-th throwing point to the center of the rectangular area.

[0015] Optionally, step S2 includes:

[0016] Step S21: Calculate the satellite antenna gain in the jammer's receiving direction according to the following formula:

[0017] ,

[0018] in, The satellite antenna gain indicating the direction of reception for the jammer; This represents the antenna gain of the ground target. This indicates the received power of the ground target. This indicates the receiving power of the jammer;

[0019] Step S22: For the same time, based on the satellite antenna gain corresponding to different jammers, the jammer with the highest satellite antenna gain in the receiving direction is determined as the optimal jammer, thereby obtaining the optimal jammers corresponding to different times.

[0020] Step S23: For the same moment, the MUSIC algorithm is used to predict the low-orbit satellite signal received by the optimal jammer, and the three-dimensional coordinates of the low-orbit satellite are calculated. Then, a spatial cone with the jammer as the cone apex, the satellite-jammer direction as the axis, and a preset half-cone angle is constructed, and the projection prediction circle of the spatial cone and the ground plane is obtained.

[0021] Optionally, step S23 includes:

[0022] For the same moment, calculate the covariance matrix of the low-orbit satellite signal received by the optimal jammer, and perform eigenvalue decomposition on the covariance matrix to obtain the signal subspace and noise subspace;

[0023] Based on the following formula, the angle corresponding to the peak value of the spectrum is determined as the azimuth angle of the low-Earth orbit satellite signal. and pitch angle :

[0024] ,

[0025] in, Indicates direction and angle The corresponding signal spectrum value at that time; The steering vector represents the direction of the low-Earth orbit satellite signal. The array response under the following conditions "H" represents the noise subspace; "H" represents the conjugate transpose.

[0026] Calculate the satellite's three-dimensional coordinates based on its azimuth, elevation, and the altitude of the low-Earth orbit satellite;

[0027] Based on the three-dimensional coordinates of the satellite and the jammer, a spatial cone is constructed with the jammer as the apex, the satellite-jammer direction as the axis, and a preset half-cone angle.

[0028] Calculate the intersection of the spatial cone and the ground plane to obtain the predicted projection circle of the jammer's predicted directional beam on the ground.

[0029] Optionally, the method further includes:

[0030] Step S4: Calculate the angular offset between the current direction of the optimal jammer and the direction of maximum main lobe according to the following formula:

[0031] ,

[0032] in, This indicates the satellite antenna gain in the current direction. It is the offset value between the current direction and the maximum direction of the main lobe; This indicates the maximum gain of the antenna in the direction of the main lobe center. It is the half-power angle;

[0033] On the plane formed by the optimal jammer, the ground target, and the satellite, the position of the optimal jammer is adjusted based on the angular offset. The projection prediction circle is recalculated based on the adjusted position of the optimal jammer. Then, step S3 is executed to obtain the corrected positioning result of the ground target.

[0034] The embodiments described in this invention have the following advantages:

[0035] This invention provides a blind user positioning method based on a jammer cluster. After the jammer cluster acquires low-Earth orbit (LEO) satellite signals at different times, the MUSIC algorithm is used simultaneously to predict the acquired LEO satellite signals, calculating the three-dimensional coordinates of the LEO satellites. This constructs a spatial cone with the jammer as the apex, the satellite-jammer direction as the axis, and a preset half-cone angle. The projected prediction circle of this spatial cone and the ground plane is then obtained. The intersection area of ​​the projected prediction circles at different times is then determined as the location of the ground target, and the centroid is calculated to obtain the positioning result of the ground target. In this method, a jammer cluster is used to receive signals transmitted by LEO satellites, and these signals are calculated to form an irregular prediction area on the ground. The Monte Carlo algorithm is then applied to this prediction area to accurately locate the position of the ground target. This method achieves non-cooperative positioning under special conditions such as limited network conditions and remote locations, and has good positioning performance and immediacy. Attached Figure Description

[0036] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0037] Figure 1 A flowchart illustrating an embodiment of a blind user localization method based on an interference machine cluster provided by the present invention;

[0038] Figure 2 A system schematic diagram illustrating an embodiment of a blind user localization method based on an interference machine cluster provided by the present invention;

[0039] Figure 3 A schematic diagram of a minimum rectangular region provided by the present invention;

[0040] Figure 4 A schematic diagram of weight selection provided by the present invention;

[0041] Figure 5 A schematic diagram of a satellite antenna gain provided by the present invention;

[0042] Figure 6 A side view of a positioning result provided by the present invention;

[0043] Figure 7 A simulation positioning result diagram provided by the present invention;

[0044] Figure 8 A simulation result localization map based on the selection of the optimal jammer is provided for this invention;

[0045] Figure 9 This invention provides a simulation result positioning diagram based on optimal interference machine selection and angle correction. Detailed Implementation

[0046] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0047] To achieve non-cooperative positioning under special conditions such as limited network conditions and remote areas. Figure 1 A flowchart of an embodiment of a blind user localization method based on an interference machine cluster provided by the present invention is given, which specifically includes:

[0048] Step S1: The jamming cluster acquires low-Earth orbit (LEO) satellite signals at different times, where the LEO satellite signals are signals transmitted by LEO satellites to ground targets.

[0049] Low-Earth orbit (LEO) satellite signals refer to signals transmitted by LEO satellites to ground targets, including but not limited to positioning signals and communication signals.

[0050] like Figure 2 The diagram illustrates a system schematic of an embodiment of a blind user positioning method based on a jammer swarm provided by this invention. The diagram constructs a positioning model consisting of low-Earth orbit satellites, a jammer swarm / array, and a ground target. Here, 1 represents a satellite orbiting along its orbit, 2 represents the jammer swarm, 3 represents the predicted direction of the satellite signal, 4 represents the intersection of the estimated target location areas, and 5 represents the actual target location. Based on this model, the signals transmitted by the satellites are reflected by the jammers and projected onto the ground, forming multiple projection areas, i.e., prediction circles. By analyzing the intersection of these areas, the ground target can be located, thus achieving non-cooperative positioning under special conditions such as limited network conditions and remote locations. This method achieves good real-time performance while also obtaining good positioning accuracy.

[0051] Step S2: For the same moment, the MUSIC algorithm is used to predict the acquired low-orbit satellite signal and calculate the three-dimensional coordinates of the low-orbit satellite. Then, a spatial cone with the jammer as the cone apex, the satellite-jammer direction as the axis, and a preset half-cone angle is constructed. The projection prediction circle of the spatial cone and the ground plane is then obtained.

[0052] To improve positioning accuracy, this invention acquires and processes low-Earth orbit (LEO) satellite signals at different times, and uses the MUSIC (Multiple Signal Classification) algorithm to predict the direction of the LEO satellite signal acquired by the jammer at the current moment. Combined with the altitude of the LEO satellite, the position of the LEO satellite is determined. This allows the construction of a spatial cone with the jammer as the apex, the satellite-jammer direction as the axis, and a preset semi-cone angle. The relationship between the spatial cone and the ground plane is then calculated. The intersection line is obtained, and the least squares method is used to fit the intersection line into a circle, thereby obtaining the projection coverage area of ​​the jammer's predicted directional beam on the ground, i.e., each prediction circle.

[0053] The MUSIC algorithm decomposes the received low-Earth orbit satellite signal into "signal" and "noise" subspaces, and uses the orthogonality between the signal steering vector and the noise subspace to transform the parameter estimation problem into a spectral peak search problem. That is, it determines the elevation and azimuth angles of the low-Earth orbit satellite signal based on the angles corresponding to the spectral peaks. Its high resolution helps to improve positioning accuracy.

[0054] In addition, at the same time, there may be multiple jammer clusters that can receive low-orbit satellite signals. Considering that there is a certain error in the direction of the jammers, the gain of the satellite transmitting antenna can be used to reduce the superposition of errors caused by multiple jammers. At the same time, it is only necessary to select one or two jammers in the jammer cluster with the most suitable receiving angle.

[0055] Step S3: Determine the intersection area of ​​the projection prediction circles at different times as the area where the ground target is located, and calculate the centroid to obtain the positioning result of the ground target.

[0056] For multiple predicted circles on the ground, their sizes can be changed to obtain the intersection region. The centroid of the intersection region can be calculated using the Monte Carlo algorithm to obtain the position of the ground target.

[0057] Specifically, step S3 may include:

[0058] Determine the intersection region of the projected prediction circles at different times;

[0059] Determine the smallest rectangular region that encompasses the intersecting areas;

[0060] The centroid of the intersection region is calculated using the Monte Carlo algorithm according to the following formula to obtain the localization result of the ground target:

[0061] (1)

[0062] Where C represents the centroid coordinates, The coordinates of the i-th throw point that lands in the intersection area are represented by , and n represents the number of throw points that land in the intersection area. This represents the weight coefficient corresponding to the i-th throwing point. , This represents the minimum distance from the i-th throwing point to the vertex of the region. This represents the distance from the i-th throwing point to the center of the rectangular area.

[0063] First, find the smallest rectangle that encloses the intersection area. For example... Figure 3 The diagram illustrates a minimum rectangular region provided by this invention. The gray area represents an irregular polygonal curve region, and points 6, 7, and 8 represent the vertices of this irregular polygonal curve region, obtained by the intersection of various projected circles. If the rectangular region is directly obtained through the coordinates of the vertices, it may result in… Figure 3 In this case, the rectangular area does not completely enclose the irregular polygonal curve area, and the arc is convex. Therefore, point 9 needs to be introduced, which is the point where the radius is added to or subtracted from the center coordinates. For example, in the x-axis and y-axis directions, adding or subtracting the radius from the center coordinates yields four coordinate points: directly above, directly below, directly to the left, and directly to the right of the center. Figure 3 Point 9 in the diagram is the point where the center coordinates are added or subtracted from the radius. Points 6, 7, and 8 are the intersection points. By comparing points 6, 7, 8, and 9, the final rectangle is the smallest rectangular area that can completely enclose the irregular polygonal curve region.

[0064] Traditional Monte Carlo algorithms obtain the centroid by calculating the average coordinates of the throwing points within the region. In this invention, to reduce computational complexity and improve positioning speed, a weighting mechanism is introduced, as shown in formula (1) and... Figure 4 As shown in the weight selection diagram, the minimum distance between the throwing point and the vertex of the region is calculated for each throwing point in the region. At the same time, the Euclidean distance between each throwing point in the region and the point at the center of the rectangle is calculated, and the ratio of the two is used as the weight. The closer the point is to the center of the rectangle, the higher the weight. In this way, 10,000 throwing points can achieve the stability that would otherwise require 100,000 throwing points, and the time can be reduced to nearly one-tenth of the original, which can effectively improve the speed and immediacy of positioning.

[0065] In summary, this invention provides a blind user positioning method based on a jammer swarm. After the jammer swarm acquires low-Earth orbit (LEO) satellite signals at different times, the MUSIC algorithm is used simultaneously to predict the acquired LEO satellite signals, calculating the three-dimensional coordinates of the LEO satellites. This constructs a spatial cone with the jammer as the apex, the satellite-jammer direction as the axis, and a preset half-cone angle, resulting in a projection prediction circle between the spatial cone and the ground plane. The intersection area of ​​the projection prediction circles at different times is then determined as the location of the ground target, and the centroid is calculated to obtain the positioning result of the ground target. In this method, a jammer swarm is used to receive signals transmitted by LEO satellites, and these signals are calculated to form an irregular prediction area on the ground. The Monte Carlo algorithm is then applied to this prediction area, enabling accurate positioning of ground targets. This method achieves non-cooperative positioning under special conditions such as limited network conditions and remote locations, and has good positioning performance and immediacy.

[0066] Optionally, step S2 may include:

[0067] Step S21: Calculate the satellite antenna gain in the jammer's receiving direction according to the following formula:

[0068] (2)

[0069] in, The satellite antenna gain indicating the direction of reception for the jammer; This represents the antenna gain of the ground target. This indicates the received power of the ground target. This indicates the receiving power of the jammer;

[0070] Step S22: For the same time, based on the satellite antenna gain corresponding to different jammers, the jammer with the highest satellite antenna gain in the receiving direction is determined as the optimal jammer, thereby obtaining the optimal jammers corresponding to different times.

[0071] Step S23: For the same moment, the MUSIC algorithm is used to predict the low-orbit satellite signal received by the optimal jammer, and the three-dimensional coordinates of the low-orbit satellite are calculated. Then, a spatial cone with the jammer as the cone apex, the satellite-jammer direction as the axis, and a preset half-cone angle is constructed, and the projection prediction circle of the spatial cone and the ground plane is obtained.

[0072] For a satellite operating at the same time, there may be multiple jammers in a jamming cluster capable of receiving its signal. Each jammer that receives the signal projects a circular area on the ground. These circular areas intertwine, and the resulting irregular common area represents the user's predicted area. Considering the inherent directional errors of the jammers, this invention utilizes the satellite transmitting antenna gain to reduce the cumulative errors caused by multiple jammers in order to improve positioning accuracy. At any given time, only the jammer with the most suitable receiving angle in the jamming cluster is selected for positioning. The satellite transmitting antenna gain is as follows: Figure 5 As shown.

[0073] To better explain step S21, the derivation of formula (2) can be referred to the following process:

[0074] Jammer signal power in ideal free space:

[0075] (3)

[0076] Where Pr is the received power, Pt is the satellite transmit power, Gt is the satellite transmit antenna gain, and Gr is the receive antenna gain. This is due to distance attenuation.

[0077] In the above formula, if the receiving antenna is an omnidirectional antenna, then the value of Gr is 0, as shown in the following formula.

[0078] , (4)

[0079] Meanwhile, the receiving power of ground targets It can be represented as:

[0080] (5)

[0081] jammer's receiving power It can be represented as:

[0082] (6)

[0083] It can be understood that the satellite's transmit power Pt remains constant, therefore Pt0 = Pt1. Low-Earth orbit satellites typically operate at an altitude of 550 km, while jammers can operate at an altitude of 10 km. On the same plane, the distance difference between the jammer's trajectory along the received signal and the target point on the ground, and the distance between the ground target and the satellite, is minimal. Therefore, the distance attenuation can be considered equal, i.e., d0 = d1. The two can be combined as follows:

[0084] (7)

[0085] Subtracting them gives the satellite antenna gain in the jammer's receiving direction:

[0086] (2)

[0087] Given the antenna gain Gt0 and received power Pr0 of the ground target, Pr1 can be obtained by the jammer calculating the current direction of the attack on the ground. Then, the satellite antenna gain Gt1 of the jammer's receiving direction can be deduced. By comparing the satellite antenna gains Gt of each jammer in the jammer array in the receiving direction, the jammer with the maximum received antenna gain can be obtained, and the signal receiving angle calculated and predicted by this jammer can be confirmed as the optimal receiving angle.

[0088] Optionally, step S23 may include:

[0089] For the same moment, calculate the covariance matrix of the low-orbit satellite signal received by the optimal jammer, and perform eigenvalue decomposition on the covariance matrix to obtain the signal subspace and noise subspace;

[0090] Based on the following formula, the angles corresponding to the peak values ​​of the spectrum are determined as the azimuth and elevation angles of the low-Earth orbit satellite signal:

[0091] (8)

[0092] in, Indicates direction and angle The corresponding signal spectrum value at that time; The steering vector represents the direction of the low-Earth orbit satellite signal. The array response under the following conditions "H" represents the noise subspace; "H" represents the conjugate transpose.

[0093] Calculate the satellite's three-dimensional coordinates based on its azimuth, elevation, and the altitude of the low-Earth orbit satellite;

[0094] Based on the three-dimensional coordinates of the satellite and the jammer, a spatial cone is constructed with the jammer as the apex, the satellite-jammer direction as the axis, and a preset half-cone angle.

[0095] Calculate the intersection of the spatial cone and the ground plane to obtain the predicted projection circle of the jammer's predicted directional beam on the ground.

[0096] The satellite signal received by the jammer can be represented as:

[0097] (9)

[0098] in, This represents the received signal of a uniform rectangular array. The steering vector characterizes the signal in direction. The array response under the following conditions Indicates the azimuth angle of the satellite signal. Indicates the elevation angle of the satellite signal. For narrowband signals transmitted by satellites, It is Gaussian white noise.

[0099] To address the high-speed movement characteristics of low-Earth orbit satellites, the array response along the x and y axes needs to be rapidly matched to the signal incident direction, as shown below:

[0100] x-axis response:

[0101] (10)

[0102] y-axis response:

[0103] (11)

[0104] Composite guide vector:

[0105] (12)

[0106] in, and , represents the array response along the x-axis and y-axis respectively, d is the element spacing, M represents the number of elements in the uniform rectangular array along the x-axis, and N represents the number of elements in the uniform rectangular array along the y-axis. "This indicates the Kronecker accumulation."

[0107] Covariance matrix calculation:

[0108] (13)

[0109] covariance matrix It reflects the statistical characteristics of signal and noise; in practice, time averaging can be used to replace the expected calculation, where T is the number of snapshots.

[0110] Eigenvalue decomposition:

[0111] (14)

[0112] right Perform eigenvalue decomposition to obtain the eigenvalue matrix. and eigenvector matrix The eigenvectors corresponding to the top K largest eigenvalues, sorted by eigenvalue size, form the signal subspace. K represents the number of signal sources, and the remaining eigenvectors form the noise subspace. Furthermore, when the number of satellites is uncertain, the signal subspace and noise subspace can be divided according to the percentage of energy.

[0113] Quick estimation of azimuth and elevation angles:

[0114] (8)

[0115] Noise subspace With satellite signal steering vector When orthogonal, the denominator approaches 0, and the spectral value... A peak appears; the spectral peak corresponds to These are the azimuth and elevation angles of the satellite signal.

[0116] Based on the satellite's altitude H and the azimuth angle α and elevation angle β calculated in the previous step, the satellite's coordinates in three-dimensional space can be calculated. : ).

[0117] Then, by constructing a spatial cone with the jammer as the apex, the satellite-jammer direction as the axis, and a given semi-cone angle, the relationship between the cone and the ground plane is calculated. The intersection line is obtained, and the least squares method is used to fit the intersection line into a circle, thereby obtaining the projection coverage area of ​​the jammer's predicted directional beam on the ground, i.e., each prediction circle.

[0118] Optionally, the method may further include:

[0119] Step S4: Calculate the angular offset between the current direction of the optimal jammer and the direction of maximum main lobe according to the following formula:

[0120] (15)

[0121] in, This indicates the satellite antenna gain in the current direction. It is the offset value between the current direction and the maximum direction of the main lobe; This indicates the maximum gain of the antenna in the direction of the main lobe center. It is the half-power angle;

[0122] On the plane formed by the optimal jammer, the ground target, and the satellite, the position of the optimal jammer is adjusted based on the angular offset. The projection prediction circle is recalculated based on the adjusted position of the optimal jammer. Then, step S3 is executed to obtain the corrected positioning result of the ground target.

[0123] like Figure 6 The diagram shown is a side view of a positioning result, where 10 represents a satellite at a certain moment, 11 is the jammer in the optimal direction corresponding to the satellite, 12 represents the predicted target, 13 represents the actual target, and 14 represents the ground. There is always an error between the predicted user location and the actual user location on the ground. Therefore, to further reduce the error and improve accuracy, the satellite antenna gain model formula based on the Gaussian model is used:

[0124] (15)

[0125] For the same moment, based on the optimal jammer obtained in step S22 The angle shift at this point can be obtained by inverse calculation using the antenna gain model. Subsequently, on the plane formed by the optimal jammer, the satellite, and the predicted user, the azimuth of the optimal jammer is corrected by adjusting its angle to align it with the predicted target. The angle offset is calculated, meaning the corrected jammer position is located in the direction of the maximum main lobe of the satellite antenna gain. Then, a new ground prediction circle is calculated using the corrected jammer position and the satellite at the same time. Step S3 is executed to obtain the corrected positioning result of the ground target. Based on the initial target prediction, the corrected target azimuth is obtained, realizing real-time correction of the prediction angle, thereby further improving the positioning accuracy while meeting the immediacy requirement.

[0126] Table 1: Basic Experimental Parameter Settings

[0127]

[0128] To better explain the blind user localization method based on an interference machine cluster provided by this invention, this invention provides, as follows: Figure 7 , Figure 8 and Figure 9 The simulation results are shown in Table 1. The basic experimental parameters are set as shown in Table 1. The frequency, speed of light, wavelength, array elements, number of snapshots, and signal-to-noise ratio ensure the normal use of the scheme described in this invention. The gain of the ground target received signal determines the peak gain of the satellite transmitting antenna, and the half-power width of the main lobe controls the width of the Gaussian curve.

[0129] exist Figure 7 In this process, the positioning system directly uses a swarm of jammers to capture the satellite's transmitted signals. The satellite's position is calculated using the methods described in steps S1-S3. A spatial cone with the jammer receiving the signal as its apex, the satellite-jammer direction as its axis, and a given half-cone angle is used to calculate its relationship with the ground plane. The intersection lines of the jammers' predicted directional beams are calculated, and the least squares method is used to fit these lines into circles, thus obtaining the projected coverage areas on the ground, i.e., the predicted circles. These projected circles intertwine, creating an irregular polygonal curved region. The initial predicted location of the user can be obtained by applying a geometric centroid estimation algorithm to this predicted region. As can be seen, the positioning speed is very fast, achieving successful positioning in almost one second under given conditions.

[0130] exist Figure 8In the process, the positioning system uses the method described in steps S21-S22 to filter the jammers that receive the signal. Based on the satellite antenna gain in the receiving direction, it selects the jammer with the optimal receiving angle at each time moment, i.e., the optimal jammer. The remaining jammers at each time moment are then eliminated. The positioning operation is repeated using a spatial cone with the optimal jammer as the apex, the satellite-optimal jammer direction as the axis, and a given half-cone angle. It can be seen that after selecting the optimal jammer and eliminating redundant jammers, the positioning speed is improved, the prediction error is significantly reduced, and the positioning accuracy is greatly improved.

[0131] exist Figure 9 In this process, the positioning system corrects the angle of the optimal jammer, making the satellite-optimal jammer axis closer to the satellite-real user axis, and then repeats the positioning operation. It can be seen that after angle correction, the prediction error is significantly reduced and the positioning accuracy is significantly improved.

[0132] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0133] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0134] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A blind user localization method based on a cluster of jamming machines, characterized in that, The method includes: Step S1: The jamming machine cluster acquires low-Earth orbit satellite signals at different times, wherein the low-Earth orbit satellite signals are signals transmitted by low-Earth orbit satellites to ground targets; Step S2: For the same moment, the MUSIC algorithm is used to predict the acquired low-orbit satellite signal and calculate the three-dimensional coordinates of the low-orbit satellite. Then, a spatial cone with the jammer as the cone apex, the satellite-jammer direction as the axis, and a preset half-cone angle is constructed. Then, the projection prediction circle of the spatial cone and the ground plane is obtained. Step S3: Determine the intersection area of ​​the projection prediction circles at different times as the area where the ground target is located, and calculate the centroid to obtain the positioning result of the ground target.

2. The method according to claim 1, characterized in that, Step S3 includes: Determine the intersection region of the projected prediction circles at different times; Determine the smallest rectangular region that encompasses the intersecting areas; The centroid of the intersection region is calculated using the Monte Carlo algorithm according to the following formula to obtain the localization result of the ground target: ， Where C represents the centroid coordinates, The coordinates of the i-th throw point that lands in the intersection area are represented by , and n represents the number of throw points that land in the intersection area. This represents the weight coefficient corresponding to the i-th throwing point. , This represents the minimum distance from the i-th throwing point to the vertex of the region. This represents the distance from the i-th throwing point to the center of the rectangular area.

3. The method according to claim 1, characterized in that, Step S2 includes: Step S21: Calculate the satellite antenna gain in the jammer's receiving direction according to the following formula: ， in, The satellite antenna gain indicating the direction of reception for the jammer; This represents the antenna gain of the ground target. This indicates the received power of the ground target. This indicates the receiving power of the jammer; Step S22: For the same time, based on the satellite antenna gain corresponding to different jammers, the jammer with the highest satellite antenna gain in the receiving direction is determined as the optimal jammer, thereby obtaining the optimal jammers corresponding to different times. Step S23: For the same moment, the MUSIC algorithm is used to predict the low-orbit satellite signal received by the optimal jammer, and the three-dimensional coordinates of the low-orbit satellite are calculated. Then, a spatial cone with the jammer as the cone apex, the satellite-jammer direction as the axis, and a preset half-cone angle is constructed, and the projection prediction circle of the spatial cone and the ground plane is obtained.

4. The method according to claim 3, characterized in that, Step S23 includes: For the same moment, calculate the covariance matrix of the low-orbit satellite signal received by the optimal jammer, and perform eigenvalue decomposition on the covariance matrix to obtain the signal subspace and noise subspace; Based on the following formula, the angle corresponding to the peak value of the spectrum is determined as the azimuth angle of the low-Earth orbit satellite signal. and pitch angle : ， in, Indicates direction and angle The corresponding signal spectrum value at that time; The steering vector represents the direction of the low-Earth orbit satellite signal. The array response under the following conditions "H" represents the noise subspace; "H" represents the conjugate transpose. Calculate the satellite's three-dimensional coordinates based on its azimuth, elevation, and the altitude of the low-Earth orbit satellite; Based on the three-dimensional coordinates of the satellite and the jammer, a spatial cone is constructed with the jammer as the apex, the satellite-jammer direction as the axis, and a preset half-cone angle. Calculate the intersection of the spatial cone and the ground plane to obtain the predicted projection circle of the jammer's predicted directional beam on the ground.

5. The method according to claim 3, characterized in that, The method further includes: Step S4: Calculate the angular offset between the current direction of the optimal jammer and the direction of maximum main lobe according to the following formula: ， in, This indicates the satellite antenna gain in the current direction. It is the offset value between the current direction and the maximum direction of the main lobe; This indicates the maximum gain of the antenna in the direction of the main lobe center. It is the half-power angle; On the plane formed by the optimal jammer, the ground target, and the satellite, the position of the optimal jammer is adjusted based on the angular offset. The projection prediction circle is recalculated based on the adjusted position of the optimal jammer. Then, step S3 is executed to obtain the corrected positioning result of the ground target.

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