Method and System for Locating Mobile GNSS Interference Sources Based on LEO Satellites

Abstract

This invention belongs to the field of satellite navigation and radio monitoring technology, and discloses a method and system for locating mobile GNSS interference sources based on LEO satellites. The method utilizes LEO satellites to locate mobile ground interference sources, overcoming the limitations of traditional ground positioning methods with their small range, and enabling interference source location over a large area. Furthermore, the method comprehensively utilizes TDOA and FDOA measurements to construct a more complete and universal dynamic solution model, i.e., the objective equation, and employs a two-step weighted least squares method and a semi-definite relaxation method to solve the objective equation, thereby improving the ability to calculate the position and velocity parameters of the interference source. The two-step weighted least squares method can solve the objective equation in real time and achieve positioning accuracy at the hundred-meter level, significantly meeting the requirements of high-time-sensitivity scenarios. The semi-definite relaxation method can reconstruct and convexly relax the non-convex optimization model involved in the positioning problem, significantly expanding the applicable scenarios of the method.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and radio monitoring technology, specifically relating to a method and system for locating mobile GNSS interference sources based on LEO satellites. Background Technology

[0002] With its technological advantages of all-weather, all-time, and global coverage, the Global Navigation Satellite System (GNSS) has become a key infrastructure in modern transportation, surveying and mapping, communications and other fields.

[0003] However, GNSS has significant security vulnerabilities, primarily manifested in its vulnerability to physical layer signal attacks launched by commercially available jammers and spoofers. This security threat is particularly prominent in fields such as intelligent transportation, shipping, and aviation. For example, in intelligent transportation systems, vehicle terminals rely on GNSS for precise positioning and route planning; interference can lead to widespread navigation errors and even traffic accidents. The problems encountered in practical applications fully reveal the vulnerability of GNSS to interference and spoofing attacks, highlighting the urgency and importance of building an efficient and reliable GNSS interference detection and positioning system.

[0004] Low Earth Orbit (LEO) satellites, located within 2000 kilometers above the Earth, offer advantages such as wide coverage and fast response, effectively enabling the detection and location of large-scale ground-based GNSS interference. Although LEO satellite-based interference source localization methods have made some progress, many challenges remain in practical application scenarios such as high-noise environments and complex ionospheric disturbances.

[0005] First, most existing methods primarily target static or quasi-static interference sources, exhibiting limited continuous tracking and localization capabilities for ground-based mobile interference sources. Traditional algorithms based on Time Difference of Arrival (TDOA) or Frequency Difference of Arrival (FDOA) perform poorly in such scenarios. Second, single TDOA or FDOA-based measurement methods struggle to maintain stable computational performance under highly nonlinear constraints. Most importantly, in regions with frequent ionospheric or tropospheric disturbances, the positioning accuracy and robustness of traditional algorithms significantly decrease. For example, the error of single-satellite positioning methods can reach as high as 100 kilometers, and the accuracy of TDOA or FDOA-based algorithms drops sharply under high noise or atmospheric delay conditions. Furthermore, existing commercial systems such as Hawkeye360 have not disclosed their adaptive computational strategies for handling complex scenarios, leaving their actual performance in variable environments uncertain. Summary of the Invention

[0006] The purpose of this invention is to propose a method for locating mobile GNSS interference sources based on LEO satellites. This method can improve the positioning accuracy and robust positioning capability of mobile ground interference sources in complex electromagnetic environments.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for locating mobile GNSS interference sources based on LEO satellites includes the following steps:

[0009] Step 1. Based on the two lines of TLE data from the LEO satellite orbits, calculate the spatial position and velocity of each LEO satellite sensor at the observation time;

[0010] Step 2. Based on the spatial position and velocity of LEO satellite sensors, construct TDOA and FDOA observation models for the position and velocity parameters of ground-based mobile interference sources, and establish a joint TDOA and FDOA positioning target equation;

[0011] Step 3. Solve the joint positioning target equation of TDOA and FDOA using the two-step weighted least squares method (TSWLS) and the semi-definite relaxation method (SDR) respectively to obtain the position and velocity estimates of the ground mobile interference source.

[0012] Furthermore, based on the LEO satellite-based method for locating mobile GNSS interference sources, this invention also proposes a corresponding LEO satellite-based system for locating mobile GNSS interference sources, the technical solution of which is as follows:

[0013] A mobile GNSS interference source localization system based on LEO satellites, comprising:

[0014] The position and velocity calculation module is used to calculate the spatial position and velocity of each LEO satellite sensor at the observation time based on the two lines of TLE data from the LEO satellite orbits.

[0015] The objective equation establishment module is used to construct TDOA and FDOA observation models based on the spatial position and velocity of ground mobile interference sources using LEO satellite sensors, and to establish the joint TDOA and FDOA positioning objective equation.

[0016] And an interference source localization module, which is used to solve the joint localization target equation of TDOA and FDOA by using the two-step weighted least squares method (TSWLS) and the semi-definite relaxation method (SDR) respectively, to obtain the position estimate and velocity estimate of the ground mobile interference source.

[0017] Furthermore, based on the above-mentioned method for locating mobile GNSS interference sources based on LEO satellites, this invention also proposes a computer device, which includes a memory and one or more processors;

[0018] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the LEO satellite-based mobile GNSS interference source localization method described above.

[0019] Furthermore, based on the aforementioned method for locating mobile GNSS interference sources based on LEO satellites, this invention also proposes a computer-readable storage medium storing a program thereon; when executed by a processor, this program is used to implement the steps of the aforementioned method for locating mobile GNSS interference sources based on LEO satellites.

[0020] The present invention has the following advantages:

[0021] As described above, this invention discloses a method for locating mobile GNSS interference sources based on LEO satellites. This method utilizes LEO satellites to locate mobile ground-based interference sources, overcoming the limitations of traditional ground-based positioning methods with limited range, and enabling interference source location over a large area. Furthermore, this invention constructs a more complete and universal dynamic solution model, i.e., the target equation, by comprehensively utilizing TDOA and FDOA measurements. It then employs a two-step weighted least squares method and a semi-definite relaxation method to solve the target equation, thereby improving the ability to calculate the position and velocity parameters of the interference source. Based on real-time solution of the target equation using the two-step weighted least squares method, it can achieve positioning accuracy at the hundred-meter level, with a root mean square error of no more than [value missing]. The root mean square error of the speed is no greater than This significantly meets the needs of high-time-sensitivity scenarios. By reconstructing and convexly relaxing the non-convex optimization model involved in the positioning problem using the semi-definite relaxation method, the applicable scenarios can be significantly expanded. This allows the method of the present invention to maintain excellent robustness and solution accuracy even under challenging conditions such as complex dynamics, high-noise environments, and atmospheric errors such as tropospheric delay and ionospheric delay. Attached Figure Description

[0022] Figure 1 This is a flowchart of a mobile GNSS interference source localization method based on LEO satellites in an embodiment of the present invention.

[0023] Figure 2 This is the RMSE curve of the target location estimation obtained using the method of this invention.

[0024] Figure 3 The RMSE curve for the target velocity estimation obtained using the method of this invention.

[0025] Figure 4The RMSE curve for target position estimation obtained by the method of this invention is obtained after introducing interference from ionospheric delay and tropospheric delay. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0027] Example 1

[0028] This embodiment discloses a high-precision positioning method for interference sources in mobile global navigation satellite systems based on low-Earth orbit (LEO) satellites, using joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA). This method constructs a collaborative observation network of multiple LEO satellites, fuses TDOA and FDOA measurement information, and employs a scenario-adaptive hybrid solution strategy combining two-stage weighted least squares (TSWLS) and semidefinite relaxation (SDR) to achieve real-time high-precision positioning of ground-based mobile interference sources. First, TDOA and FDOA observations are obtained by accurately simulating LEO satellite orbital parameters. Second, the optimal solution algorithm is selected based on the signal-to-noise ratio and environmental complexity of the actual application scenario: the computationally efficient TSWLS algorithm is used in low-noise environments, while the robust SDR algorithm is used in complex environments with high noise or ionospheric / tropospheric delays. This invention solves the problems of insufficient accuracy in traditional single-satellite positioning methods and poor stability of existing algorithms in complex electromagnetic environments. It also overcomes the limitation of static interference source positioning technology in tracking moving targets, providing an efficient and reliable technical means for GNSS interference monitoring and countermeasures.

[0029] The general idea of ​​this invention is to first obtain TDOA and FDOA measurements, then construct a nonlinear expression containing the location and velocity of the interference source, and then use the TSWLS algorithm and SDR to calculate the target location and velocity. Finally, ionospheric delay and tropospheric delay are introduced to calculate the positioning accuracy of the two calculation methods under complex environments. The following is a detailed description of the LEO satellite-based mobile GNSS interference source localization method proposed in this invention.

[0030] like Figure 1 As shown, the method for locating mobile GNSS interference sources based on LEO satellites specifically includes the following steps:

[0031] Step 1. Based on the two lines of TLE data from the LEO satellite orbits, calculate the spatial position and velocity of each LEO satellite sensor at the observation time.

[0032] In step 1 of this embodiment, the TLE data includes parameters such as orbital altitude, perigee angle, orbital inclination, right ascension of the ascending node, mean perigee angle, mean perigee time, and angular velocity, which are used to calculate the satellite's position and velocity at a certain moment.

[0033] The spatial position and velocity of each LEO satellite sensor at the observation time were obtained by analyzing the TLE orbital elements and applying the SGP4 propagation model.

[0034] In this embodiment, the location and velocity of the interference source are as follows: The unit is meters (m). The unit is m / s.

[0035] Step 2. Based on the spatial position and velocity of LEO satellite sensors, construct TDOA and FDOA observation models for the position and velocity parameters of ground mobile interference sources, and establish the joint TDOA and FDOA positioning target equation.

[0036] In this embodiment, step 2 specifically includes:

[0037] consider In a three-dimensional spatial motion interference source localization scenario where multiple LEO satellite sensors work in collaboration, let the first... The spatial position and velocity of the LEO satellite sensors are known.

[0038] No. Spatial location of LEO satellite sensors and speed They are represented as follows: , .

[0039] in, , , , Indicates the first The three-dimensional coordinate components of each LEO satellite sensor in the Earth-centered Earth-fixed coordinate system.

[0040] Location of ground-based mobile interference sources and speed They are represented as follows: , .

[0041] in, , , This represents the three-dimensional coordinate components of a ground-based mobile interference source in the Earth-centered Earth-fixed coordinate system.

[0042] The first LEO satellite sensor was used as a reference.

[0043] Ground-based mobile interference sources and the first Distance between LEO satellite sensors for:

[0044] (1)

[0045] If the first The time difference of arrival (TDOA) between the signals received by the first LEO satellite sensor and the first LEO satellite sensor is: The speed of signal propagation is The equation relating the time difference of arrival to the location of the interference source is shown in equation (2):

[0046] (2)

[0047] in, This represents the actual distance difference between satellite sensors.

[0048] Based on formula (2), we get Squaring both sides and substituting into formula (1), we get:

[0049] (3)

[0050] Taking the time derivative of formula (1), we obtain the rate of change of the correlation distance. The equation relating the target parameters is shown in formula (4), where the target parameters are the locations of the interference sources. and speed :

[0051] (4)

[0052] To obtain the FDOA equation, we take the time derivative of equation (3) and get:

[0053] (5)

[0054] The joint positioning target equation of TDOA and FDOA is established as follows:

[0055] .

[0056] Let the noisy distance difference vector The difference vector of the rate of change of distance with noise They are respectively:

[0057] , .

[0058] In practical applications, when performing passive localization of target interference sources, each satellite sensor can only obtain observations of time difference and frequency difference data, and these observations contain measurement noise. Therefore, this invention considers representing the TDOA and FDOA observations using additive Gaussian noise, and the range difference vector... and the difference vector of the rate of change of distance The TDOA and FDOA measurements are described by the additive noise model:

[0059] (6)

[0060] in, This represents the true value of the distance difference vector. This represents the true value of the distance difference vector. Indicates time difference measurement noise. , to These represent the TDOA measurement noise of the 2nd to Mth LEO satellites relative to the 1st LEO satellite. Indicates frequency difference measurement noise. , to These represent the FDOA measurement noise of the 2nd to Mth LEO satellites relative to the 1st LEO satellite.

[0061] and It has zero mean and its covariance matrix is:

[0062] (7)

[0063] (8)

[0064] in, Expressing expectations, Let represent the covariance matrix.

[0065] Step 3. Solve the joint positioning target equation of TDOA and FDOA using the two-step weighted least squares method (TSWLS) and the semi-definite relaxation method (SDR) respectively to obtain the position and velocity estimates of the ground mobile interference source.

[0066] In step 3 of this embodiment, the process of solving the joint TDOA and FDOA positioning target equation using the two-step weighted least squares method is as follows:

[0067] Define auxiliary vector for: .

[0068] The resulting matrix equation is: .

[0069] in, This represents the residual of the objective function in the first step of the weighted least squares method.

[0070] matrix As shown in formula (9):

[0071] (9)

[0072] matrix As shown in formula (10):

[0073] (10)

[0074] in, express A zero vector matrix.

[0075] The solution obtained by the first step of the weighted least squares method is:

[0076] (11)

[0077] Among them, the weight matrix As shown in formula (12):

[0078] (12)

[0079] Among them, matrix Represented as: .

[0080] in, Represents the zero matrix. , .

[0081] In solving At that time, the interference variable was assumed. and It is independent of the position and velocity of the ground-based moving interference source, but in reality... and Using formulas (1) and (4) with the location of the ground mobile interference source and speed Related, that is:

[0082] (13)

[0083] The final estimation of the location and velocity of the interference source needs to achieve a dual optimization objective: it should be as close as possible to... While including the source location value, minimize the equation error in formula (13).

[0084] make , .

[0085] in, to They represent auxiliary vectors respectively. The first to seventh elements.

[0086] This leads to the second step of the two-step weighted least squares method, which involves constructing another set of equations.

[0087] Introducing auxiliary vectors for: .

[0088] Construct the equation matrix: .

[0089] in, This represents the residual of the objective function in the second step of the weighted least squares method.

[0090] matrix As shown in formula (14):

[0091] (14)

[0092] in, Representing auxiliary vectors The 8th element.

[0093] matrix As shown in formula (15):

[0094] (15)

[0095] in, express The identity matrix, express A vector of all 1s.

[0096] The solution for the second step of the weighted least squares method is:

[0097] .

[0098] weight matrix for: .

[0099] in, Represents convolution. .

[0100] The final location and velocity of the ground-based mobile interference source are shown in formula (16):

[0101] (16)

[0102] in, to They represent auxiliary vectors respectively. The first to sixth elements. .

[0103] The core idea of ​​the SDR method is to use SDR technology to transform a constrained optimization problem into a semidefinite programming problem, which can then be solved using a convex optimization toolkit. In this embodiment, step 3, specifically, involves using the semidefinite relaxation method to solve the joint localization objective equation of TDOA and FDOA as follows:

[0104] Define auxiliary vector for: .

[0105] Introducing positive semidefinite matrices for: .

[0106] The objective function for constructing SDR is:

[0107] (17)

[0108] The objective function of SDR shown in formula (17) can be written as:

[0109] (18)

[0110] in, Representing auxiliary vectors The 4th element, Representing auxiliary vectors The 8th element, namely , . Representing auxiliary vectors The first to third elements are the location vectors of the ground-based mobile interference sources. Representing auxiliary vectors The 5th to 7th elements are the velocity vectors of the ground-based mobile interference source.

[0111] The objective function of SDR can be further expressed as: .

[0112] Among them, matrix and Represented as:

[0113] (19)

[0114] The constraint shown in formula (18) can be further expressed as:

[0115] (20)

[0116] in:

[0117] (twenty one)

[0118] By further tightening the constraints using the Cauchy-Schwarz inequality, we obtain:

[0119] (twenty two)

[0120] Formula (22) is equivalent to .

[0121] in, , .

[0122] Further tightening the constraints yields:

[0123] (twenty three)

[0124] Formula (23) is equivalent to .

[0125] because Non-negative, multiply both sides of formula (23) by The results are as follows:

[0126] (twenty four)

[0127] Formula (24) is equivalent to .

[0128] in, .

[0129] Adding all constraints to the objective function of SDR, the final semidefinite programming problem is obtained as follows:

[0130] (25)

[0131] Its constraints are:

[0132] (26)

[0133] Furthermore, in step 3 of this embodiment, after solving the joint positioning target equation of TDOA and FDOA using TSWLS and SDR, the root mean square error (RMSE) and Cramer-Rhodes lower bound (CRLB) are used to evaluate the solution methods TSWLS and SDR. The specific process is as follows:

[0134] The root mean square error is used to evaluate positioning performance, as defined in equations (27) and (28):

[0135] (27)

[0136] (28)

[0137] in, , Indicates the number of Monte Carlo runs; This represents the root mean square error of the position. Indicates the root mean square error of the velocity; This indicates the ground mobile interference source obtained using the solution method. The next position estimate, The expression represents the ground mobile interference source obtained using the solution method. The estimated velocity for this time.

[0138] The Cramer-Rhodes lower bound is the lowest possible variance achievable by an unbiased linear estimator, which is equal to the inverse of the Fisher information matrix. The definition is as follows:

[0139] (29)

[0140] in, This represents the distance difference derived from TDOA and FDOA measurements. and distance change rate The vector formed . Represented by auxiliary vectors conditional The probability density function. This represents the true value of the parameter vector containing the position and velocity of the ground-based moving interference source. The theoretical derivations in this embodiment are all performed near the true parameter values.

[0141] Crame-Lo lower world Equal to the inverse of the Fisher information matrix:

[0142] (30)

[0143] in, This represents the theoretical lower bound of the estimation error covariance matrix when performing unbiased estimation of the position and velocity of a moving source under given TDOA and FDOA measurement noise models.

[0144] Figure 2 and Figure 3The position RMSE and velocity RMSE obtained using the method of this invention are given. CRLB is the lower bound of CRLB. TDOA combined with FDOA TSWLS indicates that the objective equation is established using the method of this invention, and the objective equation is solved for localization using the two-step weighted least squares method, i.e., the TSWLS algorithm. TDOA combined with FDOA SDR indicates that the objective equation is established using the method of this invention, and the objective equation is solved for localization using the semidefinite relaxation method, i.e., the SDR algorithm.

[0145] Figure 2 This demonstrates a comparison of the RMSE performance of the TSWLS and SDR algorithms in location estimation. (The text also mentions noise variance.) No more than 10dB, that is At that time, the TSWLS algorithm demonstrated extremely high localization accuracy, with its position RMSE consistently close to the lower bound of CRLB, validating its effectiveness and fast convergence capability in low-noise scenarios. However, as the noise variance increases... As the noise level gradually rises above 15dB, the TSWLS algorithm's positioning error increases rapidly, exceeding 4000 meters at 30dB, significantly deviating from the theoretical limit. In contrast, the SDR algorithm performs more stably across the entire noise range, with its RMSE curve rising slowly with increasing noise, and its noise variance... Even at 30dB, the position RMSE can still be maintained at around 1000 meters, demonstrating a significant noise reduction advantage.

[0146] Figure 3 This paper presents a comparison of the RMSE performance of the TSWLS and SDR algorithms in velocity estimation. (Noise variance...) No more than 5dB, that is Initially, both the TSWLS and SDR algorithms showed RMSEs close to CRLB, with errors remaining below 22 m / s, demonstrating good initial computational capabilities. However, when the noise variance increased from no more than 10 dB to above 10 dB, the TSWLS algorithm's estimation error increased sharply, with RMSE exceeding 50 m / s. In contrast, the SDR algorithm maintained a more gradual error growth trend across the entire noise range, with a lower noise variance. At a speed of 30dB, the RMSE can still be maintained at around 400m / s, demonstrating significant robustness and adaptability to tracking highly dynamic targets.

[0147] This invention proposes a method for locating interference sources by fusing measurement information from multiple LEO satellite sensors. This method comprehensively utilizes TDOA and FDOA measurements to jointly calculate the position and velocity of ground-based moving interference sources. Considering the high nonlinearity and noise sensitivity of the TDOA-FDOA joint model, two calculation strategies are designed: one is the TSWLS algorithm based on linearization of the measurement values, and the other is the SDR algorithm, which relaxes the original non-convex problem into a semidefinite programming form through convex optimization. Simulation results show that the TSWLS algorithm exhibits extremely high calculation accuracy and computational efficiency in low-noise scenarios, making it suitable for applications with high real-time requirements; while the SDR algorithm demonstrates stronger robustness in both low-noise and high-noise scenarios, especially maintaining good calculation performance in the presence of interference factors such as ionospheric and tropospheric delays.

[0148] In addition, in step 3 of this embodiment, based on the complex environment of adding ionospheric delay parameters and tropospheric delay parameters, RMSE and CRLB are used to evaluate the solution methods TSWLS and SDR.

[0149] The process of introducing the ionospheric delay parameter is as follows:

[0150] Calculate the total electron content in the zenith direction for:

[0151] (31)

[0152] in, Indicates the electron density along the propagation path. Let be the length of the differential arc segment along the path in the zenith direction.

[0153] Depend on The total electron content along the oblique propagation path required for calculating ionospheric delay is obtained by transforming the projection function. :

[0154] (32)

[0155] in, A function representing the zenith distance of the satellite relative to the station. express The projection function, This represents the zenith distance of the satellite relative to the ionospheric puncture point. The ionospheric puncture point is the intersection of the line connecting the satellite and the station with the thin layer of the ionosphere. The projection function is directly derived from the geometric relationships between the station, the satellite, and the puncture point. The average radius of the Earth This refers to the thickness of the thin layer.

[0156] By expanding the integrand using the zenith distance trigonometric function for two-level integration, and inputting the actual meteorological parameters measured by the observation station, the zenith tropospheric delay and ionospheric delay can be directly calculated. for:

[0157] (33)

[0158] in, Indicates the frequency of signal propagation.

[0159] Introducing tropospheric delay parameters The process is as follows:

[0160] (34)

[0161] (35)

[0162] in, Indicates the latitude of the interference source. For elevation, This represents a correction for the gravitational acceleration caused by the Earth's rotation. This indicates the temperature at the location of the ground-based mobile interference source. This indicates the air pressure at the location of the ground-based mobile interference source.

[0163] For complex environments with added ionospheric and tropospheric delay parameters, when using RMSE to evaluate the solution methods TSWLS and SDR, the root mean square error is defined as shown in Equations (27) and (28).

[0164] When evaluating the solution methods TSWLS and SDR using CRLB in complex environments with added ionospheric and tropospheric delay parameters, the Fisher information matrix... The definition is shown in formula (29), and the Cramer-Rhodes lower bound is shown in formula (30). Equal to Fisher's information matrix The reverse.

[0165] covariance matrix TDOA noise vector and FDOA noise vector They are respectively:

[0166] .

[0167] .

[0168] in, to This indicates the time propagation error caused by ionospheric propagation error to TDOA and FDOA. to This indicates the time propagation error caused by tropospheric propagation error to TDOA and FDOA.

[0169] Figure 4 The position RMSE with added delay obtained using the method of this invention. Figure 4 The TSWLS with added delay represents the objective equation established using the method of this invention for complex environments with added ionospheric and tropospheric delay parameters, and the objective equation is solved by a two-step weighted least squares method. Figure 4 The SDR with added delay represents the objective equation established using the method of this invention for complex environments with added ionospheric and tropospheric delay parameters, and the objective equation is solved by the semi-definite relaxation method.

[0170] Figure 4 This paper demonstrates a comparison of the RMSE performance of the TSWLS and SDR algorithms in position estimation under complex environments with added ionospheric and tropospheric delay parameters. Figure 4 As shown, after introducing ionospheric and tropospheric delay interference, the robustness of the TSWLS algorithm further decreases, and its position RMSE curve generally rises, compared to Figure 2 There is a significant deviation when the noise variance At a noise level of 30 dB, the error exceeds 4000 m, indicating its high sensitivity to atmospheric delay model disturbances. In contrast, the SDR algorithm demonstrates significant advantages in complex disturbance environments; even under the combined effects of high noise and atmospheric delay, its position RMSE remains within 1000 m. At a value of 30dB, the position RMSE error after adding delay remains at approximately 1000 meters.

[0171] In summary, the TSWLS algorithm demonstrates high accuracy and efficiency in low-noise environments, making it suitable for applications with high real-time requirements. SDR, on the other hand, exhibits superior robustness in complex electromagnetic interference environments, making it suitable for precise positioning needs under high-dynamic and high-noise conditions.

[0172] The method of the present invention is in In low-noise environments, based on the two-step weighted least squares method, the target equation can be solved in real time, achieving a positioning accuracy of 100 meters, with a root mean square error of no more than [value missing]. The root mean square error of the speed is no greater than This significantly meets the needs of high-time-efficiency scenarios. When When complex disturbances such as ionospheric and tropospheric delays exist, a semidefinite relaxation method is introduced. By constructing auxiliary decision variables and constraining them with the Cauchy-Schwarz inequality, the instability problem of the non-convex optimization model is effectively solved, demonstrating strong robustness. The SDR technology is used to reconstruct and convexly relax the non-convex optimization model involved in the positioning problem, which significantly expands the applicable scenarios of the solution. Under challenging conditions such as complex dynamics, high-noise environments, and atmospheric errors such as tropospheric and ionospheric delays, it still maintains excellent robustness and solution accuracy.

[0173] Example 2

[0174] This embodiment 2 describes a mobile GNSS interference source localization system based on LEO satellites, which is based on the same inventive concept as the mobile GNSS interference source localization method based on LEO satellites in embodiment 1.

[0175] Specifically, this LEO satellite-based mobile GNSS interference source localization system includes the following modules:

[0176] The position and velocity calculation module is used to calculate the spatial position and velocity of each LEO satellite sensor at the observation time based on the two lines of TLE data from the LEO satellite orbit.

[0177] The objective equation establishment module is used to construct TDOA and FDOA observation models based on the spatial position and velocity of ground moving interference sources using LEO satellite sensors, and to establish the joint TDOA and FDOA positioning objective equation.

[0178] And an interference source localization module, which is used to solve the joint localization target equation of TDOA and FDOA by using the two-step weighted least squares method (TSWLS) and the semi-definite relaxation method (SDR) respectively, to obtain the position estimate and velocity estimate of the ground mobile interference source.

[0179] It should be noted that the implementation process of the functions and roles of each functional module in the LEO satellite-based mobile GNSS interference source localization system is detailed in the corresponding steps of the method in Example 1, and will not be repeated here.

[0180] Example 3

[0181] This embodiment 3 describes a computer device that includes a memory and one or more processors.

[0182] The memory stores executable code, which, when executed by the processor, is used to implement the steps of the mobile GNSS interference source localization method based on LEO satellites in Embodiment 1 above.

[0183] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0184] Example 4

[0185] This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of a method for locating mobile GNSS interference sources based on LEO satellites.

[0186] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0187] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for locating mobile GNSS interference sources based on LEO satellites, characterized in that, Includes the following steps: Step 1. Based on the two lines of TLE data from the LEO satellite orbits, calculate the spatial position and velocity of each LEO satellite sensor at the observation time; Step 2. Based on the spatial position and velocity of LEO satellite sensors, construct TDOA and FDOA observation models for the position and velocity parameters of ground-based mobile interference sources, and establish a joint TDOA and FDOA positioning target equation; Step 3. Solve the joint positioning target equation of TDOA and FDOA using the two-step weighted least squares method (TSWLS) and the semi-definite relaxation method (SDR) respectively to obtain the position and velocity estimates of the ground moving interference source. Step 2 specifically involves: consider In a three-dimensional spatial motion interference source localization scenario where multiple LEO satellite sensors work in collaboration, let the first... The spatial position and velocity of the LEO satellite sensors are known; No. Spatial location of LEO satellite sensors and speed They are represented as follows: , ; in, , , , Indicates the first Three-dimensional coordinate components of each LEO satellite sensor in the geocentric-geofixed coordinate system; Location of ground-based mobile interference sources and speed They are represented as follows: , ; in, , , This represents the three-dimensional coordinate components of a ground-based mobile interference source in the Earth-centered Earth-fixed coordinate system. The first LEO satellite sensor was used as a reference. Ground-based mobile interference sources and the first Distance between LEO satellite sensors for: (1) No. The time difference of arrival (TDOA) between the signals received by the first LEO satellite sensor and the first LEO satellite sensor is: The speed of signal propagation is The equation relating the time difference of arrival to the location of the interference source is shown in equation (2): (2) in, This represents the actual distance difference between satellite sensors; Based on formula (2), we get Squaring both sides and substituting into formula (1), we get: (3) Taking the time derivative of formula (1), we obtain the rate of change of the correlation distance. The equation relating the target parameters is shown in formula (4), where the target parameters are the locations of the interference sources. and speed : (4) To obtain the FDOA equation, we take the time derivative of equation (3) and get: (5) The joint positioning target equation of TDOA and FDOA is established as follows: ； Let the noisy distance difference vector The difference vector of the rate of change of distance with noise They are respectively: ， ； Distance difference vector and the difference vector of the rate of change of distance The TDOA and FDOA measurements are described by the additive noise model: (6) in, This represents the true value of the distance difference vector; This represents the true value of the distance difference vector. Indicates time difference measurement noise. , to These represent the TDOA measurement noise of the 2nd to Mth LEO satellites relative to the 1st LEO satellite, respectively. Indicates frequency difference measurement noise. , to These represent the FDOA measurement noise of the 2nd to Mth LEO satellites relative to the 1st LEO satellite, respectively. and It has zero mean and its covariance matrix is: (7) (8) in, Expressing expectations, Let represent the covariance matrix.

2. The method for locating mobile GNSS interference sources based on LEO satellites according to claim 1, characterized in that, In step 1, the TLE data includes orbital altitude, perigee angle, orbital inclination, right ascension of the ascending node, mean perigee angle, mean perigee time, and angular velocity; the spatial position and velocity of each LEO satellite sensor at the observation time are obtained by analyzing the TLE orbital elements and applying the SGP4 propagation model.

3. The method for locating mobile GNSS interference sources based on LEO satellites according to claim 2, characterized in that, In step 3, the process of solving the joint TDOA and FDOA positioning target equation using the two-step weighted least squares method is as follows: Define auxiliary vector for: ; The resulting matrix equation is: ; in, This represents the residual of the objective function in the first step of the weighted least squares method; matrix As shown in formula (9): (9) matrix As shown in formula (10): (10) in, express 0 vector matrix; The solution obtained by the first step of the weighted least squares method is: (11) Among them, the weight matrix As shown in formula (12): (12) Among them, matrix Represented as: ; in, Represents the zero matrix. , ; In solving When assuming the disturbance variable and It is independent of the position and velocity of the ground-based moving interference source; in fact... and Using formulas (1) and (4) with the location of the ground mobile interference source and speed Related, that is: (13) make , ; in, to They represent auxiliary vectors respectively. The first to seventh elements; This leads to the second step of the two-step weighted least squares method, which constructs another set of equations; Introducing auxiliary vectors for: ; Construct the equation matrix: ; in, This represents the residual of the objective function in the second step of the weighted least squares method; matrix As shown in formula (14): (14) in, Representing auxiliary vectors The 8th element; matrix As shown in formula (15): (15) in, express The identity matrix, express A vector of all 1s; The solution for the second step of the weighted least squares method is: ； weight matrix for: ; in, Represents convolution. ; The final location and velocity of the ground-based mobile interference source are shown in formula (16): (16) in, to They represent auxiliary vectors respectively. The first to sixth elements; .

4. The method for locating mobile GNSS interference sources based on LEO satellites according to claim 3, characterized in that, In step 3, the process of solving the joint TDOA and FDOA localization target equation using the semi-definite relaxation method is as follows: Define auxiliary vector for: ; Introducing positive semidefinite matrices for: ; The objective function for constructing SDR is: (17) The objective function of SDR shown in formula (17) can be written as: (18) in, Representing auxiliary vectors The 4th element, Representing auxiliary vectors The 8th element, namely , ; Representing auxiliary vectors The first to third elements are the location vectors of the ground-based mobile interference source; Representing auxiliary vectors The 5th to 7th elements are the velocity vectors of the ground-based mobile interference source; The objective function of SDR can be further expressed as: ; Among them, matrix and Represented as: (19) The constraint shown in formula (18) can be further expressed as: (20) in: (21) By further tightening the constraints using the Cauchy-Schwarz inequality, we obtain: (22) Formula (22) is equivalent to ; in, , ; Further tightening the constraints yields: (23) Formula (23) is equivalent to ; because Non-negative, multiply both sides of formula (23) by The results are as follows: (24) Formula (24) is equivalent to ; in, ; Adding all constraints to the objective function of SDR, the final semidefinite programming problem is obtained as follows: (25) Its constraints are: (26)。 5. The method for locating mobile GNSS interference sources based on LEO satellites according to claim 4, characterized in that, In step 3, after solving the joint positioning target equation of TDOA and FDOA using TSWLS and SDR, the root mean square error (RMSE) and Cramer-Rhodes lower bound (CRLB) are used to evaluate the solution methods TSWLS and SDR. The specific process is as follows: The root mean square error is used to evaluate positioning performance, as defined in equations (27) and (28): (27) (28) in, , Indicates the number of Monte Carlo runs; This represents the root mean square error of the position. Indicates the root mean square error of the velocity; This indicates the ground mobile interference source obtained using the solution method. The next position estimate, The expression represents the ground mobile interference source obtained using the solution method. The estimated velocity value for the next step; Fisher Information Matrix The definition is as follows: (29) in, This represents the distance difference derived from TDOA and FDOA measurements. and distance change rate The vector formed ; Represented by auxiliary vectors conditional The probability density function; This represents the true value of a parameter vector containing the position and velocity of a ground-based moving interference source; Crame-Lo lower world Equal to the inverse of the Fisher information matrix: (30)。 6. The method for locating mobile GNSS interference sources based on LEO satellites according to claim 5, characterized in that, In step 3, the TSWLS and SDR solution methods are evaluated using RMSE and CRLB, based on the complex environment of adding ionospheric delay parameters and tropospheric delay parameters. The process of introducing the ionospheric delay parameter is as follows: Calculate the total electron content in the zenith direction for: (31) in, Indicates the electron density along the propagation path. Let be the length of the differential arc segment along the path in the zenith direction; Depend on The total electron content along the oblique propagation path required for calculating ionospheric delay is obtained by transforming the projection function. : (32) in, A function representing the zenith distance of the satellite relative to the station. express The projection function, This represents the zenith distance of the satellite relative to the ionospheric puncture point; The average radius of the Earth The thickness is the height of the thin layer; Ionospheric delay for: (33) in, Indicates the signal propagation frequency; Introducing tropospheric delay parameters The process is as follows: (34) (35) in, Indicates the latitude of the interference source. For elevation, This represents a correction for the gravitational acceleration caused by the Earth's rotation. This indicates the temperature at the location of the ground-based mobile interference source. This indicates the air pressure at the location of the ground-based mobile interference source; For complex environments with added ionospheric and tropospheric delay parameters, when using RMSE to evaluate the solution methods TSWLS and SDR, the root mean square error is defined as shown in Equations (27) and (28). When evaluating the solution methods TSWLS and SDR using CRLB in complex environments with added ionospheric and tropospheric delay parameters, the Fisher information matrix... The definition is shown in formula (29), and the Cramer-Rhodes lower bound is shown in formula (30). Equal to Fisher's information matrix The reverse; covariance matrix TDOA noise vector and FDOA noise vector They are respectively: ； ； in, to This indicates the time propagation error caused by ionospheric propagation error to TDOA and FDOA. to This indicates the time propagation error caused by tropospheric propagation error to TDOA and FDOA.

7. A LEO satellite-based mobile GNSS interference source localization system for implementing the LEO satellite-based mobile GNSS interference source localization method as described in claim 1, characterized in that, The LEO satellite-based mobile GNSS interference source localization system includes: The position and velocity calculation module is used to calculate the spatial position and velocity of each LEO satellite sensor at the observation time based on the two lines of TLE data from the LEO satellite orbits. The objective equation establishment module is used to construct TDOA and FDOA observation models based on the spatial position and velocity of ground mobile interference sources using LEO satellite sensors, and to establish the joint TDOA and FDOA positioning objective equation. And an interference source localization module, which is used to solve the joint localization target equation of TDOA and FDOA by using the two-step weighted least squares method (TSWLS) and the semi-definite relaxation method (SDR) respectively, to obtain the position estimate and velocity estimate of the ground mobile interference source.

8. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the mobile GNSS interference source localization method based on LEO satellites as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method for locating mobile GNSS interference sources based on LEO satellites as described in any one of claims 1 to 6.

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