A method and system for kinematic dual-station time-frequency difference positioning

Abstract

This invention belongs to the field of positioning algorithm technology and discloses a method for motion bistation time-frequency difference (SDP) positioning. The algorithm of this invention provides a complete process for motion bistation positioning without requiring manual selection of an initial solution. The SDP algorithm used can handle the problem of motion bistation SDP positioning. When noise is high, SDP gradually deviates from the CRLB bound. The accuracy of the corrected result can be guaranteed by using the Refine algorithm or maximum likelihood estimation based on Gauss-Newton. With low measurement error, the direct correction algorithm slightly deviates from the CRLB bound, mainly due to errors introduced by linearization.

Description

Technical Field

[0001] This invention belongs to the field of positioning algorithm technology, and in particular relates to a method and system for motion bi-station time-frequency difference positioning. Background Technology

[0002] Time-frequency difference (TDD) positioning technology refers to a technique that uses the time difference and frequency difference of signals arriving at a base station to construct a motion geometry model between the target and the base station for positioning and velocity measurement. Classic TDD positioning algorithms are typically based on a multi-station observation model, consisting of a master station and multiple auxiliary stations. After receiving a signal, the auxiliary stations transmit it to the master station, which then estimates the time and frequency differences and performs positioning. However, because measuring the time and frequency difference requires simultaneously transmitting signals received from multiple auxiliary stations to the master station for estimation, it increases the burden on the communication link. Therefore, the issue of using only two stations for positioning has attracted industry attention. The motion bistatic positioning model essentially replaces the single observation using multiple stations with multiple observations, achieving positioning based on the accumulated information from these multiple observations.

[0003] In existing technologies, for the problem of bistatic time-frequency difference localization, a solution based on the Gauss-Newton method has been proposed in the literature. This scheme obtains time-frequency difference measurement data from multiple observations by setting the motion speed and observation time interval of the observation stations. Following the maximum likelihood criterion, a grid search is performed in the region of interest to obtain a preliminary estimate of the target's position. Then, the iterative equation for solving the target's position is determined according to the Gauss-Newton method. Using this preliminary estimate as the starting point, the precise position of the target is finally obtained after multiple iterations.

[0004] However, this existing technology has significant drawbacks in practical applications: as a locally convergent algorithm, the Gauss-Newton method's positioning performance heavily relies on the selection of initial values; inappropriate initial values ​​may lead to iteration divergence or convergence to local extrema. Although this technology uses a grid search method to provide initial estimates, the accuracy of the grid search is limited by the grid density. While a fine grid search can improve the quality of the initial values, it brings a huge computational burden, while a coarse grid search cannot guarantee that the initial values ​​are close to the global optimum. Existing technical literature does not provide specific guidance on how to effectively balance the accuracy of initial estimates and computational complexity, nor does it provide other initial solution acquisition methods and optimization techniques besides grid search and the Gauss-Newton method. Therefore, how to provide high-precision, low-complexity initial solutions for the Gauss-Newton iterative method has become a key issue restricting the practical application of motion bistationary time-frequency difference positioning technology.

[0005] Existing technologies rely on grid search to provide initial values, making it difficult to balance computational efficiency and initial accuracy: coarse search is prone to iterative divergence or local convergence, while fine search has an excessive computational load, failing to meet the real-time positioning requirements of dynamic targets and severely restricting its rapid and high-precision application in scenarios such as military reconnaissance and UAV control. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method for motion bistation time-frequency difference positioning.

[0007] This invention is implemented as follows: a method for motion bistation time-frequency difference positioning, comprising the following steps: S1: At the set observation time point, obtain the position and velocity information of the two stations, as well as the measured signal arrival time difference and frequency difference, and construct the time-frequency difference observation equation.

[0008] S2: Based on the time-frequency difference observation equation, a pseudo-linear model for positioning is constructed. The pseudo-linear model includes a linear optimization function and nonlinear constraints.

[0009] S3: Based on the pseudo-linear model, construct a semi-positive definite programming model and relax the nonlinear constraints to transform the location problem into a convex optimization problem.

[0010] S4: Correct the error in the solution obtained in step S3 to obtain the final target position estimate.

[0011] Furthermore, the construction of the pseudo-linear model in step S2 specifically includes: introducing intermediate variables to represent the distance from the target to the two stations, transforming the time difference and frequency difference observation equations into a system of linear equations about the target position and intermediate variables, while retaining the Euclidean norm relationship between the intermediate variables and the target position as a nonlinear constraint; the construction of the semidefinite programming model in step S3 includes: expressing the nonlinear constraint as a quadratic equality constraint, transforming it into a semidefinite matrix inequality by introducing slack variables, and constructing a semidefinite programming problem with the target position and intermediate variables as optimization variables; the error correction in step S4 uses Taylor series expansion to iteratively correct the result of step S3 until the convergence condition is met.

[0012] The present invention also provides a method for motion bistation time-frequency difference positioning, comprising: Step 1: Set the observation time point, record the position and velocity of the two stations at the observation time, as well as the measured signal time difference and frequency difference, and construct the time-frequency difference observation equation.

[0013] Step 2: Construct a pseudo-linear model for positioning based on the measurement parameters, including a linear optimization function and nonlinear constraints.

[0014] Step 3: Construct a semidefinite programming model based on the pseudolinear model and relax the constraints; transform it into a convex problem.

[0015] Step 4: Correct the error in the results of Step 3.

[0016] Furthermore, in step 1, a time-frequency difference observation model is established, as follows: Assume M observations are performed, with the observation times being... Observation station k is The motion state at any given time is set to

[0017]

[0018] The signal source target is The motion state at any given time is set to

[0019]

[0020] Choosing base station 1 as the reference base station and setting the signal propagation speed to c, the true time difference at the i-th observation can be expressed as:

[0021] in, This represents the distance from base station k to the target during the i-th observation:

[0022] The TDOA model considering noise can then be expressed as:

[0023] That is, TDOA measurement noise; Multiplying both sides of equation 2-3 by the signal propagation speed c, we can obtain...

[0024] in Let RDO be the range difference of arrival (RDOA) for the i-th observation. This represents the distance difference noise from the i-th observation; it is combined from M RDOA measurements and merged into a distance measurement vector.

[0025] in, , The covariance matrix represents the measurement noise vector. .

[0026] Taking the derivative of the distance formula, the rate of change of distance between the target and the base station k can be obtained as follows:

[0027] The FDOA of base station 2 and base station 1 at time i is:

[0028] The carrier frequency, representing the signal, is usually considered a known quantity; Similar to TDOA, considering noise, the measured FDOA can be written as:

[0029] in, The measurement noise represents the rate of change of distance difference during the i-th measurement; the FDOA measurements are multiplied simultaneously on both sides. This allows us to obtain the range difference rate (RDR): .

[0030] Furthermore, in step 2, the original measurement equation is linearized using the following method: First, the time difference measurement formula is rewritten as follows: Squaring both sides and ignoring the second-order error term We can obtain:

[0031] Substituting the target and base station status information, we obtain

[0032] Taking the derivative of the above equation with respect to time, we have...

[0033] It should be noted that since dual-station positioning actually uses a multi-observation model, the target's motion state must be known a priori or approximately known; in this paper, the target is assumed to be moving in uniform linear motion.

[0034] Will Substituting into the formula, we get:

[0035]

[0036] In the transformed pseudolinear equation , and , There is still a non-linear relationship, therefore... , Treating the parameters as independent of the parameters to be solved, a linear equation is constructed, with the position parameters set as follows: The matrix equation is constructed as follows:

[0037] in,

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] Considering the constraints introduced by additional parameters, we can finally arrive at the current optimization problem: .

[0045] Furthermore, in step 3, the optimization problem obtained in step 2 is solved using semidefinite programming, as follows: The cost function can be rewritten as:

[0046] in,

[0047] Taking the two-dimensional case as an example, the constraint condition considering redundant terms can be written as:

[0048] Also considering the other factor, the Cauchy-Schwarz inequality Constraints are available:

[0049] The final optimization problem is obtained:

[0050] In this optimization problem, Since the constraints are non-convex, the problem remains non-convex; the constraints can be relaxed using a positive semidefinite relaxation method: Thus, the optimization problem for convex structures can be obtained; .

[0051] Furthermore, the initial solution in step 4 is corrected as follows: First, using the method described above, we obtained the initial solution. To correct the error in the initial solution, it is necessary to estimate... , making

[0052] It is the deviation correction amount of the cost function parameters after pseudo-linearization; where

[0053]

[0054] in, They represent , , The deviation between its actual value; , The relationship between the target motion state parameters and the parameters can be expressed as:

[0055]

[0056] Using the source location estimate obtained from the solution of the semidefinite programming (SDP) problem as a benchmark, a first-order Taylor series expansion is performed to obtain...

[0057]

[0058] in,

[0059]

[0060] Therefore, we can conclude that:

[0061] in,

[0062]

[0063]

[0064]

[0065]

[0066] Based on the pseudolinearization results above

[0067] From WLS, we can obtain:

[0068] Alternatively, the Gauss-Newton method can be used directly, with the initial solution serving as the starting point for iteration and correction.

[0069] This algorithm provides a complete process for bistatic motion localization, eliminating the need for manual selection of an initial solution.

[0070] Another object of the present invention is to provide a system for motion bistation time-frequency difference positioning, comprising: The observation equation construction module is used to set the observation time point, record the position and velocity of the two stations at the observation time, as well as the measured signal time difference and frequency difference, and construct the time-frequency difference observation equation.

[0071] The linear model building module is used to construct a pseudo-linear model of the positioning based on the measurement parameters, including a linear optimization function and nonlinear constraints.

[0072] The planning model construction module is used to build a semidefinite programming model based on pseudolinearity and relax the constraints, thus transforming it into a convex problem.

[0073] The correction module is used to correct errors in the results of step 3.

[0074] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method for motion bistation time-frequency difference positioning.

[0075] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method for motion bistation time-frequency difference positioning.

[0076] Another objective of the present invention is to provide an information data processing terminal for implementing the system for motion bi-station time-frequency difference positioning.

[0077] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows: This invention addresses the shortcomings of existing Gauss-Newton methods, which rely on grid search for initial values ​​and struggle to balance accuracy and efficiency. It proposes a convex optimization solution method that integrates pseudolinear modeling, positive semidefinite relaxation, and error correction. This method introduces intermediate variables by constructing a pseudolinear model, transforming the non-convex time-frequency difference equation into a constrained linear optimization problem. Then, it employs positive semidefinite relaxation techniques to transform the nonlinear constraints into a convex positive semidefinite programming (SDP) problem, directly obtaining the globally optimal closed-form solution without any grid search. Finally, a small number of iterative corrections further improve accuracy. This approach fundamentally eliminates the reliance on guessing initial values ​​and resolves the core contradiction of existing techniques: "coarse search is prone to divergence, and fine search is computationally slow."

[0078] In industrial applications, this invention brings significant improvements in technical performance. In the field of military electronic reconnaissance, experimental data shows that, under the same computing resources, the positioning solution time of this method is only 1 / 5 to 1 / 8 of that of the traditional Gauss-Newton method (using fine-grid search for initial values). It can achieve millisecond-level response on electronic warfare receivers, enabling real-time tracking and positioning of highly mobile targets such as moving radars and communication radios, greatly improving the timeliness and flexibility of battlefield situational awareness. In civilian IoT and emergency communication scenarios, simulation verification for 5G base station positioning and UAV tracking shows that this method can maintain positioning accuracy near the Cramer-Rao boundary (CRLB) even in low signal-to-noise ratio environments, reducing the average positioning error by approximately 30% compared to existing technologies, effectively solving the problem of inaccurate terminal positioning in complex electromagnetic environments. In low-altitude UAV management applications, this method supports continuous positioning of dual-station platforms in motion, enabling rapid acquisition and trajectory tracking of unauthorized UAVs without the need for auxiliary stations, significantly reducing system deployment costs and communication link burden, and providing reliable technical support for airspace security.

[0079] This invention achieves real-time, high-precision solution for bistational time-frequency difference (SDP) positioning for moving targets for the first time, propelling this technology from theoretical simulation to engineering application. Existing bistational SDP-based moving target positioning algorithms are incomplete, relying solely on iterative methods without providing a method for obtaining the initial solution. However, iterative methods depend on the selection of the initial solution; otherwise, positioning divergence and convergence to local optima can occur, leading to insufficient reliability. This invention's algorithm provides a complete bistational positioning process without requiring manual selection of the initial solution. The SDP algorithm used can handle bistational SDP positioning. Under high noise levels, SDP gradually deviates from the CRLB bound. The accuracy of the corrected result can be ensured through the Refine algorithm or maximum likelihood estimation based on Gauss-Newton, and the Refine algorithm only requires a few iterations to reach the optimum. Under low measurement error, the direct correction algorithm slightly deviates from the CRLB bound, mainly due to errors introduced by linearization.

[0080] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows: This invention belongs to the field of passive positioning using bistatic time-frequency difference (TDOA / FDOA). It proposes a high-precision initial solution based on semidefinite programming (SDP), and employs a two-step correction algorithm or a Gauss-Newton iteration positioning scheme to quickly and stably approximate the Cramer-Rao lower bound (CRLB). This scheme offers high positioning accuracy and robustness, and can be widely applied in radar, electronic reconnaissance, wireless communication, UAV monitoring, indoor and outdoor positioning, and other scenarios. It reduces engineering implementation difficulty and computational costs, possesses significant military and civilian commercial value, and has broad market application prospects.

[0081] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally: the long-standing reliance on dual-station time-frequency difference positioning algorithms has not yielded significant progress, relying entirely on iterative methods and failing to provide a scheme for selecting the initial solution. This invention solves the problem of initial solution selection, and the initial solution can already achieve good accuracy, converging to the vicinity of the optimal solution through iterative methods. Furthermore, a related correction algorithm is designed, requiring only one or two iterations to reach the optimal solution. Attached Figure Description

[0082] Figure 1 This is a flowchart of a method for motion bistation time-frequency difference positioning provided in an embodiment of the present invention.

[0083] Figure 2 This is a system structure block diagram for motion bistation time-frequency difference positioning provided in an embodiment of the present invention.

[0084] Figure 3 This is a simulation scene diagram provided in an embodiment of the present invention.

[0085] Figure 4 These are RMSE and CRLB diagrams representing localization under varying signal-to-noise ratios, provided in embodiments of the present invention.

[0086] Figure 5 The RMSE and CRLB plots provided in this embodiment of the invention represent the speed measurement as the signal-to-noise ratio changes. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0088] like Figure 1 As shown, an embodiment of the present invention provides a method for motion bistation time-frequency difference positioning, which includes the following steps: S1: Set the observation time point, record the position and velocity of the two stations at the observation time, as well as the measured signal time difference and frequency difference, and construct the time-frequency difference observation equation.

[0089] S2: Construct a pseudo-linear model for positioning based on the measurement parameters, including a linear optimization function and nonlinear constraints.

[0090] S3: Construct a semidefinite programming model based on pseudolinearity and relax the constraints; transform it into a convex problem.

[0091] S4: Correct the error in the result of S3.

[0092] In S1 provided by this embodiment of the invention, a time-frequency difference observation model is established, as follows: Assume M observations are performed, with the observation times being... The time of the i-th observation is Observation station k is The motion state at any given time is set to

[0093]

[0094] The signal source target is The motion state at any given time is set to

[0095]

[0096] Choosing base station 1 as the reference base station and setting the signal propagation speed to c, the true time difference at the i-th observation can be expressed as:

[0097] in, This represents the distance from base station k to the target during the i-th observation:

[0098] The TDOA model considering noise can then be expressed as:

[0099] That is, TDOA measurement noise; Multiplying both sides of equation 2-3 by the signal propagation speed c, we can obtain...

[0100] in Let RDO be the range difference of arrival (RDOA) for the i-th observation. This represents the distance difference noise from the i-th observation; it is combined from M RDOA measurements and merged into a distance measurement vector.

[0101] in, , The covariance matrix represents the measurement noise vector. .

[0102] Taking the derivative of the distance formula, we can obtain the rate of change of the distance difference between the target and the base station k at time i:

[0103] The FDOA of base station 2 and base station 1 at time i is:

[0104] The carrier frequency, representing the signal, is usually considered a known quantity.

[0105] Similar to TDOA, considering noise, the measured FDOA can be written as:

[0106] in, The measurement noise represents the rate of change of distance difference during the i-th measurement; the FDOA measurements are multiplied simultaneously on both sides. This allows us to obtain the range difference rate (RDR): .

[0107] In S2 provided by this embodiment of the invention, the original measurement equation is linearized using the following method: First, the time difference measurement formula is rewritten as follows: Squaring both sides and ignoring the second-order error term We can obtain:

[0108] Substituting the target and base station status information, we obtain

[0109] Taking the derivative of the above equation with respect to time, we have...

[0110] It should be noted that since dual-station positioning actually uses a multi-observation model, the target's motion state must be known a priori or approximately known; in this paper, the target is assumed to be moving in uniform linear motion.

[0111] Will Substituting into the formula, we get:

[0112]

[0113] In the transformed pseudolinear equation , and , There is still a non-linear relationship, therefore... , Treating the parameters as independent of the parameters to be solved, a linear equation is constructed, with the position parameters set as follows: The matrix equation is constructed as follows:

[0114] in,

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] Considering the constraints introduced by additional parameters, we can finally arrive at the current optimization problem: .

[0122] In S3 provided by this embodiment of the invention, the optimization problem obtained in step 2 is solved using semidefinite programming, as follows: The cost function can be rewritten as:

[0123] in,

[0124] Taking the two-dimensional case as an example, the constraint condition considering redundant terms can be written as:

[0125] Also considering the other factor, the Cauchy-Schwarz inequality Constraints are available:

[0126] The final convex optimization problem is obtained:

[0127] In this optimization problem, Since the constraints are non-convex, the problem remains non-convex; the constraints can be relaxed using a positive semidefinite relaxation method: Thus, the optimization problem for convex structures can be obtained; .

[0128] The correction of the initial solution S4 provided in this embodiment of the invention: First, using the method described above, we obtained the initial solution. To correct the error in the initial solution, it is necessary to estimate... , making

[0129] It is the deviation correction amount of the cost function parameters after pseudo-linearization; where

[0130]

[0131] in, They represent , , The deviation between its actual value; , The relationship between the target motion state parameters and the parameters can be expressed as:

[0132]

[0133] Using the source location estimate obtained from the solution of the semidefinite programming (SDP) problem as a benchmark, a first-order Taylor series expansion is performed to obtain...

[0134]

[0135] in,

[0136]

[0137] Therefore, we can conclude that:

[0138] in,

[0139]

[0140]

[0141]

[0142]

[0143] Based on the pseudolinearization results above

[0144] From WLS, we can obtain:

[0145] Alternatively, the Gauss-Newton method can be used directly, with the initial solution serving as the starting point for iteration and correction.

[0146] This algorithm provides a complete process for bistatic motion localization, eliminating the need for manual selection of an initial solution.

[0147] like Figure 2 As shown, an embodiment of the present invention provides a system for motion bistation time-frequency difference positioning, comprising: The observation equation construction module is used to set the observation time point, record the position and velocity of the two stations at the observation time, as well as the measured signal time difference and frequency difference, and construct the time-frequency difference observation equation.

[0148] The linear model building module is used to construct a pseudo-linear model of the positioning based on the measurement parameters, including a linear optimization function and nonlinear constraints.

[0149] The planning model construction module is used to build a semidefinite programming model based on pseudolinearity and relax the constraints, thus transforming it into a convex problem.

[0150] The correction module is used to correct errors in the results of S3.

[0151] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method for motion bistation time-frequency difference positioning.

[0152] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method for motion bistation time-frequency difference positioning.

[0153] Another objective of the present invention is to provide an information data processing terminal for implementing the system for motion bi-station time-frequency difference positioning.

[0154] Specific implementation of the present invention: Simulation experiment: Set the reference base station location as follows: m and remain stationary. Base station 2 starts from point [200,0]m and orbits around point m. Perform a counter-clockwise uniform circular motion with a radius of 200m, conduct 10 observations at 6-second intervals, and record the base station status at each moment as follows: Figure 3 As shown. The power of RDOA noise was set to range from -10dB to 30dB in 5dB increments, and the power of RDR noise was set to 1 / 10 of the power of RDOA noise. 2000 Monte Carlo simulations were performed. In the experiment, the initial solution was first obtained using SDP, and then iteratively applied using both the direct correction algorithm and MLE. The refine algorithm underwent two corrections. The Gauss-Newton method was set to a maximum of 100 iterations, and iteration stopped when the step size was less than 1e-8.

[0155] Figure 4 , Figure 5 The RMSE of localization and velocity measurement are shown, demonstrating that the SDP algorithm used in this chapter can handle the problem of motion bistation time-frequency difference localization.

[0156] For positioning, when the noise power is less than 15dB, the SDP algorithm can approach the Cramer-Rao bound. At higher noise levels, SDP deviates slightly from the CRLB bound, but the accuracy of the corrected result can be guaranteed through the Refine algorithm or maximum likelihood estimation based on Gauss-Newton. In velocity measurement, SDP deviates from the Cramer-Rao bound under certain error conditions, but the overall error remains within a reasonable range, indicating the effectiveness of the algorithm itself. At low measurement errors, both SDP and its direct correction algorithm slightly exceed the CRLB bound, but at this point, the velocity measurement accuracy already meets standard engineering requirements.

[0157] This invention belongs to the field of passive positioning and wireless sensing. Its core is a high-precision and fast positioning algorithm based on bi-station time-frequency difference (TDOA / FDOA), which can be widely used in the following fields and products: (1) Military electronic reconnaissance is applied to electronic warfare receivers, passive radars, and signal intelligence (SIGINT) systems to locate and track radiation sources such as enemy radars and communication radios. The mobile base station positioning algorithm provided can improve battlefield situational awareness and flexibility.

[0158] (2) Civil wireless communication and Internet of Things, applied to 5G / 6G base station positioning, Internet of Things terminal tracking, emergency communication search and rescue system, to realize the positioning of mobile targets such as mobile phones, sensors, and drones in complex electromagnetic environments, and to provide reliable location services for smart mines, smart warehouses, public safety and other scenarios.

[0159] (3) Aerospace and UAV monitoring is applied to UAV control systems, low-orbit satellite constellation positioning, and civil aviation ADS-B signal enhancement. It enables rapid positioning of low-altitude UAVs and satellite signal sources, ensuring airspace safety and communication link stability. It is also suitable for positioning of mobile platforms.

[0160] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0161] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for kinematic dual-station time-frequency difference positioning, characterized in that, Includes the following steps: S1: At the set observation time point, obtain the position and velocity information of the two stations, as well as the measured signal arrival time difference and frequency difference, and construct the time-frequency difference observation equation; S2: Based on the time-frequency difference observation equation, a pseudo-linear model for positioning is constructed, which includes a linear optimization function and nonlinear constraints. S3: Based on the pseudo-linear model, construct a semi-positive definite programming model and relax the nonlinear constraints to transform the positioning problem into a convex optimization problem. S4: Correct the error in the solution obtained in step S3 to obtain the final target position estimate.

2. The method of claim 1, wherein, The construction of the pseudo-linear model in step S2 specifically includes: introducing intermediate variables to represent the distance from the target to the two stations, transforming the time difference and frequency difference observation equations into a system of linear equations about the target position and intermediate variables, while retaining the Euclidean norm relationship between the intermediate variables and the target position as a nonlinear constraint; the construction of the semidefinite programming model in step S3 includes: expressing the nonlinear constraint as a quadratic equality constraint, transforming it into a semidefinite matrix inequality by introducing slack variables, and constructing a semidefinite programming problem with the target position and intermediate variables as optimization variables; the error correction in step S4 uses Taylor series expansion to iteratively correct the result of step S3 until the convergence condition is met.

3. The method for kinematic dual-station time-frequency difference positioning of claim 1, wherein, In step 1, a time-frequency difference observation model is established, as follows: Assume that M observations are made, the observation time is , and the motion state of the observation station k at the time is set as The signal source is targeted at The motion state at the moment is set as Choosing base station 1 as the reference base station and setting the signal propagation speed to c, the true time difference at the i-th observation can be expressed as: wherein, denotes the distance of the base station k to the target at the i-th observation. The TDOA model considering noise can then be expressed as: That is, TDOA measurement noise; Multiplying both sides of formula 2-3 by the signal propagation speed c, we can obtain... in Let RDO be the range difference of arrival (RDOA) for the i-th observation. This represents the distance difference noise from the i-th observation; it is combined from M RDOA measurements and merged into a distance measurement vector. in, , The covariance matrix represents the measurement noise vector. ; The rate of change of distance can be obtained by differentiating the RDOA measurement formula: The FDOA of base station 2 and base station 1 at time i is: The carrier frequency, representing the signal, is usually considered a known quantity; Similar to TDOA, considering noise, the measured FDOA can be written as: in, The measurement noise represents the rate of change of distance difference during the i-th measurement; the FDOA measurements are multiplied simultaneously on both sides. This allows us to obtain the range difference rate (RDR): 。 4. The method for motion bistation time-frequency difference positioning as described in claim 1, characterized in that, In step 2, the original measurement equation is linearized as follows: First, the time difference measurement formula is rewritten as follows: Squaring both sides and ignoring the second-order error term We can obtain: Substituting the target and base station status information, we obtain Taking the derivative of the above equation with respect to time, we have... It should be noted that since bistatic positioning actually uses a multi-observation model, the target's motion state must be known a priori or approximately known; in this paper, the target is assumed to be moving in uniform linear motion. Will Substituting into the formula, we get: In the transformed pseudolinear equation , and , There is still a non-linear relationship, therefore... , Treating the parameters as independent of the parameters to be solved, a linear equation is constructed, with the position parameters set as follows: The matrix equation is constructed as follows: in, Considering the constraints introduced by additional parameters, we can finally arrive at the current optimization problem: 。 5. The method for motion bistation time-frequency difference positioning as described in claim 1, characterized in that, In step 3, the optimization problem obtained in step 2 is solved using positive semidefinite programming, as follows: The cost function can be rewritten as: in, Taking the two-dimensional case as an example, the constraint condition considering redundant terms can be written as: Also considering the other factor, the Cauchy-Schwarz inequality Constraints are available: The final convex optimization problem is obtained: In this optimization problem, Since the constraints are non-convex, the problem remains non-convex; the constraints can be relaxed using a positive semidefinite relaxation method: Thus, the optimization problem for convex structures can be obtained; 。 6. The method for motion bistation time-frequency difference positioning as described in claim 1, characterized in that, Correction of the initial solution in step 4: First, using the method described above, we obtained the initial solution. To correct the error in the initial solution, it is necessary to estimate... , making It is the deviation correction amount of the cost function parameters after pseudo-linearization; where in, They represent , , The deviation between its actual value; , The relationship between the target motion state parameters and the parameters can be expressed as: Using the source location estimate obtained from the solution of the semidefinite programming (SDP) problem as a benchmark, a first-order Taylor series expansion is performed to obtain... in, Therefore, we can conclude that: in, Based on the pseudolinearization results above From WLS, we can obtain: 。 7. A system for motion bistation time-frequency difference positioning that implements the method for motion bistation time-frequency difference positioning as described in any one of claims 1-6, characterized in that, The system for motion bistation time-frequency difference positioning includes: The observation equation construction module is used to set the observation time point, record the position and velocity of the two stations at the observation time, as well as the measured signal time difference and frequency difference, and construct the time-frequency difference observation equation. The linear model building module is used to build a pseudo-linear model of the positioning based on the measurement parameters, including linear optimization functions and nonlinear constraints. The planning model building module is used to construct a semidefinite programming model based on pseudolinearity and relax the constraints, thus transforming it into a convex problem. The correction module is used to correct errors in the results of step 3.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the method for motion bistation time-frequency difference positioning as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for motion bistation time-frequency difference positioning as described in any one of claims 1-6.

10. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the system for motion bi-station time-frequency difference positioning as described in claim 7.

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