An Elliptic Positioning Method and System Based on the Master Optimization Minimization Algorithm

Abstract

This invention proposes an elliptic positioning method and system based on a master optimization minimization algorithm. The method includes: acquiring the position information of the transmitter and receiver and bistatic distance measurements; estimating the position of a target object; wherein, the target object position estimation process includes the following steps: generating an initial solution for the target object position using the weighted least squares method; constructing a surrogate function satisfying upper bounds, compactness, and gradient consistency to transform the nonlinear, non-convex maximum likelihood estimation problem into an iterable convex optimization subproblem; obtaining the analytical solution of the iterable convex optimization subproblem and updating the target object position. This invention can significantly reduce computational complexity while improving the accuracy of target object position estimation.

Description

[Technical Field] This invention relates to the field of wireless communication technology, and in particular to an elliptic positioning method and system based on a master optimization minimization algorithm. [Background Technology] Passive target localization technology plays a crucial role in modern wireless communication, sonar, and radar systems. With continuous technological advancements, the demand for high-precision and high-efficiency localization methods is increasing. Traditional distance-based localization methods, such as measuring direct distance, distance difference, and distance sum, can meet localization requirements to some extent, but these methods often rely on precise clock synchronization, which is often difficult to achieve in practical applications. Furthermore, these methods often suffer from insufficient accuracy and high computational complexity when dealing with localization problems in complex environments.

[0001] Elliptic positioning methods based on bistatic distance measurement have attracted attention due to their advantages such as not requiring strict clock synchronization and flexible deployment. This method estimates the target's position by constructing an elliptic positioning model by measuring the distance the signal propagates from the transmitter to the receiver after reflection from the target. However, the elliptic positioning problem is inherently a nonlinear, nonconvex optimization problem, and traditional solution methods have significant limitations.

[0002] Maximum likelihood estimation (MLE) is a well-known method when measurement noise follows a Gaussian distribution. However, because the MLE problem is inherently nonlinear, its solution process is often complex and prone to getting trapped in local optima. To address this issue, weighted least squares (WLS) simplifies the computation by transforming the nonlinear problem into a pseudolinear expression. However, the WLS method requires the introduction of numerous auxiliary variables when generating the pseudolinear expression, which not only increases computational complexity but also leads to performance degradation when measurement data is insufficient.

[0003] In summary, how to achieve high-precision and rapid target positioning by efficiently solving nonlinear and nonconvex optimization problems in complex noisy environments is one of the important problems that urgently need to be solved in this field. [Summary of the Invention] The purpose of this invention is to provide an elliptical positioning method and system based on a master optimization minimization algorithm to overcome the shortcomings of the prior art. It can significantly reduce computational complexity while improving the accuracy of target position estimation.

[0004] This invention provides an elliptic positioning method based on a master optimization minimization algorithm, including: Acquire the position information of the transmitter and receiver, and the bistatic distance measurement; The location of the target object is estimated; the process of estimating the location of the target object includes the following steps: The initial solution for the target object's position is generated using the weighted least squares method. A surrogate function that satisfies the upper bound, compactness, and gradient consistency is constructed to transform the nonlinear and non-convex maximum likelihood estimation problem into an iterable convex optimization subproblem. Calculate the analytical solution to the iterable convex optimization subproblem and update the target object's position.

[0005] In the elliptic localization method based on the master optimization minimization algorithm described above, the surrogate function may optionally be: ; in, Here are the position coordinates of the target object to be located, M is the number of transmitters, and N is the number of receivers. These are the weighting coefficients. This is the offset vector.

[0006] In the elliptic localization method based on the master optimization minimization algorithm described above, optionally, the process of estimating the target object's position includes the following steps: Use the WLS method to obtain the initial solution; The MM algorithm is used for iterative solution until the relative error of the target object position estimate is less than the convergence tolerance.

[0007] In the elliptic positioning method based on the master optimization minimization algorithm described above, optionally, the formula for the closed-form solution of the subproblem in the (k+1)th iteration is: ; in, Indicates the weighting coefficient. Represents the offset vector. These are the coordinates of the transmitter or receiver.

[0008] In the elliptic localization method based on the master optimization minimization algorithm described above, optionally, the formulas for the offset vector and weight coefficients are as follows: ; in, for The largest eigenvalue, , ; For vectors The i-th term, and Q= I; To measure the covariance matrix of the noise, This is a matrix of bistatic distance measurements.

[0009] In the elliptical localization method based on the master optimization minimization algorithm described above, optionally, the formula for determining whether the relative error of the target object's position estimate is less than the convergence tolerance is as follows: ; in, This is the closed-form solution to the subproblem in the (k+1)th iteration. This is the closed-form solution to the subproblem in the k-th iteration. To achieve convergence tolerance.

[0010] In the elliptic localization method based on the master optimization minimization algorithm described above, optionally, the convergence tolerance is no greater than [value missing]. .

[0011] This invention also proposes an elliptic positioning system based on a master optimization minimization algorithm, comprising: At least one transmitter for transmitting signals; At least two receivers for receiving measurement signals; The processor, transmitter, and receiver are all communicatively connected to the processor. The processor is used to acquire the position coordinates of each transmitter and receiver, as well as the measurement results from each receiver, and to estimate the position of the target object; among them, The processor uses the method described in any of the above methods to estimate the location of the target object.

[0012] In the elliptic positioning system based on the master optimization minimization algorithm described above, optionally, the number of transmitters is 1-20 and they are deployed separately; the number of receivers is 2-20 and they are deployed separately.

[0013] In the elliptic positioning system based on the master optimization minimization algorithm described above, optionally, the measurement results of each receiver include the corresponding bistatic distance measurement value of each receiver.

[0014] Compared with existing technologies, this invention has the following advantages: During estimation, an initial solution for the target object's position is generated using the Weighted Least Squares (WLS) method; by constructing a surrogate function that satisfies upper bounds, compactness, and gradient consistency, the nonlinear, non-convex maximum likelihood estimation (MLE) problem is transformed into an iterable convex optimization subproblem; the analytical solution of the subproblem is iteratively solved to update the target object's position, while simultaneously achieving superlinear convergence using the quadratic iteration method. This invention can significantly reduce computational complexity while improving the accuracy of target object position estimation, with positioning accuracy approaching the Cramer-Rao lower bound. Furthermore, by transforming the complex optimization problem into a surrogate function subproblem with an analytical solution, this invention can effectively simplify the computation process. [Attached Image Description] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 A schematic diagram of the elliptic positioning method and system based on the master optimization minimization algorithm provided in an embodiment of the present invention; Figure 2 The flowchart illustrates the steps of the elliptic positioning method based on the master optimization minimization algorithm for a single transmitter provided in an embodiment of the present invention. Figure 3 The flowchart illustrates the steps of the elliptic positioning method based on the master optimization minimization algorithm for multiple transmitters provided in this embodiment of the invention. Figure 4 A structural block diagram of an elliptical positioning system based on a master optimization minimization algorithm is provided for embodiments of the present invention.

Detailed Implementation Methods

[0016] In the description of this invention, it should be understood that the terms "longitudinal," "lateral," "thickness," "upper," "lower," "top," "bottom," "inner," "outer," and "radial," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the 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, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, unless otherwise stated, "a plurality of" means two or more. In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0017] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] To address the problems raised in the background section, existing elliptic positioning solutions either suffer from large estimation errors and are prone to getting trapped in local optima, or have high computational complexity and slow convergence speed, making it difficult to balance positioning accuracy and real-time requirements.

[0019] To overcome the limitations of the aforementioned methods, this invention introduces the Master Minimization (MM) algorithm into the localization problem. The key to this invention lies in constructing a surrogate function to transform the complex non-convex nonlinear problem into a convex optimization subproblem, thereby iteratively solving its closed-form solution. This effectively simplifies the computation process and demonstrates fast processing and good convergence performance.

[0020] To further clarify the innovations and underlying principles of this invention, some basic concepts are first introduced: A transmitter is a device capable of transmitting signals; its location is known, and it can be single or multiple. A receiver is a device capable of receiving signals; its location is known, and it is generally at least two in number. The signals received by the receiver include signals reflected by a target object. A target object is an object capable of reflecting radar wave signals; it is single, and its position coordinates are the result to be calculated. The bistatic distance measurement refers to the measured propagation distance from the transmitter to the target object and then back to the receiver after the radar wave signal is reflected by the target object. Elliptical positioning calculation is based on the geometric properties of an ellipse with the transmitter and receiver as foci and the bistatic distance as the major axis; the target object's position is determined by the intersection of multiple sets of measurements.

[0021] Using bistatic distance measurements between the transmitter, target, and receiver, a pseudo-linear equation is established by introducing some auxiliary variables, and the MM algorithm is used to accurately estimate the target's position. However, due to the large number of auxiliary variables generated in this process, WLS and SDP schemes are inefficient when the number of receivers is insufficient. This invention simplifies the solution process through the principal optimization minimization (MM) method, achieving efficient and accurate estimation, and proceeds as follows: I. System Deployment: Deploy M transmitters, one target, and N receivers within a K-dimensional monitoring area to locate the target object. The positions of the transmitters and receivers are known. The value of K is typically 2.

[0022] II. Bistatic Distance Measurement: The transmitter sends a signal, which is reflected by the target and received by the receiver. All bistatic distance measurements between the transmitter, target, and receiver are recorded, and the results are sent to a server or centralized processor. In other words, the location information of the transmitter and receiver, as well as the bistatic distance measurements, are obtained. The location information of the transmitter and receiver includes their identification numbers and coordinates.

[0023] III. Target Location Estimation: The MM algorithm is used on a server or processor to estimate the target location. By constructing a surrogate function, the location problem is transformed into an iteratively solvable subproblem, and its analytical solution is obtained. The key improvement in this invention is the transformation of the location problem into an iteratively solvable subproblem by constructing a surrogate function and obtaining its analytical solution. Specifically, during estimation, an initial solution for the target location is generated using the Weighted Least Squares (WLS) method; by constructing a surrogate function that satisfies upper bounds, compactness, and gradient consistency, the nonlinear and non-convex maximum likelihood estimation (MLE) problem is transformed into an iterative convex optimization subproblem; the analytical solution of the subproblem is iteratively solved, and the target location is updated.

[0024] IV. Communication between sensors: In this positioning system, the transmitter, receiver and main processor communicate in a closed loop of “synchronous triggering-data acquisition-real-time upload-command feedback” to achieve accurate transmission of bistatic distance measurement data and device synchronization, providing high-quality input data for the MM algorithm and ensuring positioning accuracy and real-time performance.

[0025] Suppose a passive target localization system is deployed in a K-dimensional (K is typically equal to 2) space. The system consists of M targets located in... The transmitter and N located in The receiver consists of, among which , .like Figure 1 The example shown is A schematic diagram of a split-type radar target localization system containing two transmitters and two receivers within a 3D spatial region. The position coordinates of the two receivers are known, denoted as follows: , The position coordinates of the two transmitters are also known, and are represented as follows: , Within this monitoring area, there is also a target object to be located, whose location coordinates are represented as follows: .like Figure 1 As shown, the path of the radar wave signal from the transmitter to the target. The path that the object reflects off and reaches the receiver The signal comes from the transmitter Through the target object Reflected to the receiver The bistatic distance to the true distance is related by the following formula: in, for and The true value of the bistatic distance; These are the position coordinates of the target object.

[0026] Due to measurement errors and environmental interference, the true value of the bistatic distance is... It cannot be measured precisely, and its measured values ​​all contain noise. Therefore, it can be expressed as: in, To measure noise, This is a bistatic distance measurement.

[0027] Combining all measurements into a vector form, we have the expression: in, Ideally, the measurement noise n follows a zero mean and a covariance of . The Gaussian distribution.

[0028] The maximum likelihood estimation (MLE) of elliptic localization based on bistatic measurements described above can be expressed as the following optimization problem: in Let be a function of the target object's position. , This is the covariance matrix for measuring noise.

[0029] Through the above process, the problem of locating the target object can be transformed into the minimization problem in formula (4).

[0030] Depending on the number of transmitters, the problem is divided into single-transmitter problems and multi-transmitter problems. The following descriptions will be based on single-transmitter and multi-transmitter problems, with Example 1 and Example 2 respectively.

[0031] Example 1 This embodiment provides a detailed explanation of the formula derivation process and positioning method for the master optimization minimization algorithm for a single transmitter.

[0032] For the single-transmitter MM problem, the Master Minimization (MM) algorithm transforms the original problem into an iteratively solved convex optimization problem by constructing a surrogate function. The original optimization problem can be expressed as: Here, f(x) is a nonlinear, non-convex continuous function, and its solution contains a non-empty set. If the traditional method is used to solve it directly, it will lead to inefficiency and low accuracy.

[0033] set up As the initial solution to the above optimization problem, a surrogate function is used. The MM algorithm produced the solution in the k-th iteration. The proxy function is required to have the following characteristics: in, .

[0034] In the (k+1)th iteration, The value is obtained by solving Obtaining, that is, representing: According to (6) and (7), we have the following inequalities: Therefore, the function value As the number of iterations increases, the algorithm becomes non-incremental, and the MM algorithm described above has good convergence performance.

[0035] Regarding the single transmitter problem, the signal originates from a single transmitter. Reflected by the target to the receiver The true value of the bistatic distance is: in ; for and The true value of the bistatic distance; The position coordinates of the target object, Let N be the location coordinates of the receiver, and N be the number of receivers.

[0036] Due to measurement errors and environmental interference, the true value of the bistatic distance is... It cannot be measured precisely, and its measured values ​​all contain noise. Therefore, it can be expressed as: in To measure noise, This is a bistatic distance measurement.

[0037] Combining all measurements into a vector form, we have the expression: in, Ideally, the measurement noise n follows a zero mean and a covariance of . The Gaussian distribution.

[0038] The maximum likelihood estimation (MLE) of elliptic localization based on bistatic measurements described above can be expressed as the following optimization problem: in Let be a function of the target object's position. , To measure the covariance of noise.

[0039] To design the MM algorithm for problem (12), define Therefore, the optimization problem (12) is changed to: in ,in , .

[0040] The objective function f(x) can be further expanded to express: Through quadratic functions (in, Surrogate functions for (positive semi-definite matrices): in .

[0041] According to the surrogate function (15), substituting the first term on the right side of equation (14) results in an inequality: in Q= I, = This indicates taking the largest eigenvalue of matrix P.

[0042] Therefore, substituting equation (16) into equation (14), we have the following inequality: in, .

[0043] right Expand the item to make Then the following inequality holds: Vector norm The proxy function is constructed using the following inequality: because Applying inequality (19) and substituting it into equation (18), we can obtain the following inequality: in , When it is the kth iteration The estimated value.

[0044] Since x is a function of u, equation (17) can be expanded as follows: Combining equations (17), (18), and (20), we can obtain: in .

[0045] Combining equations (21) and (22), equation (21) can be further expressed as: in; According to equations (6) and (23), the surrogate function of f(u) Represented as: Therefore, to solve the elliptic positioning problem, the MM algorithm iteratively solves the following minimization problem: The following will explain how to solve formula (25). Solving formula (25) is equivalent to solving... Then we can obtain the equation: Based on equation (26), the analytical solution expression is further obtained: The above is the theoretical basis for transforming the original positioning problem into the minimization problem corresponding to formula (24). In practical applications, when estimating the position of the target object, iterative calculations are required, and the minimization problem of the surrogate function is solved in each iteration.

[0046] The stopping criterion for iterative calculation is determined based on the relative error of the target object's position estimate being less than a preset threshold, and the corresponding expression is: in To achieve convergence tolerance, set it to a value that is sufficiently close to zero; for example, it could be... ; This is an estimate of the target object's location. The estimated location of the target object is obtained when the algorithm iteration stops. .

[0047] For this source localization problem, the MM algorithm's elliptic localization steps are as follows: Input parameters include: ; Output parameters include: ; Please refer to Figure 2 The steps of the MM algorithm are as follows: S11: Initialize parameters, obtain input parameters, including receiver position. Transmitter position Bistatic distance measurement value Measurement noise covariance matrix Convergence tolerance ; S12: Import according to formula (12) ; S13: Generate an initial solution using the WLS method ; S14: Enter the MM algorithm iteration loop, with the initial iteration count set to k=1; S15: Update Specifically, update according to formula (23) and formula (27) ; S16: Update k=k+1; S17: Determine whether the iteration termination condition is met. That is, if the calculated relative error satisfies formula (28), the iteration calculation is terminated. If the formula does not satisfy formula (28), repeat steps S15 to S17. In other words, determine whether the accuracy satisfies formula (28). That is, the iteration stopping condition is that the relative error of the target object position estimate is less than the convergence tolerance.

[0048] After the above steps, the location of the target object can be obtained. The value of is thus obtained. In other words, the location of the target object has been estimated.

[0049] The surrogate function (24) constructed by the MM algorithm is equivalent to the MLE minimization problem (12) and has linear constraints. The MM algorithm ensures that the objective function value does not increase with the number of iterations through the surrogate function, and has good convergence performance. The compactness and gradient consistency of the surrogate function ensure that the estimation result is unbiased. Combining the WLS initial solution and the SQUAREM accelerator, both convergence stability and convergence speed are taken into account, ensuring that the expected value of the final estimator converges to the actual position. The mean square error (MSE) of the final estimator can reach the Cramer-Rao lower bound, and the deviation approaches zero.

[0050] Example 2 This embodiment is an improvement on the first embodiment, that is, it extends the method from a single transmitter problem to a multi-transmitter problem.

[0051] Therefore, to solve the nonlinear and nonconvex optimization problem (4), this embodiment employs the Master Minimization (MM) algorithm, which transforms the original problem into an iteratively solved convex optimization problem by constructing a surrogate function. It should be noted that in this embodiment, Let be the transmitter's position coordinates, where , Let be the position coordinates of the receiver, where .

[0052] To design the MM algorithm for problem (4), define Therefore, the optimization problem (4) is changed to: in ,in , .

[0053] Expanding the objective function f(x), it can be further expressed as: Through quadratic functions The surrogate function for (where P is a positive semi-definite matrix): in ; According to the surrogate function (31), substituting the first term on the right side of equation (30) results in an inequality: in Q= I, = Indicates taking the matrix The largest eigenvalue.

[0054] Therefore, substituting equation (32) into equation (30), we have the following inequality: in, .

[0055] right Expand the item to make Then the following inequality holds: Vector norm The proxy function is constructed using the following inequality: because Applying inequality (35) and substituting it into equation (34), we can obtain the following inequality: in This is the estimated value at the k-th iteration.

[0056] Since x is a function of u, equation (33) can be expanded as follows: Combining equations (33), (34), and (36), we can obtain: ; (38) in .

[0057] Combining equations (37) and (38), equation (37) can be further expressed as: in; According to equations (6) and (39), the surrogate function of f(u) Represented as: Therefore, to solve the elliptic positioning problem, the MM algorithm iteratively solves the following minimization problem: The following will explain how to solve formula (41). Solving formula (41) is equivalent to solving... Then we can obtain the equation: Based on equation (42), the analytical solution expression is further obtained: The above is the theoretical basis for transforming the original positioning problem into the minimization problem corresponding to formula (40). In practical applications, when estimating the position of the target object, iterative calculations are required, and the minimization problem of the surrogate function is solved in each iteration.

[0058] The stopping criterion for iterative calculation is determined based on the relative error of the target object's position estimate being less than a preset threshold, and the corresponding expression is: in To achieve convergence tolerance, set it to a value that is sufficiently close to zero; for example, it could be... ; This is an estimate of the target object's location. The estimated location of the target object is obtained when the algorithm iteration stops. .

[0059] For this source localization problem, the MM algorithm's elliptic localization steps are as follows: Input parameters include: ; Output parameters include: ; Please refer to Figure 3 The steps of the MM algorithm are as follows: S21: Initialize parameters, obtain input parameters, including receiver position. Transmitter position Measured values Noise covariance matrix Convergence tolerance ϵ; S22: Import according to (4) ; S23: Generate an initial solution using the WLS method ; S24: Enter the MM algorithm iteration loop, with the initial iteration count set to k=1; S25: Update That is, update according to formula (39) and formula (43) ; S26: Update k=k+1; S27: Determine whether the iteration termination condition is met. That is, if the calculated relative error satisfies formula (44), then terminate the iteration calculation. If the formula does not satisfy formula (44), repeat steps S25 to S27. That is, determine whether the iteration termination condition is met by checking whether the accuracy satisfies formula (44). In other words, the iteration stopping condition is that the relative error of the target object position estimate is less than the convergence tolerance.

[0060] After the above steps, the location of the target object can be obtained. The value of is thus obtained. In other words, the location of the target object has been estimated.

[0061] Based on the schemes disclosed in Embodiments 1 and 2 above, this invention proposes an innovative and efficient estimation method for the elliptical localization problem under bibase distance measurement, using the Master Minimum Optimization (MM) algorithm. By constructing a surrogate function that satisfies upper bounds, compactness, and gradient consistency, the original non-convex maximum likelihood estimation (MLE) problem is transformed into a series of convex optimization subproblems with analytical solutions, effectively overcoming the shortcomings of traditional methods in terms of convergence and computational efficiency. By introducing a weighted least squares (WLS) initial solution and an accelerated convergence strategy, the localization accuracy and algorithm stability are significantly improved while ensuring global convergence.

[0062] Compared to existing technologies, the first and second embodiments proposed in this invention have at least the following beneficial effects: Strong convergence performance: The MM algorithm has a monotonically decreasing property, ensuring that the objective function continuously decreases during the iteration process, exhibiting good global convergence characteristics. Efficient solution: By constructing a convex surrogate function and deriving a closed-form iterative solution, complex numerical optimization processes are avoided, significantly improving computational efficiency. Wide applicability: The proposed method can be extended to various distance-based positioning systems, such as bistatic radar and multi-station time difference positioning, possessing broad application prospects.

[0063] Example 3 This embodiment proposes a system applicable to the methods described in Embodiments 1 and 2, wherein please refer to... Figure 4 The system includes: at least one transmitter for transmitting measurement signals; multiple receivers for receiving measurement signals; and a processor communicatively connected to the transmitters and receivers. The processor acquires the position information of each transmitter and receiver, as well as the measurement results of each receiver, and estimates the position of a target object. The processor uses the method described in Embodiment 1 or Embodiment 2 to solve the target object localization problem by transforming it into a subproblem with an analytical solution. The measurement results of each receiver include the bistatic distance measurement value corresponding to each receiver. The number of transmitters is 1-20, and they are deployed separately; the number of receivers is 2-20, and they are also deployed separately.

[0064] This embodiment is used in conjunction with Embodiment 1 or Embodiment 2; that is, based on the hardware provided in this embodiment, the method described in Embodiment 1 or Embodiment 2 is implemented. Regarding the positioning method, please refer to Embodiment 1 or Embodiment 2, and it will not be repeated here.

[0065] Through the above embodiments up to Embodiment 3, in Embodiment 1, the target localization based on bistatic distance measurements is constructed into a principal optimization minimization (MM) algorithm, which includes a surrogate function. The analytical solution of this surrogate function is obtained through iteration to solve the problem. In Embodiment 2, the single-transmitter problem is extended to a multi-transmitter target localization scenario, and an MM solution method is designed for this target localization. Since the transformed subproblem is convex, MM has natural global convergence. This invention uses a principal optimization minimization (MM) algorithm based on bistatic distance measurements to achieve efficient and accurate estimation of the target's position. In the MM solution process, the complex optimization problem is transformed into an iteratively solvable surrogate function, effectively simplifying the calculation process. Therefore, the MM solution method exhibits its fast processing speed and good convergence. This method has also been extended to multi-transmitter scenarios, showing good performance. It should be noted that this invention requires precise clock synchronization, which can be achieved using hardware-level device synchronization, i.e., the transmitter and receiver share a high-precision clock source to ensure clock synchronization, thus reducing the requirements for clock synchronization.

[0066] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0067] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. An elliptic localization method based on a master optimization minimization algorithm, comprising: Acquire the transmitter's position information, the receiver's position information, and bistatic distance measurements; The location of the target object is estimated; characterized in that, The process of estimating the location of a target object includes the following steps: The initial solution for the target object's location is generated using the weighted least squares method; Construct a surrogate function that satisfies the upper bound, compactness and gradient consistency to transform the nonlinear and nonconvex maximum likelihood estimation problem into an iterable convex optimization subproblem; Calculate the analytical solution to the iterable convex optimization subproblem and update the target object's position.

2. The elliptic positioning method based on the master optimization minimization algorithm according to claim 1, characterized in that, The proxy function is: ； in, Here are the coordinates of the target object to be located, M is the number of transmitters, and N is the number of receivers. These are the weighting coefficients. For offset vectors, These are the coordinates of the transmitter or receiver.

3. The elliptic positioning method based on the master optimization minimization algorithm according to claim 2, characterized in that, The process of estimating the location of a target object includes the following steps: The initial solution is calculated using the weighted least squares method; The main optimization minimization algorithm is used for iterative solution until the relative error of the estimated target position is less than the convergence tolerance.

4. The elliptic positioning method based on the master optimization minimization algorithm according to claim 3, characterized in that, The formula for the closed-form solution of the subproblem in the (k+1)th iteration is: ； in, Indicates the weighting coefficient. Represents the offset vector. These are the coordinates of the transmitter or receiver.

5. The elliptic positioning method based on the master optimization minimization algorithm according to claim 4, characterized in that, The formulas for the offset vector and weight coefficients are as follows: ； in, for The largest eigenvalue, , , For vectors The i-th term, and Q= I; To measure the covariance matrix of the noise, This is a matrix of bistatic distance measurements.

6. The elliptic positioning method based on the master optimization minimization algorithm according to claim 3, characterized in that, The formula for determining whether the relative error of the estimated target location is less than the convergence tolerance is as follows: ； in, This is the closed-form solution to the subproblem in the (k+1)th iteration. This is the closed-form solution to the subproblem in the k-th iteration. To achieve convergence tolerance.

7. The elliptic positioning method based on the master optimization minimization algorithm according to claim 3, characterized in that, Convergence tolerance no greater than .

8. An elliptic positioning system based on a master optimization minimization algorithm, comprising: At least one transmitter for transmitting signals; At least two receivers for receiving measurement signals; The processor, transmitter, and receiver are all communicatively connected to the processor. The processor is used to acquire the position information of each transmitter, the position information of each receiver, and the measurement results of each receiver, and to estimate the position of the target object; its characteristic is that... The processor estimates the location of the target object using the method described in any one of claims 1-7.

9. The elliptical positioning system based on the master optimization minimization algorithm according to claim 8, characterized in that, The number of transmitters is 1-20, and they are deployed separately; the number of receivers is 2-20, and they are deployed separately.

10. The elliptical positioning system based on the master optimization minimization algorithm according to claim 8, characterized in that, The measurement results for each receiver include the corresponding bistatic distance measurement values ​​for each receiver.

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