A multi-station time difference and frequency difference fusion positioning method, system, device and medium

Abstract

This application discloses a multi-station time difference and frequency difference fusion positioning method, system, device, and medium. It transforms the projected position of a low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in a geodetic coordinate system. The current radiation source position is substituted into the time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix. The radiation source position after the (k+1)-th iteration is calculated. The height of the radiation source position is corrected using a global elevation map to obtain the radiation source position in the Earth-fixed coordinate system. Finally, the current radiation source position is replaced and iterated. The optimal estimate of the radiation source position is obtained when the difference is less than a preset threshold or when the preset number of iterations is reached. By combining time difference and frequency difference data, and combining the time-frequency difference fusion positioning equation set and global elevation map information, high-precision three-dimensional positioning of the target is achieved.

Description

Technical Field

[0001] This application relates to the field of radio monitoring technology, and more specifically, to a multi-station time difference and frequency difference fusion positioning method, system, device and medium. Background Technology

[0002] Space-based observation stations, by intercepting and processing electromagnetic signals emitted by various electromagnetic radiation sources, can extract various observables, including phase difference of arrival (PDOA), time difference of arrival (TDOA), frequency difference of arrival (FDOA), and their rates of change. Combined with information such as the station's position and velocity, these observables are used for spatial positioning of the radiation source. Based on the number of observation stations, this positioning technology can be divided into two main categories: single-station passive positioning and multi-station cooperative passive positioning.

[0003] Single-station positioning techniques mainly include direction finding, phase difference rate of change, Doppler rate of change, and direct signal positioning. The advantage of these techniques lies in their simple equipment configuration; they do not require time and frequency synchronization or correction strategies between multiple stations, reducing system complexity and cost. However, single-station positioning techniques also have significant limitations: direction finding positioning suffers from low accuracy due to short baselines, especially when the radiation source is located at the edge of Earth's coverage area, where the curvature of the Earth significantly affects positioning accuracy, making it impossible to ensure high-precision positioning across the entire area. While phase difference rate and Doppler rate of change positioning methods can achieve longer virtual baselines through long-term signal accumulation, improving positioning accuracy, this requires the radiation source signal to remain observable for an extended period, limiting their application scenarios. Direct signal positioning requires a high duty cycle and performs poorly in complex environments.

[0004] In contrast, multi-station cooperative positioning technology utilizes long baselines (typically tens to hundreds of kilometers) and short observation times (usually no more than a hundred milliseconds) between multiple observation stations to achieve rapid and high-precision positioning across the entire airspace. However, the bi-station time-frequency difference positioning algorithm has unlocatable areas and positioning mirror ambiguities under certain conditions, requiring additional direction finding and other auxiliary methods to determine the unique radiation source location. A three-star time-difference positioning method based on Newton's iteration method is widely used in engineering practice, offering advantages such as simple computation and no unlocatable areas. However, this method relies entirely on time-difference observations, and the accuracy of time-difference measurements is insufficient for certain types of signals (e.g., narrowband continuous waves), especially in areas with edge coverage, where time-difference accuracy is easily severely affected. Furthermore, positioning accuracy is closely related to the geometric layout of the observation stations; when the three observation stations are almost aligned in a straight line, the positioning effect drops significantly, and may even fail.

[0005] To overcome these challenges, researchers have also explored methods to improve long-range positioning accuracy using Doppler frequency difference observations. Doppler frequency difference observations can achieve high measurement accuracy in a relatively short time (tens to hundreds of milliseconds) and have low requirements for the configuration of the observation stations. However, relying solely on the three-station frequency difference positioning algorithm also faces the problem of unlocatable areas, making it difficult to guarantee high-precision positioning throughout the entire coverage area. Therefore, how to comprehensively utilize multiple observations and optimize positioning algorithms to achieve broader and more accurate radiation source positioning has become one of the key research directions. Summary of the Invention

[0006] The purpose of this application is to overcome the shortcomings of existing technologies and provide a multi-station time difference and frequency difference fusion positioning method, system, device and medium. By combining time difference and frequency difference data, and combining time and frequency difference fusion positioning equations and global elevation map information, high-precision three-dimensional positioning of the target can be achieved.

[0007] The objective of this application is achieved through the following technical solution:

[0008] In a first aspect, this application proposes a multi-station time difference and frequency difference fusion positioning method, which is applied to a multi-station time difference and frequency difference fusion positioning model, the model including multiple low-Earth orbit observation stations and ground radiation sources, and the method comprising:

[0009] Step S1: Convert the projected position of the low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in the geodetic coordinate system;

[0010] Step S2: Based on the three-dimensional geographic coordinates, substitute the current radiation source location into the constructed time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix.

[0011] Step S3: Calculate the radiation source location after the (k+1)th iteration based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix;

[0012] Step S4: Based on the longitude and latitude of the radiation source location after the (k+1)th iteration, use the global elevation map to correct the height of the radiation source location after the (k+1)th iteration to obtain the radiation source location in the Earth-fixed coordinate system.

[0013] Step S5: Replace the current radiation source position in step S2 with the radiation source position in the Earth-fixed coordinate system. Iterate from step S2 to S4. If the difference between the final radiation source position and the previous radiation source position is less than a preset threshold, or if the preset number of iterations is reached, obtain the optimal estimated value of the radiation source position.

[0014] In one possible implementation, step S1 includes:

[0015] The projection position of the low-orbit observation station on the Earth's surface was selected, and the initial three-station time difference positioning was performed based on the Chan method to obtain the three-station time difference positioning results;

[0016] The three-station time difference positioning results are used as the initial position, and the initial position is converted into three-dimensional geographic coordinates in the geodetic coordinate system.

[0017] In one possible implementation, step S2 includes:

[0018] Calculate the distance difference, the rate of change of the distance difference, the time difference equation, and the frequency difference equation for the low-orbit observation stations;

[0019] Based on the distance difference and the rate of change of the distance difference, the Earth constraint equation of the ellipsoid model is combined with the time difference equation and the frequency difference equation to construct a time-frequency difference fusion positioning equation set;

[0020] Constructing a cost function transforms the localization problem into a problem of finding the minimum value of the cost function. When the conditions for minimizing the problem are met, the time-frequency difference fusion localization equations are expanded into a first-order Taylor series at the current radiation source location to obtain the residuals of the time-frequency difference fusion localization equations.

[0021] Substituting the current radiation source location into the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation system yields the processed Jacobian matrix.

[0022] In one possible implementation, step S3 includes:

[0023] Based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix, an iterative equation for the radiation source location based on the least squares algorithm is obtained.

[0024] Input the current radiation source location into the iterative equation to obtain the radiation source location after the (k+1)th iteration.

[0025] Secondly, this application proposes a multi-station time difference and frequency difference fusion positioning system, the system comprising:

[0026] The conversion module is used to convert the projected position of a low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in a geodetic coordinate system.

[0027] The generation module is used to substitute the current radiation source location into the constructed time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set based on three-dimensional geographic coordinates to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix.

[0028] The calculation module is used to calculate the radiation source position after the (k+1)th iteration based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix.

[0029] The correction module is used to correct the height of the radiation source location after the (k+1)th iteration using a global elevation map to obtain the radiation source location in the Earth-fixed coordinate system based on the longitude and latitude of the radiation source location after the (k+1)th iteration.

[0030] The iteration module is used to replace the current radiation source position with the radiation source position in the Earth-fixed coordinate system. The optimal estimated value of the radiation source position is obtained when the difference between the final radiation source position and the previous radiation source position is less than a preset threshold value, or when the preset number of iterations is reached.

[0031] In one possible implementation, the conversion module is used for:

[0032] The projection position of the low-orbit observation station on the Earth's surface was selected, and the initial three-station time difference positioning was performed based on the Chan method to obtain the three-station time difference positioning results;

[0033] The three-station time difference positioning results are used as the initial position, and the initial position is converted into three-dimensional geographic coordinates in the geodetic coordinate system.

[0034] In one possible implementation, the generation module is used for:

[0035] Calculate the distance difference, the rate of change of the distance difference, the time difference equation, and the frequency difference equation for the low-orbit observation stations;

[0036] Based on the distance difference and the rate of change of the distance difference, the Earth constraint equation of the ellipsoid model is combined with the time difference equation and the frequency difference equation to construct a time-frequency difference fusion positioning equation set;

[0037] Constructing a cost function transforms the localization problem into a problem of finding the minimum value of the cost function. When the conditions for minimizing the problem are met, the time-frequency difference fusion localization equations are expanded into a first-order Taylor series at the current radiation source location to obtain the residuals of the time-frequency difference fusion localization equations.

[0038] Substituting the current radiation source location into the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation system yields the processed Jacobian matrix.

[0039] In one possible implementation, the computing module is used for:

[0040] Based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix, an iterative equation for the radiation source location based on the least squares algorithm is obtained.

[0041] Input the current radiation source location into the iterative equation to obtain the radiation source location after the (k+1)th iteration.

[0042] Thirdly, this application also proposes a computer device comprising a processor and a memory, wherein the memory stores a computer program, which is loaded and executed by the processor to implement the multi-station time difference and frequency difference fusion positioning method as described in any of the first aspects.

[0043] Fourthly, this application also proposes a computer-readable storage medium storing a computer program that is loaded and executed by a processor to implement the multi-station time difference and frequency difference fusion positioning method as described in any of the first aspects.

[0044] The main solution and its various further alternatives described above can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application; furthermore, the (non-conflicting alternatives) can also be freely combined with each other and with other alternatives. Those skilled in the art, after understanding the solution of this application, will realize from the prior art and common general knowledge that there are many combinations, all of which are technical solutions to be protected by this application, and will not be exhaustively listed here.

[0045] This application discloses a multi-station time difference and frequency difference fusion positioning method, system, device, and medium. It transforms the projected position of a low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in a geodetic coordinate system. The current radiation source position is substituted into the time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix. The radiation source position after the (k+1)-th iteration is calculated. The height of the radiation source position is corrected using a global elevation map to obtain the radiation source position in the Earth-fixed coordinate system. Finally, the current radiation source position is replaced and iterated. The optimal estimate of the radiation source position is obtained when the difference is less than a preset threshold or when the preset number of iterations is reached. By combining time difference and frequency difference data, and combining the time-frequency difference fusion positioning equation set and global elevation map information, high-precision three-dimensional positioning of the target is achieved. Attached Figure Description

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0047] Figure 1 The diagram shows a flowchart of a multi-station time difference and frequency difference fusion positioning method proposed in an embodiment of this application.

[0048] Figure 2 A schematic diagram of the multi-station time difference and frequency difference fusion positioning model proposed in an embodiment of this application is shown.

[0049] Figure 3a The diagram shows the distribution of GDOP (Ground Difference Positioning) accuracy for the three stations.

[0050] Figure 3b The diagram shows the distribution of the GDOP (Ground-Difference Positioning Accuracy) of the three stations.

[0051] Figure 4a The diagram shows the distribution of GDOP (Ground Difference Positioning) accuracy at four stations.

[0052] Figure 4b The diagram shows the distribution of the GDOP (Ground-Difference Positioning Accuracy) of the three stations.

[0053] Figure 5a The diagram shows the relationship between the positioning accuracy in the longitude direction and the coverage distance for the four positioning methods shown.

[0054] Figure 5b The diagram shows the relationship between the positioning accuracy in the latitudinal direction and the coverage distance for the four positioning methods.

[0055] Figure 6a This diagram illustrates the relationship between the positioning accuracy of the three-station time difference and time-frequency difference as a function of the signal carrier frequency, as proposed in the embodiments of this application, along the longitude direction.

[0056] Figure 6b This diagram illustrates the latitudinal direction of the relationship between the positioning accuracy of the three-station time difference and time-frequency difference as proposed in the embodiments of this application and the change of signal carrier frequency.

[0057] Figure 7a This diagram illustrates the relationship between the positioning accuracy of four-station time difference and time-frequency difference as a function of signal carrier frequency, as proposed in the embodiments of this application, along the longitude direction.

[0058] Figure 7b This diagram illustrates the latitudinal direction of the relationship between the positioning accuracy of the four-station time difference and time-frequency difference as proposed in the embodiments of this application and the change of signal carrier frequency. Detailed Implementation

[0059] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0060] Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] While traditional three-station time difference positioning technology is widely used for target location, it has several limitations. These limitations include insufficient accuracy in measuring the time difference for certain signals (such as narrowband continuous waves) and decreased positioning accuracy in distant areas. Furthermore, positioning accuracy significantly decreases or even fails when the three observation stations are almost in a straight line.

[0062] To achieve observation-level fusion positioning in multi-station time difference and frequency difference positioning equations, and to make the time difference and frequency difference fusion positioning algorithm more universal and practical, this application proposes a multi-station time difference and frequency difference fusion positioning method, system, device, and medium for stationary targets on land or slow-moving targets at sea. It is based on arbitrary multi-station (≥3) time difference and frequency difference fusion using Taylor expansion plus least squares iteration (Taylor-LS), which not only considers time difference information but also combines frequency difference information, and uses the Earth elliptical model and global elevation map for constraints, thereby improving positioning accuracy. The following is a detailed description of it.

[0063] Please refer to Figure 1 , Figure 1 This illustration shows a flowchart of a multi-station time difference and frequency difference fusion positioning method proposed in an embodiment of this application. The method includes applying a multi-station time difference and frequency difference fusion positioning model. Figure 2 The diagram illustrates a multi-station time-difference-frequency-difference fusion positioning model proposed in this application, including multiple low-Earth orbit (LEO) observation stations and a ground-based radiation source. The diagram shows three LEO observation stations (A, B, and C) and one ground-based radiation source. The observation stations determine the location of the radiation source by measuring the time difference of arrival (TDOA) and frequency difference of arrival (FDOA).

[0064] Observation stations A, B, and C acquire data by receiving signals emitted by ground radiation sources. Dashed lines represent the TDOA lines between observation stations A and B, and between observation stations A and C. Solid lines represent the FDOA lines between observation stations A and B, and between observation stations A and C. A single point represents the location of the ground radiation source. By analyzing TDOA and FDOA data, the specific location of the radiation source can be determined. Through the coordinated work of multiple observation stations, the location of the ground radiation source can be accurately pinpointed.

[0065] At any given time, N (N≥3) low-Earth orbit (LEO) observation stations receive and process signals from ground-based radiation sources. The position vector of the N observation stations is p. i =[x i ,y i ,z i ]T i = 0, 1, ..., N-1, and the velocity vector is v. i =[v xi ,v yi ,v zi ] T The values ​​of i are 0, 1, ..., N-1, and the position vector of the radiation source is p = [x, y, z]. T The velocity vector is v = [v x ,v y ,v z ] T Taking observation station 0 as the master station, the distances of N observation stations from the ground radiation source are... The distance difference Δr between the i-th observation station and the main station i,0 With time difference τ i,0 The relationship between them is Δr i,0 =r i -r0=||pp i ||-||p-p0||=τ i,0 c, where c is the speed of light, relative to r i The rate of change of distance from N observation stations to the radiation source is obtained by taking the first derivative in the time dimension. Correspondingly, the rate of change of the distance difference between the i-th observation station and the main station is... With Doppler frequency difference Δf di,0 The relationship between them is:

[0066] ,in This is the first derivative of the location of the ground radiation source with respect to time. The first derivative of the position of observation station 0 with respect to time. Let λ be the first derivative of the position of the i-th observation station with respect to time, and λ be the signal wavelength. It is easy to see that the distance difference Δr... i,0 With time difference τ i,0 There is a direct proportional relationship, with the scaling factor being the speed of light c, and the rate of change of the distance difference. With Doppler frequency difference Δf di,0 There is a direct proportional relationship between them, and the scaling factor is the signal wavelength λ.

[0067] based on Figure 1 The multi-station time difference and frequency difference fusion positioning method proposed in this application includes the following steps:

[0068] Step S1: Convert the projected position of the low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in the geodetic coordinate system.

[0069] To determine the initial location of the radiation source, the projected positions of multiple low-Earth orbit (LEO) stations were first selected, their multi-station spatial centers were calculated, and projected onto the Earth's surface. Then, three stations were selected, and the initial location of the radiation source was calculated by measuring the time difference of arrival (TDOA) and applying the Chan method. Finally, this initial location was converted from the Earth-centered Earth-fixed (ECEF) coordinate system to the WGS-84 geodetic coordinate system (latitude, longitude, and altitude) to obtain the three-dimensional geographic coordinates of the radiation source, which were used in subsequent iterative positioning algorithms to further improve positioning accuracy.

[0070] Step S1 includes:

[0071] The projection position of the low-orbit observation station on the Earth's surface was selected, and the initial three-station time difference positioning was performed based on the Chan method to obtain the three-station time difference positioning results;

[0072] The three-station time difference positioning results are used as the initial position, and the initial position is converted into three-dimensional geographic coordinates in the geodetic coordinate system.

[0073] First, determine the positions of all low-Earth orbit (LEO) observation stations involved in the positioning process. These positions can be obtained through satellite navigation systems or other means and are typically represented as coordinates in the geocentric-earth-fixed (ECEF) coordinate system. Then, calculate the average position of all observation stations to determine the spatial center point of the multi-station system. Use the spatial center point as a rough estimate of the initial position and project the calculated spatial center point of the multi-station system onto the Earth's surface to find the nearest point on the Earth's surface.

[0074] Three stations are selected from all available observation stations for time difference positioning. The selection criteria can be the relative positions between the three stations. The time difference between each pair of stations is calculated based on the time when the signals are received by the three stations. The Chan method is used to calculate the initial position of the radiation source. By linearizing the TDOA equation, the number of iterations is reduced and the computational efficiency is improved.

[0075] The initial position calculated using the Chan method is converted from the Earth-centered Earth-fixed coordinate system (ECEF) to the WGS-84 geodetic coordinate system (latitude, longitude, and altitude). The initial position, p, is based on the three-station time difference positioning results. 1 =p ini =[x 0 ,y 0 ,z 0 ] T k=1, and convert the initial p1 coordinates to WGS-84 geodetic coordinate system latitude, longitude, and altitude.

[0076] Step S2: Based on the three-dimensional geographic coordinates, substitute the current radiation source location into the constructed time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix.

[0077] Based on three-dimensional geographic coordinates, the current radiation source location p k Substituting the distance difference, the rate of change of distance difference, and the Earth constraint equations, the time-frequency difference fusion positioning equations F(p) are constructed. k ) and its Jacobian matrix F'(p k The residuals of the time-frequency difference fusion positioning equations and the processed Jacobian matrix are obtained, and the current radiation source position p is set. k Coordinates converted to WGS-84 geodetic coordinate system (latitude, longitude, and altitude) Three-dimensional high-precision positioning of the radiation source.

[0078] Step S2 includes:

[0079] Calculate the distance difference, the rate of change of the distance difference, the time difference equation, and the frequency difference equation for the low-orbit observation stations;

[0080] Based on the distance difference and the rate of change of the distance difference, the Earth constraint equation of the ellipsoid model is combined with the time difference equation and the frequency difference equation to construct a time-frequency difference fusion positioning equation set;

[0081] Constructing a cost function transforms the localization problem into a problem of finding the minimum value of the cost function. When the conditions for minimizing the problem are met, the time-frequency difference fusion localization equations are expanded into a first-order Taylor series at the current radiation source location to obtain the residuals of the time-frequency difference fusion localization equations.

[0082] Substituting the current radiation source location into the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation system yields the processed Jacobian matrix.

[0083] Since there are N (N≥3) low-Earth orbit observation stations, N-1 time difference equations and N-1 frequency difference equations are obtained. By simultaneously solving the Earth equations, a set of 2N-1 time-frequency difference fusion positioning equations is obtained. This set of equations contains at least 5 equations to solve for the 3 unknowns of the radiation source location. Therefore, this set of equations exhibits nonlinearity and overdeterminism. Passive positioning solutions based on TDOA / FDOA can employ analytical methods, iterative methods, and search methods. To reduce the number of iterations and lower the computational complexity of the algorithm, initial positioning based on the Chan method is first implemented using the three-station time difference, which serves as the initial value for the radiation source location iteration.

[0084] Specifically, for any N (N≥3) observation stations, the 0th observation station is selected as the master station, and the distance difference, time difference, frequency difference, radial velocity difference, and rate of change of distance difference between the remaining observation stations and the master station are respectively Δri0 , τ i0 , Δf di,0 ,Δν i,0 and To improve positioning accuracy, the Earth constraint equations of the ellipsoid model are combined with the aforementioned Δr i,0 =r i -r0=||pp i ||-||p-p0||=τ i,0 c and

[0085] By combining the equations, we obtain the time-frequency difference fusion positioning equation set:

[0086]

[0087] Where e is the Earth's first eccentricity and N is the Earth's maximal curvature radius, these are further transformed into mathematical expressions for time difference, frequency difference observations, and Earth's constraint equations:

[0088]

[0089] The mathematical expression is transformed into: F(p) = [f1(p),...,f N (p),...,f 2N-1 (p)] T Then construct the cost function. The localization problem is transformed into finding the minimum of the cost function. If F(p) is differentiable, the gradient of the multivariate function satisfies the following at the minimum: At that time, F(p) is placed at the current radiation source location p. k The residual of the time-frequency difference fusion positioning equation system is obtained by performing a first-order Taylor series expansion: F(p) = F(p) k )+F'(p k (pp) k ).

[0090] Solving for the Jacobian matrix F'(p) involves the Jacobian matrix of the distance difference, the rate of change of the distance difference, and the Jacobian matrix of the elliptical Earth model coordinate system transformation. The distance difference and rate of change of the distance difference equations in the time-frequency difference fusion positioning equation set are respectively applied at the radiation source target location p = [x, y, z]. T The gradient is calculated to construct the Jacobian matrix of the distance difference and the rate of change of the distance difference. The x, y, z coordinates in the constraint equations of the elliptical Earth model are converted to longitude, latitude, and altitude in the WGS-84 geodetic coordinate system, and their gradients in the longitude and latitude directions at the radiation source target location are calculated to construct the Jacobian matrix of the coordinate transformation of the elliptical Earth model.

[0091] First, the distance difference Δr between a certain observation station and the main station is calculated. i,0For i = 1, 2, ..., N-1, take the partial derivatives at x, y, and z respectively, which are the distance differences Δr. i,0 In p = [x, y, z] T The gradient at point is expressed as: The rate of change of distance difference between a certain observation station and the main station Take the partial derivatives at x, y, and z respectively, which is the distance difference. In p = [x, y, z] T The gradient at is: Construct the Jacobian matrix H relating the distance difference and the rate of change of the distance difference. tf for:

[0092]

[0093] The matrix dimension is (2N-2)×3.

[0094] The Jacobian matrix for coordinate system transformation in the ellipsoidal model is derived. Since the motion of the ground radiation source and the low-Earth orbit observation station is related to the Earth ellipsoidal model, the latitude, longitude, and altitude of the WGS-84 world geodetic coordinate system are chosen to represent the location p of the radiation source. LBh =[L,B,h] T The positioning calculation process involves both the geodetic coordinate system and the Earth-fixed geocentric coordinate system p = [x, y, z]. T Regarding the coordinate transformation between the two coordinate systems, for the elliptical Earth constraint equation in equation (14), the transformation relationship between the two coordinate systems is as follows: The first eccentricity of the Earth is generally taken as e = 0.0818191908426214957, and the radius of curvature of the Earth is... R e Let N be the Earth's semi-major axis. Taking the first derivative of the Earth's radial-major radius of curvature N with respect to latitude B yields the rate of change of the Earth's radial-major radius of curvature. for: Let the radiation source location be p = [x, y, z] T Represented as position p in WGS-84 geodetic coordinate system LBh =[L,B,h] T Taking the partial derivatives at longitudes L, B, and h respectively, we obtain the radiation source location p = [x, y, z]. T In p LBh =[L,B,h] T Find the gradient at the given point.

[0095] It is worth noting that radiation sources usually move or are distributed along the same elevation of the Earth, meaning that the elevation direction does not change and is constant. Therefore, the velocity in the elevation direction is also 0, so there is no need to calculate the partial derivative with respect to the height h.

[0096] Construct the Jacobian matrix H of N (N≥3) observation stations for the location of the radiation source from the geocentric coordinate system to the WGS-84 coordinate system.LB for: Under the constraints of an ellipsoidal model and a global elevation map, the Jacobian matrix F'(p) in the arbitrary multi-station time difference and frequency difference fusion positioning iteration based on Taylor expansion and least squares (Taylor-LS) is: F'(p) = H tf ×H LB .

[0097] Step S3: Calculate the radiation source location after the (k+1)th iteration based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix.

[0098] Residuals of the time-frequency difference fusion positioning equations, processed Jacobian matrix, and current radiation source location The location of the radiation source after the (k+1)th iteration is calculated.

[0099] Step S3 includes:

[0100] Based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix, an iterative equation for the radiation source location based on the least squares algorithm is obtained.

[0101] Input the current radiation source location into the iterative equation to obtain the radiation source location after the (k+1)th iteration.

[0102] Let F(p) = F(p) k )+F'(p k (pp) k Substitute The iterative equation for the radiation source location based on the least squares (LS) algorithm is obtained: p k+1 =p k -[F'(p k ) T F'(p k )] -1 F'(p k ) T F(p k ) T In the iterative equation, the direction of the iterative update is related to the gradient value of the cost function, F'(p k This represents the distance difference, the rate of change of the distance difference, and the Jacobian matrix of the k-th iteration of the Earth constraint equations F(p). Solving the nonlinear equations requires satisfying F'(p)... k ) T F'(p k Since the matrix is ​​invertible and the equation is a non-positive definite matrix, it is necessary to solve for F'(p). k ) T F'(p kThe generalized inverse matrix of ), and the location of the radiation source p. k The initial value is p, which is based on the Chan method for time difference positioning. ini =[x 0 ,y 0 ,z 0 ] T .

[0103] Step S4: Based on the longitude and latitude of the radiation source location after the (k+1)th iteration, use the global elevation map to correct the height of the radiation source location after the (k+1)th iteration to obtain the radiation source location in the Earth-fixed coordinate system.

[0104] After the (k+1)th iteration, the longitude L of the radiation source was obtained. k+1 and latitude B k+1 To query and correct the height on a global elevation map, use a global elevation map (such as SRTM, ASTER GDEM, etc.). To query the height value h on a global elevation map, use a global elevation map. k+1 Corrected to h (k+1) ', based on the longitude L of the radiation source obtained through iteration k+1 and latitude B k+1 The corresponding elevation value is queried to ensure the accuracy of the radiation source's altitude, as the radiation source may be located on different terrains. The latitude, longitude, and altitude of the radiation source location are updated by combining the longitude and latitude of the radiation source location after the (k+1)th iteration with the altitude obtained from the global elevation map. Transform latitude, longitude and altitude coordinates To convert the updated latitude, longitude, and altitude coordinates to the geocentric coordinate system p, the updated latitude, longitude, and altitude coordinates will be converted to the geocentric coordinate system p. k+1 This yields the precise location of the radiation source in the Earth-fixed geocentric coordinate system after the (k+1)th iteration, ensuring high accuracy and reliability of the positioning results.

[0105] Step S5: Replace the current radiation source position in step S2 with the radiation source position in the Earth-fixed coordinate system. Iterate from step S2 to S4. If the difference between the final radiation source position and the previous radiation source position is less than a preset threshold, or if the preset number of iterations is reached, obtain the optimal estimated value of the radiation source position.

[0106] The loop condition repeats steps S2 to S4 until the convergence condition is met or the maximum number of iterations is reached. Finally, the difference between the radiation source location and the radiation source location from the previous iteration is less than a preset threshold value |p. k+1 -p k|<ε, where ε is a very small positive number used to determine whether the position is sufficiently close to the true position. The iteration is forcibly stopped when the number of iterations exceeds the preset maximum number of iterations M. During each iteration, the radiation source position in the Earth-fixed coordinate system is replaced with the current radiation source position in the current coordinate system, and subsequent iterations are performed. The iteration stops when any of the above conditions are met. The obtained radiation source position at this point is the optimal estimate of the true position of the radiation source. This ensures that the iteration process stops when the accuracy requirements are met or the maximum number of iterations is reached, thus obtaining the optimal estimate of the radiation source position, improving the robustness of the algorithm, and guaranteeing the efficiency and accuracy of the calculation.

[0107] In one possible embodiment, taking typical three-station (A, B, C) and four-station (A, B, C, D) scenarios as examples, a simulation analysis of multi-station time difference and frequency difference fusion positioning performance is conducted. The relevant verification conclusions can be extended to scenarios with more than four stations. The simulation conditions are set as follows: A scenario is set up with four stations (A, B, C, D) observing motion at an altitude of 860 km above the Earth's surface. Stations A and B are located on the same orbital plane, with their center position at point O projected onto the Earth's surface. Stations C and D are located on a different orbital plane. The distance between each pair of observation stations is set to 75 km to 90 km. The position and velocity parameters of each observation station are set as shown in Figure 0.

[0108] Table 1

[0109]

[0110] Assuming the radiation source is located on the Earth's surface and is stationary, the time difference measurement accuracy of the ground radiation source signal at stations AB, AC, and AD is 50 ns (rms), the frequency difference measurement accuracy is 1 Hz (rms), the random error of the observation station site is 5 m (rms), and the random error of the observation station velocity is 0.1 m / s (rms).

[0111] Before obtaining the simulation results, a comparative analysis of the positioning accuracy of different positioning systems was conducted. Based on traditional three-station time difference positioning and the multi-station time difference and frequency difference fusion positioning proposed in this paper, the simulation results were obtained. Figure 3a The diagram showing the GDOP distribution of the three-station time difference positioning accuracy is as follows: Figure 3b The diagram showing the distribution of the GDOP (Ground-Difference Positioning Accuracy) for the three stations is provided. Figure 4a The diagram showing the GDOP distribution of the four-station time difference positioning accuracy is provided. Figure 4b The diagram shows the GDOP distribution of positioning accuracy for three-station time-frequency difference (TFD) positioning. Simulation analysis is performed using a typical signal frequency of 3GHz as an example for both three-station and four-station TFD positioning. One-dimensional slices are plotted on (ordinate: 0km, abscissa: 0km~2200km) and (bscissa: 0km, ordinate: 0km~2200km) to obtain the relationship between the positioning accuracy of the four positioning methods and the coverage distance in the longitude and latitude directions. Figure 5aThe graphs shown in Figure 5b illustrate the relationship between the positioning accuracy of the four positioning methods in the longitude direction and the coverage distance, and Tables 2 and 3 respectively show the positioning accuracy of the four positioning methods in the longitude and latitude directions at distances of 0km, 1000km, and 2000km from the observation station.

[0112] Table 2

[0113]

[0114] Table 3

[0115]

[0116] It can be seen that, by calculating the root mean square of the positioning accuracy of the four methods within a two-dimensional latitude and longitude coverage radius of approximately 2200km, the time difference error of three stations is 7.79km (rms) > the time difference error of four stations is 4.77km (rms) > the time frequency difference error of three stations is 1.62km (rms) > the time frequency difference error of four stations is 1.28km (rms). It is not difficult to see that introducing frequency difference information into the multi-station positioning model can effectively improve positioning accuracy.

[0117] Figure 6a This diagram illustrates the relationship between the positioning accuracy of the three-station time difference and time-frequency difference as a function of the signal carrier frequency, according to an embodiment of this application. Figure 6b This diagram illustrates the latitudinal direction of the relationship between the positioning accuracy of the three-station time difference and time-frequency difference as proposed in the embodiments of this application and the variation of the signal carrier frequency. Figure 7a This diagram illustrates the relationship between the positioning accuracy of four-station time difference and time-frequency difference as a function of signal carrier frequency, according to an embodiment of this application. Figure 7b The diagram illustrates the relationship between the positioning accuracy of four-station time difference and time-frequency difference positioning and the signal carrier frequency as proposed in this application. Within a distance of 0 to 1000 km from the observation station, the positioning accuracy of the four methods is similar. In general, time difference and frequency difference fusion positioning is slightly better than single time difference positioning, and four-station positioning is slightly better than three-station positioning. At a distance of 2000 km from the observation station, taking the longitude direction as an example, with the three-station time difference positioning accuracy of 3.032 km (rms) as a reference, the three-station time-frequency difference positioning accuracy is 1.329 (rms), which is improved by 2.89 times; the four-station time difference positioning accuracy is 2.594 (rms), which is improved by 1.17 times; and the four-station time-frequency difference positioning accuracy is 1.007 (rms), which is improved by 3 times.

[0118] Therefore, time difference and frequency difference fusion positioning methods show higher accuracy in both near and far areas, especially in far areas and under high-frequency signal conditions, where the improvement is particularly significant.

[0119] Compared with the prior art, the embodiments of this application have the following beneficial effects:

[0120] First, the nonlinear equations are linearized using Taylor expansion, and then iteratively solved using the least squares method to improve positioning accuracy.

[0121] Second, the elliptical Earth model and global elevation map information are integrated into the time difference and frequency difference positioning iterative algorithm. Through multiple Earth model corrections and elevation iterations, the three-dimensional high-precision positioning of the target is achieved.

[0122] The following is a possible implementation of a multi-station time difference and frequency difference fusion positioning system, which is used to perform the various execution steps and corresponding technical effects of the multi-station time difference and frequency difference fusion positioning method shown in the above embodiments and possible implementations.

[0123] The system includes:

[0124] The conversion module is used to convert the projected position of a low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in a geodetic coordinate system.

[0125] The generation module is used to substitute the current radiation source location into the constructed time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set based on three-dimensional geographic coordinates to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix.

[0126] The calculation module is used to calculate the radiation source position after the (k+1)th iteration based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix.

[0127] The correction module is used to correct the height of the radiation source location after the (k+1)th iteration using a global elevation map to obtain the radiation source location in the Earth-fixed coordinate system based on the longitude and latitude of the radiation source location after the (k+1)th iteration.

[0128] The iteration module is used to replace the current radiation source position with the radiation source position in the Earth-fixed coordinate system. The optimal estimated value of the radiation source position is obtained when the difference between the final radiation source position and the previous radiation source position is less than a preset threshold value, or when the preset number of iterations is reached.

[0129] In one possible implementation, the conversion module is used for:

[0130] The projection position of the low-orbit observation station on the Earth's surface was selected, and the initial three-station time difference positioning was performed based on the Chan method to obtain the three-station time difference positioning results;

[0131] The three-station time difference positioning results are used as the initial position, and the initial position is converted into three-dimensional geographic coordinates in the geodetic coordinate system.

[0132] In one possible implementation, the generation module is used for:

[0133] Calculate the distance difference, the rate of change of the distance difference, the time difference equation, and the frequency difference equation for the low-orbit observation stations;

[0134] Based on the distance difference and the rate of change of the distance difference, the Earth constraint equation of the ellipsoid model is combined with the time difference equation and the frequency difference equation to construct a time-frequency difference fusion positioning equation set;

[0135] Constructing a cost function transforms the localization problem into a problem of finding the minimum value of the cost function. When the conditions for minimizing the problem are met, the time-frequency difference fusion localization equations are expanded into a first-order Taylor series at the current radiation source location to obtain the residuals of the time-frequency difference fusion localization equations.

[0136] Substituting the current radiation source location into the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation system yields the processed Jacobian matrix.

[0137] In one possible implementation, the computing module is used for:

[0138] Based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix, an iterative equation for the radiation source location based on the least squares algorithm is obtained.

[0139] Input the current radiation source location into the iterative equation to obtain the radiation source location after the (k+1)th iteration.

[0140] This preferred embodiment provides a computer device that can implement the steps in any embodiment of the multi-station time difference and frequency difference fusion positioning method provided in this application. Therefore, it can achieve the beneficial effects of the multi-station time difference and frequency difference fusion positioning method provided in this application. For details, please refer to the previous embodiments, which will not be repeated here.

[0141] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor. Therefore, embodiments of this application provide a storage medium storing multiple instructions that can be loaded by a processor to execute the steps of any embodiment of the multi-station time difference and frequency difference fusion positioning method provided in this application.

[0142] The storage medium may include: read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0143] Since the instructions stored in the storage medium can execute the steps in any of the multi-station time difference and frequency difference fusion positioning method embodiments provided in this application, the beneficial effects that any of the multi-station time difference and frequency difference fusion positioning methods provided in this application can achieve can be realized. For details, please refer to the previous embodiments, which will not be repeated here.

[0144] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A multi-station time difference and frequency difference fusion positioning method, characterized in that, The method is applied to a multi-station time-frequency fusion positioning model, which includes multiple low-Earth orbit observation stations and ground-based radiation sources. The method includes: Step S1: Convert the projected position of the low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in the geodetic coordinate system; Step S2: Based on the three-dimensional geographic coordinates, substitute the current radiation source location into the constructed time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix. Step S3: Calculate the radiation source location after the (k+1)th iteration based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix; Step S4: Based on the longitude and latitude of the radiation source location after the (k+1)th iteration, use the global elevation map to correct the height of the radiation source location after the (k+1)th iteration to obtain the radiation source location in the Earth-fixed coordinate system. Step S5: Replace the current radiation source position in step S2 with the radiation source position in the Earth-fixed coordinate system. Iterate from step S2 to S4. If the difference between the final radiation source position and the previous radiation source position is less than a preset threshold, or if the preset number of iterations is reached, obtain the optimal estimated value of the radiation source position.

2. The fusion positioning method as described in claim 1, characterized in that, Step S1 includes: The projection position of the low-orbit observation station on the Earth's surface was selected, and the initial three-station time difference positioning was performed based on the Chan method to obtain the three-station time difference positioning results; The three-station time difference positioning results are used as the initial position, and the initial position is converted into three-dimensional geographic coordinates in the geodetic coordinate system.

3. The fusion positioning method as described in claim 1, characterized in that, Step S2 includes: Calculate the distance difference, the rate of change of the distance difference, the time difference equation, and the frequency difference equation for the low-orbit observation stations; Based on the distance difference and the rate of change of the distance difference, the Earth constraint equation of the ellipsoid model is combined with the time difference equation and the frequency difference equation to construct a time-frequency difference fusion positioning equation set; Constructing a cost function transforms the localization problem into a problem of finding the minimum value of the cost function. When the conditions for minimizing the problem are met, the time-frequency difference fusion localization equations are expanded into a first-order Taylor series at the current radiation source location to obtain the residuals of the time-frequency difference fusion localization equations. Substituting the current radiation source location into the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation system yields the processed Jacobian matrix.

4. The fusion positioning method as described in claim 3, characterized in that, Step S3 includes: Based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix, an iterative equation for the radiation source location based on the least squares algorithm is obtained. Input the current radiation source location into the iterative equation to obtain the radiation source location after the (k+1)th iteration.

5. A multi-station time difference and frequency difference fusion positioning system, characterized in that, The system includes: The conversion module is used to convert the projected position of a low-orbit observation station on the Earth's surface into three-dimensional geographic coordinates in a geodetic coordinate system. The generation module is used to substitute the current radiation source location into the constructed time-frequency difference fusion positioning equation set and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation set based on three-dimensional geographic coordinates to obtain the residual of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix. The calculation module is used to calculate the radiation source position after the (k+1)th iteration based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix. The correction module is used to correct the height of the radiation source location after the (k+1)th iteration using a global elevation map to obtain the radiation source location in the Earth-fixed coordinate system based on the longitude and latitude of the radiation source location after the (k+1)th iteration. The iteration module is used to replace the current radiation source position with the radiation source position in the Earth-fixed coordinate system. The optimal estimated value of the radiation source position is obtained when the difference between the final radiation source position and the previous radiation source position is less than a preset threshold value, or when the preset number of iterations is reached.

6. The fusion positioning system as described in claim 5, characterized in that, The conversion module is used for: The projection position of the low-orbit observation station on the Earth's surface was selected, and the initial three-station time difference positioning was performed based on the Chan method to obtain the three-station time difference positioning results; The three-station time difference positioning results are used as the initial position, and the initial position is converted into three-dimensional geographic coordinates in the geodetic coordinate system.

7. The fusion positioning system as described in claim 5, characterized in that, Generate modules for: Calculate the distance difference, the rate of change of the distance difference, the time difference equation, and the frequency difference equation for the low-orbit observation stations; Based on the distance difference and the rate of change of the distance difference, the Earth constraint equation of the ellipsoid model is combined with the time difference equation and the frequency difference equation to construct a time-frequency difference fusion positioning equation set; Constructing a cost function transforms the localization problem into a problem of finding the minimum value of the cost function. When the conditions for minimizing the problem are met, the time-frequency difference fusion localization equations are expanded into a first-order Taylor series at the current radiation source location to obtain the residuals of the time-frequency difference fusion localization equations. Substituting the current radiation source location into the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation system yields the processed Jacobian matrix.

8. The fusion positioning system as described in claim 7, characterized in that, The calculation module is used for: Based on the current radiation source location, the residual of the time-frequency difference fusion positioning equation set, and the processed Jacobian matrix, an iterative equation for the radiation source location based on the least squares algorithm is obtained. Input the current radiation source location into the iterative equation to obtain the radiation source location after the (k+1)th iteration.

9. A computer device, characterized in that, The computer device includes a processor and a memory, the memory storing a computer program, which is loaded and executed by the processor to implement the fusion positioning method as described in any one of claims 1-4.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which is loaded and executed by a processor to implement the fusion positioning method as described in any one of claims 1-4.

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