Multi-station time difference and frequency difference fusion positioning method, system, equipment and medium

Abstract

The invention discloses a multi-station time difference and frequency difference fusion positioning method, system and device and a medium, and the method comprises the steps: converting a projection position of a low-orbit observation station on the earth surface into a three-dimensional geographic coordinate in a geodetic coordinate system; and respectively substituting the current radiation source position into the time-frequency difference fusion positioning equation set and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation set to obtain the residual error of the time-frequency difference fusion positioning equation set and the processed Jacobian matrix, and calculating to obtain the radiation source position after the (k + 1) th iteration, and correcting the height of the radiation source position by using a global elevation map to obtain the radiation source position in the earth-fixed coordinate system, finally replacing the current radiation source position for iteration, and obtaining the optimal estimation value of the radiation source position under the condition that the difference value is smaller than a preset threshold value or the cycle reaches the preset iteration times. And high-precision three-dimensional positioning of a target is realized by combining time difference and frequency difference data and combining a time-frequency difference fusion positioning equation set and global elevation map information.

Description

Technical Field

[0001] The present application relates to the field of radio monitoring technology, and in particular to a multi-station time difference and frequency difference fusion positioning method, system, device and medium. Background Art

[0002] Space-based observatories can extract various observation quantities such as phase difference of arrival (PDOA), time difference of arrival (TDOA), frequency difference of arrival (FDOA) and their rate of change by intercepting and processing electromagnetic signals emitted by various electromagnetic radiation sources. Combined with the position, speed and other information of the observation station, these observation quantities are used for spatial positioning of the radiation source. According to the number of observation stations, this positioning technology can be divided into two categories: single-station passive positioning and multi-station collaborative passive positioning.

[0003] Single-station positioning technology mainly includes direction finding, phase difference change rate, Doppler change rate and signal direct positioning methods. The advantage of this type of technology is that the equipment configuration is simple, and there is no need for time, frequency synchronization and correction strategies between multiple stations, which reduces the complexity and cost of the system. However, single-station positioning technology also has obvious limitations: due to the short baseline of direction finding positioning (resulting in low direction finding accuracy), especially when the radiation source is located at the edge of the ground coverage area, the positioning accuracy will be significantly reduced due to the influence of the earth's curvature, and high-precision positioning in the entire area cannot be ensured. Although the phase change rate and Doppler change rate positioning methods can achieve a longer virtual baseline through long-term signal accumulation and improve positioning accuracy, this requires the radiation source signal to remain observable for a long time, which limits its application scenarios. The signal direct positioning law has high requirements for the high duty cycle of the signal and performs poorly in complex environments.

[0004] In contrast, multi-station collaborative positioning technology utilizes the long baselines (generally tens to hundreds of kilometers) and short observation times (usually no more than 100 milliseconds) between multiple observation stations, and can achieve fast and high-precision positioning in the entire airspace. Among them, the dual-station time-frequency difference positioning algorithm has unlocatable areas and positioning mirror ambiguity points under certain conditions, and requires additional auxiliary means such as direction finding to determine the unique location of the radiation source. A three-star time difference positioning method based on Newton iteration method is widely used in engineering practice, with the advantages of simple calculation and no unlocatable areas. However, this method relies entirely on time difference observations. For certain types of signals (such as narrowband continuous waves), the accuracy of time difference measurements is difficult to meet the requirements, especially when the edge area of ​​ground coverage is easily affected. In addition, the positioning accuracy is closely related to the geometric layout of the observation station. When the three observation stations are almost arranged in a line, the positioning effect will be greatly reduced, or even ineffective.

[0005] In order to overcome the above challenges, researchers have also explored the use of Doppler frequency difference observations to improve the accuracy of far-field positioning. Doppler frequency difference observations can achieve high measurement accuracy in a shorter period of time (tens to hundreds of milliseconds) and have lower requirements for the configuration of the observation station. However, relying solely on the three-station frequency difference positioning algorithm also faces the problem of unpositionable areas, and it is difficult to ensure high-precision positioning in the entire coverage area. Therefore, how to comprehensively use multiple observations and optimize the positioning algorithm to achieve wider and more accurate radiation source positioning has become one of the key directions of current research. Summary of the invention

[0006] The purpose of this application is to overcome the existing technical defects and provide a multi-station time difference and frequency difference fusion positioning method, system, equipment and medium, which realizes high-precision three-dimensional positioning of the target by combining time difference and frequency difference data, and combining time-frequency difference fusion positioning equation group and global elevation map information.

[0007] The purpose of this application is achieved through the following technical solutions:

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

[0009] Step S1, converting the projection 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, the current radiation source position is substituted into the constructed time-frequency difference fusion positioning equation group and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix;

[0011] Step S3, calculating the radiation source position after the k+1th iteration based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix;

[0012] Step S4, based on the longitude and latitude of the radiation source position after the k+1th iteration, use the global elevation map to correct the height of the radiation source position after the k+1th iteration to obtain the radiation source position 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 ground-fixed coordinate system, iterate steps S2 to S4, and obtain the optimal estimate of the radiation source position 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 cycle reaches a preset number of iterations.

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

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

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

[0017] In a possible implementation, the steps of step S2 include:

[0018] Calculate the distance difference, distance difference change rate, time difference equation, and frequency difference equation of 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 the time-frequency difference fusion positioning equation group;

[0020] Construct a cost function to transform the positioning problem into a problem of solving the minimum value of the cost function. When the conditions for solving the minimization problem are met, perform a first-order Taylor series expansion of the time-frequency difference fusion positioning equation group at the current radiation source position to obtain the residual of the time-frequency difference fusion positioning equation group.

[0021] Substitute the current radiation source position into the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the processed Jacobian matrix.

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

[0023] Based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the iterative equation of the radiation source position based on the least squares algorithm is obtained;

[0024] The current radiation source position is input into the iterative equation to obtain the radiation source position after the k+1th iteration.

[0025] In a second aspect, the present application proposes a multi-station time difference and frequency difference fusion positioning system, the system comprising:

[0026] A conversion module, used to convert the projection position of the low-orbit observation station on the earth's surface into three-dimensional geographic coordinates in the geodetic coordinate system;

[0027] A generation module is used to substitute the current radiation source position into the constructed time-frequency difference fusion positioning equation group and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group based on the three-dimensional geographic coordinates to obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix;

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

[0029] A correction module, for correcting the height of the radiation source position after the k+1th iteration using a global elevation map based on the longitude and latitude of the radiation source position after the k+1th iteration to obtain the radiation source position in the earth-fixed coordinate system;

[0030] The iterative module is used to replace the current radiation source position with the radiation source position in the ground-fixed coordinate system, and obtain the optimal estimate of the radiation source position 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 cycle reaches a preset number of iterations.

[0031] In a possible implementation, the conversion module is used to:

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

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

[0034] In a possible implementation, a generating module is used to:

[0035] Calculate the distance difference, distance difference change rate, time difference equation, and frequency difference equation of 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 the time-frequency difference fusion positioning equation group;

[0037] Construct a cost function to transform the positioning problem into a problem of solving the minimum value of the cost function. When the conditions for solving the minimization problem are met, perform a first-order Taylor series expansion of the time-frequency difference fusion positioning equation group at the current radiation source position to obtain the residual of the time-frequency difference fusion positioning equation group.

[0038] Substitute the current radiation source position into the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the processed Jacobian matrix.

[0039] In a possible implementation, the computing module is used to:

[0040] Based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the iterative equation of the radiation source position based on the least squares algorithm is obtained;

[0041] The current radiation source position is input into the iterative equation to obtain the radiation source position after the k+1th iteration.

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

[0043] In a fourth aspect, the present application also proposes a computer-readable storage medium, in which a computer program is stored. The computer program is loaded and executed by a processor to implement the multi-station time difference and frequency difference fusion positioning method as described in any one of the first aspects.

[0044] The above-mentioned main scheme of the present application and its further options can be freely combined to form multiple schemes, all of which are schemes that can be adopted and claimed for protection in the present application; and in the present application, (non-conflicting options) options and other options can also be freely combined. After understanding the scheme of the present application, those skilled in the art can understand that there are multiple combinations based on the prior art and common knowledge, all of which are technical schemes to be protected by the present application, and they are not exhaustively listed here.

[0045] The present application discloses a multi-station time difference and frequency difference fusion positioning method, system, equipment and medium, which converts the projection position of a low-orbit observation station on the earth's surface into a three-dimensional geographic coordinate in a geodetic coordinate system, substitutes the current radiation source position into a time-frequency difference fusion positioning equation group and the Jacobian matrix of the k-th iteration of the time-frequency difference fusion positioning equation group, respectively, to obtain the residual and processed Jacobian matrix of the time-frequency difference fusion positioning equation group, calculates the radiation source position after the k+1-th iteration, uses a global elevation map to correct the height of the radiation source position to obtain the radiation source position in the earth-fixed coordinate system, and finally replaces the current radiation source position for iteration. When the difference is less than a preset threshold value or the cycle reaches a preset number of iterations, the optimal estimate of the radiation source position is obtained. By combining time difference and frequency difference data, and combining the time-frequency difference fusion positioning equation group and global elevation map information, high-precision three-dimensional positioning of the target is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. 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 related drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 A flow chart of a multi-station time difference and frequency difference fusion positioning method proposed in an embodiment of the present application is shown.

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

[0049] Figure 3a The GDOP distribution diagram of the time difference positioning accuracy of the three stations is shown.

[0050] Figure 3b The GDOP distribution diagram of the time-frequency difference positioning accuracy of the three stations is shown.

[0051] Figure 4a The GDOP distribution diagram of the time difference positioning accuracy of the four stations is shown.

[0052] Figure 4b The GDOP distribution diagram of the time-frequency difference positioning accuracy of the three stations is shown.

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

[0054] Figure 5b The relationship between the positioning accuracy in the latitude direction and the coverage distance of the four positioning methods is shown.

[0055] Figure 6a A schematic diagram in the longitude direction showing the relationship between the positioning accuracy of the three-station time difference and time-frequency difference proposed in the embodiment of the present application and the change of the signal carrier frequency.

[0056] Figure 6b A schematic diagram in the latitude direction showing the relationship between the positioning accuracy of the three-station time difference and time-frequency difference and the change in signal carrier frequency proposed in the embodiment of the present application.

[0057] Figure 7a A schematic diagram in the longitude direction showing the relationship between the positioning accuracy of the four-station time difference and time-frequency difference and the change of the signal carrier frequency proposed in the embodiment of the present application.

[0058] Figure 7b A schematic diagram in the latitude direction showing the relationship between the positioning accuracy of the four-station time difference and time-frequency difference and the change in signal carrier frequency proposed in the embodiment of the present application. DETAILED DESCRIPTION

[0059] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0060] Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative work shall fall within the scope of protection of this application.

[0061] In the existing technology, although the traditional three-station time difference positioning technology is widely used for target positioning, it has some limitations. These limitations include insufficient time difference measurement accuracy for certain specific signals (such as narrowband continuous waves) and reduced positioning accuracy in far areas. In addition, when the three observation stations are almost in a straight line, the positioning accuracy will be significantly reduced or even fail.

[0062] In order to realize observation-level fusion positioning in the multi-station time difference and frequency difference positioning equations, and make the fusion positioning algorithm of time difference and frequency difference more universal and practical, for stationary targets on land or slow-moving targets at sea, the present application proposes a multi-station time difference and frequency difference fusion positioning method, system, equipment and medium, which is based on the Taylor expansion plus least squares iteration (Taylor-LS) fusion of arbitrary multi-station (≥3) time difference and frequency difference, which not only considers the time difference information, but also combines the frequency difference information, and uses the earth ellipse model and the global elevation map for constraints, thereby improving the positioning accuracy, which is described in detail below.

[0063] Please refer to Figure 1 , Figure 1 A schematic flow chart of a multi-station time difference and frequency difference fusion positioning method proposed in an embodiment of the present application is shown. The method includes applying a multi-station time difference and frequency difference fusion positioning model, Figure 2 The schematic diagram of the multi-station time difference and frequency difference fusion positioning model proposed in the embodiment of the present application is shown, including multiple low-orbit observation stations and ground radiation sources, including three low-orbit observation stations A, B, C and one ground radiation source. The observation station determines the position of the radiation source by measuring the arrival time difference (TDOA) and frequency difference (FDOA).

[0064] Observation stations A, B, and C obtain data by receiving signals from ground radiation sources. The TDOA line between observation stations A and B and the TDOA line between observation stations A and C are represented by dotted lines. The FDOA line between observation stations A and B and the FDOA line between observation stations A and C are represented by solid lines in the figure. The position of the ground radiation source is represented by a point in the figure. By analyzing the TDOA and FDOA data, the specific position of the radiation source can be determined. Through the collaborative work of multiple observation stations, the position of the ground radiation source can be accurately located.

[0065] At any time, N (N ≥ 3) low-orbit observation stations detect and process the target signal of the ground radiation source. The position vector of N observation stations is p i =[x i ,y i ,z i ]T ,i=0,1,...,N-1, the velocity vector is v i =[v xi ,v yi ,v zi ] T ,i=0,1,...,N-1, 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 With the No. 0 observation station as the main station, the N observation stations are located at a distance of Then the distance difference between the i-th observation station and the main station is Δr i,0 With the 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, for r i The first-order derivative in the time dimension is used to obtain the rate of change of the distance from N observation stations to the radiation source. Correspondingly, the rate of change of the distance difference between the i-th observation station and the main station is and Doppler frequency difference Δf di,0 The relationship between them is:

[0066] ,in is the first-order derivative of the ground radiation source position with respect to time, is the first-order derivative of the position of observation station No. 0 with respect to time, is the first-order derivative of the position of the i-th observation station with respect to time, and λ is the signal wavelength. It is not difficult to see that the distance difference Δr i,0 With the time difference τ i,0 There is a direct proportional relationship, the proportional factor is the speed of light c, and the rate of change of the distance difference and Doppler frequency difference Δf di,0 There is a positive proportional relationship between them, and the proportional factor is the signal wavelength λ.

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

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

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

[0070] The steps of step S1 include:

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

[0072] The time difference positioning results of the three stations 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-orbit observation stations involved in positioning, which can be obtained through satellite navigation systems or other means, usually expressed as coordinates in the Earth-centered Earth-fixed coordinate system (ECEF). Then calculate the average of the positions of all observation stations to determine the spatial center point of multiple stations. Use the spatial center point as a rough estimate of the initial position and project the calculated multi-station spatial center point onto the earth's surface, that is, find the nearest point to the point on the earth's surface.

[0074] Select three observation stations from all available observation stations for time difference positioning. The selection criterion can be the relative positions between the three stations. According to the time when the three observation stations receive the signals, the time difference between every two stations is calculated. 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 calculation efficiency is improved.

[0075] The initial position calculated by the Chan method is converted from the Earth-centered Earth-fixed coordinate system (ECEF) to the WGS-84 geodetic coordinate system (latitude, longitude and height), and the positioning result based on the time difference of the three stations is used as the initial position, i.e., p 1 =p ini =[x 0 ,y 0 ,z 0 ] T , k = 1, and convert the initial value p1 coordinates into the longitude, latitude and height of the WGS-84 geodetic coordinate system

[0076] Step S2: Based on the three-dimensional geographic coordinates, the current radiation source position is substituted into the constructed time-frequency difference fusion positioning equation group and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix.

[0077] Based on the three-dimensional geographic coordinates, the current radiation source position p k Substituting the distance difference, the distance difference change rate and the earth constraint equation group into the time-frequency difference fusion positioning equation group F(p k ) and its Jacobian matrix F'(p k ), obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, and convert the current radiation source position p k Coordinates are converted to WGS-84 geodetic coordinate system longitude, latitude and height Perform three-dimensional high-precision positioning of radiation sources.

[0078] The steps of step S2 include:

[0079] Calculate the distance difference, distance difference change rate, time difference equation, and frequency difference equation of 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 the time-frequency difference fusion positioning equation group;

[0081] Construct a cost function to transform the positioning problem into a problem of solving the minimum value of the cost function. When the conditions for solving the minimization problem are met, perform a first-order Taylor series expansion of the time-frequency difference fusion positioning equation group at the current radiation source position to obtain the residual of the time-frequency difference fusion positioning equation group.

[0082] Substitute the current radiation source position into the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the processed Jacobian matrix.

[0083] Since there are N (N≥3) low-orbit observation stations, N-1 time difference equations and N-1 frequency difference equations are obtained based on this. The combined earth equation constraints can obtain a time-frequency difference fusion positioning equation group consisting of 2N-1 equations. This equation group contains at least 5 equations to solve the three unknowns of the radiation source position. Therefore, this equation group has the characteristics of nonlinearity and overdetermined. The passive positioning solution based on TDOA / FDOA can be solved by analytical method, iterative method and search method. In order to reduce the number of iterations and reduce the complexity of the algorithm, the initial positioning of the three-station time difference is firstly realized based on the Chan method, which is used as the initial value of the radiation source position iteration.

[0084] Specifically, for any N (N ≥ 3) observation stations, the observation station No. 0 is selected as the master station, and the distance difference, time difference, frequency difference, radial velocity difference, and distance difference change rate between the remaining observation stations and the master station are Δri0 , τ i0 , Δf di,0 , Δν i,0 and In order to improve the positioning accuracy, the ellipsoid model earth constraint equation is combined with the above Δr i,0 =r i -r0=||pp i ||-||p-p0||=τ i,0 c and

[0085] By combining them, we get the time-frequency difference fusion positioning equation group:

[0086]

[0087] Where e is the first eccentricity of the earth, N is the radius of curvature of the earth, which is further converted into the mathematical expression of time difference, frequency difference observation and earth constraint equation:

[0088]

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

[0090] The Jacobian matrix F'(p) solution includes the distance difference, the distance difference change rate Jacobian matrix and the elliptical earth model coordinate system conversion Jacobian matrix. The distance difference and the distance difference change rate equations in the time-frequency difference fusion positioning equation group are respectively calculated at the radiation source target position p = [x, y, z] T The gradient is calculated at , so as 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 equation of the elliptical earth model are converted to the longitude and latitude of the WGS-84 geodetic coordinate system, and the gradient is calculated in the longitude and latitude directions of the target position of the radiation source, so as to construct the Jacobian matrix of the coordinate conversion of the elliptical earth model.

[0091] First, the distance difference Δr between a certain observation station and the main station i,0i=1,2,...,N-1, calculate partial derivatives at x,y,z respectively, i.e., the distance difference Δr i,0 At p = [x, y, z] T The gradient at is expressed as: The rate of change of the distance difference between a certain observation station and the main station Find the partial derivative at x, y, and z, that is, the distance difference At p = [x, y, z] T The gradient at is: Construct the Jacobian matrix H related to 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 of the ellipsoid model coordinate system transformation is derived. Since the motion of the ground radiation source and the low-orbit observation station is related to the earth ellipsoid model, the longitude and latitude of the WGS-84 world geodetic coordinate system are selected to represent the radiation source position p LBh =[L,B,h] T The positioning solution process involves the geodetic coordinate system and the earth-fixed geocentric coordinate system p = [x, y, z] T For the elliptical earth constraint equation in formula (14), the conversion relationship between the two coordinate systems is: The first eccentricity of the earth is generally taken as e = 0.0818191908426214957, and the radius of curvature of the earth is R e is the semi-major axis of the earth. Taking the first-order derivative of the earth's unitary curvature radius N with respect to latitude B, we can get the rate of change of the earth's unitary curvature radius for: The radiation source position p = [x, y, z] T Expressed as WGS-84 geodetic coordinate system position p LBh =[L,B,h] T , calculate the partial derivative at longitudes L, B and h respectively, and get the radiation source position p = [x, y, z] T In p LBh =[L,B,h] T Find the gradient.

[0095] It is worth mentioning that the radiation source usually moves or is distributed along the earth's constant altitude, that is, the altitude direction does not change, that is, it is a constant, so the speed in the altitude direction is also 0, so there is no need to find the partial derivative of the height h.

[0096] Construct the Jacobian matrix H of N (N≥3) observation stations from the Earth-fixed geocentric coordinate system to the WGS-84 coordinate system for the radiation source positionLB for: Under the constraints of the ellipsoid model + global elevation map, the Jacobian matrix F'(p) in the iterative positioning of the time difference and frequency difference fusion of any multiple stations based on Taylor expansion + least squares (Taylor-LS) is: F'(p) = H tf ×H LB .

[0097] Step S3, based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the radiation source position after the k+1th iteration is calculated.

[0098] Residual of the positioning equations based on time-frequency difference fusion, processed Jacobian matrix and current radiation source position Calculate the radiation source position after the k+1th iteration

[0099] The steps of step S3 include:

[0100] Based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the iterative equation of the radiation source position based on the least squares algorithm is obtained;

[0101] The current radiation source position is input into the iterative equation to obtain the radiation source position after the k+1th iteration.

[0102] F(p) = F(p k )+F'(p k )(pp k ) The iterative equation of the radiation source position based on the least squares (LS) algorithm is obtained: 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 of the equation is related to the gradient value of the cost function, F'(p k ) is the Jacobian matrix of the kth iteration of the distance difference, distance difference change rate and earth constraint equations F(p). In the process of solving the nonlinear equations, it is necessary to satisfy F'(p k ) T F'(p k ) matrix is ​​invertible. Since the equation is a non-positive definite matrix, we need to solve F'(p k ) T F'(p k), in addition, the radiation source position p k The initial value is the initial value p based on the Chan method time difference positioning ini =[x 0 ,y 0 ,z 0 ] T .

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

[0104] After the k+1th iteration, the radiation source longitude and latitude are obtained. k+1 and latitude B k+1 , query the global elevation map to correct the height. Use the global elevation map (such as SRTM, ASTER GDEM, etc.) to query the global elevation map for the height value h k+1 Corrected to h (k+1) ', according to the iterative radiation source longitude L k+1 and latitude B k+1 , query the corresponding elevation value to ensure that the height value of the radiation source is more accurate, because the radiation source may be located on different terrains. Update the longitude and latitude of the radiation source position after the k+1th iteration. Combine the longitude and latitude of the radiation source position and the height queried through the global elevation map to update the longitude and latitude coordinates of the radiation source position. Convert longitude and latitude coordinates Convert the updated latitude and longitude coordinates to the earth-fixed geocentric coordinate system p k+1 , the precise position of the radiation source in the ground-fixed geocentric coordinate system after the k+1th iteration is obtained, ensuring the 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 ground-fixed coordinate system, iterate steps S2 to S4, and obtain the optimal estimate of the radiation source position 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 cycle reaches a preset number of iterations.

[0106] The loop condition repeats steps S2 to S4 until the convergence condition is met or the maximum number of iterations is reached, and the difference between the final radiation source position and the radiation source position of the previous iteration is less than the preset threshold value |p k+1 -p k|<ε, where ε is a very small positive number, which is used to determine whether the position is close enough to the true position. When the number of iterations exceeds the preset maximum number of iterations M, the iteration is forced to stop. During each iteration, the radiation source position in the ground-fixed coordinate system is replaced with the current radiation source position in , and subsequent iterative calculations are continued. When any of the above conditions is met, the iteration stops. The radiation source position obtained at this time is the optimal estimate of the true position of the radiation source. This ensures that the iterative process stops when the accuracy requirements are met or the maximum number of iterations is reached, thereby obtaining the optimal estimate of the radiation source position, which improves the robustness of the algorithm and ensures the efficiency and accuracy of the calculation.

[0107] In a possible embodiment, taking typical three stations (A, B, C) and four stations (A, B, C, D) as examples, a simulation analysis of the fusion positioning performance of multi-station time difference and frequency difference is carried out. The relevant verification conclusions can be extended to scenarios with more than four stations. The simulation conditions are set first: the four stations A, B, C, and D are set to observe the motion scene, 860km above the earth's surface, where stations A and B are located on the same orbital plane, and their center positions are projected as point O on the earth, and stations C and D are located on another orbital plane. The distance between the observation stations is set to 75km to 90km, and the position and speed parameter settings of each observation station are shown in 0:

[0108] Table 1

[0109]

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

[0111] Before obtaining the simulation results, a comparative analysis of the positioning accuracy of different positioning systems was conducted. Based on the 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 Figure 3a The distribution diagram of the time difference positioning accuracy GDOP of the three stations is shown. Figure 3b The distribution diagram of the GDOP of the time-frequency difference positioning accuracy of the three stations is shown. Figure 4a The distribution diagram of the time difference positioning accuracy GDOP of the four stations is shown. Figure 4b The distribution diagram of the three-station time-frequency difference positioning accuracy GDOP is shown. For the three-station time-frequency difference and four-station time-frequency difference positioning, a simulation analysis is performed using a typical signal frequency of 3GHz as an example. One-dimensional slices are made at (ordinate: 0km, abscissa: 0km~2200km) and (abscissa: 0km, ordinate: 0km~2200km), and the relationship between the positioning accuracy of the four positioning methods in the longitude and latitude directions and the coverage distance is obtained. Figure 5aThe relationship between the positioning accuracy of the four positioning methods in the longitude direction and the coverage distance is shown in Figure 5a. The relationship between the positioning accuracy of the four positioning methods in the latitude direction and the coverage distance is shown in Figure 5b. Tables 2 and 3 respectively statistically calculate the positioning accuracy of the four positioning methods in the longitude and latitude directions at 0km, 1000km and 2000km from the observation station:

[0112] Table 2

[0113]

[0114] Table 3

[0115]

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

[0117] Figure 6a A schematic diagram of the longitude direction of the relationship between the three-station time difference and time-frequency difference positioning accuracy and the signal carrier frequency proposed in the embodiment of the present application is shown, Figure 6b The latitude direction schematic diagram shows the relationship between the three-station time difference and time-frequency difference positioning accuracy and the signal carrier frequency proposed in the embodiment of the present application, Figure 7a The longitude direction schematic diagram shows the relationship between the positioning accuracy of the four-station time difference and the time-frequency difference and the signal carrier frequency proposed in the embodiment of the present application, Figure 7b A schematic diagram of the latitude direction of the relationship between the positioning accuracy of the four-station time difference and time-frequency difference and the signal carrier frequency proposed in the embodiment of the present application is shown. Within 0 to 1000 km from the lower point of the observation station, the positioning accuracy of the four methods is similar. In general, the fusion positioning of time difference and frequency difference is slightly better than the single time difference positioning, and the four-station positioning is slightly better than the three-station positioning; when the distance from the lower point of the observation station is 2000 km, taking the longitude direction as an example, taking the three-station time difference positioning accuracy: 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, in positioning near and far areas, the time difference and frequency difference fusion positioning methods show higher accuracy, especially in far areas and high-frequency signal conditions, the improvement is particularly significant.

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

[0120] First, the nonlinear equation is linearized using Taylor expansion, and then it is solved iteratively 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, and the three-dimensional high-precision positioning of the target is achieved through multiple earth model corrections and elevation iterations.

[0122] A possible implementation of a multi-station time difference and frequency difference fusion positioning system is given below, which is used to execute each execution step 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] A conversion module, used to convert the projection position of the low-orbit observation station on the earth's surface into three-dimensional geographic coordinates in the geodetic coordinate system;

[0125] A generation module is used to substitute the current radiation source position into the constructed time-frequency difference fusion positioning equation group and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group based on the three-dimensional geographic coordinates to obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix;

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

[0127] A correction module, for correcting the height of the radiation source position after the k+1th iteration using a global elevation map based on the longitude and latitude of the radiation source position after the k+1th iteration to obtain the radiation source position in the earth-fixed coordinate system;

[0128] The iterative module is used to replace the current radiation source position with the radiation source position in the ground-fixed coordinate system, and obtain the optimal estimate of the radiation source position 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 cycle reaches a preset number of iterations.

[0129] In a possible implementation, the conversion module is used to:

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

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

[0132] In a possible implementation, a generating module is used to:

[0133] Calculate the distance difference, distance difference change rate, time difference equation, and frequency difference equation of 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 the time-frequency difference fusion positioning equation group;

[0135] Construct a cost function to transform the positioning problem into a problem of solving the minimum value of the cost function. When the conditions for solving the minimization problem are met, perform a first-order Taylor series expansion of the time-frequency difference fusion positioning equation group at the current radiation source position to obtain the residual of the time-frequency difference fusion positioning equation group.

[0136] Substitute the current radiation source position into the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the processed Jacobian matrix.

[0137] In a possible implementation, the computing module is used to:

[0138] Based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the iterative equation of the radiation source position based on the least squares algorithm is obtained;

[0139] The current radiation source position is input into the iterative equation to obtain the radiation source position after the k+1th iteration.

[0140] This preferred embodiment provides a computer device, which can implement the steps in any embodiment of the multi-station time difference and frequency difference fusion positioning method provided in the embodiments of the present application. Therefore, the beneficial effects of the multi-station time difference and frequency difference fusion positioning method provided in the embodiments of the present application can be achieved. Please see the previous embodiments for details and will not be repeated here.

[0141] Those skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructions, or by controlling related hardware through instructions, and the instructions can be stored in a computer-readable storage medium and loaded and executed by a processor. To this end, an embodiment of the present application provides a storage medium, in which a plurality of instructions are stored, and the instructions 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 the embodiment of the present application.

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

[0143] Since the instructions stored in the storage medium can execute the steps in any embodiment of the multi-station time difference and frequency difference fusion positioning method provided in the embodiments of the present application, the beneficial effects that can be achieved by any multi-station time difference and frequency difference fusion positioning method provided in the embodiments of the present application can be achieved. Please see the previous embodiments for details and will not be repeated here.

[0144] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present 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 difference and frequency difference fusion positioning model, the model includes multiple low-orbit observation stations and ground radiation sources, and the method includes: Step S1, converting the projection 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, the current radiation source position is substituted into the constructed time-frequency difference fusion positioning equation group and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix; Step S3, calculating the radiation source position after the k+1th iteration based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix; Step S4, based on the longitude and latitude of the radiation source position after the k+1th iteration, use the global elevation map to correct the height of the radiation source position after the k+1th iteration to obtain the radiation source position in the earth-fixed coordinate system; Step S5, replace the current radiation source position in step S2 with the radiation source position in the ground-fixed coordinate system, iterate steps S2 to S4, and obtain the optimal estimate of the radiation source position 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 cycle reaches a preset number of iterations.

2. The fusion positioning method according to claim 1, characterized in that: The steps of step S1 include: The projection position of the low-orbit observation station on the earth's surface is selected, and the three-station time difference initial positioning is performed based on the Chan method to obtain the three-station time difference positioning result; The time difference positioning results of the three stations 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 according to claim 1, characterized in that: The steps of step S2 include: Calculate the distance difference, distance difference change rate, time difference equation, and frequency difference equation of 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 the time-frequency difference fusion positioning equation group; Construct a cost function to transform the positioning problem into a problem of solving the minimum value of the cost function. When the conditions for solving the minimization problem are met, perform a first-order Taylor series expansion of the time-frequency difference fusion positioning equation group at the current radiation source position to obtain the residual of the time-frequency difference fusion positioning equation group. Substitute the current radiation source position into the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the processed Jacobian matrix.

4. The fusion positioning method according to claim 3, characterized in that: The steps of step S3 include: Based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the iterative equation of the radiation source position based on the least squares algorithm is obtained; The current radiation source position is input into the iterative equation to obtain the radiation source position after the k+1th iteration.

5. A multi-station time difference and frequency difference fusion positioning system, characterized in that: The system comprises: A conversion module, used to convert the projection position of the low-orbit observation station on the earth's surface into three-dimensional geographic coordinates in the geodetic coordinate system; A generation module is used to substitute the current radiation source position into the constructed time-frequency difference fusion positioning equation group and the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group based on the three-dimensional geographic coordinates to obtain the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix; A calculation module is used to calculate the radiation source position after the k+1th iteration based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix; A correction module, for correcting the height of the radiation source position after the k+1th iteration using a global elevation map based on the longitude and latitude of the radiation source position after the k+1th iteration to obtain the radiation source position in the earth-fixed coordinate system; The iterative module is used to replace the current radiation source position with the radiation source position in the ground-fixed coordinate system, and obtain the optimal estimate of the radiation source position 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 cycle reaches a preset number of iterations.

6. The fusion positioning system according to claim 5, characterized in that: Conversion module, used to: The projection position of the low-orbit observation station on the earth's surface is selected, and the three-station time difference initial positioning is performed based on the Chan method to obtain the three-station time difference positioning result; The time difference positioning results of the three stations 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 according to claim 5, characterized in that: Generate modules for: Calculate the distance difference, distance difference change rate, time difference equation, and frequency difference equation of 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 the time-frequency difference fusion positioning equation group; Construct a cost function to transform the positioning problem into a problem of solving the minimum value of the cost function. When the conditions for solving the minimization problem are met, perform a first-order Taylor series expansion of the time-frequency difference fusion positioning equation group at the current radiation source position to obtain the residual of the time-frequency difference fusion positioning equation group. Substitute the current radiation source position into the Jacobian matrix of the kth iteration of the time-frequency difference fusion positioning equation group to obtain the processed Jacobian matrix.

8. The fusion positioning system according to claim 7, characterized in that: Compute module for: Based on the current radiation source position, the residual of the time-frequency difference fusion positioning equation group and the processed Jacobian matrix, the iterative equation of the radiation source position based on the least squares algorithm is obtained; The current radiation source position is input into the iterative equation to obtain the radiation source position after the k+1th iteration.

9. A computer device, characterized in that: The computer device includes a processor and a memory, wherein a computer program is stored in the memory, and the computer program is loaded and executed by the processor to implement the fusion positioning method according to any one of claims 1 to 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 according to any one of claims 1 to 4.

Images