Single-satellite doppler geo-navigation jammer location initial solution estimation method, system, and media

Abstract

This application discloses an initial solution estimation method, system, and medium for single-satellite Doppler localization of ground-based navigation interference sources. The method includes receiving a segment of multi-epoch Doppler data from a navigation interference signal emitted by a ground-based interference source during the overhead transit of a single low-Earth orbit satellite. This yields N zero-Doppler nadir points. These N zero-Doppler nadir points are then fused to obtain the zero-Doppler point positioning coordinates based on the multi-epoch Doppler data. A first perpendicular line is drawn from these zero-Doppler point positioning coordinates to the nadir trajectory curve of the single satellite. A binary search method is used on this first perpendicular line to find the point with the minimum Doppler residual; the location of this point is the initial solution location of the ground-based interference source. This method is applicable to the monitoring and localization of ground-based interference sources in satellite navigation systems. By processing the Doppler frequency shift information of the received signal from a single satellite, an initial solution estimation of the interference source location is performed, providing iterative initial values ​​for subsequent precise localization.

Description

Technical Field

[0001] This application relates to the field of positioning technology, and in particular to an initial solution estimation method, system and medium for single-satellite Doppler Earth navigation interference source localization. Background Technology

[0002] In the existing technology, when ground navigation interference sources interfere with navigation signals, it is difficult to determine the actual location of the interference source, and there is a lack of effective technical means to detect and eliminate the interference source. Summary of the Invention

[0003] The main technical problem addressed in this application is to provide an initial solution estimation method, system, and medium for single-satellite Doppler localization of ground navigation interference sources. This method utilizes a single low-Earth orbit satellite for passive localization of ground navigation interference sources. By processing the Doppler frequency shift information of the received signal from the single satellite, an initial solution estimation of the interference source location is performed, providing iterative initial values ​​for subsequent precise localization.

[0004] To address the aforementioned technical problems, this application provides a method for estimating the initial solution for locating a single-satellite Doppler ground-based navigation interference source. The method includes the following steps: during the overhead transit of a single low-Earth orbit satellite, receiving a segment of multi-epoch Doppler data from a navigation interference signal emitted by a ground-based interference source, corresponding to N Doppler data points; using the Doppler data acquired at each single epoch, locating the corresponding zero-Doppler nadir point, resulting in N zero-Doppler nadir points; fusing the N zero-Doppler nadir points to obtain the zero-Doppler point location coordinates based on the multi-epoch Doppler data; drawing a first perpendicular line from the zero-Doppler point location coordinates to the nadir point trajectory curve of the single satellite; and using a binary search method on the first perpendicular line to find the point with the minimum Doppler residual, the location of which corresponds to the point with the minimum Doppler residual is the initial solution location of the ground-based interference source.

[0005] In some embodiments, the Doppler data includes Doppler frequency shift. and Doppler rate of change The corresponding first expression: , in, The carrier wavelength of the monitored navigation interference signal; The frequency of the monitored navigation interference signal; The speed of light; The coordinates of the ground interference source; For satellite position; This refers to the satellite's radial acceleration. For the satellite's inertial acceleration; For satellite speed; The radial velocity of the ground interference source relative to the satellite. It is the radial angle of the ground interference source relative to the satellite.

[0006] In some embodiments, a second expression is constructed based on the first expression: , in, For Doppler residuals, These are Doppler frequency shift observations. This is the calculated value for the Doppler frequency shift; For the Doppler rate of change residual, These are Doppler rate of change observations. This is the calculated value for the Doppler rate of change. Let be the ECEF coordinate vector of the ground interference source, and satisfy the constraint equations: , The radius of the Earth's equator; The Earth's polar radius; Minimizing the Doppler observation residuals of the second expression above can be represented as a formal expression of a least-squares optimization problem with equality constraints, namely: , in, The Jacobian matrix of the observation model is represented as follows: .

[0007] In some embodiments, further Convert to Lagrange formula: , in, For Lagrange multipliers; And, further, we obtain: , in, It is the identity matrix, and the regularization coefficient is... gradient of constraint function The mechanism for jointly determining the update step size, the position correction to be determined is: Solve and The location estimate was subsequently updated to The zero-Doppler nadir localization result corresponding to the single-epoch Doppler data was obtained: .

[0008] In some embodiments, N zero-Doppler nadir points are fused to obtain the zero-Doppler point positioning coordinates corresponding to the Doppler data acquired in the multi-epoch acquisition: , in, Locate the coordinates of the zero Doppler point. This is the zero-Doppler sub-point localization result for the i-th epoch.

[0009] In some embodiments, during the observation period when the satellite passes overhead, a smooth nadir trajectory curve is obtained by fitting the coordinate sequence of the satellite's nadir point; using the zero Doppler point positioning coordinates as the origin, a first perpendicular line is drawn relative to the nadir trajectory curve to obtain an initial reference point that passes through the nadir trajectory curve. .

[0010] In some embodiments, with the initial reference point Using a fixed step size as the initial search starting point. A binary search is performed along the target direction of the first vertical line to determine the optimal solution point A with the minimum Doppler residual on the first vertical line; Then, taking point A as the center, with Calculate the step length on both sides of point A on the first perpendicular line. , Point residuals are calculated, and the point with the smallest residual among the three points is selected. Let's assume the point with the smallest residual is... Point, then with Centered on point, with Step size calculation Points on both sides , The two residuals are calculated until the step size threshold setting requirement is met, and the point F with the smallest residual on the first vertical line is obtained.

[0011] In some embodiments, after finding the point F with the minimum Doppler observation residual on the first perpendicular line, a perpendicular line is drawn through point F to the first perpendicular line, which is the second perpendicular line. The point with the minimum residual is then searched on the second perpendicular line using the same binary search strategy to obtain the final positioning result.

[0012] This application also provides an initial solution estimation system for locating interference sources in single-satellite Doppler Earth navigation, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the initial solution estimation method as described above.

[0013] This application also provides a storage medium storing a computer program that, when executed by a processor, implements the steps of the initial solution estimation method as described above.

[0014] The beneficial effects of this application are as follows: This application discloses an initial solution estimation method, system, and medium for single-satellite Doppler localization of ground navigation interference sources. The method includes receiving a segment of multi-epoch Doppler data from a navigation interference signal emitted by a ground interference source during the overhead transit of a single low-Earth orbit satellite, obtaining N zero-Doppler nadir points, fusing these N zero-Doppler nadir points to obtain the zero-Doppler point positioning coordinates based on the multi-epoch Doppler data; drawing a first perpendicular line from these zero-Doppler point positioning coordinates to the nadir point trajectory curve of the single satellite, and using a binary search method on this first perpendicular line to find the point with the minimum Doppler residual; the corresponding location is the initial solution location of the ground interference source. This method is applicable to the monitoring and localization of ground interference sources in satellite navigation systems. By processing the Doppler frequency shift information of the received signal from a single satellite, it provides an initial solution estimation of the interference source location, offering iterative initial values ​​for subsequent precise localization. Attached Figure Description

[0015] Figure 1 This is a flowchart of an embodiment of the initial solution estimation method for single-satellite Doppler Earth navigation interference source localization in this application; Figure 2 This is a schematic diagram of the spatial principle of an embodiment of the initial solution estimation method for single-satellite Doppler Earth navigation interference source localization in this application; Figure 3 This is a schematic diagram of the distribution of the minimum Doppler residual points on the first vertical line in one embodiment of the initial solution estimation method for single-satellite Doppler-to-ground navigation interference source localization in this application. Figure 4 This is a schematic diagram of the binary search method for finding the minimum Doppler residual in one embodiment of the initial solution estimation method for single-satellite Doppler-based Earth navigation interference source localization in this application. Detailed Implementation

[0016] To facilitate understanding of this application, a more detailed description is provided below with reference to the accompanying drawings and specific embodiments. Preferred embodiments of this application are shown in the drawings. However, this application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application.

[0017] It should be noted that, unless otherwise defined, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The term "and / or" as used in this specification includes any and all combinations of one or more of the associated listed items.

[0018] Ground navigation and positioning interference sources typically emit interference signals at the same frequency as the real navigation signals to interfere with the normal reception of real navigation signals by ground navigation receivers. Therefore, this application utilizes low-Earth orbit (LEO) satellites to locate and identify ground navigation and positioning interference sources. This is achieved by using LEO satellites as they pass overhead to receive interference signals emitted by the source, thus making an initial determination of the source's location.

[0019] like Figure 1 The diagram shown is a flowchart of an embodiment of the initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to this application. The method includes the following steps: Step S1: During the overhead transit of a single low-orbit satellite, receive a segment of Doppler data collected at multiple epochs from the navigation interference signal emitted by the ground interference source, corresponding to N Doppler data points; Step S2: Using the Doppler data collected in each single epoch, locate the corresponding zero-Doppler nadir point, and obtain N zero-Doppler nadir points; Step S3: Merge the N zero-Doppler sub-satellite points to obtain the zero-Doppler point positioning coordinates corresponding to the Doppler data acquired based on multi-epoch data; Step S4: Using the zero Doppler point positioning coordinates, draw a first perpendicular line relative to the nadir trajectory curve of the single satellite; Step S5: Use a binary search method to find the point of minimum Doppler residual on the first vertical line. The location of the point of minimum Doppler residual is the initial solution location of the ground interference source.

[0020] like Figure 2 As shown, during step S1, as a single satellite passes overhead from a ground-based navigation interference source, it will receive navigation interference signals emitted by the source within this time frame. This is referred to as multi-epoch Doppler data. This is because navigation interference signals are usually on the same frequency as normal navigation signals, allowing for co-frequency suppression of normal navigation signals.

[0021] The satellite is in relative motion with respect to the ground interference source, therefore the actual frequency value of the received navigation interference signal will be affected by the Doppler effect. In this application, the nadir curve of the satellite is used as a reference. Theoretically, the ground interference source should be located on a vertical line that intersects the nadir curve (hereinafter referred to as the first vertical line), and this intersection point serves as an initial reference point for the satellite on the nadir curve.

[0022] Furthermore, in step S2, the ground interference source is located on the Earth's surface, and the Doppler data received by a single low-orbit satellite from the ground interference source includes: Doppler frequency shift. With Doppler rate of change The observation equation is expressed in the first form: , in, The carrier wavelength of the monitored navigation interference signal; The frequency of the monitored navigation interference signal; The speed of light; The coordinates of the ground interference source; For satellite position; This refers to the satellite's radial acceleration. For the satellite's inertial acceleration; For satellite speed; The radial velocity of the ground interference source relative to the satellite. It is the radial angle of the ground interference source relative to the satellite.

[0023] The following further explains the technical solution for determining the zero-Doppler sub-satellite point based on Doppler data.

[0024] This application uses Doppler data acquired at a single epoch. The core objective of locating the corresponding zero Doppler nadir point is to minimize the residual matrix of the Doppler observation residuals under ellipsoidal constraints. The second expression for this residual matrix is ​​shown below: , in, For Doppler residuals, These are Doppler frequency shift observations. This is the calculated value for the Doppler frequency shift; For the Doppler rate of change residual, These are Doppler rate of change observations. This is the calculated value for the Doppler rate of change. Let be the ECEF (Earth-Centered, Earth-Fixed) coordinate vector of the ground disturbance source, and in the WGS84 ellipsoidal coordinate system, satisfy the constraint equations:

[0025] The radius of the Earth's equator; This is the Earth's polar radius.

[0026] Furthermore, minimizing the Doppler observation residuals in the second expression above can be represented as a formal expression of a least-squares optimization problem with equality constraints, namely: , in, The Jacobian matrix of the observation model is represented as follows: .

[0027] Furthermore, in order to improve solution efficiency, for Optimization problems with equality constraints can be transformed into unconstrained optimization problems by using the Lagrange multiplier method while preserving the constraints.

[0028] Therefore, the Lagrange function is constructed as follows: , in, It is a Lagrange multiplier.

[0029] Find the position correction vector for the above equation. and Lagrange multipliers The partial derivatives are taken and set to zero. According to the fundamental rules of matrix differentiation, the squared term of the residual norm 2 is... right The partial derivatives are Constraints right The partial derivatives are Therefore, we can obtain the third expression: .

[0030] For Lagrange multipliers Taking the partial derivatives and setting them to zero, we can directly restore the original equality constraints: Considering the iterative solution process, the current position estimate... It does not strictly satisfy the WGS84 ellipsoidal constraint, and the constraint function needs to be modified. At the current iteration point Perform a first-order Taylor expansion at that point.

[0031] Let the position estimate of the current iteration be The position correction to be determined is That is, the position estimate for the next iteration is Then the constraint function The linearized approximation is: , By uniformly simplifying the variables to the symbolic form of the current iteration point, we obtain the fourth expression corresponding to the linearized constraint conditions: , The third expression Divide both sides by 2 and replace the variables with the iteration correction values. Since multiplying both sides of the equation by a non-zero constant does not change the equivalence of the solutions, rearranging and simplifying, we get: , make (The Lagrange multipliers are undetermined constants; redefining them does not affect the final numerical value of the localized solution.) After rearranging and simplifying, we obtain the fifth expression: .

[0032] Therefore, the fifth expression can be combined. and the fourth expression The two calculation formulas can be written in standard block matrix form: , Further implicit introduction of regularization terms , Become Repeat the above steps. Revised to: .

[0033] Will Rewritten as , and the fourth expression mentioned above By combining the two equations, we obtain: , Among them, when hour, yes The largest diagonal element has a radial update coefficient of approximately 0.5, which means that the observation information is reasonably adopted, driving the solution vector to move in the direction of smaller Doppler residuals, and gradually approaching the zero Doppler isosurface under the constraint of the nadir point trajectory. The gradient vector of the constraint function reflects the normal of the ellipsoid at the current position; This is a correction vector for the location of the interference source, used to update the localization solution.

[0034] It can be obtained by inverting the matrix: , in, It is the identity matrix, revealing the regularization coefficients. gradient of constraint function The mechanism that jointly determines the update step size. Solving this linear system yields... and The location estimate was subsequently updated to The process is repeated iteratively until the convergence condition is met.

[0035] To strictly enforce the ellipsoidal constraints, the updated position is projected onto the WGS84 ellipsoid, thus obtaining the zero-Doppler nadir positioning result for the low-Earth orbit satellite with single epoch data: , in, .

[0036] In step S3, N zero-Doppler sub-satellite points are fused to obtain the zero-Doppler point positioning coordinates corresponding to the Doppler data acquired through multi-epoch acquisition:

[0037] in, To determine the coordinates of the final zero Doppler point, The total number of observed epochs, This is the zero-Doppler sub-point localization result for the i-th epoch.

[0038] like Figure 2 As shown, theoretically, the location of the ground interference source is consistent with the zero-Doppler point positioning coordinates. However, since the zero-Doppler point positioning coordinates are selected as an average value, due to errors, they are not the actual location of the ground interference source. Further calculations are needed to improve the accuracy of the positioning calculation.

[0039] Furthermore, after obtaining the zero-Doppler point location coordinates, the location error is mainly concentrated in the direction passing through the target point (the actual location of the interference source) and orthogonal to the nadir point trajectory. To achieve accurate error suppression in this direction, this application further proposes a binary search optimization strategy along the direction passing through the zero-Doppler nadir point and orthogonal to the nadir point trajectory. This transforms the two-dimensional spatial search into a refined one-dimensional iterative search along this orthogonal direction, significantly improving computational efficiency while ensuring global optimality.

[0040] Specifically, during the observation period when the satellite passes overhead, the coordinate sequence of the nadir point can be fitted using cubic spline interpolation to obtain a smooth nadir point trajectory curve: ,in, It is a cubic spline interpolation operator that ensures the smoothness of the nadir point trajectory by minimizing the trajectory curvature; This represents the sub-satellite point of the nth sampling epoch.

[0041] To simplify geometric calculations, a local coordinate system is established, with the zero Doppler point used for coordinate positioning. Using angular coordinates as the origin This indicates that the eastward direction along the trajectory of the nadir point is the x-axis, the northward direction perpendicular to the trajectory of the nadir point is the y-axis, and the z-axis has a value of 0.

[0042] The coordinate transformation relationships are as follows: , 111 indicates that the longitude distance at the equator is 111 kilometers. The projection curve of the nadir point trajectory in this local coordinate system is denoted as... . origin The slope at point is calculated using the central difference method, as shown below: , Based on geometric orthogonality, we obtain the first perpendicular line, which passes through the initial reference point of the trajectory below the star. The equation of the first perpendicular line: The slope of the first perpendicular is ,in, for In the local coordinate system, this line represents the unique path for one-dimensional optimization.

[0043] Step S5: Search for the minimum point of the Doppler residual using the bisection method. The core of the optimization along the first vertical line is to search for the minimum value of the Doppler observation residual norm based on the bisection method.

[0044] Define the objective function as: ,in, Represents the target coordinates on the optimized path along the first vertical line; It is the theoretical Doppler value calculated based on the optimization point; These are Doppler observations.

[0045] The theoretical distribution of Doppler residuals along the first vertical line is as follows: Figure 3 As shown. Using the initial reference point... Using the center point as an example, as we move along the first perpendicular line from the center point to both sides, a minimum residual value will be observed on each side.

[0046] These two minimum values ​​correspond to point P1 on the first vertical line that is closest to the true coordinates of the interference source, and its mirror image point P2 on the other side of the nadir trajectory. Additional information is needed to eliminate these mirror image solutions before performing optimization on the first vertical line.

[0047] After the mirror ambiguity is eliminated, the zero Doppler sub-point location obtained on the target side extends towards the true location of the interference source to the nearest approximation point. During this process, the Doppler observation residual shows a strictly monotonically decreasing trend. When the nearest approximation point P1 is reached, the residual drops to a minimum value. After passing point P1, the residual shows a strictly monotonically increasing trend in the direction away from the true location.

[0048] like Figure 4 As shown, based on this residual distribution characteristic, with the initial reference point... Using a fixed step size as the initial search starting point. A bisection search is performed along the target direction of the first vertical line to determine the optimal solution point A with the minimum Doppler residual on the first vertical line.

[0049] Then, taking point A as the center, with Calculate the step length on both sides of point A on the first perpendicular line. , Point residuals are calculated, and the point with the smallest residual among the three points is selected. Let's assume the point with the smallest residual is... Point, then with Centered on point, with Step size calculation Points on both sides , Two-point residuals, until the step size threshold is met (e.g.) Set requirements to obtain the point F with the smallest residual on the first vertical line.

[0050] After finding the point F with the minimum Doppler observation residual on the first perpendicular line, draw a perpendicular line from point F to the first perpendicular line, which is the second perpendicular line. This second perpendicular line is parallel to the trajectory of the nadir point. On this parallel line, use the same binary search strategy to find the point with the minimum residual, and obtain the final positioning result.

[0051] Based on the same inventive concept, this application also provides an initial solution estimation system for locating interference sources in single-satellite Doppler Earth navigation, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the initial solution estimation method as described above.

[0052] This application also provides a computer-readable storage medium storing program code that can be called by a processor to execute the methods described in the above method embodiments.

[0053] Computer-readable storage media can be electronic storage devices such as flash memory, EEPROM (Electrically Erasable Programmable Read-Only Memory), EPROM, hard disk, or ROM. Optionally, computer-readable storage media include nontransitory computer-readable media. A computer-readable storage medium has storage space for program code that performs any of the method steps described above. This program code can be read from or written to one or more computer program products. The program code can be compressed in an appropriate form.

[0054] Therefore, this application discloses an initial solution estimation method, system, and medium for single-satellite Doppler localization of ground navigation interference sources. The method includes receiving a segment of multi-epoch Doppler data from a navigation interference signal emitted by a ground interference source during the overhead transit of a single low-Earth orbit satellite, obtaining N zero-Doppler nadir points, fusing these N zero-Doppler nadir points to obtain the zero-Doppler point positioning coordinates based on the multi-epoch Doppler data; drawing a first perpendicular line from these zero-Doppler point positioning coordinates to the nadir point trajectory curve of the single satellite, and using a binary search method on this first perpendicular line to find the point with the minimum Doppler residual; the corresponding location is the initial solution location of the ground interference source. This method is applicable to the monitoring and localization of ground interference sources in satellite navigation systems. By processing the Doppler frequency shift information of the received signal from a single satellite, it provides an initial solution estimation of the interference source location, offering iterative initial values ​​for subsequent precise localization.

[0055] The above are merely embodiments of this application and do not limit the scope of this patent application. Any equivalent structural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A method for estimating the initial solution for locating interference sources in single-satellite Doppler Earth navigation, characterized in that, Including the following steps: During the overhead transit of a single low-Earth orbit satellite, a segment of Doppler data collected at multiple epochs is received from the navigation interference signal transmitted by the ground interference source, corresponding to N Doppler data points; Using the Doppler data collected in each single epoch, the corresponding zero-Doppler nadir point is located, resulting in N zero-Doppler nadir points; By fusing the N zero-Doppler sub-satellite points, the zero-Doppler point positioning coordinates corresponding to the Doppler data acquired based on multi-epoch data are obtained; Draw a first perpendicular line from the zero Doppler point positioning coordinates to the nadir trajectory curve of the single satellite. The Doppler residual minimum point is found by using a binary search method on the first vertical line. The location of the Doppler residual minimum point is the initial solution location of the ground interference source.

2. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 1, characterized in that, The Doppler data includes Doppler frequency shift. and Doppler rate of change The corresponding first expression: ， in, The carrier wavelength of the monitored navigation interference signal; The frequency of the monitored navigation interference signal; The speed of light; The coordinates of the ground interference source; For satellite position; This refers to the satellite's radial acceleration. For the satellite's inertial acceleration; For satellite speed; The radial velocity of the ground interference source relative to the satellite. It is the radial angle of the ground interference source relative to the satellite.

3. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 2, characterized in that, Based on the first expression, construct the second expression: ， in, For Doppler residuals, These are Doppler frequency shift observations. This is the calculated value for the Doppler frequency shift; For the Doppler rate of change residual, These are Doppler rate of change observations. This is the calculated value for the Doppler rate of change. Let be the ECEF coordinate vector of the ground interference source, and satisfy the constraint equations: ， The radius of the Earth's equator; The Earth's polar radius; Minimizing the Doppler observation residuals of the second expression above can be represented as a formal expression of a least-squares optimization problem with equality constraints, namely: ， in, The Jacobian matrix of the observation model is represented as follows: 。 4. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 3, characterized in that, Further Convert to Lagrange formula: ， in, For Lagrange multipliers; And, further, we obtain: ， in, It is the identity matrix, and the regularization coefficient is... gradient of constraint function The mechanism for jointly determining the update step size, the position correction to be determined is: Solve and The location estimate was subsequently updated to The zero-Doppler nadir localization result corresponding to the single-epoch Doppler data was obtained: 。 5. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 4, characterized in that, By fusing N zero-Doppler sub-satellite points, the zero-Doppler point positioning coordinates corresponding to the Doppler data acquired over the multi-epoch period are obtained: ， in, Locate the coordinates of the zero Doppler point. This is the zero-Doppler sub-point localization result for the i-th epoch.

6. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 5, characterized in that, During the observation period when the satellite passes overhead, a smooth nadir trajectory curve is obtained by fitting the coordinate sequence of the satellite's nadir point. Taking the zero Doppler point positioning coordinates as the origin, a first perpendicular line is drawn relative to the nadir trajectory curve to obtain an initial reference point that passes through the nadir trajectory curve. .

7. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 5, characterized in that, With the initial reference point Using a fixed step size as the initial search starting point. A binary search is performed along the target direction of the first vertical line to determine the optimal solution point A with the minimum Doppler residual on the first vertical line; Then, taking point A as the center, with Calculate the step length on both sides of point A on the first perpendicular line. , Point residuals are calculated, and the point with the smallest residual among the three points is selected. Let's assume the point with the smallest residual is... Point, then with Centered on point, with Step size calculation Points on both sides , The two residuals are calculated until the step size threshold setting requirement is met, and the point F with the smallest residual on the first vertical line is obtained.

8. The initial solution estimation method for single-satellite Doppler Earth navigation interference source localization according to claim 4, characterized in that, After finding the point F with the minimum Doppler observation residual on the first perpendicular line, draw a perpendicular line from point F to the first perpendicular line, which is the second perpendicular line. On the second perpendicular line, use the same binary search strategy to find the point with the minimum residual, and obtain the final positioning result.

9. An initial solution estimation system for locating interference sources in single-satellite Doppler Earth navigation, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the initial solution estimation method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, implements the steps of the initial solution estimation method as described in any one of claims 1 to 8.

Images