A stereobaseline interferometer direction finding method based on coordinate system conversion

Abstract

The application belongs to the field of electronic reconnaissance, and particularly relates to a stereoscopic baseline interferometer direction finding method based on coordinate system conversion. The method comprises the following steps: S1, selecting a guide baseline and a deblurring baseline; S2, constructing a coordinate system conversion matrix according to the guide baseline; S3, traversing a blur array combination, and acquiring a pitch angle and an azimuth angle under different blur array combinations according to the guide baseline and the coordinate system conversion matrix; and S4, constructing an evaluation function according to the deblurring baseline, and selecting the pitch angle and the azimuth angle corresponding to the maximum evaluation function as the final direction finding result. The stereoscopic baseline interferometer direction finding method based on coordinate system conversion converts the stereoscopic baseline problem into a planar baseline problem through coordinate system conversion, so that the fast and high-precision direction finding of the coming wave direction is realized by direct analytical solution.

Description

Technical Field

[0001] This application belongs to the field of electronic reconnaissance, and specifically relates to a direction finding method for a stereo baseline interferometer based on coordinate system transformation. Background Technology

[0002] Interferometer-based direction finding systems are widely used due to their simple structure and high accuracy. Traditional two-dimensional direction finding is mostly based on coplanar arrays, whose azimuth and elevation angles can be directly solved using a system of two linear equations. However, in applications such as airborne conformal systems, array elements are often non-coplanar due to mounting surfaces or tolerances, resulting in a stereo baseline interferometer. Existing methods suffer from drawbacks such as iterative non-convergence, stringent requirements on baseline layout, and low efficiency.

[0003] Therefore, there is an urgent need for a technical solution to overcome or mitigate at least one of the aforementioned defects in the existing technology. Summary of the Invention

[0004] The purpose of this application is to provide a stereo baseline interferometer direction finding method based on coordinate system transformation to solve at least one problem existing in the prior art.

[0005] The technical solution of this application is:

[0006] A direction finding method for a stereo baseline interferometer based on coordinate system transformation, comprising:

[0007] Step S1: Select the guiding baseline and the deblurred baseline;

[0008] Step S2: Construct a coordinate system transformation matrix based on the guiding baseline;

[0009] Step S3: Traverse the combinations of ambiguities and obtain the elevation and azimuth angles under different combinations of ambiguities based on the guiding baseline and the coordinate system transformation matrix;

[0010] Step S4: Construct an evaluation function based on the defuzzified baseline, and select the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result.

[0011] In at least one embodiment of this application, step S1, selecting the guiding baseline and the deblurred baseline, includes:

[0012] From all of the interferometers From the root baselines, two baselines that meet the length requirements and are approximately orthogonal are selected as guide baselines, denoted as vectors. and N is the number of interferometer elements, N≥4;

[0013] The remaining M baselines are used as the unblurred baselines, denoted as... .

[0014] In at least one embodiment of this application, step S2, constructing a coordinate system transformation matrix based on the guiding baseline, includes:

[0015] Step S21: Calculate the unit normal vector of the plane forming the guiding baseline, including:

[0016] Calculate the normal vector of the plane formed by the guiding baselines:

[0017] ;

[0018] ;

[0019] ;

[0020] Calculate the magnitude of the normal vector:

[0021] ;

[0022] Calculate the unit normal vector:

[0023] ;

[0024] Step S22: Calculate the rotation angle based on the unit normal vector:

[0025] ;

[0026] Where α is the pitch angle and β is the azimuth angle. , , They are the unit normal vectors The X, Y, and Z components;

[0027] Step S23: Construct the basic rotation matrix based on the rotation angle:

[0028] ;

[0029] Step S24: Construct the coordinate system transformation matrix based on the basic rotation matrix:

[0030] ;

[0031] The coordinate system transformation matrix T satisfies ,in, Let be the vector to be transformed. This is the transformed vector.

[0032] In at least one embodiment of this application, in step S21, if the unit normal vector Z component Then let Ensure unit normal vector Z component .

[0033] In at least one embodiment of this application, step S3 involves iterating through the combinations of ambiguities and obtaining the elevation and azimuth angles under different combinations of ambiguities based on the guiding baseline and the coordinate system transformation matrix, including:

[0034] Step S31: Determine the range of ambiguity values ​​corresponding to the two guide baselines:

[0035] ;

[0036] ;

[0037] in, To guide the baseline Fuzzy numbers, To guide the baseline Fuzzy numbers;

[0038] Step S32: For each group of fuzzy number combinations Calculate the candidate pitch and azimuth angles, and collect all candidate pitch and azimuth angles into a set. middle.

[0039] In at least one embodiment of this application, in step S32, for each group of fuzzy number combinations Calculate the candidate pitch and azimuth angles, and collect all candidate pitch and azimuth angles into a set. Includes:

[0040] Transform the guiding baseline according to the coordinate system transformation matrix:

[0041] ;

[0042] in, , The converted guide baseline;

[0043] The ambiguous phase difference between the two guide baselines is restored to an unambiguous phase difference:

[0044] ;

[0045] ;

[0046] in, , These represent the ambiguous phase difference between the two guide baselines. , These are the unambiguous phase differences between the two guide baselines;

[0047] according to Incoming wave direction vector in coordinate system A system of linear equations is constructed to relate the unambiguous phase difference between the two guide baselines:

[0048] ;

[0049] in, , These are the vector components of the two guide baselines, respectively;

[0050] Solving the system of linear equations, we obtain... , The value is determined by ,get ;

[0051] Two candidate direction vectors are obtained:

[0052] ;

[0053] Inversely transform the candidate direction vector back to the original coordinate system:

[0054] ;

[0055] Based on the candidate direction vector in the original coordinate system Calculate the candidate pitch and azimuth angles:

[0056] ;

[0057] Repeat the above steps to iterate through all combinations of fuzzy numbers and collect all candidate pitch and azimuth angles into a set. middle.

[0058] In at least one embodiment of this application, step S4, which involves constructing an evaluation function based on the de-fuzzy baseline and selecting the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result, includes:

[0059] Step S41, from set Extract the candidate pitch angle and azimuth angle to be determined, and obtain the candidate direction vectors corresponding to the current candidate pitch angle and azimuth angle. ;

[0060] Step S42: Construct an evaluation function based on the unfuzzy baseline:

[0061] ;

[0062] in, For evaluation functions;

[0063] Step S43: Select the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result.

[0064] The invention has at least the following beneficial technical effects:

[0065] The coordinate system transformation-based stereo baseline interferometer direction finding method of this application transforms the stereo baseline problem into a planar baseline problem through coordinate system transformation, thereby realizing fast and high-precision direction finding by directly and analytically solving the direction of incoming waves. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the geometric model of a stereo baseline interferometer according to one embodiment of this application;

[0067] Figure 2 This is a schematic diagram of coordinate system transformation according to one embodiment of this application;

[0068] Figure 3 This is a flowchart of the correlation unfuzzing process for one embodiment of this application;

[0069] Figure 4 This is a flowchart of an angle calculation algorithm based on coordinate system transformation according to one embodiment of this application;

[0070] Figure 5 This is a schematic diagram of the positions of the elements of a five-element stereo baseline interferometer according to one embodiment of this application;

[0071] Figure 6 This is a schematic diagram of the mean square error of the azimuth direction finding of a stereo baseline interferometer according to one embodiment of this application;

[0072] Figure 7 This is a schematic diagram of the pitch angle direction finding mean square error of a stereo baseline interferometer according to one embodiment of this application;

[0073] Figure 8 This is a schematic diagram illustrating the success probability of deblurring using a stereo baseline interferometer according to one embodiment of this application. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0075] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this application.

[0076] The following is in conjunction with the appendix Figures 1 to 8 This application provides further details.

[0077] This application provides a stereo baseline interferometer direction finding method based on coordinate system transformation, including the following steps:

[0078] Step S1: Select the guiding baseline and the deblurred baseline;

[0079] Step S2: Construct a coordinate system transformation matrix based on the guiding baseline;

[0080] Step S3: Traverse the combinations of ambiguities and obtain the elevation and azimuth angles under different combinations of ambiguities based on the guiding baseline and the coordinate system transformation matrix;

[0081] Step S4: Construct an evaluation function based on the defuzzified baseline, and select the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result.

[0082] In the preferred embodiment of this application, such as Figure 1 As shown, in step S1, selecting the guiding baseline and the deblurring baseline includes:

[0083] From all of the interferometers From the root baselines, two baselines that meet the length requirements and are approximately orthogonal are selected as guide baselines, denoted as vectors. and N is the number of interferometer elements, N≥4;

[0084] The remaining M baselines are used as the unblurred baselines, denoted as... .

[0085] In this embodiment, the two longest, approximately orthogonal baselines are selected as the guiding baselines.

[0086] In the preferred embodiment of this application, such as Figure 2 As shown, in step S2, the coordinate system transformation matrix is ​​constructed based on the guiding baseline, including:

[0087] Step S21: Calculate the unit normal vector of the plane forming the guiding baseline, including:

[0088] Calculate the normal vector of the plane formed by the guiding baselines:

[0089] ;

[0090] ;

[0091] ;

[0092] Calculate the magnitude of the normal vector:

[0093] ;

[0094] Calculate the unit normal vector:

[0095] ;

[0096] Step S22: Calculate the rotation angle based on the unit normal vector:

[0097] ;

[0098] Where α is the pitch angle and β is the azimuth angle. , , They are the unit normal vectors The X, Y, and Z components;

[0099] In this embodiment, α and β represent the angles of rotation around the X-axis and the Y-axis, respectively.

[0100] Step S23: Construct the basic rotation matrix based on the rotation angle:

[0101] ;

[0102] Step S24: Construct the coordinate system transformation matrix based on the basic rotation matrix:

[0103] ;

[0104] The coordinate system transformation matrix T satisfies ,in, Let be the vector to be transformed. This is the transformed vector.

[0105] In this embodiment, in step S21, if the unit normal vector Z component Then let Ensure unit normal vector Z component This ensures that subsequent rotations yield the true angle, not a mirror image.

[0106] In at least one embodiment of this application, such as Figure 3-4 As shown, in step S3, the ambiguity combinations are traversed, and the elevation and azimuth angles under different ambiguity combinations are obtained based on the guiding baseline and the coordinate system transformation matrix, including:

[0107] Step S31: Determine the range of ambiguity values ​​corresponding to the two guide baselines:

[0108] ;

[0109] ;

[0110] in, To guide the baseline Fuzzy numbers, To guide the baseline Fuzzy numbers;

[0111] Step S32: For each group of fuzzy number combinations Calculate the candidate pitch and azimuth angles, and collect all candidate pitch and azimuth angles into a set. middle.

[0112] In at least one embodiment of this application, in step S32, for each group of fuzzy number combinations Calculate the candidate pitch and azimuth angles, and collect all candidate pitch and azimuth angles into a set. Includes:

[0113] Transform the guiding baseline according to the coordinate system transformation matrix:

[0114] ;

[0115] in, , The converted guide baseline;

[0116] The ambiguous phase difference between the two guide baselines is restored to an unambiguous phase difference:

[0117] ;

[0118] ;

[0119] in, , These represent the ambiguous phase difference between the two guide baselines. , These are the unambiguous phase differences between the two guide baselines;

[0120] according to Incoming wave direction vector in coordinate system A system of linear equations is constructed to relate the unambiguous phase difference between the two guide baselines:

[0121] ;

[0122] in, , These are the vector components of the two guide baselines, respectively;

[0123] Solving the system of linear equations, we obtain... , The value is determined by ,get ;

[0124] Two candidate direction vectors are obtained:

[0125] ;

[0126] Inversely transform the candidate direction vector back to the original coordinate system:

[0127] ;

[0128] Based on the candidate direction vector in the original coordinate system Calculate the candidate pitch and azimuth angles:

[0129] ;

[0130] This allows us to obtain two sets of potential angles. and One set of angles is a false angle, which can be removed by the evaluation function calculated in the subsequent step S4.

[0131] Repeat the above steps to iterate through all combinations of fuzzy numbers and collect all candidate pitch and azimuth angles into a set. middle.

[0132] In a preferred embodiment of this application, step S4, which involves constructing an evaluation function based on the de-fuzzy baseline and selecting the elevation and azimuth angles corresponding to the maximum value of the evaluation function as the final direction finding result, includes:

[0133] Step S41, from set Extract the candidate pitch angle and azimuth angle to be determined, and obtain the candidate direction vectors corresponding to the current candidate pitch angle and azimuth angle. ;

[0134] Step S42: Construct an evaluation function based on the unfuzzy baseline:

[0135] ;

[0136] in, For evaluation functions;

[0137] Step S43: Select the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result.

[0138] In one specific embodiment of this application, such as Figure 5 As shown, the calculation process is explained in detail below using a five-element stereo baseline interferometer as an example, combined with specific numerical values. System operating parameters: System parameters: signal frequency 5 GHz, wavelength λ=0.06 m. The coordinates of the five antenna elements (unit: meters) are shown in Table 1. Guide baseline selection: Element 1 and element 3 are selected to form guide baseline 1, and element 2 and element 4 are selected to form guide baseline 2.

[0139] Table 1

[0140]

[0141] Monte Carlo simulations were performed in 1° increments within the range of azimuth ∈ [-45°, 45°] and elevation ∈ [-30°, 30°] (1000 independent trials were conducted at each angle point). The simulation results are as follows: Figures 6-8 As shown, the method of this application has a direction finding mean square error better than 0.8° and a success rate of deambiguity resolution close to 100%. The experimental results fully demonstrate the effectiveness and engineering value of this application.

[0142] The coordinate system transformation-based stereo baseline interferometer direction finding method of this application has strong applicability and can be applied to any spatial array; it reduces the three-dimensional nonlinear angle solution problem to a two-dimensional linear problem, avoids iteration and approximation, and has a simple closed-loop solution form.

[0143] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A direction finding method for a stereo baseline interferometer based on coordinate system transformation, characterized in that, include: Step S1: Select the guiding baseline and the deblurred baseline; Step S2: Construct a coordinate system transformation matrix based on the guiding baseline; Step S3: Traverse the combinations of ambiguities and obtain the elevation and azimuth angles under different combinations of ambiguities based on the guiding baseline and the coordinate system transformation matrix; Step S4: Construct an evaluation function based on the defuzzified baseline, and select the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result.

2. The stereo baseline interferometer direction finding method based on coordinate system transformation according to claim 1, characterized in that, In step S1, selecting the guiding baseline and the deblurred baseline includes: From all of the interferometers From the root baselines, two baselines that meet the length requirements and are approximately orthogonal are selected as guide baselines, denoted as vectors. and N is the number of interferometer elements, N≥4; The remaining M baselines are used as the unblurred baselines, denoted as... .

3. The stereo baseline interferometer direction finding method based on coordinate system transformation according to claim 2, characterized in that, In step S2, a coordinate system transformation matrix is ​​constructed based on the guiding baseline, including: Step S21: Calculate the unit normal vector of the plane forming the guiding baseline, including: Calculate the normal vector of the plane formed by the guiding baselines: ； ； ； Calculate the magnitude of the normal vector: ； Calculate the unit normal vector: ； Step S22: Calculate the rotation angle based on the unit normal vector: ； Where α is the pitch angle and β is the azimuth angle. , , They are the unit normal vectors The X, Y, and Z components; Step S23: Construct the basic rotation matrix based on the rotation angle: ； Step S24: Construct the coordinate system transformation matrix based on the basic rotation matrix: ； The coordinate system transformation matrix T satisfies ,in, Let be the vector to be transformed. This is the transformed vector.

4. The stereo baseline interferometer direction finding method based on coordinate system transformation according to claim 3, characterized in that, In step S21, if the unit normal vector Z component Then let Ensure unit normal vector Z component .

5. The stereo baseline interferometer direction finding method based on coordinate system transformation according to claim 4, characterized in that, In step S3, the combinations of ambiguities are traversed, and the elevation and azimuth angles under different combinations of ambiguities are obtained based on the guiding baseline and the coordinate system transformation matrix, including: Step S31: Determine the range of ambiguity values ​​corresponding to the two guide baselines: ； ； in, To guide the baseline Fuzzy numbers, To guide the baseline Fuzzy numbers; Step S32: For each group of fuzzy number combinations Calculate the candidate pitch and azimuth angles, and collect all candidate pitch and azimuth angles into a set. middle.

6. The stereo baseline interferometer direction finding method based on coordinate system transformation according to claim 5, characterized in that, In step S32, for each group of fuzzy number combinations Calculate the candidate pitch and azimuth angles, and collect all candidate pitch and azimuth angles into a set. Includes: Transform the guiding baseline according to the coordinate system transformation matrix: ； in, , The converted guide baseline; The ambiguous phase difference between the two guide baselines is restored to an unambiguous phase difference: ； ； in, , These represent the ambiguous phase difference between the two guide baselines. , These are the unambiguous phase differences between the two guide baselines; according to Incoming wave direction vector in coordinate system A system of linear equations is constructed to relate the unambiguous phase difference between the two guide baselines: ； in, , These are the vector components of the two guide baselines, respectively; Solving the system of linear equations, we obtain... , The value is determined by ,get ; Two candidate direction vectors are obtained: ； Inversely transform the candidate direction vector back to the original coordinate system: ； Based on the candidate direction vector in the original coordinate system Calculate the candidate pitch and azimuth angles: ； Repeat the above steps to iterate through all combinations of fuzzy numbers and collect all candidate pitch and azimuth angles into a set. middle.

7. The stereo baseline interferometer direction finding method based on coordinate system transformation according to claim 6, characterized in that, In step S4, an evaluation function is constructed based on the defuzzified baseline, and the elevation and azimuth angles corresponding to the maximum value of the evaluation function are selected as the final direction finding results, including: Step S41, from set Extract the candidate pitch angle and azimuth angle to be determined, and obtain the candidate direction vectors corresponding to the current candidate pitch angle and azimuth angle. ; Step S42: Construct an evaluation function based on the unfuzzy baseline: ； in, For evaluation functions; Step S43: Select the elevation angle and azimuth angle corresponding to the maximum value of the evaluation function as the final direction finding result.

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