A plane arbitrary configuration interferometer demisting optimization arrangement method
By optimizing the array of a planar arbitrary configuration interferometer using an iterative convex optimization algorithm, the problem of lack of closed mapping in ambiguity resolution performance is solved, achieving efficient configuration optimization and stable ambiguity-free direction finding.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-02
- Publication Date
- 2026-07-10
AI Technical Summary
The unfuzzy resolution performance of planar arbitrary configuration interferometers lacks a closed mapping relationship, which leads to traditional design methods relying on a large number of model Carlo simulations, resulting in low optimization efficiency and difficulty in quickly obtaining the optimized configuration.
An iterative convex optimization algorithm based on the phase residual cost function is adopted. By determining the direction-finding baseline, constructing the phase residual cost function, and performing linearized neighborhood optimization in the neighborhood, combined with the array structure and geometric constraints, rapid configuration optimization is achieved.
It effectively avoids the concentration of fuzzy probabilities, improves the stability and optimization efficiency of configuration defuzzification, is applicable to various layout constraints, and enhances the defuzzification performance of planar interferometers.
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Figure CN122362270A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of passive direction finding and positioning technology, specifically relating to a defuzzification optimization design method for a planar arbitrary configuration interferometer. Background Technology
[0002] Planar interferometers consist of spatially distributed two-dimensional phase interference nodes. They estimate the direction of arrival by measuring the wavefront phase difference of the signal at each node. They possess the capability to achieve wide-field-of-view, high-precision direction finding with fewer nodes and are widely used in frequency monitoring, navigation, and positioning. However, due to limitations such as accuracy requirements and antenna size, the baseline length within the interferometer often exceeds half a wavelength, leading to direction-finding ambiguity. Therefore, the configuration of the interference nodes needs to be optimized to enable the system to achieve ambiguity-free direction finding.
[0003] Given the correlation between the defuzzification performance and the implementation algorithm of an interferometer, its layout is usually strongly correlated with the defuzzification method. Unlike dual (multi)-dimensional linear arrays and uniform circular arrays, planar arbitrary configuration interferometers lack closed-loop defuzzification methods. Their unfuzzy direction finding is often based on fuzzy number hypothesis testing, i.e., by traversing the phase residuals of the system under different fuzzy number conditions, a cost function is designed to determine the minimum fuzzy number of the residuals. Since there is no closed-loop mapping relationship between defuzzification performance and interferometer configuration, heuristic optimization and traversal search methods are often used in practice to obtain the optimal configuration. However, these methods rely on a large number of model Carlow simulations to evaluate the defuzzification performance of the configuration, resulting in low optimization efficiency and difficulty in quickly obtaining the optimal configuration. Summary of the Invention
[0004] To address the lack of a closed-form mapping relationship in the defuzzification performance of planar arbitrary configuration interferometers, traditional design methods rely on numerous model Carlow simulations to evaluate the defuzzification performance of the configuration, resulting in low optimization efficiency. This invention proposes an iterative convex optimization configuration algorithm based on the phase residual cost function to achieve rapid tuning of the interferometer array.
[0005] The technical solution for achieving the present invention is as follows: a method for defuzzification optimization array arrangement of a planar arbitrary configuration interferometer, comprising the following steps:
[0006] Step 1: Determine the initial configuration of the planar interferometer based on the constraints, and determine two sets of direction-finding baselines in conjunction with the maximum outer product criterion.
[0007] Step 2: Based on the unambiguous direction finding range and the two selected direction finding baselines, determine the set of ambiguity numbers corresponding to the wave arrival ambiguity offset vector within the field of view.
[0008] Step 3: Based on the two selected direction-finding baselines, determine the minimum effective non-redundant phase difference observation set, construct the phase residual cost function, traverse all fuzzy number sets under the current configuration, calculate the replacement cost function and corresponding gradient, and generate neighborhood optimization cost constraints.
[0009] Step 4: Based on the array structure and neighborhood size constraints, generate linearized neighborhood optimization geometric constraints.
[0010] Step 5: Under the constraints of cost and geometry, solve for the optimal configuration correction vector in the neighborhood and update the initial configuration.
[0011] Step 6: Repeat steps 2 to 5 until the L2 norm of the optimal configuration correction vector in the neighborhood is less than one-thousandth of the shortest wavelength in the target frequency band, thus obtaining the optimal configuration.
[0012] Compared with the prior art, the significant advantages of this invention are:
[0013] (1) The present invention effectively avoids the concentration of fuzzy probabilities and ensures the stability of configuration defuzzification.
[0014] (2) There are no special requirements for the array form of the planar interferometer, and it can be combined with specific layout constraints, making it highly applicable.
[0015] (3) Based on the construction of a closed ambiguity cost function, configuration optimization is achieved by using the asymptotic convex optimization method, which greatly improves the configuration optimization efficiency. Attached Figure Description
[0016] Figure 1 This is a flowchart of a method for defuzzification optimization array arrangement of a planar arbitrary configuration interferometer.
[0017] Figure 2 This is a schematic diagram of the iterative optimization of the configuration of a planar arbitrary configuration interferometer.
[0018] Figure 3 This is a comparison diagram of the interferometer configuration before and after optimization of the method of the present invention.
[0019] Figure 4 This is a comparison chart of the interferometer's defuzzification performance before and after optimization of the method of this invention. Detailed Implementation
[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0021] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.
[0022] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly and specifically defined.
[0023] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixing," etc., should be interpreted broadly. For example, "fixing" can mean a fixed connection, a detachable connection, or an integral part; "connection" can mean a mechanical connection or an electrical connection. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0024] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible to those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.
[0025] The following section will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention, using this design example as an example.
[0026] Combination Figures 1-2 The present invention provides a method for unfuzzy optimization array arrangement of a planar arbitrary configuration interferometer, comprising the following steps:
[0027] Step 1: Determine the initial configuration of the planar interferometer based on the constraints, and determine two sets of direction-finding baselines in conjunction with the maximum outer product criterion. This includes the following steps:
[0028] Step 1-1: Assume the planar interferometer includes Let the nth phase interference node be denoted as . The position coordinates of each phase interference node , ,in This represents the matrix transpose; in this case, configuration vectors are used. To characterize the overall configuration of the interferometer:
[0029] .
[0030] Steps 1-2, in Two sets of baselines are selected from each phase interferometer node as the direction-finding baselines. According to the direction-finding principle of a plane interferometer, the direction-finding accuracy is positively correlated with the baseline length. To achieve optimal two-dimensional direction-finding accuracy, the two sets of baselines with the largest outer product are selected as the direction-finding baselines. These two sets of direction-finding baselines are denoted as follows: , They are respectively:
[0031] ,
[0032] It satisfies:
[0033] .
[0034] in, This refers to the sequence number of the phase interferometer node within the first set of direction-finding baselines. This refers to the sequence number of the phase interference node within the second set of direction finding baselines.
[0035] Step 2: Based on the unambiguous direction finding range and the two selected direction finding baselines, determine the set of ambiguity numbers corresponding to the arrival ambiguity offset vector within the field of view. This specifically includes the following steps:
[0036] Step 2-1: Record the shortest wavelength within the target frequency band as... The signal arrival offset vector generated by the phase ambiguity corresponding to the direction finding baseline at the highest frequency is... ;in The phase difference ambiguity number between the two sets of direction-finding baselines. All are integers. Let be the unit arrival offset vector caused by phase ambiguity of two sets of direction-finding baselines, which satisfies:
[0037] ,
[0038] in for 3D identity matrix.
[0039] Step 2-2: Record the maximum off-axis angle of the target wave arriving at the plane interferometer as . Then the signal arrival offset vector satisfy ,in This represents the 2-norm of a vector.
[0040] Therefore, it is determined The range of values for is:
[0041] ,
[0042] in Indicates rounding up. The ambiguity amplification factor is determined by the included angle of the direction-finding baseline, i.e.:
[0043] ,
[0044] This gives the set of fuzzy numbers corresponding to the fuzzy offset vector of arrival within the field of view. ,Right now:
[0045] .
[0046] Step 3: Based on the selected two sets of direction-finding baselines, determine the minimum effective non-redundant phase difference observation set, construct the phase residual cost function, traverse all fuzzy number sets under the current configuration, calculate the cost function and corresponding gradient, and generate neighborhood optimization cost constraints. This specifically includes the following steps:
[0047] Step 3-1: Without loss of generality, take the minimum set of non-redundant baselines for the interferometer. for:
[0048] .
[0049] Due to the two sets of direction-finding baselines Since it does not contribute to the phase residual, removing it from the above set yields the minimum effective set of baselines without redundancy. :
[0050] .
[0051] Step 3-2: Record the fuzzy number The corresponding effective phase residual vector for:
[0052] .
[0053] in, Baseline The normalized fuzzy phase residual that exists under the corresponding fuzzy offset vector is:
[0054] .
[0055] in Denotes a modulo-1 function that satisfies , It is the shortest wavelength within the target frequency band.
[0056] At this time, the fuzzy number Corresponding phase residual cost function for:
[0057] ,
[0058] Where the matrix for The phase detection error covariance matrix corresponding to each baseline.
[0059] matrix for:
[0060] .
[0061] Where the matrix ,represent Each element is concatenated and transposed row by row. Select a matrix for the direction finding baseline. Here is the non-directional baseline selection matrix, which satisfies:
[0062] .
[0063] in for 3D identity matrix for A zero-dimensional matrix, where N represents the phase interference nodes contained in the planar interferometer.
[0064] Step 3-3: Calculate the set of fuzzy numbers The cost function corresponding to all possible combinations of fuzzy numbers. and seek configuration vector gradient Its expression is:
[0065] .
[0066] in Configuration vector The Middle One element, Represents the effective phase residual vector Relative configuration vector The Jacobian matrix.
[0067] right Taking the partial derivative, we get:
[0068] .
[0069] Step 3-4: Let the global minimum phase residual cost function be... The interferometer configuration correction vector is Then for any fuzzy number Construct the following neighborhood linearization cost constraint:
[0070] ,
[0071] in Represents the vector dot product. This represents the set of fuzzy numbers corresponding to the wave arrival fuzzy offset vector within the field of view.
[0072] Step 4: Based on the array structure and neighborhood size constraints, generate linearized neighborhood optimization geometric constraints, which specifically includes the following steps:
[0073] Step 4-1: The array layout constraints for minimum node spacing and deployable area are uniformly described using the following constraint model:
[0074] .
[0075] in For equality constraints, For inequality constraints, For constraint sequence number, This represents the total number of equality constraints. This represents the total number of inequality constraints.
[0076] To each and Perform neighborhood linearization and construct linearized geometric constraints, i.e.:
[0077] .
[0078] in, For interferometer configuration correction vector, Equality constraints configuration vector gradient, Inequality constraints configuration vector The gradient.
[0079] Step 4-2: Since the cost constraint constructed in Step 3-4 and the geometric constraint constructed in Step 4-1 both only apply if the configuration correction vector... The condition is only valid when the changes in each element are sufficiently small, and a high-dimensional spherical neighborhood is used. The value is constrained, and the radius of the spherical neighborhood is denoted as . Then, a neighborhood range constraint can be constructed:
[0080] .
[0081] Step 5: Under cost and geometric constraints, solve for the optimal configuration correction vector in the neighborhood and update the initial configuration. This includes the following steps:
[0082] Step 5-1: Based on cost constraints and geometric constraints, construct the following second-order cone programming problem:
[0083] ,
[0084] The above problem is solved using a solver to obtain the optimal configuration correction vector in the neighborhood space under approximate constraints.
[0085] Step 5-2: Calculate the updated configuration vector To verify the validity of the array layout constraints, namely:
[0086] ,
[0087] If all the above equations hold true, then the initial configuration vector is directly updated as follows: If the condition is met, then step 5 ends; otherwise, proceed to step 5-3.
[0088] Step 5-3, due to Unable to meet array constraints, for shrinkage factor Perform a binary search to satisfy:
[0089] ,
[0090] The initial configuration vector is then updated to... .
[0091] Step 6: Repeat steps 2 to 5 until the L2 norm of the optimal configuration correction vector in the neighborhood is less than one-thousandth of the shortest wavelength in the target frequency band, thus obtaining the optimal configuration.
[0092] The above method has no special requirements for the interferometer layout and is compatible with various layout constraints, making it highly applicable. By fully utilizing the statistical characteristics of the phase residuals used in hypothesis testing during the defuzzification calculation to construct a closed-form cost function, it effectively improves the system's defuzzification performance while ensuring efficient iterative optimization, avoiding fuzziness concentration on a specific set of fuzzy numbers, and guaranteeing the stability of configuration defuzzification.
[0093] Example 1
[0094] Experiments have shown that the unfuzzy optimization array method for planar arbitrary configuration interferometers described in this invention can quickly achieve configuration optimization of planar interferometers. Taking the unit interferometer configuration as an example for optimization, the shortest wavelength in the target frequency band is designed. Take 29.979mm (corresponding to a maximum frequency of 10GHz), maximum field of view Take 67deg. Figure 3 The comparison of the configurations before and after optimization is given. Baselines 1-2 and 1-3 were selected as direction-finding baselines. During the optimization process, the positions of antennas 1, 2, and 3 were fixed to ensure that the positioning performance did not deteriorate. The coordinates of each node before and after optimization are shown in the table below:
[0095]
[0096] It can be seen that the algorithm completes configuration optimization after fine-tuning the structure. (Comparison) Figure 4 The deblurring probabilities before and after optimization show that the deblurring performance of the planar interferometer array is significantly improved after optimization, and the single-pulse deblurring probability can meet the requirement of being better than 90% at the highest frequency of 10GHz.
Claims
1. A method for defuzzification and optimization array arrangement of a planar arbitrary configuration interferometer, characterized in that, The steps are as follows: Step 1: Determine the initial configuration of the planar interferometer based on the constraints, and determine two sets of direction-finding baselines in conjunction with the maximum outer product criterion, then proceed to Step 2; Step 2: Based on the unambiguous direction finding range and the two selected direction finding baselines, determine the set of ambiguity numbers corresponding to the wave arrival ambiguity offset vector within the field of view, and proceed to Step 3; Step 3: Based on the two selected direction-finding baselines, determine the minimum effective non-redundant phase difference observation set, construct the phase residual cost function, traverse all fuzzy number sets under the current configuration, calculate the replacement cost function and corresponding gradient, generate neighborhood optimization cost constraints, and proceed to step 4. Step 4: Based on the array structure and neighborhood size constraints, generate linearized neighborhood optimization geometric constraints, and proceed to step 5; Step 5: Under the constraints of cost and geometry, solve for the optimal configuration correction vector in the neighborhood and update the initial configuration, then proceed to step 6. Step 6: Repeat steps 2 to 5 until the L2 norm of the optimal configuration correction vector in the neighborhood is less than one-thousandth of the shortest wavelength in the target frequency band, thus obtaining the optimal configuration.
2. The method for defuzzification optimization array arrangement of a planar arbitrary configuration interferometer according to claim 1, characterized in that, Step 1 is detailed as follows: Step 1-1: Assume the planar interferometer includes Let the nth phase interference node be denoted as . The position coordinates of each phase interference node , At this point, configuration vectors are used. To characterize the overall configuration of the interferometer: ， in Indicates matrix transpose; Steps 1-2, in Two sets of baselines are selected from each phase interferometer node as the direction-finding baselines. According to the direction-finding principle of a plane interferometer, the direction-finding accuracy is positively correlated with the baseline length. To achieve optimal two-dimensional direction-finding accuracy, the two sets of baselines with the largest outer product are selected as the direction-finding baselines. These two sets of direction-finding baselines are denoted as follows: , They are respectively: ， It satisfies: ， in, This refers to the sequence number of the phase interferometer node within the first set of direction-finding baselines. This refers to the sequence number of the phase interference node within the second set of direction finding baselines.
3. The method for defuzzification optimization of the array of a planar arbitrary configuration interferometer according to claim 2, characterized in that, Step 2 is detailed as follows: Step 2-1: Record the shortest wavelength within the target frequency band as... The signal arrival offset vector generated by the phase ambiguity corresponding to the direction finding baseline at the highest frequency is... ;in The phase difference ambiguity number between the two sets of direction-finding baselines. All are integers. Let be the unit arrival offset vector caused by phase ambiguity of two sets of direction-finding baselines, which satisfies: ， in, for 3D identity matrix; Step 2-2: Record the maximum off-axis angle of the target wave arriving at the plane interferometer as . Then the signal arrival offset vector satisfy ,in Represents the 2-norm of a vector; Therefore, it is determined The range of values for is: ， in Indicates rounding up. The ambiguity amplification factor is determined by the included angle of the direction-finding baseline, i.e.: ， This gives the set of fuzzy numbers corresponding to the fuzzy offset vector of arrival within the field of view. ,Right now: 。 4. The method for unfuzzy optimization array arrangement of a planar arbitrary configuration interferometer according to claim 3, characterized in that, Step 3 is detailed as follows: Step 3-1: Obtain the minimum set of non-redundant baselines for the interferometer. for: ， Due to the two sets of direction-finding baselines Since it does not contribute to the phase residual, removing it from the above set yields the minimum effective set of baselines without redundancy. : ， in, Represents the minimum effective set of baselines without redundancy. Elements in; Step 3-2: Record the fuzzy number The corresponding effective phase residual vector for: ， in, Indicates baseline The normalized fuzzy phase residual existing under the corresponding fuzzy offset vector; Then the baseline Normalized fuzzy phase residuals existing under the corresponding fuzzy offset vector for: ， in Denotes a modulo-1 function that satisfies , The shortest wavelength within the target frequency band; The unit arrival-arrival offset vector caused by phase ambiguity of the two sets of direction-finding baselines; At this time, the fuzzy number Corresponding phase residual cost function for: ， Among them, matrix for The phase detection error covariance matrix corresponding to each baseline; matrix for: ， Among them, matrix , represent Each element is concatenated and transposed row by row. Select a matrix for the direction finding baseline. Here is the non-directional baseline selection matrix, which satisfies: ， in for 3D identity matrix for A zero-matrix, where N represents the phase interference nodes contained in the planar interferometer; Step 3-3: Calculate the set of fuzzy numbers The cost function corresponding to all possible combinations of fuzzy numbers. and seek configuration vector gradient Its expression is: ， in, Configuration vector The Middle One element, Represents the effective phase residual vector Relative configuration vector The Jacobian matrix; right Taking the partial derivative, we get: ， Step 3-4: Let the global minimum phase residual cost function be... The interferometer configuration correction vector is Then for any fuzzy number Construct the following neighborhood linearization cost constraint: ， in Represents the vector dot product. This represents the set of fuzzy numbers corresponding to the wave arrival fuzzy offset vector within the field of view.
5. The method for unfuzzy optimization array arrangement of a planar arbitrary configuration interferometer according to claim 4, characterized in that, Step 4 is detailed as follows: Step 4-1: The array layout constraints for minimum node spacing and deployable area are uniformly described using the following constraint model: ， in, For equality constraints, For inequality constraints, For constraint sequence number, This represents the total number of equality constraints. This represents the total number of inequality constraints. To each and Perform neighborhood linearization and construct linearized geometric constraints, i.e.: ， in, For interferometer configuration correction vector, Equality constraints configuration vector gradient, Inequality constraints configuration vector The gradient; Step 4-2: Since the cost constraint constructed in Step 3-4 and the geometric constraint constructed in Step 4-1 both only apply if the configuration correction vector... The condition is only valid when the changes in each element are sufficiently small, and a high-dimensional spherical neighborhood is used. The value is constrained, and the radius of the spherical neighborhood is denoted as . Then, a neighborhood range constraint can be constructed: 。 6. The method for unfuzzy optimization array arrangement of a planar arbitrary configuration interferometer according to claim 5, characterized in that, Step 5 is detailed below: Step 5-1: Based on cost constraints and geometric constraints, construct the following second-order cone programming problem: ， The above problem is solved using a solver to obtain the optimal configuration correction vector in the neighborhood space under approximate constraints; Step 5-2: Calculate the updated configuration vector To verify the validity of the array layout constraints, namely: ， If all the above equations hold true, then the initial configuration vector is directly updated as follows: If the condition is met, then end step 5; otherwise, proceed to step 5-3. Step 5-3, due to Unable to meet array constraints, for shrinkage factor Perform a binary search to satisfy: ， The initial configuration vector is then updated to... .