Interferometer three-dimensional ambiguity resolution direction finding method

Abstract

The invention discloses a three-dimensional ambiguity resolution direction finding method for an interferometer, and belongs to the field of electronic monitoring. The method comprises the following steps: firstly, selecting two short base lines, and respectively calculating fuzzy number ranges of the two short base lines; secondly, traversing all fuzzy number combinations in the fuzzy number range of the two short baselines, and calculating to obtain an azimuth-pitch hypothesis set; then, constructing a cost function, screening out hypotheses with the cost function smaller than a threshold value in the azimuth-pitching hypothesis set according to the set threshold value, and obtaining an azimuth-pitching effective set; flatness error correction values of the two longest base lines are calculated according to the azimuth-pitching effective set, and a corrected non-fuzzy phase difference hypothesis set is obtained; and constructing a cost function, calculating a cost function value corresponding to the corrected azimuth-pitch hypothesis set, finding out an estimation result enabling the cost function to be minimum, and finally obtaining azimuth-pitch estimation.

Description

Technical Field

[0001] The invention belongs to the field of electronic monitoring, and in particular relates to a three-dimensional deambiguation direction finding method of an interferometer. Background Art

[0002] Passive direction finding technology is a key technology for electronic monitoring. The performance of the passive direction finding system directly affects the performance of electronic monitoring satellites in practical tasks such as radiation source positioning, interference guidance, and threat warning. Common passive direction finding technologies include phase interferometer direction finding, amplitude comparison direction finding, and spatial spectrum direction finding. Among them, phase interferometer direction finding technology has the advantages of high direction finding accuracy and easy engineering implementation, and is a technology widely used in the field of electronic monitoring.

[0003] The traditional single-baseline phase interferometer has a contradiction between direction-finding accuracy and phase ambiguity. In order to take into account the two key performances of deambiguation capability and direction-finding accuracy, a multi-baseline phase interferometer is usually used. Whether the deambiguation can be correctly resolved is the key to whether the multi-baseline phase interferometer can achieve high-precision direction-finding. Existing deambiguation methods can be divided into two categories. One is the standard deambiguation method that solves the ambiguity number in real time through multiple sets of baselines. Among them, the long and short baseline method, the virtual baseline method, and the staggered baseline method have small computational complexity, but have strict constraints on the arrangement of antenna array elements, and are often used in linear arrays or orthogonal arrays. In practice, antenna arrays often do not have the conditions to be arranged according to the constraints. To address this problem, Chinese Patent Publication No. CN114063065A discloses a method for measuring angles of a two-dimensional multi-baseline interferometer with a special-shaped array. This method reduces the constraints on the antenna array, but still requires a linear array in at least one direction. The stereo baseline method has no requirements for the antenna array arrangement. The paper "Arbitrary Planar Array Interferometer Direction Finding Method Based on Hybrid Baseline" improves the traditional stereo baseline method, overcomes the limitations of the traditional stereo baseline method in baseline pair selection, and makes full use of the antenna array. However, it is necessary to traverse the fuzzy numbers of multiple groups of baseline pairs, which is computationally intensive. In addition to the above problems, the existing standard deambiguation methods are all based on the assumption that the antenna array is an ideal planar array. In actual applications, due to factors such as installation and antenna deployment, the antenna array will have flatness errors, especially for long baselines that ensure direction finding accuracy, which leads to a sharp decline in the performance of the standard deambiguation method, or even failure to resolve the ambiguity.

[0004] Another type of deambiguation method is the correlation method, which compares the similarity between the measured phase difference and the pre-established original phase difference sample library. Since the table is pre-built, this method can overcome the impact of the flatness error of the antenna array. However, the direction finding accuracy of the correlation method depends on the fineness of the original phase difference sample library, and the large amount of sample library data will greatly reduce the real-time performance of direction finding and cannot meet engineering requirements, especially in scenarios where azimuth-elevation two-dimensional angle measurement is required. Summary of the invention

[0005] The present invention proposes an interferometer three-dimensional deambiguation direction finding method, which solves the problem that the existing method cannot deambiguate direction finding when there is a flatness error in the antenna array in engineering applications.

[0006] The technical solution to realize the present invention is: an interferometer three-dimensional deambiguation direction finding method, comprising the following steps:

[0007] Step 1: Select two short baselines and calculate the fuzzy number ranges of the two short baselines respectively.

[0008] Step 2: Traverse all fuzzy number combinations within the fuzzy number range of the two short baselines and calculate the azimuth-elevation hypothesis set.

[0009] Step 3: construct a cost function, and filter out hypotheses whose cost functions are less than the threshold value in the azimuth-elevation hypothesis set according to the set threshold value, to obtain the azimuth-elevation valid set.

[0010] Step 4: Calculate the flatness error correction values ​​of the two longest baselines according to the azimuth-elevation valid set to obtain a corrected unambiguous phase difference hypothesis set.

[0011] Step 5: Construct a cost function, calculate the cost function value corresponding to the corrected azimuth-elevation hypothesis set, find the estimation result that minimizes the cost function, and finally obtain the azimuth-elevation estimation.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] 1) The present invention makes full use of baseline information to ensure the stability of defuzzification.

[0014] 2) There are no special requirements for antenna layout and it has strong applicability.

[0015] 3) Only one set of baseline pairs needs to be defuzzified, which requires little computation and can meet the real-time requirements of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The invention is a flow chart of a three-dimensional interferometer deambiguation direction finding method.

[0017] Figure 2 It is a schematic diagram of the antenna array coordinate system.

[0018] Figure 3 It is a schematic diagram comparing the defuzzification probability of the method of the present invention and that of the method without considering the flatness error.

[0019] Figure 4 It is a schematic diagram comparing the direction finding accuracy of the method of the present invention and that of the method without considering the flatness error. DETAILED DESCRIPTION

[0020] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0022] In addition, in the present invention, the descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0023] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation" and the like should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; "connection" can be a mechanical connection or an electrical connection. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0024] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0025] The following will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention in combination with this design example.

[0026] Combination Figure 1-2 The present invention provides an interferometer three-dimensional deambiguation direction finding method, comprising the following steps:

[0027] Step 1: Select two short baselines and calculate the fuzzy number ranges of the two short baselines respectively, which specifically includes the following steps:

[0028] Step 11. Assume that the antenna array consists of M+N array elements. The antenna is designed to be in an unfolded form, that is, the 1st to Mth array elements are fixed on the antenna disk, and the M+1th to Nth array elements are obtained by unfolding the antenna array; the position coordinate of the i-th array element in the antenna array coordinate system is denoted as p i =[x i ,y i ,z i ] T , i=1,2,…,M+N, the element flatness error on the antenna plate is negligible, that is, z i =0, i = 1, 2, ..., M, the array elements outside the antenna disk cause flatness error due to antenna expansion, that is, z i ≠0, i=M+1,M+2,…,M+N; select four array elements from the 1st array element to the Mth array element, numbered as i1, i2, i3, i4, to form two short baselines, and the corresponding baseline vectors are d1 and d2:

[0029]

[0030] in, For number i l The coordinate of the array element on the X-axis of the antenna array coordinate system, For number i l The coordinate of the array element on the Y axis of the antenna array coordinate system, For number i l The coordinates of the array element on the Z axis of the antenna array coordinate system, l = 1, 2, 3, 4; T represents transposition;

[0031] Step 12: Let the wavelength of the radiation source signal be λ, and calculate the maximum ambiguity values ​​K1 and K2 of the phase difference measured by the two short baselines according to the unambiguous phase difference formula:

[0032]

[0033] Among them, d1 and d2 are the lengths of the two baselines, d1=||d1||, d2=||d2||, and ||·|| represents the 2-norm. represents rounding up; the fuzzy number ranges corresponding to the two short baselines are n1 and n2 respectively:

[0034] n1∈[-K1,K1]

[0035] n2∈[-K2,K2].

[0036] Step 2: Traverse all fuzzy number combinations within the fuzzy number range of the two short baselines to calculate the azimuth-elevation hypothesis set, which specifically includes the following steps:

[0037] Step 21: For the jth fuzzy number combination <n1, n2>, assuming that it is a true fuzzy number combination, the unambiguous phase difference of the two short baselines is obtained: for

[0038]

[0039] in, are the measured phase differences of the two short baselines respectively;

[0040] Step 22: Note the sight line vector u = [u x ,u y ,u z ] T According to the unambiguous phase difference formula, we get

[0041]

[0042]

[0043] Where the coefficient κ = λ / 2π; Solving the above equation, the coordinates of the line of sight vector on the X-axis and Y-axis of the antenna array coordinate system are u x 、u y :

[0044]

[0045] Step 23, define the azimuth angle θ as the angle between the projection of the incident signal in the XOY plane of the antenna array coordinate system and the positive direction of the X axis, and the elevation angle ε as the angle between the incident signal and the Z axis of the antenna array coordinate system. According to the conversion relationship between the line of sight vector and the angle, the azimuth-elevation hypothesis (θ j ,ε j ),in

[0046]

[0047] Step 24: Traverse all fuzzy number combinations to obtain the azimuth-elevation hypothesis set H:

[0048] H={(θ1,ε1),…,(θ j ,ε j ),…,(θ L ,ε L )}

[0049] Among them, the number of fuzzy number combinations L = (2K1+1)(2K2+1).

[0050] Step 3: construct a cost function, and select hypotheses whose cost functions are less than the threshold value in the azimuth-elevation hypothesis set according to the set threshold value, and obtain the azimuth-elevation valid set, which specifically includes the following steps:

[0051] Step 31: Based on the j-th azimuth-pitch hypothesis (θ j ,ε j ) Calculate the corresponding phase φ of other array elements i , select several baselines to calculate the phase difference and form a vector ψ j :

[0052] ψ j =[ψ (1) ψ (2) …ψ (q) …ψ (Q) ] T

[0053] Among them, number i a with i b The phase difference of the baseline formed by the array elements q=1,2,…,Q, Q is the number of selected baselines, a=1,2,…,M, b=1,2,…,M, and a≠b;

[0054] Step 32: According to the measured phase difference Construct the residual and cost function C1(θ j ,ε j ):

[0055]

[0056] Among them, ||·||1 represents the 1-norm;

[0057] Step 33: Determine the size of the cost function and the set threshold value T′. If C1(θ j ,ε j )<T′, then the jth azimuth-pitch hypothesis (θ j ,ε j ) is the effective azimuth-elevation;

[0058] Step 34: Repeat steps 31 to 33 to obtain an azimuth-elevation effective set H consisting of effective azimuth-elevation components. v :

[0059] H v ={(θ1,ε1),…,(θ j' ,ε j' ),…,(θ L' ,ε L' )}

[0060] Obviously, H v is a subset of H, (θ j' ,ε j' ) is the j'th valid azimuth-elevation pair, and L' is the number of valid azimuth-elevation pairs.

[0061] Step 4: Calculate the flatness error correction values ​​of the two longest baselines according to the azimuth-elevation valid set to obtain a corrected unambiguous phase difference hypothesis set, which specifically includes the following steps:

[0062] Step 41, assuming that the flatness errors of the two longest baselines are dz1 and dz2 respectively, for the j'th effective azimuth-pitch pair in the azimuth-pitch effective set, calculate the flatness error correction values ​​ν1 and ν2:

[0063]

[0064] Step 42: Calculate the corrected unambiguous phase difference hypothesis set

[0065]

[0066] in, is the measured phase difference of the two longest baselines, g1 and g2 are the fuzzy number center values ​​calculated according to the correction value, and R1 and R2 are the set fuzzy number expansion ranges;

[0067] g1,g2 are expressed as

[0068]

[0069] in, Indicates rounding.

[0070] Step 43: According to steps 22 to 24, substitute the corrected unambiguous phase difference hypothesis to calculate the corrected azimuth-elevation hypothesis set H c :

[0071] H c ={(θ 1c ,ε 1c ),…,(θ jc ,ε jc ),…,(θ Lc ,ε Lc )}

[0072] Among them, the number of corrected azimuth-elevation hypotheses Lc=(2R1+1)(2R2+1); the present invention proposes for the first time an interferometer three-dimensional deambiguation direction-finding method that uses the azimuth-elevation hypothesis to perform correction before direction-finding. After correction, it solves the problem that the existing method cannot deambiguate direction-finding when there is a flatness error in the antenna array.

[0073] Step 5: construct a cost function, calculate the cost function value corresponding to the modified azimuth-elevation hypothesis set, find the estimation result that minimizes the cost function, and finally obtain the azimuth-elevation estimation, which specifically includes the following steps:

[0074] Step 51: According to the jc azimuth-pitch hypothesis (θ jc ,ε jc ) calculates the phase difference of all baselines and forms a vector

[0075]

[0076] in, is the phase difference of the baseline formed by any two array elements, p = 1, 2, ..., P, P is the total number of baselines; here all baseline information is fully utilized, so the method is robust;

[0077] Step 52: Record the measured phase difference of all baselines Calculate the residual and cost function C2(θ jc ,ε jc ):

[0078]

[0079] Step 53, repeating steps 51 to 52, and calculating the cost function value sequence C2 corresponding to each orientation-elevation hypothesis in the corrected orientation-elevation hypothesis set:

[0080] C2={C2(θ 1c ,ε 1c ),C2(θ 2c ,ε 2c ),…,C2(θ jc ,ε jc )…,C2(θ Lc ,ε Lc )}

[0081] Step 54: Find the estimation result with the minimum cost function value and obtain the azimuth-pitch estimation.

[0082]

[0083] The above method has no special requirements for antenna array, so it is highly applicable. Moreover, the amount of calculation is not large, the steps are easy to implement, and it can meet the real-time requirements of the project.

[0084] Example 1

[0085] Through experiments, the interferometer three-dimensional deambiguation direction finding method described in the present invention can realize deambiguation direction finding when there is a flatness error. The deambiguation probability is compared with the two-dimensional deambiguation direction finding method without considering the flatness error. Figure 3 As shown, it can be seen that when the flatness error is not considered, the deambiguation probability decreases sharply with the increase of frequency, and the method of the present invention can maintain a relatively high deambiguation probability.

[0086] The direction finding accuracy of the method of the present invention is compared with that of the two-dimensional deambiguation direction finding method without considering the flatness error. Figure 4 As shown, it can be seen that as the frequency increases, direction measurement will be impossible if the flatness error is not considered. The method of the present invention can overcome the flatness error, and the direction measurement accuracy is significantly better than the two-dimensional deambiguation direction measurement method that does not consider the flatness error, and the accuracy increases with the increase of frequency.

Claims

1. An interferometer three-dimensional deambiguation direction finding method, characterized in that: The following steps are involved: Step 1: Select two short baselines and calculate the fuzzy number ranges of the two short baselines respectively; Step 2, traverse all fuzzy number combinations within the fuzzy number range of the two short baselines, and calculate the azimuth-pitch hypothesis set; Step 3: construct a cost function, and select hypotheses whose cost functions are less than the threshold value in the azimuth-elevation hypothesis set according to the set threshold value, so as to obtain the azimuth-elevation valid set; Step 4: Calculate the flatness error correction values ​​of the two longest baselines according to the azimuth-elevation valid set to obtain a corrected unambiguous phase difference hypothesis set; Step 5: Construct a cost function, calculate the cost function value corresponding to the corrected azimuth-elevation hypothesis set, find the estimation result that minimizes the cost function, and finally obtain the azimuth-elevation estimation.

2. The interferometer three-dimensional deambiguation direction finding method according to claim 1, characterized in that: In step 1, two short baselines are selected and the fuzzy number ranges of the two short baselines are calculated respectively, which specifically includes the following steps: Step 11. Assume that the antenna array consists of M+N array elements. The antenna is designed to be in an unfolded form, that is, the 1st to Mth array elements are fixed on the antenna disk, and the M+1th to Nth array elements are obtained by unfolding the antenna array; the position coordinate of the i-th array element in the antenna array coordinate system is denoted as p i =[x i ,y i ,z i ] T , i=1,2,…,M+N, the element flatness error on the antenna plate is negligible, that is, z i =0, i = 1, 2, ..., M, the array elements outside the antenna disk cause flatness error due to antenna expansion, that is, z i ≠0, i=M+1,M+2,…,M+N; select four array elements from the 1st array element to the Mth array element, numbered as i1, i2, i3, i4, to form two short baselines, and the corresponding baseline vectors are d1 and d2: in, For number i l The coordinate of the array element on the X-axis of the antenna array coordinate system, For number i l The coordinate of the array element on the Y axis of the antenna array coordinate system, For number i l The coordinates of the array element on the Z axis of the antenna array coordinate system, l = 1, 2, 3, 4; T represents transposition; Step 12: Let the wavelength of the radiation source signal be λ, and calculate the maximum ambiguity values ​​K1 and K2 of the phase difference measured by the two short baselines according to the unambiguous phase difference formula: Among them, d1 and d2 are the lengths of the two baselines, d1=||d1||, d2=||d2||, and ||·|| represents the 2-norm. represents rounding up; the fuzzy number ranges corresponding to the two short baselines are n1 and n2 respectively:

3. The interferometer three-dimensional deambiguation direction finding method according to claim 2, characterized in that: In step 2, all fuzzy number combinations within the fuzzy number range of the two short baselines are traversed to calculate the azimuth-elevation hypothesis set, which specifically includes the following steps: Step 21: For the jth fuzzy number combination <n1, n2>, assuming that it is a true fuzzy number combination, the unambiguous phase difference of the two short baselines is obtained: for in, are the measured phase differences of the two short baselines respectively; Step 22: Note the sight vector u = [u x ,u y ,u z ] T According to the unambiguous phase difference formula, we get Where the coefficient κ = λ / 2π; Solving the above equation, the coordinates of the line of sight vector on the X-axis and Y-axis of the antenna array coordinate system are u x 、u y : Step 23, define the azimuth angle θ as the angle between the projection of the incident signal in the XOY plane of the antenna array coordinate system and the positive direction of the X axis, and the elevation angle ε as the angle between the incident signal and the Z axis of the antenna array coordinate system. According to the conversion relationship between the line of sight vector and the angle, the azimuth-elevation hypothesis (θ j ,ε j ),in Step 24: Traverse all fuzzy number combinations to obtain the azimuth-elevation hypothesis set H: H={(θ1,ε1),…,(θ j ,he j ),…,(θ L ,he L )} Among them, the number of fuzzy number combinations L = (2K1+1)(2K2+1).

4. The interferometer three-dimensional deambiguation direction finding method according to claim 3, characterized in that: In step 3, a cost function is constructed, and hypotheses whose cost functions are less than the threshold value in the azimuth-elevation hypothesis set are screened out according to the set threshold value, so as to obtain the azimuth-elevation valid set, which specifically includes the following steps: Step 31: Based on the j-th azimuth-pitch hypothesis (θ j ,ε j ) Calculate the corresponding phase φ of other array elements i , select several baselines to calculate the phase difference and form a vector ψ j : ψ j =[ψ (1) ψ (2) …ψ (q) …ψ (Q) ] T Among them, number i a with i b The phase difference of the baseline formed by the array elements Q is the number of selected baselines, serial number a=1,2,…,M, serial number b=1,2,…,M, and a≠b; Step 32: According to the measured phase difference Construct the residual and cost function C1(θ j ,ε j ): Among them, ||·||1 represents the 1-norm; Step 33: Determine the size of the cost function and the set threshold value T′. If C1(θ j ,ε j )<T′, then the jth azimuth-pitch hypothesis (θ j ,ε j ) is the effective azimuth-elevation; Step 34: Repeat steps 31 to 33 to obtain an azimuth-elevation effective set H consisting of effective azimuth-elevation components. v : H v ={(θ1,ε1),…,(θ j' ,he j' ),…,(θ L' ,he L' )} Obviously, H v is a subset of H, (θ j' ,ε j' ) is the j'th valid azimuth-elevation pair, and L' is the number of valid azimuth-elevation pairs.

5. The interferometer three-dimensional deambiguation direction finding method according to claim 4, characterized in that: In step 4, the flatness error correction values ​​of the two longest baselines are calculated according to the azimuth-elevation valid set to obtain a corrected unambiguous phase difference hypothesis set, which specifically includes the following steps: Step 41, assuming that the flatness errors of the two longest baselines are dz1 and dz2 respectively, for the j'th effective azimuth-pitch pair in the azimuth-pitch effective set, calculate the flatness error correction values ​​ν1 and ν2: Step 42: Calculate the corrected unambiguous phase difference hypothesis set and in, is the measured phase difference of the two longest baselines, g1 and g2 are the fuzzy number center values ​​calculated according to the correction value, and R1 and R2 are the set fuzzy number expansion ranges; g1,g2 are expressed as in, Indicates rounding; Step 43: According to steps 22 to 24, substitute the corrected unambiguous phase difference hypothesis to calculate the corrected azimuth-elevation hypothesis set H c : H c ={(θ 1c ,he 1c ),…,(θ jc ,he jc ),…,(θ Lc ,he Lc )} Among them, the corrected azimuth-elevation hypothesis number Lc=(2R1+1)(2R2+1).

6. The interferometer three-dimensional deambiguation direction finding method according to claim 5, characterized in that: In step 5, a cost function is constructed, the cost function value corresponding to the modified azimuth-elevation hypothesis set is calculated, and the estimation result that minimizes the cost function is found, and finally the azimuth-elevation estimation is obtained, which specifically includes the following steps: Step 51: According to the jc azimuth-pitch hypothesis (θ jc ,ε jc ) calculates the phase difference of all baselines and forms a vector in, is the phase difference of the baseline formed by any two array elements, p = 1, 2, ..., P, P is the total number of baselines; Step 52: Record the measured phase difference of all baselines Calculate the residual and cost function C2(θ jc ,ε jc ): Step 53, repeating steps 51 to 52, and calculating the cost function value sequence C2 corresponding to each orientation-elevation hypothesis in the corrected orientation-elevation hypothesis set: C2={C2(θ 1c ,he 1c ),C2(θ 2c ,he 2c ),…,C2(θ jc ,he jc )…,C2(θ Lc ,he Lc )} Step 54: Find the estimation result with the minimum cost function value and obtain the azimuth-pitch estimation.

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