Interferometer three-dimensional ambiguity resolution direction finding method based on amplitude-phase combination

Abstract

The invention discloses an interferometer three-dimensional ambiguity resolution direction finding method based on amplitude-phase combination, and belongs to the field of signal processing. The method comprises the following steps: firstly, selecting two vertical long base lines, and respectively calculating fuzzy number ranges of the two vertical long base lines based on azimuth-pitching coarse estimation measured by amplitude; traversing all fuzzy number combinations in the fuzzy number range of the two vertical long baselines, and calculating to obtain an initial fuzzy-free phase difference hypothesis set of the two vertical long baselines; calculating flatness error correction values of the two vertical long base lines based on azimuth-pitch coarse estimation obtained by amplitude measurement, and calculating according to the initial non-fuzzy phase difference hypothesis set to obtain a corrected non-fuzzy phase difference hypothesis set; according to the corrected non-fuzzy phase difference hypothesis set, calculating to obtain an azimuth-pitching hypothesis set; and establishing an azimuth-pitching cost function model, performing traversal calculation on the azimuth-pitching hypothesis set, selecting an estimation result which enables the cost function to be minimum, and finally obtaining azimuth-pitching estimation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of signal processing, and particularly relates to a three-dimensional deambiguating direction finding method of an interferometer based on amplitude-phase combination. BACKGROUND

[0002] The interferometer direction finding method is a classical passive direction finding method and is widely applied in radar, communication signal detection and other fields. The core principle thereof is to calculate the direction information of a signal source by analyzing the phase difference or amplitude difference between the signals received by the antennas distributed in space. However, the traditional interferometer technology is mainly based on the design of an ideal two-dimensional planar array and faces significant challenges in actual engineering applications.

[0003] Firstly, the traditional interferometer based on the phase difference assumes that the antenna array is strictly in the same plane when direction finding, but in actual deployment, the antenna array deviates from the ideal plane due to installation errors, forming a non-planar interferometer array. This structural deviation will destroy the mathematical model of the traditional two-dimensional algorithm, resulting in a significant decrease in the accuracy of the traditional two-dimensional direction finding. Due to the periodic nature of the phase, the azimuth and elevation angle measurement results of the traditional interferometer based on the phase difference have the problem of multi-value, namely "angle ambiguity". Especially in the three-dimensional non-planar interferometer scene, a single interferometer array cannot accurately distinguish the azimuth and elevation angles of the signal at the same time, is easy to produce ambiguous solution, limits the direction finding accuracy, and even causes angle ambiguity or solution failure. Secondly, the direction finding method relying only on amplitude information can partially alleviate the ambiguity problem, but is limited by the gain characteristics of the antenna array and is easily disturbed by noise in low signal-to-noise ratio or long distance scenes, resulting in performance degradation.

[0004] In recent years, some researches have tried to enhance the direction finding capability by expanding the three-dimensional array structure or introducing multi-baseline interference technology, but such schemes usually face problems such as high hardware cost, complex array calibration, and the need for redundant calculation, resulting in high system cost and insufficient real-time performance. In addition, the existing methods mainly focus on the optimization of a single dimension of phase or amplitude, and fail to fully exploit the potential of joint processing of both. SUMMARY

[0005] The application proposes a three-dimensional deambiguating direction finding method of an interferometer based on amplitude-phase combination. In view of the problems existing in the existing methods in engineering applications, the application proposes a three-dimensional deambiguating direction finding method of an interferometer based on amplitude-phase combination, which breaks through the problem of direction finding failure of the existing methods when the planeness error exists in the interferometer array; only one set of baseline pairs need to be deambiguated, eliminating the redundant calculation link, saving hardware resources and enhancing the real-time performance of the system; the complementary characteristics of amplitude and phase information are fully utilized to ensure the direction finding accuracy while reducing the calculation complexity.

[0006] The technical solution for realizing the application is as follows: a three-dimensional deambiguating direction finding method of an interferometer based on amplitude-phase combination, comprising the following steps:

[0007] Step 1, select two vertical long base lines, based on the azimuth-elevation rough estimate measured by the amplitude, calculate the ambiguity number range of the two vertical long base lines respectively.

[0008] Step 2, traverse all ambiguity combinations in the ambiguity number range of the two vertical long base lines, calculate the initial ambiguity-free phase difference hypothesis set of the two vertical long base lines.

[0009] Step 3, based on the azimuth-elevation rough estimate measured by the amplitude, calculate the flatness error correction value of the two vertical long base lines, obtain the corrected ambiguity-free phase difference hypothesis set.

[0010] Step 4, according to the corrected ambiguity-free phase difference hypothesis set, calculate the azimuth-elevation hypothesis set;

[0011] Step 5, establish an azimuth-elevation cost function model, traverse the calculation of the azimuth-elevation hypothesis set, select the minimum cost function estimation result, and finally obtain the azimuth-elevation estimation.

[0012] Compared with the prior art, the present application has the following advantages: 1) it breaks through the problem of direction finding failure of the existing method when the interferometer array has flatness error; 2) it only needs to solve the ambiguity for a group of baseline pairs, eliminates the redundant calculation link, saves hardware resources and enhances the real-time performance of the system; 3) it fully utilizes the complementary characteristics of amplitude and phase information, ensures the direction finding accuracy while reducing the calculation complexity. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 Flow chart of interferometer three-dimensional ambiguity resolution direction finding method based on amplitude-phase joint.

[0014] Figure 2 Schematic diagram of interferometer array coordinate system.

[0015] Figure 3 Comparison chart of the method of the present application and the ambiguity resolution probability without considering flatness error, wherein a) is the observation angle 30°, b) is the observation angle 15°, and c) is the observation angle 0°.

[0016] Figure 4 Comparison chart of the method of the present application and the direction finding accuracy without considering flatness error, wherein a) is the observation angle 30°, b) is the observation angle 15°, and c) is the observation angle 0°. DETAILED DESCRIPTION

[0017] The technical solutions in the various embodiments of the present application can be combined with each other, but the combination of the technical solutions should be considered not to exist and not to be within the protection scope required by the present application on the premise that the combination of the technical solutions can be realized by ordinary skilled in the art, when the combination of the technical solutions appears contradictory or cannot be realized.

[0018] The technical solutions in the various embodiments of the present application can be combined with each other, but the combination of the technical solutions should be considered not to exist and not to be within the protection scope required by the present application on the premise that the combination of the technical solutions can be realized by ordinary skilled in the art, when the combination of the technical solutions appears contradictory or cannot be realized.

[0019] The technical solutions in the various embodiments of the present application can be combined with each other, but the combination of the technical solutions should be considered not to exist and not to be within the protection scope required by the present application on the premise that the combination of the technical solutions can be realized by ordinary skilled in the art, when the combination of the technical solutions appears contradictory or cannot be realized.

[0020] In combination Figures 1-4 , the interferometer three-dimensional unambiguous direction finding method based on amplitude and phase combination of the present application comprises the following steps:

[0021] Step 1, two vertical long baselines are selected, and the ambiguity range of the two vertical long baselines is calculated based on the azimuth-elevation rough estimation measured by the amplitude, which specifically comprises the following steps:

[0022] Step 11, assuming that the interferometer array is composed of M+4 array elements, the position coordinates of the i th array element in the interferometer array coordinate system are denoted as p i =[x i ,y i ,z i ] T , i = 1, 2, …, M+4, the first array element and the second array element are located on the X axis of the interferometer array coordinate system, the third array element and the fourth array element are located on the Y axis of the interferometer array coordinate system, and each array element has a planeness error due to antenna installation, that is, z i ≠ 0, i = 1, 2, …, M+4; the first array element to the fourth array element are selected to form two vertical long baselines, and the array element numbers are denoted as i1, i2, i3, i4, and the corresponding baseline vectors are denoted as d1, d2:

[0023]

[0024] wherein, is the coordinate of the array element numbered i l on the X axis of the antenna array coordinate system, is the coordinate of the array element numbered i l on the Y axis of the antenna array coordinate system, is the coordinate of the array element numbered i lThe coordinates of the array elements in the Z-axis of the antenna array coordinate system, l = 1, 2, 3, 4; T represents transposition.

[0025] Step 12, define the azimuth angle θ as the angle between the incident signal and the positive direction of the X-axis of the interferometer array coordinate system, and the elevation angle ε as the angle between the incident signal and the positive direction of the Y-axis of the interferometer array coordinate system, denote the azimuth-elevation coarse estimate based on the amplitude as (θ ini , ε ini ), the root mean square error of the azimuth coarse estimate of the radiation source as σ θ , and the root mean square error of the elevation coarse estimate of the radiation source as σ ε , then the angle range corresponding to the azimuth angle θ and the elevation angle ε of the radiation source is R θ , R ε , respectively.

[0026]

[0027] Step 13, denote the wavelength of the radiation source signal as λ, and calculate the maximum ambiguity value K max,1 , K max,2 of the phase difference measured by the above two perpendicular long baselines according to the unambiguous phase difference formula.

[0028]

[0029] The minimum ambiguity value K min,1 , K min,2 :

[0030]

[0031] where d1 and d2 are the lengths of the two perpendicular baselines, d1 = ||d1||, d2 = ||d2||, ||·|| represents the 2-norm, represents rounding up, represents rounding down.

[0032] Then the ambiguity number range corresponding to the two perpendicular long baselines is n1, n2, respectively:

[0033]

[0034] Step 2, traverse all ambiguity combinations within the ambiguity number range of the two perpendicular long baselines, and calculate the initial unambiguous phase difference hypothesis set of the two perpendicular long baselines, which includes the following steps:

[0035] Step 21, for the jth ambiguity combination <n1, n2>, j = 1, 2, …, L, assuming it is the true ambiguity combination, then the unambiguous phase difference of the two perpendicular long baselines is:

[0036] ​

[0037] wherein, are the measured phase differences of the two perpendicular long baselines, respectively.

[0038] Step 22, traverse all the ambiguous combinations to obtain an initial set of unambiguous phase difference hypotheses P:

[0039]

[0040] wherein, the number of ambiguous combinations L = (K max,1 -K min,1 +1)(K max,2 -K min,2 +1).

[0041] Step 3, based on the azimuth-elevation coarse estimation measured by the amplitude, calculate the planarity error correction values of the two perpendicular long baselines to obtain a set of corrected unambiguous phase difference hypotheses, which specifically includes the following steps:

[0042] Step 31, according to the azimuth-elevation coarse estimation (θ ini ,ε ini ) of the radiation source, calculate the angle γ ini between the incident signal and the positive direction of the Z-axis of the interferometer array coordinate system:

[0043]

[0044] Step 32, assuming that the planarity errors of the two perpendicular long baselines are dz1 and dz2, respectively, calculate the planarity error correction values v1 and v2:

[0045]

[0046] wherein, the coefficient κ = λ / 2π.

[0047] Step 33, calculate the set of corrected unambiguous phase difference hypotheses

[0048]

[0049] wherein, the jth set of unambiguous phase difference hypotheses is:

[0050]

[0051] Step 4, according to the set of corrected unambiguous phase difference hypotheses, calculate to obtain a set of azimuth-elevation hypotheses, which specifically includes the following steps:

[0052] Step 41, record the line-of-sight vector u = [u x ,u y ,uz ] T , under the assumption of no ambiguous phase difference for the jth group, according to the no ambiguous phase difference formula, we have:

[0053]

[0054] wherein the coefficient κ = λ / 2π.

[0055] Solving the above equation, the coordinates of the line-of-sight vector in the X-axis and Y-axis of the interferometer array coordinate system are respectively u x and u y :

[0056]

[0057] Step 42, according to the conversion relationship between the line-of-sight vector and the angle, the assumption of no ambiguous phase difference for the jth group is obtained corresponding to the azimuth-elevation assumption (θ j , ε j ), wherein

[0058]

[0059] Step 43, traversing all the combinations of the assumption of no ambiguous phase difference, the azimuth-elevation assumption set H is obtained:

[0060] H = { ( θ 1, ε 1 ), …, ( θ j , ε j ), …, ( θ L , ε L )}.

[0061] The present application firstly proposes an interferometer three-dimensional deambiguating direction finding method of first correcting and then measuring direction by using the azimuth-elevation rough estimation of the radiation source measured by the amplitude information, and the problem of direction finding failure of the existing method when the planeness error exists in the interferometer array is solved.

[0062] Step 5, the azimuth-elevation cost function model is established, the azimuth-elevation assumption set is traversed and calculated, the estimation result making the cost function minimum is selected, and finally the azimuth-elevation estimation is obtained, which specifically includes the following steps:

[0063] Step 51, according to the jth azimuth-elevation assumption (θ j , ε j ), the phases φ i of the other elements corresponding thereto are calculated, a plurality of baselines are selected to calculate the phase differences, and a vector ψ j is formed:

[0064] ψ j = [ ψ (1) ψ (2) … ψ (q)…ψ (Q) ] T ,

[0065] wherein, the number is i a and i b The phase difference of the baseline composed of the array elements of a and b The number of selected baselines q=1,2,…,Q, Q is the total number of selected baselines, a=1,2,…,M+4, b=1,2,…,M+4, and a≠b.

[0066] Step 52, according to the measured phase difference The azimuth-elevation cost function model C(θ j ,ε j ) is established:

[0067]

[0068] Wherein, ||·||1 represents 1 norm.

[0069] Step 53, repeating steps 51-52, calculating the cost function value sequence C corresponding to each azimuth-elevation hypothesis in the azimuth-elevation hypothesis set:

[0070] C={C(θ1,ε1),C(θ2,ε2),…,C(θ j ,ε j )…,C(θ L ,ε L )},

[0071] Step 54, finding the estimated result with the minimum cost function value, obtaining the azimuth-elevation estimation

[0072]

[0073] The above method fully utilizes the complementary characteristics of amplitude and phase information, ensures the direction finding accuracy while reducing the calculation complexity, and only needs to solve the ambiguity for a group of baseline pairs, eliminates the redundant calculation link, saves hardware resources and enhances the system real-time performance, and can meet the engineering real-time requirements.

[0074] Embodiment 1

[0075] Through experiments, the interferometer three-dimensional ambiguity resolution direction finding method based on amplitude and phase joint can realize ambiguity resolution direction finding when the interferometer array exists flatness error, and the ambiguity resolution probability comparison of the method of the present application and the two-dimensional ambiguity resolution direction finding method without correcting the flatness error is as follows Figure 3As shown in the figure, it can be seen that the deblurring probability sharply decreases with the increase of frequency when the flatness error is not corrected, and the smaller the observation angle is, the more obvious the high-frequency deblurring probability deteriorates, and the method can keep a high deblurring probability (>95%) under different observation angles and different frequencies; the comparison of the direction finding accuracy of the method and the two-dimensional deblurring direction finding method without correcting the flatness error is as shown in the figure Figure 4 As shown in the figure, it can be seen that the deblurring probability sharply decreases with the increase of frequency when the flatness error is not corrected, and the smaller the observation angle is, the more obvious the high-frequency deblurring probability deteriorates, and the method can keep a high deblurring probability (>95%) under different observation angles and different frequencies; the comparison of the direction finding accuracy of the method and the two-dimensional deblurring direction finding method without correcting the flatness error is as shown in the figure

Claims

1. A three-dimensional deambiguation and direction finding method based on amplitude-phase interferometer is characterized by: The following steps are involved: Step 1: Select two vertical long baselines and calculate the fuzzy number ranges of the two vertical long baselines based on the azimuth-pitch rough estimate obtained by amplitude measurement; Step 2: Traverse all fuzzy number combinations within the fuzzy number range of the two vertical long baselines to calculate the initial unambiguous phase difference hypothesis set of the two vertical long baselines; Step 3: Based on the azimuth-elevation rough estimate obtained by amplitude measurement, calculate the flatness error correction value of the two vertical long baselines to obtain a corrected unambiguous phase difference hypothesis set; Step 4: Calculate the azimuth-elevation hypothesis set based on the corrected unambiguous phase difference hypothesis set; Step 5: Establish an azimuth-pitch cost function model, perform traversal calculations on the azimuth-pitch hypothesis set, select the estimation result that minimizes the cost function, and finally obtain the azimuth-pitch estimation.

2. The three-dimensional direction-finding method based on amplitude-phase interferometer according to claim 1, characterized in that: In step 1, two vertical long baselines are selected and the ambiguity number ranges of the two vertical long baselines are calculated based on the azimuth-pitch rough estimate obtained by amplitude measurement. Specifically, the following steps are included: Step 11: Assume that the interferometer array consists of M+4 array elements, and the position coordinates of the i-th array element in the interferometer array coordinate system are denoted as p i =[x i ,y i ,z i ] T , i=1,2,…,M+4, the first and second array elements are located on the X axis of the interferometer array coordinate system, the third and fourth array elements are located on the Y axis of the interferometer array coordinate system, and the flatness error of each array element due to the antenna installation is z i ≠0, i=1,2,…,M+4; select the 1st to 4th array elements to form two vertical long baselines, and denote the array elements as i1, i2, i3, i4, and the corresponding baseline vectors as d1 and d2: in, For number i l The coordinate of the array element in the X-axis of the antenna array coordinate system, For number i l The coordinate of the array element in 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: Define the azimuth angle θ as the angle between the incident signal and the positive direction of the X-axis of the interferometer array coordinate system, and the elevation angle ε as the angle between the incident signal and the positive direction of the Y-axis of the interferometer array coordinate system. The azimuth-elevation rough estimate based on the amplitude measurement is recorded as (θ ini ,ε ini ), the root mean square error of the rough estimation of the radiation source direction is σ θ , the root mean square error of the rough estimation of the radiation source pitch is σ ε , then the angle ranges corresponding to the azimuth angle θ and the elevation angle ε of the radiation source are R θ 、R ε : Step 13: Let the wavelength of the radiation source signal be λ, and calculate the maximum ambiguity value K of the phase difference measured by the two vertical long baselines according to the unambiguous phase difference formula. max,1 , K max,2 : Minimum fuzzy value K min,1 , K min,2 : Among them, d1 and d2 are the lengths of the two vertical baselines, d1=||d1||, d2=||d2||, ||·|| represents the 2-norm, Indicates rounding up. Indicates rounding down; Then the fuzzy number ranges corresponding to the two vertical long baselines are n1 and n2 respectively:

3. The three-dimensional direction-finding method based on amplitude-phase interferometer according to claim 2, characterized in that: In step 2, all fuzzy number combinations within the fuzzy number range of the two vertical long baselines are traversed to calculate the initial unambiguous phase difference hypothesis set of the two vertical long baselines, which specifically includes the following steps: Step 21: For the jth fuzzy number combination <n1,n2>, j=1,2,...L, assuming it is a true fuzzy number combination, the unambiguous phase difference of the two vertical long baselines is obtained. for: in, are the measured phase differences of two vertical long baselines; Step 22: Traverse all fuzzy number combinations to obtain the initial unambiguous phase difference hypothesis set P: Among them, the number of fuzzy number combinations L = (K max,1 -K min,1 +1)(K max,2 -K min,2 +1).

4. The three-dimensional direction-finding method based on amplitude-phase combined interferometer according to claim 3, characterized in that: In step 3, based on the rough azimuth-elevation estimate obtained from the amplitude measurement, the flatness error correction values ​​of the two vertical long baselines are calculated to obtain a corrected unambiguous phase difference hypothesis set. Specifically, the following steps are included: Step 31: Roughly estimate the azimuth-elevation of the radiation source (θ ini ,ε ini ), calculate the angle γ between the incident signal and the positive direction of the Z axis of the interferometer array coordinate system ini : Step 32: Assuming that the flatness errors of the two vertical long baselines are dz1 and dz2 respectively, calculate the flatness error correction values ​​ν1 and ν2: Where, the coefficient κ = λ / 2π; Step 33: Calculate the corrected unambiguous phase difference hypothesis set Among them, the jth group of unambiguous phase difference assumptions for:

5. The three-dimensional deambiguation direction finding method based on amplitude-phase combined interferometer according to claim 4, characterized in that: In step 4, the azimuth-elevation hypothesis set is calculated based on the corrected unambiguous phase difference hypothesis set, which specifically includes the following steps: Step 41: Note that the sight vector u = [u x ,u y ,u z ] T , for the jth group of unambiguous phase difference assumptions, according to the unambiguous phase difference formula, we can get: Where, the coefficient κ = λ / 2π; Solving the above equations, we can get the coordinates of the line of sight vector in the interferometer array coordinate system, i.e., u, on the X and Y axes respectively. x 、u y : Step 42: According to the conversion relationship between the sight vector and the angle, the jth group of unambiguous phase difference hypotheses can be obtained. The corresponding azimuth-elevation hypothesis (θ j ,ε j ),in, Step 43: Traverse all unambiguous phase difference hypothesis combinations to obtain the azimuth-elevation hypothesis set H: H={(θ1,ε1),…,(θ j ,he j ),…,(θ L ,he L )}。 6. The three-dimensional direction-finding method based on amplitude-phase interferometer according to claim 5, characterized in that: In step 5, an azimuth-to-elevation cost function model is established, the azimuth-to-elevation hypothesis set is traversed and calculated, and the estimation result that minimizes the cost function is selected to finally obtain the azimuth-to-elevation estimation. Specifically, the following steps are included: Step 51: 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 The number of selected baselines q = 1, 2, ..., Q, where Q is the total number of selected baselines, a = 1, 2, ..., M + 4, b = 1, 2, ..., M + 4, and a ≠ b; Step 52: Based on the measured phase difference Establish the azimuth-pitch cost function model C(θ j ,ε j ): Among them, ||·||1 represents the 1-norm; Step 53: Repeat steps 51 and 52 to calculate the cost function value sequence C corresponding to each azimuth-elevation hypothesis in the azimuth-elevation hypothesis set: C={C(θ1,ε1),C(θ2,ε2),…,C(θ j ,he j )…,C(θ L ,he L )}, Step 54: Find the estimation result with the minimum cost function value and obtain the azimuth-pitch estimation

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