Seven-element uniform circular array interferometer optimal direction finding baseline group selection method
By constructing and analyzing the error transmission relationship between the azimuth angle and the included angle in the seven-member uniform circular array interferometer and the pitch angle and yaw angle in the forward direction of the platform, the optimal direction finding baseline group was selected, and the existing technology was solved. The problem of uneven measurement accuracy in the middle realizes high-precision measurement of pitch angle and yaw angle and robust two-dimensional direction finding.
Patent Information
- Application Number
- CN202411403698.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-09
- Publication Date
- 2024-12-27
AI Technical Summary
When selecting the optimal direction finding baseline group of seven-member uniform circular array interferometers, the prior art failed to effectively pay attention to the measurement accuracy of the pitch angle and yaw angle of the signal incident direction relative to the direction of the platform forward, resulting in uneven measurement accuracy. Cannot meet the needs of actual engineering applications.
By constructing the error transmission relationship between the azimuth angle and the angle formed by the azimuth angle and the pitch angle and the yaw angle of the platform forward direction, the maximum angle of the seven acute angles is determined. The longest baseline group is used, and the cascade error transfer relationship between the fuzzy-free phase difference estimate and the instantaneous phase measurement value of the array element is derived. The baseline group with relatively smallest cascade error transfer coefficient and the most balanced accuracy is selected.
The accurate measurement of the pitch angle and yaw angle of the signal incident direction relative to the forward direction of the moving platform is achieved, which simplifies the engineering implementation logic and makes the two-dimensional direction finding more robust and meets the needs of actual engineering applications.
Smart Images
Figure CN119199722A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of direction finding of a moving platform interferometer, in particular to a method for selecting an optimal direction finding baseline group of a seven-element uniform circular array interferometer. Background Art
[0002] Uniform circular array interferometer has a simple structure and high real-time performance for direction finding, and is widely used in the field of passive radar seekers. In order to reduce the amount of computational complexity of deambiguation, a seven-element uniform circular array interferometer with fewer fuzzy number set elements than a five-element uniform circular array is selected when designing the array. After completing the phase deambiguation, a direction finding baseline group is selected, and a complex number is constructed from the sum and difference of the unambiguous phase differences of the two baselines. A two-dimensional angle estimate is then extracted from the complex number, and finally the two-dimensional angle estimate is converted into the pitch and yaw angles of interest to the motion platform based on the three-dimensional spatial relationship. Different direction finding baseline groups have different angle measurement accuracy. Under the constraint of limited computing resources of the motion platform, it is necessary to select the baseline group with the best comprehensive measurement accuracy.
[0003] In the prior art, the optimal direction finding baseline group selection method mostly only focuses on the azimuth of the signal incident direction projected in the circular array plane and the optimal measurement of its angle with the circular array plane. However, in actual engineering applications, the ultimate focus is on the pitch angle and yaw angle of the signal incident direction relative to the platform's forward direction. The measurement accuracy of the two is not a simple linear relationship. Summary of the invention
[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for selecting an optimal direction finding baseline group for a seven-element uniform circular array interferometer, comprising the following steps:
[0005] Step 1: The azimuth angle α of the signal incident direction projected on the plane of the seven-element uniform circular array and the angle β between the signal incident direction and the plane of the seven-element uniform circular array constitute a two-dimensional angle <α, β>; the pitch angle θ of the signal incident direction relative to the platform's forward direction and the yaw angle ψ of the signal incident direction relative to the platform's forward direction constitute a two-dimensional angle <θ, ψ>; according to the spatial geometric relationship between <α, β> and <θ, ψ>, the error transfer relationship between <α, β> and <θ, ψ> is obtained;
[0006] Step 2: Rotate counterclockwise in the plane of the circle with the center of the circle as the axis. Determine the longest baseline group with the largest seven acute angles as the direction finding baseline group to be selected;
[0007] Step 3, derive the error transfer relationship between the interferometer direction-finding two-dimensional angle <α, β> and the unambiguous phase difference estimation value;
[0008] Step 4: Based on the unambiguous phase difference estimate and the array element instantaneous phase measurement value σ φThe relationship between , the cascade error transfer coefficient distribution of the instantaneous phase measurement error of each array element in the seven candidate baseline groups transferred to <θ, ψ> is obtained, and the optimal baseline group is determined according to the cascade error transfer coefficient distribution.
[0009] Furthermore, the error transfer relationship between <α, β> and <θ, ψ> is obtained according to the spatial geometric relationship between <α, β> and <θ, ψ>, including:
[0010] Taking the geometric center of the seven-element uniform circular array plane as the origin, the forward direction of the seven-element uniform circular array is the Z axis, the vertical direction is the X axis, and the horizontal direction is the Y axis. The angle between the projection of the signal incident direction in the seven-element uniform circular array plane and the X axis is the azimuth angle α, the angle between the signal incident direction and the circular array plane is β, the angle between the projection of the signal incident direction in the XOZ plane and the Z axis is the pitch angle θ, and the angle between the projection of the signal incident direction in the YOZ plane and the Z axis is the yaw angle ψ:
[0011] Then the conversion relationship between the two-dimensional angles <α, β> and <θ, ψ> is:
[0012]
[0013] Then the error transmission relationship of the pitch angle θ is:
[0014]
[0015] The error transmission relationship of the yaw angle ψ is:
[0016]
[0017] Furthermore, the said circular array plane rotates counterclockwise with the center of the circular array as the axis. Determine the longest baseline group with the largest seven acute angles as the direction finding baseline group to be selected, including:
[0018] Rotate counterclockwise around the center of the circle Get the longest baseline group with the largest seven angles
[0019] {(14,26),(25,37),(36,41),(47,52),(51,63),(62,74),(73,15)}, where the numbers represent the serial numbers of the seven array elements. 14 represents the baseline formed by element 1 and element 4. (14,26) represents the two-dimensional direction finding baseline group formed by baseline 14 and baseline 26. The same is true for the other baseline groups.
[0020] Furthermore, the error transfer relationship between the derivation of the interferometer direction-finding two-dimensional angle (α, β) and the unambiguous phase difference estimation value includes:
[0021] The unambiguous phase difference estimate Δφ from the baseline groupk1 and Δφ k2 , measure <α, β>, the error transfer relationship between the azimuth angle α and the unambiguous phase difference estimate is:
[0022]
[0023] The error transfer relationship between the angle β and the unambiguous phase difference estimate is:
[0024]
[0025] in Δφ k1 is the unambiguous phase difference estimate of the first baseline of the kth two-dimensional direction finding baseline group, Δφ k2 is the unambiguous phase difference estimate of the second baseline in the kth two-dimensional direction finding baseline group, r is the radius of the circular array, and λ is the wavelength of the incident signal.
[0026] Furthermore, according to the unambiguous phase difference estimate and the array element instantaneous phase measurement value σ φ The relationship between the instantaneous phase measurement errors of the array elements in the seven candidate baseline groups is obtained, and the cascade error transfer coefficient distribution of the instantaneous phase measurement errors of the array elements in the seven candidate baseline groups is transferred to <θ, ψ>. The optimal baseline group is determined according to the cascade error transfer coefficient distribution, including:
[0027] The measured root mean square error σ of the pitch angle θ θ for:
[0028]
[0029] The measured root mean square error σ of the yaw angle ψ ψ for:
[0030]
[0031] The cascade error transfer coefficient G of the array element instantaneous phase measurement error transferred to the pitch angle θ and yaw angle ψ θ and G ψ for:
[0032]
[0033] According to G θ and G ψ , the distribution of cascade error transfer coefficients of the seven longest baseline groups with the largest angles is obtained respectively, and the optimal baseline group is determined according to the distribution of cascade error transfer coefficients of the seven longest baseline groups with the largest angles.
[0034] The beneficial effects of the present invention are as follows: for the pitch angle and yaw angle of the incident direction of the signal of final concern relative to the forward direction of the moving platform, the optimal direction finding baseline group is selected according to the principle that the cascade error transfer coefficient is relatively minimum and the accuracy is most balanced within the spatial domain, which is closer to the actual engineering application; the logic of engineering implementation is simplified, making the two-dimensional direction finding more robust. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 It is a schematic diagram of the implementation process of a method for selecting the optimal direction finding baseline group for a seven-element uniform circular array interferometer;
[0036] Figure 2 It is a schematic diagram of the three-dimensional spatial relationship between the incident signal and the direction-finding coordinate system OXYZ;
[0037] Figure 3 Schematic diagram of the counterclockwise rotation geometric relationship of the baseline groups (14, 26) and (25, 37) in the circular array plane;
[0038] Figure 4 Schematic diagram of the distribution of cascade error transfer coefficients of baseline groups (14, 26) and (73, 15) at a signal frequency of 2 GHz;
[0039] Figure 5 Schematic diagram of the distribution of cascade error transfer coefficients of baseline groups (25, 37) and (62, 74) at a signal frequency of 2 GHz;
[0040] Figure 6 Schematic diagram of the distribution of cascade error transfer coefficients of baseline groups (36, 41) and (51, 63) at a signal frequency of 2 GHz;
[0041] Figure 7 It is a schematic diagram of the distribution of the cascade error transfer coefficient of the baseline group (47,52) when the signal frequency is 2GHz;
[0042] Figure 8 It is a schematic diagram of the maximum value of the cascade error transfer coefficient of each baseline group under different β when the signal frequency is 2GHz;
[0043] Fig. 9 Schematic diagram of the comparison between the statistical value and theoretical value of the cascade error transfer coefficient obtained by performing 10,000 Monte Carlo simulations on each baseline group. DETAILED DESCRIPTION
[0044] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.
[0045] The features and performance of the present invention are further described in detail below in conjunction with the embodiments.
[0046] like Figure 1As shown in 1, the error transfer relationship between the two two-dimensional angles of the seven-element uniform circular array interferometer direction finding is derived, and the three-dimensional spatial relationship between the incident signal and the direction finding coordinate system OXYZ is as follows Figure 2 As shown in the figure, the Z axis is the platform forward direction, the X axis is vertically upward, and the Y axis is horizontally to the right. The circular array plane is in the XOY plane. Most of the existing literature focuses on the azimuth angle α of the signal incident direction projected in the circular array plane and its angle β with the circular array plane. In actual engineering applications, the angle θ between the projection of the signal incident direction in the XOZ plane (the surface represented by the grid shadow in the rectangular block in the figure) and the Z axis is the pitch angle, and the angle ψ between the projection of the signal incident direction in the YOZ plane (the surface represented by the oblique line shadow in the rectangular block in the figure) and the Z axis is the yaw angle. The error transmission relationship between these two two-dimensional angles is calculated as follows:
[0047] 1) The conversion relationship between <α, β> and <θ, ψ> is obtained from the three-dimensional spatial relationship:
[0048]
[0049] 2) Differentiating both sides of the above equation, we get the error transfer relationship between the two two-dimensional angles:
[0050]
[0051] 2. Determine the direction finding baseline group to be selected, which is the longest baseline group with the largest (acute angle) angle among the seven types {(14,26), (25,37), (36,41), (47,52), (51,63), (62,74), (73,15)}, where the numbers represent the serial numbers of the seven array elements, 14 represents the baseline composed of array element 1 and array element 4, (14,26) represents the two-dimensional direction finding baseline group composed of baseline 14 and baseline 26; the geometric relationship of these seven baseline groups in the circular array plane is to rotate counterclockwise by 2π / 7 with the center of the circular array as the axis, as follows: Figure 3 As shown;
[0052] 3. The error transmission relationship of the baseline group (14, 26) for two-dimensional direction finding of <α, β> is derived. The optimal direction finding baseline group selection is the operation after the interferometer completes the deambiguation, that is, at this time, the unambiguous phase difference estimation value of each baseline group has been obtained. The deambiguation process is not the focus of the present invention and will not be elaborated in detail. Referring to the error analysis method of the five-element uniform circular array interferometer two-dimensional direction finding in the existing literature, according to the unambiguous phase difference estimation value Δφ of the baseline group (14, 26) 14 and Δφ 26 When measuring <α, β>, the error transmission relationship is
[0053]
[0054] in r is the radius of the circular array, λ is the wavelength of the incident signal;
[0055] 4. Combining steps 1 and 3, we can obtain the error transfer relationship between the pitch angle θ and the unambiguous phase difference estimate when cosα<0:
[0056]
[0057] Unambiguous phase difference Δφ 14 and Δφ 26 It is obtained by the instantaneous phase φ1, φ4, φ2 and φ6 of each array element, so the above formula can be written as:
[0058]
[0059] The instantaneous phase measurements of each array element are independent of each other, and the root mean square error is σ φ , then the measured root mean square error σ of the pitch angle θ θ for:
[0060]
[0061] When cosα≥0, the same result as above can be obtained. Similar calculation can also obtain the measured root mean square error σ of the yaw angle ψ: ψ for
[0062]
[0063] Therefore, the cascade error transfer coefficient G from the array element instantaneous phase measurement error to the pitch angle θ and yaw angle ψ is θ and G ψ for
[0064]
[0065] The cascade means: taking the pitch angle as an example, the "transfer relationship between the obtained pitch angle error dθ and the azimuth error dα and the angle error dβ", the "transfer relationship between the obtained azimuth error dα and the angle error dβ and the unambiguous phase difference measurement value" and the "relationship between the unambiguous phase difference estimate and the instantaneous phase of each array element" are cascaded to obtain the error transfer coefficient between the pitch angle error dθ and the instantaneous phase measurement error of the array element.
[0066] For the seven baseline groups to be selected in step 2, the cascade error transfer coefficients of the remaining six are replaced one by one by α1 in the above formula Then, when the circular array radius is 120 mm and the signal frequency is 2 GHz, the G θ and G ψ are all related to <α, β>. Considering the actual application scenario, the measurement range of β is [30°, 90°], and Gθ and G ψ The period along α is 180°, so the value ranges of <α,β> in the figure are [0°,180°] and [30°,90°] respectively. According to G in step 4 θ and G ψ The expression draws the distribution diagram of seven kinds of cascade error transfer coefficients as follows Figures 4 to 8 As shown, it can be seen that:
[0067] 1) G θ and G ψ It is more affected by β. It decreases rapidly with the increase of β under a certain α, and changes slowly and periodically with α under a certain β.
[0068] 2) The distributions of the baseline groups (14,26) and (73,15) are consistent, except that the trend along the α direction has a proper translation. The G of the baseline groups (25,37) and (62,74), and the baseline groups (36,41) and (51,63) are θ and G ψ There is also this relationship;
[0069] 3) G in the baseline group (47,52) θ and G ψ The distribution is relatively balanced, and the periodic change with α is relatively gentle;
[0070] 4) Comparison of the maximum value curves of the cascade error transfer coefficients of the baseline groups (14, 26), (25, 37), (36, 41) and (47, 52) under different β values. Figure 8 As shown, the frequency range of the incident signal is generally [2GHz, 18GHz], G θ and G ψ are inversely proportional to the signal frequency, so the theoretical value of 2 GHz is the maximum error transfer coefficient. Assuming that the RMS error of the instantaneous phase measurement of each array element is 2°, and the RMS error of the interferometer direction finding output <θ, ψ> is required to be 1°, then any of the above baseline groups can meet the accuracy index for all frequencies. Considering the balance of accuracy distribution, (47,52) is selected as the optimal direction finding baseline group.
[0071] Specifically, taking the test parameters of a radar seeker as an example, seven array elements are evenly distributed on a circle with a radius r of 120 mm, the frequency of the far-field narrowband incident signal is 2 GHz, the azimuth angle of the signal incident direction projected in the circular array plane is α, the angle with the circular array plane is β, the pitch angle and the yaw angle are θ and ψ, and after the interferometer deambiguation is completed, the technical solution of the direction finding baseline group is selected based on the cascade error transfer relationship analysis, and its implementation steps are as follows:
[0072] 1. Derivation of the error transfer relationship between the two two-dimensional angles <α, β> and <θ, ψ> of the seven-element uniform circular array interferometer
[0073]
[0074] 2. Determine the direction finding baseline group to be selected, which is the longest baseline group with the largest (acute angle) angle among the seven types {(14,26), (25,37), (36,41), (47,52), (51,63), (62,74), (73,15)};
[0075] 3. Derivation of the error transfer relationship of the unambiguous phase difference of the baseline group (14, 26) for two-dimensional direction finding of <α, β>
[0076]
[0077] 4. Combine steps 1 and 3 to obtain the cascade error transfer coefficient of the baseline group (14, 26) from the array element instantaneous phase measurement error to the pitch angle θ and yaw angle ψ
[0078]
[0079] Under different β, the G of the baseline group (14,26) θ The maximum value is near α=118°, G ψ The maximum value is near α=154°; for G θ At α = 118°, G ψ When α=154°, β is increased by 10° from 30° to 90°, and the root mean square error of the instantaneous phase measurement of the array element is 2°. 10,000 interferometer direction finding Monte Carlo simulations are performed for each baseline group, and the root mean square error of <θ, ψ> is calculated and divided by 2° to obtain G θ and G ψ The statistical value, the comparison curve between the theoretical value and the statistical value is as follows Fig. 9 As shown, it can be seen that the statistical values of each baseline group are basically consistent with the theoretical values. Considering the balance of accuracy distribution, (47,52) is selected as the optimal direction finding baseline group.
[0080] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art do not deviate from the spirit and scope of the present invention, and should be within the scope of protection of the claims attached to the present invention.
Claims
1. A method for selecting an optimal direction finding baseline group for a seven-element uniform circular array interferometer, characterized in that: The steps include: Step 1: The azimuth angle α of the signal incident direction projected on the plane of the seven-element uniform circular array and the angle β between the signal incident direction and the plane of the seven-element uniform circular array constitute a two-dimensional angle <α, β>; the pitch angle θ of the signal incident direction relative to the platform's forward direction and the yaw angle ψ of the signal incident direction relative to the platform's forward direction constitute a two-dimensional angle <θ, ψ>; according to the spatial geometric relationship between <α, β> and <θ, ψ>, the error transfer relationship between <α, β> and <θ, ψ> is obtained; Step 2: Rotate counterclockwise in the plane of the circle with the center of the circle as the axis. Determine the longest baseline group with the largest seven acute angles as the direction finding baseline group to be selected; Step 3, deriving the error transfer relationship between the interferometer direction-finding two-dimensional angle <α, β> and the unambiguous phase difference estimation value; Step 4: Based on the unambiguous phase difference estimate and the array element instantaneous phase measurement value σ φ , the cascade error transfer coefficient distribution of the instantaneous phase measurement error of each array element in the seven candidate baseline groups transferred to <θ, ψ> is obtained, and the optimal baseline group is determined according to the cascade error transfer coefficient distribution.
2. The method for selecting an optimal direction finding baseline group for a seven-element uniform circular array interferometer according to claim 1, characterized in that: The error transmission relationship between <α, β> and <θ, ψ> is obtained based on the spatial geometric relationship between <α, β> and <θ, ψ>, including: With the geometric center of the seven-element uniform circular array plane as the origin, the forward direction of the seven-element uniform circular array is the Z axis, the vertical direction is the X axis, and the horizontal direction is the Y axis. The angle between the projection of the signal incident direction in the seven-element uniform circular array plane and the X axis is the azimuth angle α, the angle between the signal incident direction and the circular array plane is β, the angle between the projection of the signal incident direction in the XOZ plane and the Z axis is the pitch angle θ, and the angle between the projection of the signal incident direction in the Y0Z plane and the Z axis is the yaw angle ψ: Then the conversion relationship between the two-dimensional angles <α, β> and <θ, ψ> is: Then the error transmission relationship of the pitch angle θ is: The error transmission relationship of the yaw angle ψ is:
3. The method for selecting an optimal direction finding baseline group for a seven-element uniform circular array interferometer according to claim 2, characterized in that: The said rotating in a counterclockwise direction in the plane of the circular array with the center of the circular array as the axis Determine the longest baseline group with the largest seven acute angles as the direction finding baseline group to be selected, including: Rotate counterclockwise around the center of the circle The seven longest baseline groups with the largest angles are obtained: {(14, 26), (25, 37), (36, 41), (47, 52), (51, 63), (62, 74), (73, 15)}, where the numbers represent the serial numbers of the seven array elements. 14 represents the baseline formed by element 1 and element 4, (14, 26) represents the two-dimensional direction finding baseline group formed by baseline 14 and baseline 26, and the same applies to the remaining baseline groups.
4. The method for selecting an optimal direction finding baseline group for a seven-element uniform circular array interferometer according to claim 3, characterized in that: The error transfer relationship between the derivation of the interferometer direction-finding two-dimensional angle <α, β> and the unambiguous phase difference estimation value includes: According to the unambiguous phase difference estimation values Δφk1 and Δφk2 of the baseline group, <α, β> is measured, and the error transfer relationship between the azimuth angle α and the unambiguous phase difference estimation value is: The error transfer relationship between the angle β and the unambiguous phase difference estimate is: in Δφk1 is the estimated value of the unambiguous phase difference of the first baseline in the k-th two-dimensional direction finding baseline group, Δφk2 is the estimated value of the unambiguous phase difference of the second baseline in the k-th two-dimensional direction finding baseline group, r is the radius of the circular array, and λ is the wavelength of the incident signal.
5. The method for selecting an optimal direction finding baseline group for a seven-element uniform circular array interferometer according to claim 4, characterized in that: According to the relationship between the unambiguous phase difference estimation value and the array element instantaneous phase measurement value σφ, the cascade error transfer coefficient distribution of the array element instantaneous phase measurement error of each of the seven candidate baseline groups is obtained to be transferred to <θ, ψ>. According to the cascade error transfer coefficient distribution, the optimal baseline group is determined, including: The measured root mean square error σ of the pitch angle θ θ for: The measured root mean square error σψ of the yaw angle ψ is The cascade error transfer coefficient G of the array element instantaneous phase measurement error transferred to the pitch angle θ and yaw angle ψ θ and G ψ for: According to G θ and G ψ , the distribution of cascade error transfer coefficients of the seven longest baseline groups with the largest angles is obtained respectively, and the optimal baseline group is determined according to the distribution of cascade error transfer coefficients of the seven longest baseline groups with the largest angles.