Angle measurement method and device for sparse cloth double-array-element phase comparison and double-frequency phase solution ambiguity radar

Abstract

The invention relates to a sparse cloth double-array-element phase comparison and double-frequency phase solution ambiguity radar angle measurement method and device, and belongs to the technical field of radar measurement. The method specifically comprises the following steps of: 1, performing phase comparison measurement on sparse cloth double array elements at a dual-carrier frequency and a lower dual-channel to obtain a phase difference between the array elements so as to obtain a fuzzy coefficient containing a phase error; according to the fuzzy coefficient, determining constraint conditions of dual-frequency and carrier wave values; step 2, under the constraint condition determined in the step 1, selecting a radar signal working frequency, and constructing a virtual short baseline according to the dual-array-element phase difference under different frequencies; and step 3, based on a virtual baseline ambiguity resolution method, calculating to obtain a non-ambiguity high-precision one-dimensional angle measurement angle.

Description

Technical Field

[0001] The present invention relates to a sparse dual - element phase - comparison and dual - frequency phase - ambiguity - resolving radar angle - measuring method and device, belonging to the technical field of radar measurement. Background Art

[0002] In recent years, the research on high - precision angle measurement for sparse dual - element arrays has attracted extensive attention from domestic and foreign scholars. A sparse dual - element array is the smallest antenna array composed of two elements with an element spacing greater than half - wavelength. Such an array can reduce resources such as platform installation space, weight, power consumption, and cost, while improving the angle - measuring performance by increasing the element spacing and reducing the mutual coupling between elements.

[0003] However, when the element spacing is greater than half - wavelength, phase ambiguity occurs. The larger the element spacing, the more phase ambiguity numbers there are, and it is more difficult to accurately resolve the ambiguity. Due to being restricted to the scenario of the dual - element minimum antenna array, interferometer ambiguity - resolving methods based on multiple elements such as the long - short baseline method, the staggered baseline method, and the three - dimensional baseline method are not applicable. For the dual - element scenario, in 2013, Fan Xiaobo proposed a method for resolving ambiguity by exhausting the ambiguity numbers at dual frequencies in "Research on Microwave Radar Velocity and Angle Measurement for Lunar Orbit Rendezvous and Docking"; in 2022, Ma Dingkun et al. published "Frequency - Domain Phase - Ambiguity - Resolving Interferometer Direction - Finding Method", which proposed a frequency - domain phase - ambiguity - resolving method, using the principle of continuous carrier phase and the ratio of fixed baseline to variable signal wavelength to resolve phase ambiguity; however, the existing research has not given the principle of frequency selection and the frequency selection range. The existing related research has not deeply studied the principle of frequency selection and the frequency selection range, so a perfect radar angle - measuring method has not been formed in the sparse dual - element scenario. Summary of the Invention

[0004] The object of the present invention is to propose a sparse dual - element phase - comparison and dual - frequency phase - ambiguity - resolving radar angle - measuring method and device, and calculate the frequency selection constraint conditions for successful dual - frequency ambiguity resolution considering the existence of phase measurement errors, so as to ensure accurate angle measurement for sparse dual - elements.

[0005] The technical solution of the present invention is implemented as follows: In the first aspect, a sparse dual - element phase - comparison and dual - frequency phase - ambiguity - resolving radar angle - measuring method of the present invention has the following specific process: Step 1, the sparse dual - element performs dual - channel phase - comparison measurement at dual - carrier frequencies and to obtain the phase difference between elements, and further obtain the ambiguity coefficient including phase error; according to the ambiguity coefficient, determine the constraint conditions for the values of dual - frequency and carriers; Step 2: Under the constraint conditions determined in Step 1, select the operating frequency of the radar signal, and construct a virtual short baseline according to the phase differences of the dual elements at different frequencies. Step 3: Based on the virtual baseline deblurring method, calculate the unambiguous high-precision one-dimensional angle measurement angle.

[0006] Optionally, the specific process for obtaining the phase difference between the elements and the ambiguity coefficient including phase error in Step 1 of the present invention is as follows: The sparse dual elements perform two-channel phase comparison measurements under two transmission frequency conditions to obtain the phase difference between the elements as and ;

[0007] where and respectively represent and the parts without phase measurement error in and while and represent the phase measurement error parts in The ambiguity coefficient including phase error is:

[0008] where represents rounding to the nearest integer calculation, is the baseline length, is the virtual short baseline, , .

[0009] Optionally, the specific process for determining the constraint conditions of the dual-frequency and carrier values in Step 1 of the present invention according to the phase difference between the elements and the ambiguity coefficient is as follows: According to and combining that the ambiguity coefficient of the phase error needs to satisfy no influence on the rounding calculation, we can obtain

[0010] Express the maximum measurement error of the phase difference between the two channels as ; Determine the constraint conditions of the dual-frequency and carrier values as: .

[0011] Optionally, according to the constraint conditions, when the carrier frequency is selected, we get The value of should satisfy the condition:

[0012] Optionally, according to the selected carrier frequency and whose value should satisfy the condition, the operating frequency is determined, and the virtual baseline is constructed as:

[0013] Optionally, in step three of the present invention, based on the virtual baseline ambiguity resolution method, the unambiguous high-precision one-dimensional angle measurement angle is calculated as follows: According to the phase difference obtained by dual-channel phase comparison measurement, the ambiguity parameter of the physical long baseline is calculated ,

[0014] wherein , respectively represent the phase differences between two array elements obtained by dual-channel phase comparison measurement under the frequency conditions of , ; Based on the ambiguity parameter of the physical long baseline, the unambiguous high-precision one-dimensional angle measurement angle is thus solved:

[0015] wherein represents the speed of light.

[0016] In a second aspect, the present invention provides a sparse dual-array element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement device, including a sparse dual-array element, a constraint condition calculation module, a virtual short baseline construction module, and a one-dimensional angle measurement module; The constraint condition calculation module uses the sparse dual-array element to perform dual-channel phase comparison measurement at dual carrier frequencies and to obtain the phase differences between array elements, and further obtain the ambiguity coefficient including phase error; according to the ambiguity coefficient, the constraint conditions for the dual-frequency and carrier values are determined; The virtual short baseline construction module, based on the constraint conditions, selects the operating frequency of the radar signal, and constructs a virtual short baseline according to the phase differences of the dual-array elements at different frequencies; The one-dimensional angle measurement module, based on the virtual baseline ambiguity resolution method, calculates the unambiguous high-precision one-dimensional angle measurement angle.

[0017] Beneficial effects: ​​First, a sparse dual - element phase - comparison and dual - frequency phase - ambiguity - resolving radar angle - measuring method. Based on the principle of virtual short - baseline ambiguity - resolution and the influence mechanism of phase - measurement error on the estimation of ambiguity coefficients, the dual - frequency selection interval for successful ambiguity - resolution under the influence of phase - measurement error is deduced. Using dual - frequency phase - ambiguity - resolution to achieve high - precision one - dimensional angle - measurement, and then a dual - frequency ambiguity - resolving radar angle - measuring method in the scenario of sparse dual - element with strong resource constraints is formed.

[0018] Second, the sparse dual - element phase - comparison and dual - frequency phase - ambiguity - resolving radar angle - measuring method proposed in the present invention can achieve unambiguous high - precision one - dimensional angle - measurement by using dual - elements and dual - frequencies. The frequency selection range for phase - ambiguity - resolution is analyzed and deduced, providing a theoretical basis for the engineering application of this method to meet the engineering requirements of unambiguous high - precision angle - measurement under strong resource constraints such as installation space, weight, power consumption, and cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] To clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0020] Figure 1 It is a schematic diagram of the sparse array structure of dual - elements; Figure 2 It is a schematic diagram of virtual baseline generation; Figure 3 For When, the relationship between the angle - measurement accuracy after ambiguity - resolution and the correlation - resolving frequency; Figure 4 For When, the relationship between the success probability of ambiguity - resolution and the correlation - resolving frequency; Figure 5 For When, the relationship between the angle - measurement accuracy after ambiguity - resolution and the correlation - resolving frequency; Figure 6 For When, the relationship between the success probability of ambiguity - resolution and the correlation - resolving frequency. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] The following will describe the embodiments of the present invention in detail with reference to the drawings.

[0022] It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other; and, based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present disclosure.

[0023] Note that the following description pertains to various aspects of embodiments within the scope of the appended claims. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of the aspects set forth herein can be used to implement a device and / or practice a method. Additionally, this device can be implemented and this method can be practiced using other structures and / or functionality in addition to one or more of the aspects set forth herein.

[0024] The present invention utilizes the different phase differences between two array elements at dual frequencies to form an unambiguous virtual short baseline. Based on the principle of virtual short baseline ambiguity resolution and the influence mechanism of phase measurement errors on the ambiguity number estimation, the dual-frequency selection interval for successful ambiguity resolution under the influence of phase measurement errors is further theoretically analyzed, thereby obtaining an optimal dual-frequency operating system. High-precision one-dimensional angle measurement without ambiguity is achieved with relatively few resource costs, providing a new idea for high-precision angle measurement under strong constraints on resources such as installation space, weight, power consumption, and cost.

[0025] An embodiment of the present application provides a method for angle measurement of a sparse dual-array element phase comparison and dual-frequency phase ambiguity resolution radar, and the specific process is as follows: Step 1: The sparse dual-array elements perform dual-channel phase comparison measurements at dual carrier frequencies and to obtain the phase difference between the array elements, and further obtain the ambiguity coefficient including phase errors; according to the ambiguity coefficient, determine the constraint conditions for the dual frequencies and carrier values. Next, the selection principle of the dual-frequency ambiguity resolution frequency under the condition of limited frequency difference is deduced to determine the value range of the dual frequencies Figure 1 As shown in , , a sparse array means an array with an element spacing greater than half the wavelength. For far-field signals, considering a sparse dual-array with 2 array elements. Assume that the one-dimensional angle of the radar echo of a far-field spatial target is

[0026] Assume that at time, the output signal of element 1 is and the output signal of element 2 is which can be respectively expressed as: (1) where and respectively represent the thermal noise of the output signals of element 1 and element 2, is the radar echo signal, Indicates the time difference between the arrival of the radar echo signal at element 1 and element 2. Assume that the incoming wave signal propagates at the speed of light The time difference can be expressed as: (2) In the formula, represents the geometric spacing of the two elements (also known as the baseline length). Assume that the carrier frequency of the incoming wave signal is , and its corresponding wavelength is , then the carrier phase difference between the signals received by the two elements can be expressed as: (3) According to the definition of a sparse array, if the spacing between the two elements is greater than half the wavelength, i.e., , the actual phase difference and the phase difference (the principal value range is ) measured by the phase comparison of the two-channel array differ by an integer number of full cycles of phase ambiguity. The relationship between the two is: (4) where is the ambiguity coefficient of the phase difference, indicates no phase ambiguity, and a non-zero integer indicates the presence of phase ambiguity.

[0027] As shown in Figure 1 , assume that the radar transmits a signal with a carrier frequency of , its wavelength is , and the angle of the target is . At this time, the actual phase difference between the radar echo signals received by the two antenna elements can be expressed as (5) where represents the phase difference obtained by measuring the phase comparison of the signals received by the two-element receiving channel (i.e., the two-channel), represents the ambiguity coefficient corresponding to the baseline length . Considering , we can obtain (6) For auxiliary ambiguity resolution, the radar transmits a signal with a carrier frequency of , its wavelength is . Define as the equivalent baseline length. At this equivalent baseline length, the actual phase difference between the radar echo signals received by the two channels can be expressed as (7) Among them, represents the corresponding equivalent baseline length obtained by dual-channel phase comparison measurement of the phase difference, represents the corresponding equivalent baseline length of the ambiguity coefficient.

[0028] The non-negative phase difference is obtained by the following formula : (8) Among them, is defined as the virtual short baseline.

[0029] From equation (8), when the virtual short baseline satisfies , then That is, it meets the condition of non-phase-ambiguity single-value angle measurement.

[0030] Thus, it can be obtained that (9) According to equations (5) and (8), the ambiguity coefficient can be deduced as: (10) Substituting equation (10) into equation (5), the unambiguous high-precision one-dimensional angle measurement solution value under the baseline length can be obtained: (11) In practical engineering, considering the existence of phase measurement errors, the phase differences and between array elements obtained by dual-channel phase comparison measurement under two transmission frequency conditions can be rewritten as: (12) Among them, and respectively represent and the parts without phase measurement errors in and while and represent the phase measurement error parts in

[0031] Then the unambiguous phase difference estimation values between two array elements under the frequencies and can be respectively expressed as (13) The phase difference corresponding to the virtual short baseline can be expressed as: (14) Among them, denotes the part without phase measurement error in denotes the phase measurement error part in

[0032] According to the ambiguity coefficient formula shown in Equation (10), the ambiguity coefficient containing phase error is: (15) Among them, denotes rounding calculation.

[0033] Comparing Equation (12) and Equation (15), if we want to obtain the correct ambiguity coefficient value, it is necessary to ensure that the right half of Equation (15) has no influence on the rounding calculation, that is, the following conditions need to be satisfied: (16) Considering that the channel measurement accuracies are the same, and the measurement errors of ( denotes the maximum measurement error of the phase difference between channels), then under extreme conditions, there is , and the following inequality can be obtained: (17) And the standard deviation of the measured value of the phase difference between the two channels caused by thermal noise can be calculated by the following formula: (18) At different carrier frequencies, the maximum measurement error of the phase difference between the two channels can be approximately expressed as , then substituting and into Equation (17) gives: (19) In summary, the value of should satisfy: Step 2: Construct a virtual short baseline according to the phase difference between the two array elements at different frequencies The present invention uses two different frequencies to construct a virtual baseline to achieve phase ambiguity resolution and obtain an unambiguous high-precision one-dimensional angle measurement result.

[0034] According to Step 1, the operating frequencies of the signals are determined to be , , respectively, and the phase differences between the two array elements are (21) Due to the limitations of actual factors on the frequency difference of the transmitted signal, by calculating the phase difference to construct a virtual short baseline. At this time (22) Among them, 。

[0035] The phase difference is equivalent to the phase difference of a virtual baseline with a length of under the condition of frequency , as shown in Figure 2 , where , 。

[0036] Step 3: Based on the virtual baseline ambiguity resolution method, calculate the unambiguous high-precision one-dimensional angle measurement angle First, according to the phase difference obtained by the two-channel phase comparison measurement, calculate the ambiguity parameter of the physical long baseline. According to equations (5) and (8), the ambiguity parameter satisfies: (23) Among them, , respectively represent the phase differences between two array elements obtained by two-channel phase comparison measurement under the frequency conditions of , , 。

[0037] Next, based on the virtual short baseline, perform ambiguity resolution on the physical long baseline, and the unambiguous phase difference corresponding to the physical long baseline can be obtained , so as to calculate the unambiguous high-precision one-dimensional angle measurement angle: (24) An angular measurement device for sparse dual-array element phase comparison and dual-frequency phase ambiguity resolution radar according to an embodiment of the present application includes a sparse dual-array element, a constraint condition calculation module, a virtual short baseline construction module, and a one-dimensional angle measurement module; The constraint condition calculation module uses the sparse dual-array element to perform two-channel phase comparison measurement at the dual-carrier frequencies and to obtain the phase difference between array elements, and further obtain the ambiguity coefficient including the phase error; according to the ambiguity coefficient, determine the constraint conditions for the carrier values of the dual frequencies and ; The virtual short baseline construction module, based on the constraint conditions, selects the operating frequency of the radar signal, and constructs a virtual short baseline according to the phase differences of the dual-array elements at different frequencies; The one-dimensional angle measurement module, based on the virtual baseline ambiguity resolution method, calculates the unambiguous and high-precision one-dimensional angle measurement angle.

[0038] Based on the above theoretical derivation model, the MATLAB tool is used to analyze the angle measurement performance of the proposed sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method. First, the correctness of the selected range of the phase ambiguity resolution frequency is verified, and the simulation parameters are set as follows: ① Original transmission frequency GHz; ② Signal propagation speed m / s; ③ Spacing between double elements ; ④ Assume the direction of arrival angle of the far-field target is ; ⑤ The number of Monte Carlo simulations is 300; ⑥ The signal-to-noise ratio is selected as SNR = 30dB, 40dB.

[0039] Using the root mean square error (RMSE) of the one-dimensional angle measurement angle as the evaluation parameter of the estimation accuracy, when the signal-to-noise ratio is 30dB and 40dB respectively, the relationship between the root mean square error of the angle after ambiguity resolution and the ratio is as Figure 3 shown, and the corresponding relationship between the ambiguity resolution success probability and the ratio is as Figure 4 shown.

[0040] It can be seen from the simulation results that when or , that is, or , the root mean square error of the angle measurement of the direction of arrival angle after ambiguity resolution increases sharply, and the ambiguity resolution success rate drops significantly, matching the theoretical boundary. The vertical lines in the figure represent the frequency ratio boundaries and the frequency ratio boundary under different signal-to-noise ratio conditions. The simulation results show that when , due to the influence of phase error, the ambiguity resolution success rate will also drop significantly.

[0041] To further verify the conclusion, change the spacing between double elements in the simulation parameters to , and keep the other conditions unchanged. When the signal-to-noise ratio is 30dB and 40dB respectively, the relationship between the root mean square error of the angle after ambiguity resolution and the ratio is as Figure 5 shown, and the corresponding relationship between the ambiguity resolution success probability and the ratio is as Figure 6 shown.

[0042] It can be obtained from the simulation results that when or , that is or , the ambiguity resolution cannot be successfully achieved; when , due to the influence of the phase error, the success rate of ambiguity resolution will also decrease significantly.

[0043] In summary, the theoretical boundary of the selected ambiguity resolution frequency proposed in this application is consistent with the simulation results.

[0044] In conclusion, the above is only a preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method, characterized in that, The specific process is as follows: Step 1, sparse double array elements perform dual-channel phase comparison measurement at dual carrier frequencies and to obtain the phase difference between array elements, and further obtain the ambiguity coefficient containing phase error; according to the ambiguity coefficient, determine the constraint conditions for the dual-frequency and carrier values; Step 2: Under the constraint conditions determined in Step 1, select the operating frequency of the radar signal, and construct a virtual short baseline according to the phase differences of the two array elements at different frequencies. Step 3: Based on the virtual baseline deambiguation method, calculate the unambiguous high-precision one-dimensional angle measurement angle.

2. The sparse dual-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method according to claim 1, characterized in that The specific process of obtaining the phase difference between array elements and the ambiguity coefficient containing phase error in Step 1 is as follows: Sparse dual-elements perform two-channel phase comparison measurement under two emission frequency conditions, and the phase difference between the elements is obtained as and ; Among them, and respectively represent and the parts without phase measurement error in and while and represent the parts of phase measurement error in The ambiguity coefficient containing phase error is: Among them, represents rounding calculation, is the baseline length, is the virtual short baseline, , .

3. The sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method according to claim 2, wherein, In the first step, the dual frequencies are determined according to the phase difference between the array elements and the ambiguity coefficient. and The specific process of the constraint conditions for the carrier values is as follows: According to and combining with the ambiguity coefficient of the phase error which needs to satisfy no influence on the rounding calculation, we can obtain Express the maximum measurement error of the phase difference between the two channels as ; Determine the dual frequencies and The constraint conditions for the carrier values are as follows: 。 4. The sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method according to claim 3, characterized in that According to the described constraints, at the selected carrier frequency , obtain The value of should satisfy the condition: 。 5. The sparse double-array element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method according to claim 4, characterized in that, According to the selected carrier frequency and the value of which should satisfy the condition, determine the operating frequency , and construct the virtual baseline as: 。 6. The sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement method according to claim 5, characterized in that In Step 3, based on the virtual baseline deambiguation method, the unambiguous high-precision one-dimensional angle measurement angle is calculated, specifically as follows: Calculate the ambiguity parameter of the physical long baseline based on the phase difference obtained from the dual-channel phase comparison measurement , Among them, and respectively represent the phase difference between two array elements obtained by dual-channel phase comparison measurement under the frequency conditions of and , ; Fuzzy parameters based on physical long baselines , thereby resolving the unambiguous high-precision one-dimensional angle measurement angle : Among them, represents the speed of light.

7. A sparse double-array-element phase comparison and dual-frequency phase ambiguity resolution radar angle measurement device, characterized in that, It includes a sparse dual-array element, a constraint condition calculation module, a virtual short baseline construction module, and a one-dimensional angle measurement module; Constraint condition calculation module, using sparse dual-array elements for dual-channel phase comparison measurement at dual-carrier frequencies and to obtain the phase difference between array elements, and further obtain the ambiguity coefficient including phase error; according to the ambiguity coefficient, determine the constraint conditions for the dual-frequency and carrier values; The virtual short baseline construction module, based on the constraint conditions, selects the operating frequency of the radar signal, and constructs a virtual short baseline according to the phase differences of the two array elements at different frequencies. The one-dimensional angle measurement module, based on the virtual baseline deambiguation method, calculates the unambiguous high-precision one-dimensional angle measurement angle.

8. The sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measuring device according to claim 7, characterized in that, The specific process of the constraint condition calculation module obtaining the phase difference between array elements and the ambiguity coefficient containing phase error is as follows: Sparse dual-element two-channel phase comparison measurement under two emission frequency conditions to obtain the phase difference between the elements as and ; Among them, and respectively represent and the parts without phase measurement errors in and while and represent the parts of phase measurement errors in The ambiguity coefficient containing phase error is: Among them, represents rounding calculation, is the baseline length, is the virtual short baseline, , .

9. The sparse double-array element phase comparison and dual-frequency phase-unwrapping radar angle measurement device according to claim 8, wherein The constraint condition calculation module determines the constraint conditions for the double-frequency and carrier values according to the phase difference between array elements and the ambiguity coefficient. The specific process is as follows: According to Combined with the fact that the ambiguity coefficient of the phase error needs to satisfy no influence on the rounding calculation, it can be obtained that Express the maximum measurement error of the phase difference between the two channels as ; Determine the dual frequencies and The constraint conditions for the carrier values are as follows: 。 10. The sparse double-element phase comparison and dual-frequency phase ambiguity resolution radar angle measuring device according to claim 9, characterized in that, The constraint condition calculation module, according to the constraint conditions, at the selected carrier frequency , obtains whose value should satisfy the condition: 。

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