High-frequency-band signal combined direction finding method based on full-baseline fuzzy number search method
Patent Information
- Application Number
- CN202511522445.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-23
- Publication Date
- 2026-01-23
Smart Images
Figure CN121385784A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of aero-engines, and particularly relates to a high-frequency signal combined direction finding method based on a full-baseline fuzzy number search method. BACKGROUND
[0002] Common direction finding methods include amplitude comparison, phase comparison, time difference, spatial spectrum estimation, etc. The amplitude comparison method is simple and does not require the signal frequency, but the direction finding accuracy is not high; the time difference method has high accuracy, but requires high time synchronization accuracy, and multiple receiving ends usually need to be far apart, and even cannot be implemented on the same device; the spatial spectrum estimation method has high accuracy, but has large calculation amount, so the phase comparison method with high accuracy and small calculation amount is usually selected, and a phase interferometer is usually used.
[0003] Taking a one-dimensional linear array interferometer as an example, due to different lengths of the linear array, when the baseline length of two array elements is greater than one-half of the signal wavelength, phase ambiguity occurs, accurate phase difference cannot be obtained, and thus the correct incident angle cannot be calculated. There are usually three ways to deal with this situation, namely, long-short baseline ambiguity resolution, virtual baseline ambiguity resolution and remainder ambiguity resolution.
[0004] The implementation process of the commonly used long-short baseline ambiguity resolution method is as follows: the corresponding phase difference of the shortest baseline is calculated, at this time, it is required that there is no ambiguous solution, and then the non-ambiguous phase of the long baseline is calculated step by step from the non-ambiguous phase. The main shortcomings of the method are as follows:
[0005] The first main shortcoming is that it cannot be applied to high-frequency signal environment.
[0006] The method requires that the length of the shortest baseline is less than one-half of the signal wavelength to meet the requirement of no ambiguity of the shortest baseline. When facing high-frequency and large-bandwidth electronic systems, due to the inherent size and performance requirements of the antenna, it is usually difficult to meet the requirement of small enough array element spacing in actual engineering, and thus the method cannot be used.
[0007] The second main shortcoming is poor direction finding robustness.
[0008] The method uses the way of ambiguity resolution from the shortest baseline to the long baseline step by step, so as long as the phase consistency deviation of a certain array element is large, the direction finding error of the longest baseline will be large through the step-by-step transmission during ambiguity resolution. SUMMARY
[0009] In order to solve the above problems, the application provides a high-frequency signal combined direction finding method based on a full-baseline fuzzy number search method,
[0010] Step 1: Select any number of array elements of the interferometer direction finding antenna, calculate the baseline length between all array elements, and obtain the amplitude comparison direction finding error;
[0011] Step 2: determining the ambiguity number of the longest baseline according to the baseline length searching boundary; reducing the searching boundary by using the amplitude comparison direction finding error to obtain a searching range;
[0012] Step 3: calculating the direction finding result of each ambiguity number in the searching range corresponding to the residual baseline length ambiguity number set, substituting all baseline length ambiguity number sets into the loss function respectively, and taking the baseline length ambiguity number set with the minimum loss function as the optimal ambiguity number set;
[0013] Step 4: obtaining the direction finding results of all baselines according to the optimal ambiguity number set, and obtaining the final incident angle by weighted mean of all direction finding results.
[0014] Preferably, the method for obtaining the amplitude comparison direction finding error comprises:
[0015] Step 11: constructing a three-amplitude direction finding system simulation model;
[0016] Step 12: traversing all incident angles of the three-amplitude direction finding system simulation model to obtain the maximum value of the direction finding error of the three-amplitude direction finding system simulation model in all incident angles, and taking the maximum value as the amplitude comparison direction finding error.
[0017] Preferably, the expression of the searching range is: ;
[0018] wherein,
[0019] ;
[0020] ;
[0021] wherein, is the direction finding result of the amplitude comparison direction finding, is a value determined based on the amplitude comparison direction finding error.
[0022] Preferably, = standard deviation of the amplitude comparison direction finding error + β, wherein β is a set value.
[0023] Preferably, the expression of the loss function is:
[0024] (16)
[0025]
[0026] wherein, each baseline ambiguity number set is:
[0027] ;
[0028] d1-d6 represent all baseline lengths, and k1-k6 represent all baseline ambiguity numbers.
[0029] In the formula, round represents the rounding of the logarithmic value, i.e.
[0030] .
[0031] Preferably, the weight of the i-th baseline length ambiguity number is... The calculation formula is: ;
[0032] in, is the normalized fitted value of the direction finding error of the i-th baseline.
[0033] Preferably, the specific steps for weighted averaging of all direction finding results include:
[0034] The upper and lower bounds of all the direction finding results are calculated using percentiles.
[0035] Outliers in the direction finding results are removed based on the upper and lower bounds.
[0036] The direction finding results after removing outliers are weighted. Calculate the weighted mean.
[0037] Preferably, the formula for calculating the incident angle is:
[0038] .
[0039] in Indicates the baseline length is The phase difference (less than 2) of the signals received by the two receiving array elements corresponding to the baseline of the time. ), The baseline length is The fuzzy number corresponding to the baseline at that time.
[0040] Preferably, the fitting function for the direction finding error of the i-th baseline length is... The specific method for obtaining it is as follows:
[0041] Several Monte Carlo calculations are performed on the i-th baseline length to obtain several direction-finding errors. A fitting function is then obtained by fitting all these direction-finding errors to obtain the direction-finding error for the i-th baseline length. .
[0042] This application addresses the limitation in traditional interferometer direction finding systems that require the shortest baseline length to be less than half the signal wavelength when using long and short baselines for step-by-step deambiguation. This reduces the requirements for antenna element spacing. Furthermore, by designing a combined direction finding algorithm, it significantly improves the deambiguity probability and algorithm efficiency. Attached Figure Description
[0043] Figure 1 This is an antenna distribution diagram of a three-channel amplitude comparison direction finding system.
[0044] Figure 2 This is the flowchart of the combined direction finding algorithm.
[0045] Figure 3 These are the radiation patterns of a planar helical antenna at different frequencies.
[0046] Figure 4 This is a schematic diagram of amplitude and direction finding errors at different angles at different frequencies.
[0047] Figure 5 This is a schematic diagram showing the trend of direction finding accuracy as a function of signal-to-noise ratio at the same signal frequency.
[0048] Figure 6 This is a schematic diagram of direction finding errors under different baseline lengths.
[0049] Figure 7 This is a schematic diagram of the unambiguity probability under amplitude-based direction finding guidance at different incident angles.
[0050] Figure 8 This is a schematic diagram illustrating the calculated angle values for different incident angles under amplitude-based direction finding guidance. Detailed Implementation
[0051] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings. Figure 1 As shown, the combined direction-finding algorithm designed in this scheme combines three-channel amplitude comparison direction finding with phase interferometry direction finding, while leveraging the advantages of simplicity and speed of the amplitude comparison algorithm and the high accuracy of the phase interferometry. The combined direction-finding algorithm first obtains coarse direction-finding results through the amplitude comparison algorithm while simultaneously performing frequency measurements. Then, guided by the amplitude comparison results, it uses a full-baseline ambiguity number search method to traverse and search the ambiguity numbers of all baselines of the phase interferometry within a small range, thereby improving the deambiguity probability and direction-finding accuracy.
[0052] Three-channel amplitude comparison direction finding
[0053] Considering system scale and guidance requirements, a three-channel amplitude comparison direction finding system is adopted. The included angle of the antenna axes is determined based on the reconnaissance airspace range. (For a reconnaissance airspace range of ±60°, the included angle of the axes is 60°. The figure shows the antenna distribution diagram of the three-channel amplitude comparison direction finding system, with the middle channel as 0°, and the axes of the other two channels as -60° and 60° respectively. The antennas in the direction from -60° to 60° are antenna 1, antenna 2, and antenna 3, respectively.)
[0054] against The three-channel amplitude comparison direction finding system shown can be divided into two regions: region I between antenna 1 and antenna 2, and region II between antenna 2 and antenna 3. The region can be determined by comparing the amplitudes of the received signals from each channel. Specifically, by comparing the amplitudes of the signals received by antenna 1 and antenna 3, a preliminary determination of which region the signal belongs to can be made.
[0055] After determining the signal range, the power ratio of the received signals from the two adjacent antennas within that range is calculated. or This allows for the determination of the precise azimuth angle. Assuming the amplitude comparison and direction finding antenna is a planar helical antenna, when the incident signal is located in interval I, the received signal power of the two antennas can be expressed as:
[0056] (1)
[0057] In the formula The angle between the axes of two adjacent antennas. K is the 3dB beamwidth of half the antenna, and K is a scaling constant.
[0058] The azimuth angle can be solved. The expression is:
[0059] (2)
[0060] in:
[0061] (3)
[0062] Combined direction finding based on full baseline fuzzy number search method
[0063] An interferometer direction-finding system constructed using a 4-element interferometer can obtain 6 baselines of different lengths, namely... , , , , , The expressions for the incident angles of different baselines are as follows, where Indicates the baseline length is The phase difference of the signals received by the two receiving elements corresponding to the baseline at the time of the baseline (less than 2 ), The length of the baseline is The ambiguity number corresponding to the baseline at the time of the baseline:
[0064] (4)
[0065] The direction finding result obtained by using the amplitude comparison direction finding method As a reference value, the difference between the direction finding result of the longest baseline and the reference value is not more than (determined according to the direction finding accuracy of the amplitude comparison direction finding method) as the search range of the ambiguity number
[0066] (5)
[0067] Wherein:
[0068] (6)
[0069] (7)
[0070] The loss function that can optimize the direction finding accuracy is defined , and the angle measurement result of the longest baseline is taken as the reference value :
[0071] (8)
[0072] According to the range of formula (5), the ambiguity number ( is an integer), the ambiguity number of the remaining baseline can be obtained according to formula (9) , and the ambiguity number of the longest baseline at the time of the minimum loss function and the ambiguity number of the remaining baseline can also be obtained, which are taken as the global optimal solution.
[0073] (9)
[0074] In the formula, round is the rounding of the numerical value, that is
[0075] (10)
[0076] According to the ambiguity number of the longest baseline at the time of the minimum loss function , the direction finding results of different baselines can be obtained according to formula (4) and formula (9) The final incident angle can be obtained by removing outliers and calculating a weighted mean value.
[0077] (1) The application designs a direction finding method suitable for high frequency band and large bandwidth signals, and starts from the restriction that the shortest baseline length is less than one-half of the signal wavelength in the direction finding method based on long-short baseline ambiguity resolution, and proposes a combined direction finding algorithm combining three-channel amplitude comparison direction finding and interferometer direction finding for high frequency band signals, and the algorithm has the following advantages:
[0078] ① The full baseline ambiguity number search method is designed, which can be flexibly applied to ambiguity resolution when the interferometer measures the direction of high frequency band signals, and avoids the requirement for the distance between the array elements when resolving ambiguity;
[0079] ② The search range of ambiguity number is reduced by using amplitude comparison direction finding guidance, which improves the algorithm efficiency while improving the ambiguity resolution probability.
[0080] According to the above technology, a specific embodiment is:
[0081] The specific process of the combined direction finding algorithm is shown in .
[0082] Step 1: Select the array element, determine the length of different baselines between the array elements, and obtain the received signals of each array element. In the simulation environment, the number of uniform linear array elements is 4, the array element number is [0, 1, 3, 7], and the spacing is 0.06m;
[0083] Step 2, calculate the amplitude comparison direction finding error
[0084] According to the directivity pattern (as shown in ) of a certain planar spiral antenna, the direction finding error under different angles is calculated. In the simulation environment, the incident angle is-60°~60° (step 1°), the signal-to-noise ratio is 30dB, the frequency is 8GHz~18GHz (step 2GHz), and the axis angle of the three-channel antenna is 60°. The amplitude comparison direction finding error under different frequencies and angles is shown in . It can be seen that the error is maximum when the angle is 0°, so in the simulation environment, the incident angle is 0°, the signal-to-noise ratio is 15dB~30dB (step 1dB), the frequency is 8GHz~18GHz (step 2GHz), and the axis angle of the three-channel antenna is 60°. The direction finding accuracy is shown in . If the signal-to-noise ratio of the amplitude comparison direction finding antenna is greater than 15dB, the standard deviation of the direction finding error is within 7°.
[0085] Step 3: define the ambiguity number of the longest baseline formed by each array element The search boundary is limited by using the amplitude comparison direction finding result as a coarse direction finding result to guide the search range limitation.
[0086] Since the amplitude comparison direction finding has low accuracy, but considering the direction finding variance and direction finding error range, the amplitude comparison direction finding result can be used as a reference value The difference between the direction finding result of the longest baseline in the second step and the reference value is not more than a=10° (appropriately increase the deviation on the basis of a standard deviation of 7° to increase the fault tolerance) as a new search range of the fuzzy number :
[0087] (11)
[0088] Wherein:
[0089] (12)
[0090] (13)
[0091] Fourth step: 20000 times of Monte Carlo calculation are performed according to different baseline lengths to obtain direction finding errors, and the direction finding accuracy variation law of different baseline lengths is obtained by fitting the direction finding errors as shown in , and the weight values of different baseline lengths are obtained as shown in the following formula (wherein is the shortest baseline length, is the i-th baseline length, which is usually a multiple of the short baseline length, is the normalized fitting value of the direction finding error of the i-th baseline, is the weight coefficient of the long baseline when the baseline length is );
[0092] (14)
[0093] (15)
[0094] Fifth step: the fuzzy number of all other baselines is obtained according to the fuzzy number of the longest baseline, and the loss function is defined by the weighted sum of the least square deviation function , the weight is formula (15);
[0095] (16)
[0096]
[0097] Wherein
[0098] (17)
[0099] Step 6: Finally, perform a full baseline fuzzy number search to obtain the fuzzy number that minimizes the loss function, which is then used as the longest baseline. The ambiguity number is obtained, and the ambiguity number of the remaining baselines is obtained from it, so the direction finding results of all baselines can be obtained at the same time;
[0100] Step 7: Calculate the upper and lower bounds of the multi-baseline direction finding results using percentiles, remove outliers from multiple direction finding results, and then calculate the weighted average to obtain the final direction finding result.
[0101] The simulation environment uses a signal frequency of 12GHz, a signal-to-noise ratio of 30dB, a snapshot count of 20, and a direction-finding range of [missing information]. The coarse direction finding results of amplitude comparison direction finding are assumed to be true. Add a Gaussian function with a standard deviation of 7 .
[0102] (18)
[0103] The Monte Carlo method was used to perform 1000 direction-finding calculations for each incident angle (in 1° increments). The direction-finding results were compared with the actual incident angles. If the error was within 2°, the ambiguity was successfully resolved. The resolution probability of this method was then calculated, and the results are shown in the figure. The resolved angle values for each incident angle were then weighted and averaged to obtain the resolved angle values for each incident angle under this method, as shown in the figure. As shown.
[0104] from and It can be seen that the interferometric direction finding guided by amplitude comparison has a high deambiguity probability, and this method is less affected by the incident angle. Therefore, the interferometric direction finding method that uses the amplitude comparison direction finding result as the guiding value and then uses the full baseline ambiguity number search method for deambiguity can efficiently achieve deambiguity and has high direction finding accuracy. The simulation proves the effectiveness of the deambiguity method designed in this paper. The above description is only a specific embodiment of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.
Claims
1. A high-frequency signal combination direction finding method based on the full baseline fuzzy number search method, characterized in that, Step 1: Select any number of array elements of the interferometer direction-finding antenna, calculate the baseline length between all array elements, and obtain the amplitude comparison direction-finding error; Step 2: Determine the fuzzy number of the longest baseline based on the baseline length. The search boundary is determined; the search boundary is narrowed using the amplitude-based direction finding error to obtain the search range; Step 3: Calculate each fuzzy number within the search range The corresponding set of remaining baseline length fuzzy numbers is used to substitute all the sets of baseline length fuzzy numbers into the loss function, and the set of baseline length fuzzy numbers that minimizes the loss function is taken as the optimal fuzzy number set. Step 4: Obtain the direction finding results of all baselines based on the optimal fuzzy number set, and calculate the final incident angle by weighting and averaging all the direction finding results.
2. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 1, characterized in that, Methods for obtaining amplitude comparison and direction finding error include: Step 11: Construct a simulation model of the three-amplitude direction finding system; Step 12: Traverse all incident angles of the three-amplitude direction finding system simulation model, obtain the maximum direction finding error of the three-amplitude direction finding system simulation model among all incident angles, and take the maximum direction finding error as the amplitude-ratio direction finding error.
3. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 1, characterized in that, The expression for the search scope is: ; in, ； ； in, The direction finding results are from amplitude comparison direction finding. This value is determined based on the amplitude-to-direction-finding error.
4. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 3, characterized in that, =Standard deviation of amplitude-based direction finding error + β, where β is a set value.
5. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 1, characterized in that, The expression for the loss function is: （16） The sets of baseline ambiguity numbers are as follows: ； d1-d6 represent all baseline lengths, and k1-k6 represent all baseline ambiguity numbers. In the formula, round represents the rounding of the logarithmic value, i.e. 。 6. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 1, characterized in that, Weight of the i-th baseline length fuzzy number The calculation formula is: ; in, is the normalized fitted value of the direction finding error of the i-th baseline.
7. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 6, characterized in that, The specific steps for weighted averaging of all direction finding results include: The upper and lower bounds of all the direction finding results are calculated using percentiles. Outliers in the direction finding results are removed based on the upper and lower bounds. The direction finding results after removing outliers are weighted. Calculate the weighted mean.
8. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 6, characterized in that, The formula for calculating the angle of incidence is: 。 in Indicates the baseline length is The phase difference (less than 2) of the signals received by the two receiving array elements corresponding to the baseline of the time. ), The baseline length is The fuzzy number corresponding to the baseline at that time.
9. The high-frequency signal combination direction finding method based on the full baseline fuzzy number search method as described in claim 1, characterized in that, The fitting function of the i-th baseline length direction finding error The specific method for obtaining it is as follows: Several Monte Carlo calculations are performed on the i-th baseline length to obtain several direction-finding errors. A fitting function is then obtained by fitting all these direction-finding errors to obtain the direction-finding error for the i-th baseline length. .