Phase interferometer direction finding method based on multi-frequency sparse array

Abstract

This invention discloses a direction finding method based on a multi-frequency sparse array phase interferometer, aiming to solve the technical challenge of fast, high-precision, and unambiguous DOA estimation for broadband signals in scenarios with low signal-to-noise ratio and limited array platform size. The solution includes: 1) constructing an antenna array and channelizing the received broadband signals to obtain sub-band signals at different frequencies; 2) constructing an inter-element coupling matrix, selecting different channelized data based on traditional multi-baseline phase interferometer direction finding rules and mapping them to the same channel; 3) arranging and combining the mapped channel signals with a reference signal to obtain a synthetic signal; 4) calculating the covariance matrix based on the synthetic signal and extracting the phase information of the first row of data; 5) completing DOA estimation based on the phase information using the traditional multi-baseline phase interferometer procedure. This invention effectively reduces the number of physical array elements, reduces inter-element coupling effects, significantly improves direction finding efficiency, and is easy to implement in engineering.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and further relates to passive direction finding technology. Specifically, it is a phase interferometer direction finding method based on a multi-frequency sparse array, which can be used to achieve fast, high-precision and unambiguous direction finding of targets in scenarios where the antenna array arrangement space is limited and the signal-to-noise ratio is low, such as for UAVs. Background Technology

[0002] Radiation source direction finding occupies a core position in the field of array signal processing, and it has broad application prospects in many fields such as radar, wireless communication, and navigation. Phase interferometry, as a typical direction finding method, combines the advantages of high direction finding accuracy, fast response speed, and compact structure. Phase interferometry estimates the angle of arrival of a signal by extracting the phase difference information of the received signals from spatially separated array elements. Single-baseline phase interferometry, as a classic configuration of this technology, is characterized by a small number of receiving channels, but it is difficult to achieve an ideal balance between the success rate of direction finding de-ambiguity resolution and measurement accuracy. In contrast, multi-baseline phase interferometry can effectively improve the success rate of direction finding de-ambiguity resolution while maintaining high direction finding accuracy.

[0003] The most typical array structure of a multi-baseline phase interferometer is the dual-baseline structure, which represents the phase difference between the received signals from different baselines as... ,in Indicates the angle of incidence of the incoming signal. This indicates the wavelength of the incoming signal. Existing technologies similar to this invention include long-short baseline interferometers and coprime baseline interferometers. As classic representatives of multi-baseline phase interferometers, their array structures differ only in the length of the long and short baselines. and The relationships are different. In long-short baseline interferometry, the length of the short baseline... Requirement: less than or equal to This means that the corresponding phase difference will not cause phase blurring, while long baselines Requirements greater than To ensure direction finding accuracy. In a coprime baseline interferometer... and Both require greater than ,and and The elements must be integers and satisfy the coprime relation. For long-short baseline interferometers, when the frequency of the radiation source signal is high, the half-wavelength spacing will be very small, making antenna installation impossible. Even if antenna installation is physically possible, the short element spacing will introduce strong mutual coupling effects. For coprime baseline interferometers, the baselines must strictly maintain a coprime relationship, which limits their application in space-constrained scenarios. Furthermore, both interferometer direction-finding methods require a large number of elements to ensure a high unambiguity resolution success rate.

[0004] In traditional multi-baseline phase interferometers, long-short baseline interferometers are widely used due to their simple structure, low computational complexity, and excellent direction-finding accuracy. However, they require the short baseline length to be less than half the wavelength of the incident signal, and excessively close element spacing can cause strong mutual coupling effects, making them unsuitable for broadband direction-finding systems. Coprime baseline interferometers, by designing different baseline lengths to be coprime and using the remainder theorem to achieve ambiguity-free direction finding, overcome the half-wavelength constraint of the shortest baseline, but impose stringent requirements on the coprimeness of the baseline ratio, greatly limiting the design freedom of the element layout. In addition, existing multi-baseline interferometer algorithms generally suffer from a common drawback: they require the deployment of a large number of physical elements, significantly increasing the hardware load of the direction-finding system.

[0005] Currently, multi-frequency operation modes can construct multiple virtual array elements with a small number of physical array elements, using multi-frequency technology to fill the aperture gaps in sparse arrays, effectively improving the design flexibility of virtual arrays. However, existing solutions mostly use spatial spectrum estimation algorithms for direction finding, and their high computational complexity further exacerbates the computational load of the direction finding system. Subsequent research has focused on the configuration innovation of multi-frequency sparse arrays, but generally neglected the optimization of the computational complexity of the direction finding algorithm itself, making it difficult to meet the real-time and lightweight requirements of engineering applications. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by proposing a direction-finding method based on a multi-frequency sparse array phase interferometer. It aims to solve the technical problem of fast, high-precision, and unambiguous DOA estimation of broadband signals in scenarios with low signal-to-noise ratio and limited array platform size. First, the received broadband signal is channelized to obtain sub-band signals at different frequencies. Then, based on the traditional multi-baseline phase interferometer direction-finding rules, different channelized data are selected and mapped to the same channel, effectively constructing a virtual array receiving signals at the same frequency. Next, the covariance matrix of the received signal is calculated, and the phase information of the first row of data is extracted. Finally, based on the baseline phase difference of the virtual array signal, DOA estimation is completed using the traditional multi-baseline phase interferometer procedure. This invention is not only adaptable to applications with low signal-to-noise ratio and limited platform size, but also effectively reduces the number of physical array elements, reduces inter-element coupling effects, significantly improves direction-finding computation efficiency, and is easier to implement in engineering.

[0007] To achieve the above objectives, the technical solution of the present invention includes the following:

[0008] (1) Constructing a system containing A sparse array of antennas will... The vector form of the broadband signal received by each antenna is as follows:

[0009] ,

[0010] in, This represents N snapshots of a radiation source emitting a broadband signal. Indicates the first The noise component of the signal received by each antenna; Indicates the first The complex exponent of the phase difference between the signals received from the radiation source by each antenna and the first antenna. and These represent the frequency and azimuth angle of the radiation source signal, respectively.

[0011] (2) To The broadband signal received by the antenna is channelized to obtain the signal from the antenna. Vector signal model for each channel:

[0012] ,

[0013] in, express The antenna received the first... One channel signal, Let be the frequency of the i-th channel signal. Total number of channels Represents an array manifold matrix. express The Channel data, express The antenna receives the first... Noise components of the channel signal;

[0014] (3) Construct an inter-element coupling matrix that is only related to the element spacing. :

[0015] ,

[0016] in, , Represents the set of array positions after normalization based on half a wavelength; coupling coefficient , , ..., satisfy B represents the maximum element spacing;

[0017] (4) Based on the coupling matrix between array elements For the The vector signal model of each channel is transformed and expressed in the following form:

[0018] ,

[0019] (5) Select the highest frequency point narrowband signal As a reference signal, in the remaining From the available channels, select one or more channels and map their frequencies uniformly to the corresponding channels. Related equivalent frequency points ,in This represents the frequency scaling factor; the mapped channel signal is combined with the reference signal to obtain the synthesized signal. The virtual array corresponding to the synthesized signal has the same array structure as the traditional multi-baseline phase interferometer direction finding method.

[0020] (6) Based on synthetic signals Calculate its covariance matrix and extract the phase information of the first row of elements in the covariance matrix;

[0021] (7) Based on the phase information and the traditional multi-baseline array structure corresponding to the virtual array, the direction finding method of the corresponding phase interferometer is used to realize the unambiguous direction estimation of the incoming wave.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] First, because this invention maps channelized data from different frequency points to the same frequency point, it effectively constructs a single-frequency signal received by a virtual array, thus overcoming the constraints of traditional multi-baseline interferometers on the number of physical array elements and array size. Even in scenarios with limited platform size and limited space for array element deployment, the direction-finding performance of an equivalent large-aperture array can still be achieved with a small number of physical array elements, significantly reducing system hardware costs and array deployment difficulty.

[0024] Secondly, the present invention adopts a sparse physical array design, which significantly increases the spacing between array elements. This effectively weakens the electromagnetic mutual coupling effect between array elements and avoids the problem of deterioration in direction finding accuracy caused by mutual coupling in traditional dense arrays. This feature is particularly critical in broadband and high-power signal scenarios, greatly improving the stability and reliability of the direction finding system in complex electromagnetic environments and making it easier to deploy in engineering.

[0025] Third, the phase difference of the received signals of different virtual array elements is obtained by extracting the covariance phase of the received signal, thus making it applicable to low signal-to-noise ratio situations.

[0026] Fourth, because the present invention extracts the phase information of the covariance matrix of the received signal of the virtual array during signal processing and uses the statistical averaging characteristics of the covariance matrix to suppress noise interference, it can stably obtain high-precision phase difference information under low signal-to-noise ratio conditions. This solves the problem that traditional interferometer direction finding methods are easily contaminated by noise and suffer a sharp drop in direction finding accuracy in weak signal scenarios, and expands the applicable signal-to-noise ratio range of the direction finding system.

[0027] Fifth, this invention adopts the mature multi-baseline phase interferometer direction finding framework, avoiding the complex matrix decomposition and spectral peak search operations in the spatial spectrum estimation algorithm, significantly reducing the computational complexity of the direction finding algorithm, enabling fast real-time processing of broadband signals, and better meeting the core requirements of real-time performance and lightweight design for direction finding systems in engineering applications. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0029] Figure 2 This is a schematic diagram of the single-baseline array structure in this invention;

[0030] Figure 3 This is a schematic diagram of the array geometry of different baselines provided in the embodiments of the present invention;

[0031] Figure 4 This is a graph showing the relationship between the accuracy of DOA estimation without mutual coupling effect and the signal-to-noise ratio using the method of this invention.

[0032] Figure 5 The graph shows the relationship between the unambiguous DOA estimation success rate and the signal-to-noise ratio using the method of this invention;

[0033] Figure 6 This is a graph showing the relationship between the accuracy of DOA estimation with mutual coupling effect and the signal-to-noise ratio using the method of this invention.

[0034] Figure 7 The graph shows the relationship between the success rate of unfuzzing DOA estimation with mutual coupling effect and the signal-to-noise ratio using the method of this invention. Detailed Implementation

[0035] The effects of the present invention will be further explained below with reference to simulation experiments.

[0036] Example 1: Refer to Appendix Figure 1 The present invention proposes a phase interferometer direction finding method based on a multi-frequency sparse array, which specifically includes the following steps:

[0037] Step 1) Constructing a system containing A sparse array of antennas will... The vector form of the broadband signal received by each antenna is as follows:

[0038] ,

[0039] in, This represents N snapshots of a radiation source emitting a broadband signal. Indicates the first The noise component of the signal received by each antenna; Indicates the first The complex exponent of the phase difference between the signals received from the radiation source by each antenna and the first antenna. and These represent the frequency and azimuth angle of the radiation source signal, respectively.

[0040] Step 2) The broadband signal received by the antenna is channelized to obtain the signal from the antenna. Vector signal model for each channel:

[0041] ,

[0042] in, express The antenna received the first... One channel signal, Let be the frequency of the i-th channel signal. Total number of channels Represents an array manifold matrix. express The Channel data, express The antenna receives the first... Noise components of the channel signal;

[0043] Step 3) Construct an inter-element coupling matrix that is only related to the element spacing. :

[0044] ,

[0045] in, , Represents the set of array positions after normalization based on half a wavelength; coupling coefficient , , ..., satisfy B represents the maximum element spacing;

[0046] Step 4) Based on the coupling matrix between array elements For the The vector signal model of each channel is transformed and expressed in the following form:

[0047] ,

[0048] Step 5) Select the highest frequency point narrowband signal As a reference signal, in the remaining From the available channels, select one or more channels and map their frequencies uniformly to the corresponding channels. Related equivalent frequency points ,in This represents the frequency scaling factor; the mapped channel signal is combined with the reference signal to obtain the synthesized signal. The virtual array corresponding to the synthesized signal has the same array structure as the traditional multi-baseline phase interferometer direction finding method. The traditional multi-baseline phase interferometer direction finding method mentioned here adopts any one of the direction finding methods, including long and short baseline phase interferometers, coprime baseline phase interferometers, and virtual baseline phase interferometers.

[0049] In this embodiment, the frequency scaling factor mentioned above, by combining the phase difference expression, transforms the frequency difference into an array structure difference, obtaining the original array structure. The received signal corresponds to the scaled virtual subarray; the original array and the virtual subarray are arranged according to the element position and size to obtain the virtual array; the reference signal and the selected channel signal are arranged and combined in the same way to obtain the composite signal. In this embodiment, the phase difference expression is as follows: Where c represents the speed of electromagnetic wave propagation in air. Indicates the length of the physical baseline.

[0050] Step 6) Based on the synthesized signal Calculate its covariance matrix and extract the phase information of the first row of elements in the covariance matrix;

[0051] Step 7) Based on the phase information and the traditional multi-baseline array structure corresponding to the virtual array, the direction-finding method of the corresponding phase interferometer is used to achieve unambiguous estimation of the direction of arrival of the wave.

[0052] Example 2: The overall implementation steps of the direction finding method proposed in this example are the same as those in Example 1. Now, the process of achieving unambiguous arrival direction estimation using the long and short baseline phase interferometer-based direction finding method in the traditional multi-baseline phase interferometer direction finding method will be described in further detail.

[0053] Step a1. The array structure based on the long-short baseline phase interferometer direction finding method is set by the following formula. Select the range and construct a virtual short baseline:

[0054] ,

[0055] in, Indicates the length of the physical baseline.

[0056] Step a2. According to Select channel data, according to the virtual array structure and the original narrowband signal. By performing permutations and combinations, the corresponding virtual array receiving frequency points are obtained. Synthetic signal Based on this synthesized signal Calculate its covariance matrix and extract the short baseline phase difference from the elements in the first row of the covariance matrix:

[0057] ;

[0058] in, This represents the theoretically unambiguous phase difference for long baselines;

[0059] Step a3. The ambiguity of a long baseline with a blurred phase difference is represented as follows:

[0060] ;

[0061] in, The long baseline indicates an ambiguous phase difference;

[0062] Step a4. Recover the unambiguous phase difference of the long baseline according to the following formula:

[0063] ;

[0064] Step a5. Obtain the unambiguous direction finding results:

[0065] .

[0066] Example 3: The overall implementation steps of the direction finding method proposed in this example are the same as those in Example 1. Now, the process of achieving unambiguous arrival direction estimation using the coprime baseline phase interferometer-based direction finding method in the traditional multi-baseline phase interferometer direction finding method will be described in further detail.

[0067] Step b1. Based on the coprime baseline phase interferometer direction finding method, the array structure is selected by... Construct a virtual coprime baseline, where Conditions met:

[0068] ,

[0069] in, This represents the physical baseline length, and this length is an integer multiple of half the wavelength; This represents the greatest common divisor.

[0070] Step b2. According to Select channel data, according to the virtual array structure and the original narrowband signal. By performing permutations and combinations, the corresponding virtual array receiving frequency points are obtained. Synthetic signal Based on this synthesized signal Calculate its covariance matrix and extract the phase information from the elements in the first row of the covariance matrix, including the blurred phase difference of short baselines in coprime baselines. There is an ambiguous phase difference with the long baseline. :

[0071] ;

[0072] ;

[0073] in, and These represent unambiguous phase differences between short and long baselines in coprime baselines, respectively. and They represent and ambiguity;

[0074] Step b3. Define unambiguous phase difference for short baselines in coprime baselines. Unambiguous phase difference with long baseline The expression is as follows:

[0075] ;

[0076] ;

[0077] in, It is a scaling factor expressed as the ratio of coprime integers; and All are integers and are relatively prime.

[0078] Step b4. Establish a linear Diophantine equation regarding ambiguity:

[0079] ;

[0080] Step b5. Based on the general solution property of this equation, combined with fuzzy phase difference... and The ambiguity is obtained by solving. and To eliminate phase ambiguity and restore the true phase difference, the unambiguous azimuth angle of the incoming wave is finally calculated. , and complete the direction finding.

[0081] Example 4: The overall implementation steps of the direction finding method proposed in this example are the same as in Example 1, and will now be referred to... Figure 2 The overall implementation process of the present invention will be described in further detail.

[0082] Suppose a sparse array with M elements receives a broadband signal. After channelization, the frequency of the i-th signal is... ,in This indicates the number of narrowband signals. The received signal for this channel is represented as:

[0083] ,

[0084] in, Represents an array manifold matrix. express The Channel data, This indicates that M antenna array elements receive the first... The noise component of the channel signal.

[0085] The above expression for the received signal assumes that the array elements do not interfere with each other. However, in real-world scenarios, the output of any array element will be affected by its neighboring elements; this is called mutual coupling. Considering the mutual coupling effect between array elements, it can be transformed into the following equation:

[0086] ,

[0087] in, The coupling matrix between array elements is determined solely by the element spacing.

[0088] ,

[0089] in, and The coupling coefficient represents the element positions of the physical array after normalization based on half a wavelength; , , ..., satisfy B represents the maximum element spacing.

[0090] To reduce the noise sensitivity of the interferometer direction finding system, the covariance of the received signal vector matrix of the physical array is calculated, and the phase of different elements is extracted according to the array structure to obtain the phase difference corresponding to different baselines.

[0091] Reference Figure 2 The single-baseline interferometer direction-finding array configuration shown below represents the true phase difference as follows:

[0092] ;

[0093] make ,but: ;

[0094] in, Indicates the highest frequency of the received signal. Indicates the frequency selection coefficient. By scaling the physical baseline using different frequency points, multiple virtual baselines can be constructed; that is, by setting... By using numerical values, virtual baseline structures in the form of long and short baselines and coprime baselines are constructed, thereby achieving high-precision, unambiguous direction finding.

[0095] Example 5: The overall implementation process of the direction finding method proposed in this example is the same as that of the previous examples. Please refer to the appendix for details. Figure 3 Provide examples to further describe how to set The numerical values ​​are used to construct a virtual baseline structure of long and short baselines and coprime baselines to achieve high-precision, unambiguous direction finding.

[0096] (a) Constructing a virtual long-short baseline interferometer:

[0097] According to the principle of long and short baseline interferometry, the maximum baseline length of a short baseline is: Therefore, in order to construct a virtual short baseline, The selection range is: ;

[0098] make The phase difference of the short baseline at this time is expressed as follows:

[0099] ;

[0100] in, This represents the theoretically unambiguous phase difference of a long baseline; therefore, the ambiguity of a long baseline with an ambiguous phase difference is expressed as:

[0101] ;

[0102] in, This represents the output of the long baseline phase comparator.

[0103] The unambiguous phase difference of the long baseline can be recovered using the following formula:

[0104] ;

[0105] Unambiguous direction finding results obtained:

[0106] ;

[0107] (II) Constructing a virtual coprime baseline interferometer:

[0108] Referring to the principle of the virtual long and short baseline interferometer described above, by selecting Construct a virtual coprime baseline, where the physical baseline length is... for Integer multiples of.

[0109] The unambiguous phase differences of the virtual coprime baselines are respectively

[0110] ;

[0111] ;

[0112] Assuming the ambiguous phase differences between the short and long baselines of the virtual coprime baseline are respectively... and ,but:

[0113] ;

[0114] ;

[0115] in, and They represent and The degree of ambiguity.

[0116] make ,in and All are integers and are coprime; substituting them into... After simplification, we get the following expression:

[0117] ;

[0118] The above formula shows that when and When it is a solution to the equation, and Similarly, these are solutions to the same equation, where It is an integer; because and Coprime, thus obtaining and The only solution.

[0119] Traditional multi-baseline phase interferometer direction finding methods require a large number of physical array elements to ensure a high success rate in unambiguity resolution. In contrast, the method proposed in this invention, theoretically, requires only two physical array elements to obtain a large number of virtual array elements when there are a sufficient number of frequency points and a sufficiently large signal bandwidth. In practical applications, by appropriately selecting the number of frequency points and the number of physical array elements, a balance between low cost, low complexity, and high direction finding accuracy can be achieved.

[0120] The effects of the present invention will be further explained below with reference to simulation experiments.

[0121] 1. Simulation conditions:

[0122] The simulation experiments of this invention were conducted in the MATLAB 2024a software environment.

[0123] 2. Simulation content:

[0124] This section showcases the direction-finding performance of the multi-frequency virtual multi-baseline deambiguity algorithm, comparing it with the long-short baseline method and the coprime baseline method (collectively referred to as the traditional method). The simulation experiments are divided into two parts: Simulation 1 compares the direction-finding accuracy and deambiguity probability of each method under different signal-to-noise ratios without considering the mutual coupling effect; Simulation 2 repeats the above comparison experiment after introducing the mutual coupling effect. The direction-finding accuracy comparison is demonstrated through the root mean square error (RMSE) of multiple unambiguous estimation results.

[0125] Simulation 1: Comparison of direction finding performance under different signal-to-noise ratios without mutual coupling effect

[0126] Assuming the maximum frequency of the broadband signal emitted by a single radiation source is 6 GHz, the bandwidth is sufficiently large, the direction of arrival is 60°, the positions of the three array elements are [0, 0.25, 0.5] m, the signal-to-noise ratio (SNR) range is (-10:2:10) dB, and the number of snapshots N = 500. For a virtual long-short baseline interferometer, calculations show that the baseline length for unambiguous direction finding is 0.025 m. Therefore, in this experiment, we choose... For a virtual coprime baseline interferometer, the baseline ratio is set to 7 / 10, i.e. In contrast, both the long / short baseline method and the coprime baseline method construct a receiving array with 5 elements, positioned at [0, 0.225, 0.25, 0.45, 0.5] m and [0, 0.175, 0.25, 0.35, 0.5] m respectively, consistent with the element positions of the virtual long / short baseline and virtual coprime baseline methods. The specific array structure is as follows... Figure 3 As shown. Under 1000 Monte Carlo experiments, the RMSE and unambiguity resolution success rates of the direction finding results are as follows: Figure 4 and Figure 5 As shown.

[0127] Simulation 2: Comparison of direction finding performance under different signal-to-noise ratios with mutual coupling effect

[0128] In this experiment, the basic simulation conditions remain the same as in Simulation 1. The difference is the addition of a cross-coupling matrix. The elements of the cross-coupling matrix are set to... , ,in, After 1000 Monte Carlo experiments, the RMSE and unambiguity resolution success rates of the direction finding results are as follows: Figure 6 and Figure 7 As shown.

[0129] 3. Simulation Result Analysis:

[0130] Figure 3The present invention includes traditional long and short baseline interferometer array structures, coprime baseline interferometer array structures, multi-frequency sparse physical array structures, and virtual long and short baseline interferometer array structures and virtual coprime baseline interferometer array structures obtained by the method of the present invention. It can be seen that by using three physical array elements and combining the method of the present invention, the virtual array obtained is equivalent to the traditional multi-baseline interferometer array structure, and theoretically, it can obtain comparable direction finding performance.

[0131] Figure 4 The comparison of direction-finding accuracy under different signal-to-noise ratios (SNRs) without mutual coupling effects shows that the DOA estimation accuracy of all methods gradually increases with increasing SNR. Across the entire SNR range, the direction-finding accuracy of the multi-frequency virtual multi-baseline interferometer method is essentially consistent with that of the corresponding physical multi-baseline interferometer method.

[0132] Figure 5 The comparison of direction-finding deambiguity success rates under different signal-to-noise ratios (SNRs) without mutual coupling effects shows that the DOA estimation deambiguity success rates of all methods gradually increase with increasing SNR. When the SNR is -2dB, the deambiguity success rate of all methods reaches 100%. Across the entire SNR range, the direction-finding deambiguity success rates of the multi-frequency virtual multi-baseline interferometer method and its corresponding physical multi-baseline interferometer method are essentially consistent.

[0133] Figure 6 The comparison of direction-finding accuracy under different signal-to-noise ratios with mutual coupling effects reveals that the introduction of mutual coupling effects significantly alters the direction-finding accuracy of the proposed method compared to traditional methods. Specifically, due to the half-wavelength element spacing, the long-short baseline interferometer exhibits significantly lower direction-finding accuracy across the entire signal-to-noise ratio range compared to the virtual long-short baseline interferometer. In contrast, the direction-finding accuracy of the coprime baseline interferometer is only slightly lower than that of the virtual coprime baseline interferometer, as its larger element spacing mitigates the impact of mutual coupling effects to some extent. Nevertheless, the coprime baseline interferometer requires more physical sensors, highlighting the practical advantages of the virtual coprime baseline interferometer.

[0134] Figure 7 The comparison of direction-finding deambiguity success rates under different signal-to-noise ratios with mutual coupling effects shows that the mutual coupling effect also leads to differences in the direction-finding deambiguity success rates of different methods. In this case, the unambiguity probability of the long-short baseline interferometer is significantly lower than that of the virtual long-short baseline interferometer. Furthermore, the larger element spacing also weakens the impact of mutual coupling effects on the direction-finding unambiguity success rate of the coprime baseline interferometer. Therefore, the advantage of the method in this invention compared to the coprime baseline interferometer mainly lies in reducing the use of physical array elements.

[0135] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, use and processing of the relevant data must comply with the laws, regulations and standards of the relevant countries and regions, and corresponding operation portals are provided for users to choose to authorize or refuse.

[0136] The above simulation analysis proves the correctness and effectiveness of the method proposed in this invention.

[0137] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and detail without departing from the principle and structure of the present invention. However, these modifications and changes based on the concept of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A direction finding method for a phase interferometer based on a multi-frequency sparse array, characterized in that, Includes the following steps: (1) Constructing a system containing A sparse array of antennas will... The vector representation of broadband signals received by an antenna is as follows: ， in, This represents N snapshots of a radiation source emitting a broadband signal. Indicates the first The noise component of the signal received by each antenna; Indicates the first The complex exponent of the phase difference between the signals received from the radiation source by each antenna and the first antenna. and These represent the frequency and azimuth angle of the radiation source signal, respectively. (2) To The broadband signal received by the antenna is channelized to obtain the signal from the antenna. Vector signal model for each channel: ， in, express The antenna received the first... One channel signal, Let be the frequency of the i-th channel signal. Total number of channels Represents an array manifold matrix. express The Channel data, express The antenna receives the first... Noise components of the channel signal; (3) Construct an inter-element coupling matrix that is only related to the element spacing. : ， in, , Represents the set of array positions after normalization based on half a wavelength; coupling coefficient , , ..., satisfy B represents the maximum element spacing; (4) Based on the coupling matrix between array elements For the first The vector signal model of each channel is transformed and expressed in the following form: ， (5) Select the highest frequency point narrowband signal As a reference signal, in the remaining From the available channels, select one or more channels and map their frequencies uniformly to the corresponding channels. Related equivalent frequency points ,in This represents the frequency scaling factor; the mapped channel signal is combined with the reference signal to obtain the synthesized signal. The virtual array corresponding to the synthesized signal has the same array structure as the traditional multi-baseline phase interferometer direction finding method. (6) Based on synthetic signals Calculate its covariance matrix and extract the phase information of the first row of elements in the covariance matrix; (7) Based on the phase information and the traditional multi-baseline array structure corresponding to the virtual array, the direction finding method of the corresponding phase interferometer is used to realize the unambiguous direction estimation of the incoming wave.

2. The method according to claim 1, characterized in that: The frequency scaling factor, by combining the phase difference expression, transforms the frequency difference into an array structure difference, obtaining the original array structure. The received signal corresponds to the scaled virtual subarray; the original array and the virtual subarray are arranged according to the element position and size to obtain the virtual array; the reference signal and the selected channel signal are arranged and combined in the same way to obtain the composite signal. .

3. The method according to claim 2, characterized in that: The phase difference expression is as follows: ， Where c represents the speed of electromagnetic wave propagation in air. Indicates the length of the physical baseline.

4. The method according to claim 1, characterized in that: The traditional multi-baseline phase interferometer direction finding method described in step (5) includes at least the long and short baseline phase interferometer direction finding method and the coprime baseline phase interferometer direction finding method.

5. The method according to claim 4, characterized in that: Based on the array structure of the long-short baseline phase interferometer direction finding method, the following formula is used to set... Selecting the range to construct a virtual short baseline: ， in, Indicates the length of the physical baseline.

6. The method according to claim 5, characterized in that: The phase information mentioned in step (6) specifically refers to the short baseline phase difference, as shown below: ； in, This represents the theoretically unambiguous phase difference for long baselines.

7. The method according to claim 6, characterized in that: The corresponding phase interferometer direction finding method mentioned in step (7) is a long-short baseline phase interferometer direction finding method, which specifically achieves unambiguous arrival direction estimation in the following way: (7a1) The ambiguity of a long baseline with an ambiguous phase difference is represented as follows: ； in, The long baseline indicates an ambiguous phase difference; (7a2) The unambiguous phase difference of the long baseline is recovered according to the following formula: ； (7a3) The unambiguous direction finding results obtained: 。 8. The method according to claim 4, characterized in that: Based on the array structure of the coprime baseline phase interferometer direction finding method, by selecting... Construct a virtual coprime baseline, where Conditions met: ， in, This represents the physical baseline length, and this length is an integer multiple of half the wavelength; This represents the greatest common divisor.

9. The method according to claim 8, characterized in that: The phase information mentioned in step (6) includes the fuzzy phase difference between short baselines in coprime baselines. There is an ambiguous phase difference with the long baseline. : ； ； in, and These represent unambiguous phase differences between short and long baselines in coprime baselines, respectively. and They represent and The degree of ambiguity.

10. The method according to claim 9, characterized in that: The corresponding phase interferometer direction finding method described in step (7) is a coprime baseline phase interferometer direction finding method, which achieves unambiguous arrival direction estimation in the following manner: (7b1) Define the unambiguous phase difference of short baselines in coprime baselines. Unambiguous phase difference with long baseline The expression is as follows: ； ； in, It is a scaling factor expressed as the ratio of coprime integers; and All are integers and are relatively prime. (7b2) Establish a linear Diophantine equation regarding ambiguity: ； (7b3) Based on the general solution property of this equation, combined with fuzzy phase difference and The ambiguity is obtained by solving. and To eliminate phase ambiguity and restore the true phase difference, the unambiguous azimuth angle of the incoming wave is finally calculated. , and complete the direction finding.

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