Double-frequency bee colony array error multi-domain joint correction system

Abstract

The invention discloses a double-frequency bee colony array error multi-domain joint correction system, which belongs to the technical field of radar signal processing, and is characterized in that correction signals of a plurality of correction sources are obtained through time diversity, and each correction source transmits the correction signals to a bee colony array of which the position error exceeds half-wavelength through two carrier frequencies; estimating actual steering vectors of the two carrier frequencies by adopting a simplified SMSWF method; based on the actual steering vectors of the two carrier frequencies, calculating a position error by adopting an equivalent frequency method to obtain an array element position error parameter estimation value; after array element position information is updated by adopting an array element position error parameter estimation value, a position error, a phase error and a communication time delay error are estimated by respectively utilizing receiving signals of two carrier frequencies, and the error joint correction of the bee colony array of which the position error exceeds half wavelength is completed. According to the dual-frequency position error estimation based on the equivalent frequency method, the large error estimation range of the dual-frequency method is fully utilized, the advantage of high error estimation precision of a traditional method is kept, and the error is successfully corrected when the position error exceeds half wavelength.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a dual-frequency swarm array error multi-domain joint correction system. Background Art

[0002] In a swarm, the position of each drone is traditionally determined primarily by GPS positioning. Due to positioning accuracy limitations, the operating frequency band of swarm flexible arrays cannot exceed 150 MHz. Otherwise, array position errors exceeding half a wavelength will result in phase aliasing, making correction difficult. Traditional antenna array error correction methods are complex enough to correct position errors exceeding half a wavelength; lower-complexity methods cannot handle array errors exceeding half a wavelength.

[0003] Existing real-time array position error correction methods primarily rely on single-frequency active correction. This type of active real-time array error correction technology first requires accurate extraction of the actual steering vector. Zhang Ke et al. used the eigendecomposition method to extract the steering vector, achieving joint correction of array amplitude, phase, and position errors. To address the high computational complexity of the eigendecomposition method, Yuan Chunshan et al. used the simplified multi-stage Wiener filter (SMSWF) method to extract the steering vector, achieving joint correction of array element position and amplitude and phase errors. Among self-correction methods, Peng Wencan et al. proposed a gridless sparse self-correction algorithm for amplitude and phase errors, which is used to correct the amplitude and phase errors of a partially corrected array.

[0004] Among the existing methods, the active correction method only has single-frequency correction, which makes it difficult to correct position errors exceeding half a wavelength; the passive correction method not only has high computational complexity, but may also fall into a local optimal solution, resulting in correction failure. Summary of the Invention

[0005] The present invention aims to overcome the difficulty of existing methods in correcting position errors exceeding half a wavelength. It proposes a dual-frequency swarm array error multi-domain joint correction system. This system is suitable for joint correction of array phase, position, and communication delay errors in new distributed arrays, such as swarm flexible arrays.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a dual-frequency swarm array error multi-domain joint correction method, comprising the following steps: Correction signals from multiple correction sources are obtained through time diversity, with each correction source transmitting correction signals at two carrier frequencies to a swarm array with a position error exceeding half a wavelength; The simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies; Based on the actual steering vectors of the two carrier frequencies, the position error is calculated using the equivalent frequency method to obtain the estimated value of the array element position error parameter; After updating the array element position information using the estimated value of the array element position error parameter, the position error, phase error and communication delay error are estimated using the received signals of the two carrier frequencies respectively, completing the joint error correction of the swarm array with a position error exceeding half a wavelength.

[0007] Further, the plurality of correction sources include correction sources placed at four different orientations in the far field of the swarm array with a position error exceeding half a wavelength; Phase error received The correction source signal is shown as follows:

[0008]

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] in, The phase error is the received A correction source signal, is the phase and communication delay error -dimensional diagonal matrix, is the array element position error matrix, for dimensional Gaussian white noise data vector; is the steering vector of the th signal source; is the position of the element of the swarm array whose position error exceeds half wavelength, is the position error of the swarm array whose position error exceeds half a wavelength, is the phase error of the swarm array whose position error exceeds half a wavelength, is the communication delay error of the swarm array whose position error exceeds half a wavelength; Indicates the total number of array elements; For the The pitch angle of the correction source, For the The azimuth of the correction source, For the The signal power of a correction source is, For the The noise power of a correction source is, For the The emission signal of a correction source; is the first carrier frequency, The second carrier frequency.

[0016] Furthermore, a simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies. Specifically, the simplified SMSWF method is used to directly calculate the normalized multi-stage Wiener filter coefficients of the signal subspace, and the multi-stage Wiener filter coefficients are used as the actual steering vectors.

[0017] Furthermore, based on the actual steering vectors of the two carrier frequencies, the position error is calculated using the equivalent frequency method to obtain the estimated value of the array element position error parameter, specifically: The equivalent frequency and equivalent wavelength are used to express the The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the The result of dividing the corresponding elements of the normalized multi-stage Wiener filter coefficients of the second carrier frequency of the correction source; Taking the phase of the ratio of the corresponding elements in the actual steering vector and the ideal steering vector; Based on the phase and the least squares principle, the estimated value of the array element position error parameter is obtained.

[0018] Furthermore, after updating the array element position information using the estimated value of the array element position error parameter, the position error, phase error, and communication delay error are estimated using the received signals of the two carrier frequencies, specifically: The theoretical position is updated using the estimated values ​​of the array element position error parameters, and the position error and phase error are calculated using the normalized multi-stage Wiener filter coefficients of two frequencies according to the single-frequency method. The phase of the ratio of the actual steering vector to the corresponding element in the updated ideal steering vector under the preset total phase error at the two carrier frequencies is respectively calculated; based on the phase, two position error estimates are obtained from the two carrier frequencies according to the least squares principle; and the two position error estimates are averaged to obtain a residual position error estimate; The total phase error corresponding to the two carrier frequencies is obtained by using the two position error estimates and phase calculation; The total phase errors corresponding to the two carrier frequencies are combined with the preset total phase errors under the two carrier frequencies to obtain a delay error estimate and a phase error estimate; The total position error estimate is the sum of the array element position error parameter estimate and the residual position error estimate.

[0019] Furthermore, the equivalent frequency and equivalent wavelength are used to express the The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the The result of dividing the corresponding elements of the normalized multi-stage Wiener filter coefficients of the second carrier frequency of the correction source is as follows:

[0020]

[0021]

[0022] in, express The result of dividing corresponding elements, Indicates the The first carrier frequency of the correction source Normalized multi-stage Wiener filter coefficients, Indicates the Correction source second carrier frequency Normalized multi-stage Wiener filter coefficients, is the equivalent frequency, is the equivalent wavelength; The phase of the ratio of the corresponding elements in the actual steering vector and the ideal steering vector is taken as follows:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] in, represents the ideal equivalent steering vector, The actual steering vector and The ratio of the corresponding elements in ; express Phase; Based on the phase and the least squares principle, the estimated value of the array element position error parameter is obtained, as shown in the following formula:

[0030] in, Represents the estimated value of the array element position error parameter.

[0031] Furthermore, the theoretical position is updated using the estimated value of the array element position error parameter, as shown in the following formula:

[0032] The phase of the ratio of the actual steering vector to the corresponding element in the updated ideal steering vector under the preset total phase error at the two carrier frequencies is taken. Based on the phase and the least squares principle, two position error estimates are obtained from the two carrier frequencies, as shown in the following formula:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] The remaining position error estimate is obtained by averaging the two position error estimates as follows:

[0039]

[0040]

[0041] The total phase error corresponding to the two carrier frequencies is obtained by using the two position error estimates and phase calculation, as shown in the following formula:

[0042]

[0043] The total position error estimate is the sum of the array element position error parameter estimate and the residual position error estimate, as shown in the following formula:

[0044]

[0045] in, represents the updated theoretical position, is the total position error estimate, is the estimated value of the residual position error, represents the remaining phase error; Indicates the first carrier frequency The ratio of the corresponding elements in the actual steering vector to the ideal steering vector, Indicates the second carrier frequency The ratio of the corresponding elements in the actual steering vector to the ideal steering vector, Indicates the first carrier frequency The total phase error under the preset Indicates the second carrier frequency The preset total phase error under represents the phase error, Indicates the delay error; express The phase, express The phase, represents the total phase error of the first carrier frequency, Indicates the total phase error of the second carrier frequency.

[0046] In a second aspect, the present invention provides a dual-frequency swarm array error multi-domain joint correction system, comprising: A correction signal transmission module is used to obtain correction signals from multiple correction sources through time diversity, and each correction source transmits a correction signal at two carrier frequencies to a swarm array with a position error exceeding half a wavelength; An actual steering vector estimation module, used to estimate the actual steering vectors of two carrier frequencies using a simplified SMSWF method; A position error estimation module is used to calculate the position error based on the actual steering vectors of the two carrier frequencies using the equivalent frequency method to obtain an estimated value of the array element position error parameter; The error estimation and correction module is used to update the array element position information using the estimated value of the array element position error parameter, and then use the received signals of the two carrier frequencies to estimate the position error, phase error and communication delay error, and complete the joint error correction of the swarm array with a position error exceeding half a wavelength.

[0047] In a third aspect, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the dual-frequency swarm array error multi-domain joint correction method when executing the computer program.

[0048] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, and the method for multi-domain joint correction of dual-frequency swarm array errors when the computer program is executed by a processor.

[0049] Compared with the prior art, the present invention has the following beneficial technical effects: The proposed dual-frequency swarm array error multi-domain joint correction method provides a joint correction method for array position, phase, and communication delay errors when element position errors exceed half a wavelength. This method, based on the equivalent frequency method for dual-frequency position error estimation, leverages the large error estimation range of the dual-frequency method while retaining the high error estimation accuracy of traditional methods, successfully correcting errors even when position errors exceed half a wavelength. A multi-order Wiener filter (SMSWF) method is used to extract the steering vectors corresponding to the two carrier frequencies. For position errors exceeding half a wavelength that cannot be corrected, the equivalent frequency method is used to reduce the position error to within half a wavelength. After updating the position information, a single-frequency method can be used to accurately correct each error. By incorporating the dual-frequency method into array error correction, this method achieves an error correction range exceeding the half-wavelength limit. In practical applications, this method effectively avoids the difficulty in correcting swarm flexible array errors due to insufficient GPS positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the present invention in any way. In addition, the shapes and proportional dimensions of the components in the drawings are only schematic and are used to help understand the present invention, and are not intended to specifically limit the shapes and proportional dimensions of the components of the present invention. In the drawings: Figure 1 This is a flow chart of the dual-frequency swarm array error multi-domain joint correction method of the present invention.

[0051] Figure 2 This is a structural diagram of the dual-frequency swarm array error multi-domain joint correction system of the present invention.

[0052] Figure 3 This is a diagram of the electronic equipment for the dual-frequency swarm array error multi-domain joint correction method of the present invention.

[0053] Figure 4 The figure shows a comparison between the array element positions before and after correction and the ideal array element positions in an embodiment of the present invention.

[0054] Figure 5 This is the position error estimation error situation in the embodiment of the present invention.

[0055] Figure 6 1 is a comparison between the actual delay error and the corrected delay error in an embodiment of the present invention.

[0056] Figure 7 is the delay error estimation error in the embodiment of the present invention.

[0057] Figure 8 3 is a comparison between the actual phase difference and the corrected phase error in an embodiment of the present invention.

[0058] Figure 9 is the phase error estimation error in the embodiment of the present invention.

[0059] Figure 10 This is the position error correction effect of the single-frequency method when the position error exceeds half a wavelength in an embodiment of the present invention.

[0060] Figure 11 This is the result of the joint correction of the communication delay and phase error using the single-frequency method when the position error exceeds half a wavelength in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0062] Example 1 See also Figure 1 The dual-frequency swarm array error multi-domain joint correction method includes the following steps: Correction signals from multiple correction sources are obtained through time diversity, with each correction source transmitting correction signals at two carrier frequencies to a swarm array with a position error exceeding half a wavelength; The simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies; Based on the actual steering vectors of the two carrier frequencies, the position error is calculated using the equivalent frequency method to obtain the estimated value of the array element position error parameter; After updating the array element position information using the estimated value of the array element position error parameter, the position error, phase error and communication delay error are estimated using the received signals of the two carrier frequencies respectively, completing the joint error correction of the swarm array with a position error exceeding half a wavelength.

[0063] In acquiring correction signals, this embodiment uses time diversity to allow multiple correction sources to transmit at dual carrier frequencies, enriching signal sources and frequency band coverage and enhancing adaptability to different scenarios. A simplified SMSWF method is used to estimate the actual steering vector, which not only reduces computational complexity and improves operational efficiency, but also effectively suppresses interference and ensures estimation accuracy. The equivalent frequency method is used to calculate position errors, breaking through the limitations of traditional methods in handling large position errors (exceeding half a wavelength) and improving the accuracy of position error parameter estimation. Finally, a joint error correction is performed, comprehensively considering multiple error factors such as position, phase, and communication delay to achieve comprehensive and integrated correction, avoiding the shortcomings of single error correction. The method of this embodiment can effectively improve the communication quality, signal processing capabilities, and target detection accuracy of the swarm array system performance, meeting the needs of application scenarios with high real-time requirements.

[0064] Multiple correction source signals are obtained through time diversity, and the simplified multi-stage Wiener filter (SMSWF) method is used to estimate the steering vectors of the two frequencies. The equivalent frequency method is then used to calculate the position error. After the estimated results are used to update the array element position information, the position, phase, and communication delay errors are accurately estimated using the received signals of the two frequencies. The specific implementation is as follows: Step 1: Receive signal model establishment This embodiment is mainly used for joint correction of multiple errors of a swarm array with position error exceeding half a wavelength.

[0065] Consider the entire array has Array element, The position of the array element is The position error is expressed as The phase error is expressed as The delay error is expressed as express.

[0066] The element position of the entire array is , position error , phase error Communication delay error They can be expressed as: (1) (2) (3) (4) The correction is performed using correction sources placed at four different positions in the array far field. The pitch angle of the correction source is , azimuth is , the signal power is , the noise power is , the emission signal of the correction source The waveform is known, and each correction source is respectively 、 Transmit correction signals respectively.

[0067] Carrier frequency For example, the phase error of the entire array is the first Correction source signal It can be expressed as: (5) (6) (7) Where, is the phase and communication delay error -dimensional diagonal matrix, is the array element position error matrix, for dimensional Gaussian white noise data vector, and the noise and signal are uncorrelated; is the steering vector of the th signal source, which can be expressed as: (8) Step 2: Extract the actual steering vectors corresponding to the two carrier frequencies respectively. As an example, since the signal waveform is known, the simplified multi-stage Wiener filtering (SMSWF) method is used to directly calculate the normalized multi-stage Wiener filter coefficients corresponding to the signal subspace, that is: (9) In the above formula, Indicates taking Take the average of the samples, The specific form can be expressed as: (10) Step 3: It can be seen that the multi-stage Wiener filter coefficient is the actual steering vector. Indicates the Correction source carrier frequency 、 The corresponding normalized multi-stage Wiener filter coefficients The result of dividing corresponding elements, where Represents the division of corresponding elements of vectors, It can be expressed as: (11) It is not difficult to find that The form is equivalent to a frequency of The error-guided vector of the signal is usually is called the equivalent frequency.

[0068] Equivalent frequency The corresponding equivalent wavelength It can be expressed as: (12) Therefore, for convenience, the equivalent frequency is used Equivalent wavelength Will It is expressed as follows: (13) The corresponding ideal equivalent steering vector It can be expressed as: (14) make represents the ratio of the corresponding element in the actual steering vector to the ideal steering vector. From equations (14) and (11), we can get: (15) Taking the phase of equation (15), we get: (16) set up , we can get: (17) Rewrite the above formula into the following form: (18) In formula (18) (19) (20) (twenty one) According to the least squares principle, the estimated value of the array element position error parameter can be obtained as: (twenty two) Step 4: Due to the influence of noise, the position error of the array element obtained at this time is still far from the actual value, but the difference is less than half a wavelength. At this time, the theoretical position is updated with the estimated position error, and the normalized multi-stage Wiener filter coefficients of the two frequencies are used. 、 Calculate the position error and phase error according to the single frequency method. The updated theoretical position It can be expressed as: (twenty three) Correspondingly, the remaining phase error

[0069] Carrier frequency For example, the ideal array steering vector after update can be expressed as: (twenty four) set up 、 Respectively 、 The ratio of the corresponding elements in the actual steering vector of the two frequencies to the ideal steering vector is, , Correspondingly, (25) (26) Due to phase error Delay Error Both only affect the phase of the steering vector, so that the frequency 、 Under these conditions, the total phase errors caused by the two are 、 : (27) (28) Formula (25) and (26) can be re-expressed as: (29) (30) Taking the phase of (29) and (30) respectively, we get: (31) (32) Following equations (17) to (22), we can respectively use the frequency 、 Two types of position errors are estimated: (33) (34) The difference between the two estimates is due to the difference in noise. Averaging the two gives a more accurate estimate of the residual position error. : (35) Substituting equations (33) and (34) into equations (31) and (32) respectively, the total phase error corresponding to the two carrier frequencies can be calculated: (36) (37) Then 、 Substituting into equations (27) and (28), we can obtain the estimated values ​​of delay error: and the phase error estimate : (38) (39) Total position error estimate It can be expressed as: (40) This embodiment is further described with reference to the experiments: The experimental setup is as follows: an ideal 10×10 half-wavelength uniform array operating at 3 GHz with a frequency hopping interval of 300 MHz. The array element position error is randomly distributed within the range of 0.2×(-1, 1)m, the phase error is randomly distributed within the range of 20×(-1, 1)°, and the delay error is randomly distributed within the range of 100×(0, 1)ps. The two carrier frequencies used for calibration are 3 GHz and 2.7 GHz, respectively. The calibration signal bandwidth is 20 MHz, the sampling frequency is 10 times the bandwidth, the signal duration is 80 μs, and the signal-to-noise ratio is 20 dB. The signal sources are placed at angles of (0°, 90°), (40°, 0°), (-60°, 55°), and (70°, 125°). Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 The comparison between the existing method and the method of this embodiment shows that compared with the existing method, the existing method cannot correct the array error. After correction by the algorithm of this embodiment, the maximum errors of array position, communication delay, and phase are 8.738×10 -5 m, 1.186×10 -12 s, 1.186×10 -12 s, 1.214°.

[0070] Example 2 See also Figure 2 , dual-frequency swarm array error multi-domain joint correction system, including: A correction signal transmission module is used to obtain correction signals from multiple correction sources through time diversity, and each correction source transmits a correction signal at two carrier frequencies to a swarm array with a position error exceeding half a wavelength; An actual steering vector estimation module, used to estimate the actual steering vectors of two carrier frequencies using a simplified SMSWF method; A position error estimation module is used to calculate the position error based on the actual steering vectors of the two carrier frequencies using the equivalent frequency method to obtain an estimated value of the array element position error parameter; The error estimation and correction module is used to update the array element position information using the estimated value of the array element position error parameter, and then use the received signals of the two carrier frequencies to estimate the position error, phase error and communication delay error, and complete the joint error correction of the swarm array with a position error exceeding half a wavelength.

[0071] Example 3 See also Figure 3, an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the dual-frequency swarm array error multi-domain joint correction method is implemented.

[0072] Example 4 A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the dual-frequency swarm array error multi-domain joint correction method is implemented.

[0073] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, read-only optical disks, optical storage devices, etc.) containing computer-usable program code.

[0074] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0075] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0076] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the specific implementations of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be included in the scope of protection of the present invention.

Claims

1. A dual-frequency swarm array error multi-domain joint correction method, characterized in that: The following steps are involved: Correction signals from multiple correction sources are obtained through time diversity, with each correction source transmitting correction signals at two carrier frequencies to a swarm array with a position error exceeding half a wavelength; The simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies; Based on the actual steering vectors of the two carrier frequencies, the position error is calculated using the equivalent frequency method to obtain the estimated value of the array element position error parameter; After updating the array element position information using the estimated value of the array element position error parameter, the position error, phase error and communication delay error are estimated using the received signals of the two carrier frequencies respectively, completing the joint error correction of the swarm array with a position error exceeding half a wavelength.

2. The dual-frequency swarm array error multi-domain joint correction method according to claim 1, characterized in that: The plurality of correction sources include correction sources placed at four different orientations in the far field of the swarm array with a position error exceeding half a wavelength; Phase error received The correction source signal is shown as follows: in, The phase error is the received A correction source signal, is the phase and communication delay error -dimensional diagonal matrix, is the array element position error matrix, for dimensional Gaussian white noise data vector; is the steering vector of the th signal source; is the position of the element of the swarm array whose position error exceeds half wavelength, is the position error of the swarm array whose position error exceeds half a wavelength, is the phase error of the swarm array whose position error exceeds half a wavelength, is the communication delay error of the swarm array whose position error exceeds half a wavelength; Indicates the total number of array elements; For the The pitch angle of the correction source, For the The azimuth of the correction source, For the The signal power of a correction source is, For the The noise power of a correction source is, For the The emission signal of a correction source; is the first carrier frequency, The second carrier frequency.

3. The dual-frequency swarm array error multi-domain joint correction method according to claim 2, characterized in that: The simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies. Specifically, the simplified SMSWF method is used to directly calculate the normalized multi-stage Wiener filter coefficients of the signal subspace, and the multi-stage Wiener filter coefficients are used as the actual steering vectors.

4. The dual-frequency swarm array error multi-domain joint correction method according to claim 3, characterized in that: The actual steering vectors based on the two carrier frequencies are used to calculate the position error using the equivalent frequency method to obtain the estimated value of the array element position error parameter, specifically: The equivalent frequency and equivalent wavelength are used to express the The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the The result of dividing the corresponding elements of the normalized multi-stage Wiener filter coefficients of the second carrier frequency of the correction source; Taking the phase of the ratio of the corresponding elements in the actual steering vector and the ideal steering vector; Based on the phase and the least squares principle, the estimated value of the array element position error parameter is obtained.

5. The dual-frequency swarm array error multi-domain joint correction method according to claim 4, characterized in that: After the array element position error parameter estimation value is used to update the array element position information, the position error, phase error and communication delay error are estimated using the received signals of the two carrier frequencies, specifically: The theoretical position is updated using the estimated values ​​of the array element position error parameters, and the position error and phase error are calculated using the normalized multi-stage Wiener filter coefficients of two frequencies according to the single-frequency method. The phase of the ratio of the actual steering vector to the corresponding element in the updated ideal steering vector under the preset total phase error at the two carrier frequencies is respectively calculated; based on the phase, two position error estimates are obtained from the two carrier frequencies according to the least squares principle; and the two position error estimates are averaged to obtain a residual position error estimate; The total phase error corresponding to the two carrier frequencies is obtained by using the two position error estimates and phase calculation; The total phase errors corresponding to the two carrier frequencies are combined with the preset total phase errors under the two carrier frequencies to obtain a delay error estimate and a phase error estimate; The total position error estimate is the sum of the array element position error parameter estimate and the residual position error estimate.

6. The dual-frequency swarm array error multi-domain joint correction method according to claim 4, characterized in that: The equivalent frequency and the equivalent wavelength are used to express the The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the The result of dividing the corresponding elements of the normalized multi-stage Wiener filter coefficients of the second carrier frequency of the correction source is as follows: in, express The result of dividing corresponding elements, Indicates the The first carrier frequency of the correction source Normalized multi-stage Wiener filter coefficients, Indicates the Correction source second carrier frequency Normalized multi-stage Wiener filter coefficients, is the equivalent frequency, is the equivalent wavelength; The phase of the ratio of the corresponding elements in the actual steering vector and the ideal steering vector is as follows: in, represents the ideal equivalent steering vector, The actual steering vector and The ratio of the corresponding elements in ; express Phase; The phase-based least squares principle is used to obtain the estimated value of the array element position error parameter, as shown in the following formula: in, Represents the estimated value of the array element position error parameter.

7. The dual-frequency swarm array error multi-domain joint correction method according to claim 6, characterized in that: The theoretical position is updated by using the estimated value of the array element position error parameter, as shown in the following formula: The phases of the ratios of the actual steering vector and the corresponding elements of the updated ideal steering vector under the preset total phase error at the two carrier frequencies are respectively taken. Based on the phases and the least squares principle, two position error estimates are obtained from the two carrier frequencies, as shown in the following formula: The residual position error estimate obtained by averaging the two position error estimates is shown in the following formula: The total phase error corresponding to the two carrier frequencies is obtained by using the two position error estimates and the phase calculation, as shown in the following formula: The total position error estimate is the sum of the array element position error parameter estimate and the residual position error estimate, as shown in the following formula: in, represents the updated theoretical position, is the total position error estimate, is the estimated value of the residual position error, represents the remaining phase error; Indicates the first carrier frequency The ratio of the corresponding elements in the actual steering vector to the ideal steering vector, Indicates the second carrier frequency The ratio of the corresponding elements in the actual steering vector to the ideal steering vector, Indicates the first carrier frequency The total phase error under the preset Indicates the second carrier frequency The preset total phase error under represents the phase error, Indicates the delay error; express The phase, express The phase, represents the total phase error of the first carrier frequency, Indicates the total phase error of the second carrier frequency.

8. Dual-frequency swarm array error multi-domain joint correction system, characterized by: include: A correction signal transmission module is used to obtain correction signals from multiple correction sources through time diversity, and each correction source transmits a correction signal at two carrier frequencies to a swarm array with a position error exceeding half a wavelength; An actual steering vector estimation module, used to estimate the actual steering vectors of two carrier frequencies using a simplified SMSWF method; A position error estimation module is used to calculate the position error based on the actual steering vectors of the two carrier frequencies using the equivalent frequency method to obtain an estimated value of the array element position error parameter; The error estimation and correction module is used to update the array element position information using the estimated value of the array element position error parameter, and then use the received signals of the two carrier frequencies to estimate the position error, phase error and communication delay error, and complete the joint error correction of the swarm array with a position error exceeding half a wavelength.

9. An electronic device, characterized in that: The invention comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the dual-frequency swarm array error multi-domain joint correction method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the dual-frequency swarm array error multi-domain joint correction method described in any one of claims 1 to 7 is implemented.

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