Dual-frequency cellular array error multi-domain joint correction system

Abstract

This invention discloses a multi-domain joint error correction system for a dual-frequency swarm array, belonging to the field of radar signal processing technology. It obtains correction signals from multiple correction sources through time diversity, with each source transmitting correction signals to the swarm array with a position error exceeding half a wavelength via two carrier frequencies. A simplified SMSSWF method is used to estimate the actual steering vectors of the two carrier frequencies. Based on these steering vectors, the equivalent frequency method is used to calculate the position error, obtaining estimated values ​​for the array element position error parameters. After updating the array element position information using these estimated values, the received signals from the two carrier frequencies are used to estimate the position error, phase error, and communication delay error, respectively, completing the joint error correction for the swarm array with a position error exceeding half a wavelength. The dual-frequency position error estimation based on the equivalent frequency method fully utilizes the large error estimation range of the dual-frequency method while retaining the high accuracy of traditional methods, successfully correcting errors even when the position error exceeds half a wavelength.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a multi-domain joint correction system for errors in dual-frequency swarm arrays. Background Technology

[0002] In a swarm, the position of each drone is traditionally determined primarily by GPS positioning. Due to limitations in positioning accuracy, the operating frequency of a flexible swarm array cannot exceed 150MHz; otherwise, the array position error exceeding half a wavelength will cause phase aliasing, which is difficult to correct. Traditional antenna array error correction methods that can correct position errors exceeding half a wavelength are highly complex; low-complexity methods cannot handle array errors exceeding half a wavelength.

[0003] Existing real-time array position error correction methods mainly rely on single-frequency active correction. These active real-time array error correction techniques first require accurate extraction of the actual steering vector. Zhang Ke et al. used eigenvalue decomposition to extract the steering vector, achieving joint correction of array amplitude, phase, and position errors. Addressing the high computational complexity of eigenvalue decomposition, 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 / phase errors. Among self-correction methods, Peng Wencan et al. proposed a meshless sparse self-correction algorithm for amplitude and phase errors, used to correct the amplitude and phase errors of partially corrected arrays.

[0004] Among existing methods, active correction methods only have single-frequency correction, which is difficult to correct position errors exceeding half a wavelength; passive correction methods not only have high computational complexity, but may also get trapped in local optima, leading to correction failure. Summary of the Invention

[0005] The purpose of this invention is to overcome the problem that existing methods are unable to correct position errors exceeding half a wavelength, and to propose a multi-domain joint correction system for dual-frequency swarm array errors. This system is applicable to the joint correction of array phase, position, and communication delay errors in novel distributed arrays, such as flexible swarm arrays.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for multi-domain joint correction of errors in a dual-frequency bee colony array, comprising the following steps:

[0008] The correction signals of multiple correction sources are obtained by time diversity, and each correction source transmits the correction signal to the swarm array with a position error of more than half a wavelength at two carrier frequencies.

[0009] The simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies;

[0010] 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 values ​​of the array element position error parameters.

[0011] After updating the array element position information using the estimated values ​​of the array element position error parameters, the position error, phase error, and communication delay error are estimated using the received signals of two carrier frequencies respectively, thus completing the joint error correction for the swarm array with a position error exceeding half a wavelength.

[0012] Furthermore, the multiple correction sources include correction sources placed in four different orientations in the far field of the swarm array with a position error exceeding half a wavelength;

[0013] Phase error received The correction source signal is shown in the following formula:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] in, The first received phase error One correction source signal, For phase and communication delay error 3D diagonal matrix The matrix represents the position error of the array elements. for Gaussian white noise data vector; Let be the steering vector of the i-th signal source; This refers to the element positions of a bee colony array with a position error exceeding half a wavelength. For a bee colony array, the position error is greater than half a wavelength. The phase error of a bee colony array with a position error exceeding half a wavelength. The communication delay error of a swarm array with a position error exceeding half a wavelength; Indicates the total number of array elements; For the first The pitch angle of each correction source, For the first The azimuth angle of the correction source, For the first The signal power of each correction source is, For the first The noise power of each correction source is, For the first The transmitted signal of each calibration source; As the first carrier frequency, This is the second carrier frequency.

[0023] Furthermore, the simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies. Specifically, the normalized multi-stage Wiener filter coefficients of the signal subspace are directly obtained using the simplified SMSWF method, and the multi-stage Wiener filter coefficients are used as the actual steering vectors.

[0024] 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 values ​​of the array element position error parameters, specifically:

[0025] The equivalent frequency and equivalent wavelength are used to represent the first... The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the first... The result of dividing the corresponding elements of the normalized multi-stage Wiener filter coefficients of the second carrier frequency of each correction source;

[0026] Take the phase of the ratio of corresponding elements in the actual steering vector to the ideal steering vector;

[0027] Based on the phase and the least squares principle, the estimated values ​​of the array element position error parameters are obtained.

[0028] Furthermore, after updating the array element position information using the estimated values ​​of the array element position error parameters, the position error, phase error, and communication delay error are estimated using the received signals from the two carrier frequencies, specifically as follows:

[0029] The theoretical position is updated using the estimated values ​​of array element position error parameters. The position error and phase error are calculated using the coefficients of a normalized multi-stage Wiener filter at two frequencies, respectively, according to the single-frequency method.

[0030] For each of the two carrier frequencies, the ratio of the corresponding elements in the actual steering vector to the updated ideal steering vector is taken as the phase. Based on the phase and according to the least squares principle, two position error estimates are obtained from the two carrier frequencies. The average of the two position error estimates is taken to obtain the remaining position error estimate.

[0031] The total phase error corresponding to the two carrier frequencies is obtained by using two position error estimates and phase calculation.

[0032] The total phase error corresponding to the two carrier frequencies is combined with the preset total phase error under the two carrier frequencies to obtain the time delay error estimate and the phase error estimate.

[0033] The total position error estimate is the sum of the element position error parameter estimates and the remaining position error estimates.

[0034] Furthermore, the equivalent frequency and equivalent wavelength are used to represent the first... The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the first... The result of dividing the element-wise coefficients of the normalized multi-stage Wiener filter for the second carrier frequency of each correction source is shown below:

[0035]

[0036]

[0037]

[0038] in, express The result of dividing by corresponding elements Indicates the first First carrier frequency of the correction source The normalized multi-stage Wiener filter coefficients, Indicates the first Second carrier frequency of the correction source The normalized multi-stage Wiener filter coefficients, For equivalent frequency, Equivalent wavelength;

[0039] The phase ratio of corresponding elements in the actual steering vector to the ideal steering vector is taken as follows:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in, Represents the ideal equivalent steering vector. Indicates the actual steering vector and The ratio of corresponding elements in; express The phase;

[0048] Based on the phase and according to the least squares principle, the estimated values ​​of the array element position error parameters are obtained, as shown in the following formula:

[0049]

[0050] in, This represents the estimated value of the array element position error parameter.

[0051] Furthermore, the theoretical positions are updated using the estimated values ​​of the array element position error parameters, as shown in the following equation:

[0052]

[0053] For each of the two carrier frequencies, under the preset total phase error, the ratio of corresponding elements in the actual steering vector to the updated ideal steering vector is taken as the phase. Based on the phase and according to the least squares principle, two position error estimates are obtained from the two carrier frequencies, as shown in the following formula:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] The remaining position error estimate is obtained by averaging the two position error estimates, as shown in the following formula:

[0061]

[0062]

[0063]

[0064] 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:

[0065]

[0066]

[0067] The total position error estimate is the sum of the element position error parameter estimates and the remaining position error estimates, as shown in the following formula:

[0068]

[0069]

[0070] in, Indicates the updated theoretical position. This is the estimated total position error. This is the estimated value of the remaining position error. This indicates 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 preset total phase error, Indicates the second carrier frequency The preset total phase error; Indicates phase error, Indicates time delay error; express phase, express phase, This represents the total phase error of the first carrier frequency. This represents the total phase error of the second carrier frequency.

[0071] Secondly, the present invention provides a dual-frequency bee colony array error multi-domain joint correction system, comprising:

[0072] The correction signal transmission module is used to obtain correction signals from multiple correction sources through time diversity. Each correction source transmits correction signals to the swarm array with a position error exceeding half a wavelength at two carrier frequencies.

[0073] The actual steering vector estimation module is used to estimate the actual steering vectors of the two carrier frequencies using the simplified SMSWF method.

[0074] The position error estimation module is used to calculate the position error based on the actual steering vectors of the two carrier frequencies and to obtain the estimated values ​​of the array element position error parameters by using the equivalent frequency method.

[0075] The estimation error completion correction module is used to update the array element position information using the estimated values ​​of the array element position error parameters, and then use the received signals of two carrier frequencies to estimate the position error, phase error and communication delay error respectively, so as to complete the joint error correction of the swarm array with position error exceeding half a wavelength.

[0076] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the dual-frequency cellular array error multi-domain joint correction method.

[0077] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, describes a method for multi-domain joint correction of errors in a dual-frequency bee colony array.

[0078] Compared with the prior art, the present invention has the following beneficial technical effects:

[0079] This invention proposes a multi-domain joint correction method for dual-frequency cellular array errors, providing a joint correction method for array position, phase, and communication delay errors when element position errors exceed half a wavelength. Based on dual-frequency position error estimation using the equivalent frequency method, it fully utilizes the large error estimation range of the dual-frequency method while retaining the high accuracy of traditional methods, successfully correcting errors even when position errors exceed half a wavelength. The method extracts the steering vectors corresponding to the two carrier frequencies using the multi-order Wiener filtering (SMSWF) method. 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. This invention introduces the dual-frequency method into array error correction, achieving an error correction range exceeding the half-wavelength limit. In practical applications, it can effectively avoid the problem of insufficient GPS positioning accuracy leading to difficulty in correcting errors in flexible cellular arrays. Attached Figure Description

[0080] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. Furthermore, the shapes and proportions of the components in the drawings are merely schematic to aid in understanding the invention and do not specifically limit the shapes and proportions of the components. In the drawings:

[0081] Figure 1 This is a flowchart of the dual-frequency bee colony array error multi-domain joint correction method of the present invention.

[0082] Figure 2 This is a structural diagram of the dual-frequency bee colony array error multi-domain joint correction system of the present invention.

[0083] Figure 3 This is an electronic device diagram of the dual-frequency bee colony array error multi-domain joint correction method of the present invention.

[0084] Figure 4 This is a comparison of the positions of array elements before and after correction with the ideal lower array element positions in an embodiment of the present invention.

[0085] Figure 5 This describes the position error estimation error in an embodiment of the present invention.

[0086] Figure 6 This is a comparison between the actual time delay error and the corrected time delay error in an embodiment of the present invention.

[0087] Figure 7 This refers to the time delay error estimation error in the embodiments of the present invention.

[0088] Figure 8 This is a comparison between the actual phase difference and the corrected phase error in an embodiment of the present invention.

[0089] Figure 9 This refers to the phase error estimation error in the embodiments of the present invention.

[0090] Figure 10 This is the position error correction effect of the single-frequency method in the embodiment of the present invention when the position error exceeds half a wavelength.

[0091] Figure 11 This is the result of joint correction of communication delay and phase error in single-frequency method when the position error exceeds half a wavelength in the embodiment of the present invention. Detailed Implementation

[0092] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0093] Example 1

[0094] See Figure 1 A multi-domain joint correction method for errors in dual-frequency bee colony arrays includes the following steps:

[0095] The correction signals of multiple correction sources are obtained by time diversity, and each correction source transmits the correction signal to the swarm array with a position error of more than half a wavelength at two carrier frequencies.

[0096] The simplified SMSWF method is used to estimate the actual steering vectors of the two carrier frequencies;

[0097] 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 values ​​of the array element position error parameters.

[0098] After updating the array element position information using the estimated values ​​of the array element position error parameters, the position error, phase error, and communication delay error are estimated using the received signals of two carrier frequencies respectively, thus completing the joint error correction for the swarm array with a position error exceeding half a wavelength.

[0099] In this embodiment, time diversity is used to allow multiple correction sources to transmit at dual carrier frequencies, enriching the signal sources and frequency band coverage, and enhancing adaptability to different scenarios. A simplified SMSWF method is employed to estimate the actual steering vector, reducing computational complexity, improving operational efficiency, effectively suppressing interference, and ensuring estimation accuracy. The equivalent frequency method is used to calculate the position error, overcoming the limitations of traditional methods in handling large position errors (exceeding half a wavelength) and improving the accuracy of position error parameter estimation. Finally, joint error correction is performed, comprehensively considering multiple error factors such as position, phase, and communication delay to achieve comprehensive correction, avoiding the shortcomings of single error correction. This embodiment's method effectively improves the communication quality, signal processing capabilities, and target detection accuracy of the swarm array, meeting the needs of applications with high real-time requirements.

[0100] Multiple correction source signals are obtained through time diversity. The simplified multi-stage Wiener filter (SMSWF) method is used to estimate the steering vectors at two frequencies. Then, the equivalent frequency method is used to calculate the position error. After updating the array element position information with the estimation results, the position, phase, and communication delay errors are accurately estimated using the received signals at the two frequencies. Specifically, the following steps are followed:

[0101] Step 1: Establishing the Received Signal Model

[0102] This embodiment is mainly used for the joint correction of multiple errors in a swarm array with a position error exceeding half a wavelength.

[0103] Considering the total number of arrays The array element, the first The position of each element is used The position error is expressed as... Phase error is represented by Indicated, the time delay error is expressed as... express.

[0104] Then the positions of the array elements of the entire array Position error Phase error With communication delay error They can be represented as follows:

[0105] (1)

[0106] (2)

[0107] (3)

[0108] (4)

[0109] Correction was performed using correction sources placed at four different locations in the far field of the array. The pitch angle of each correction source is azimuth angle is The signal power is The noise power is The transmission signal of the correction source The waveform is known, and each correction source uses a carrier frequency. , Each transmits a correction signal.

[0110] With carrier frequency For example, the phase error of the entire array received by the array is the first... One calibration source signal It can be represented as:

[0111] (5)

[0112] (6)

[0113] (7)

[0114] In the formula, For phase and communication delay error 3D diagonal matrix The matrix represents the position error of the array elements. for The data vector contains Gaussian white noise, and the noise and signal are uncorrelated.

[0115] Let the steering vector of the i-th signal source be expressed as:

[0116] (8)

[0117] Step 2: Extract the actual steering vectors corresponding to the two carrier frequencies respectively. Still using the carrier frequency... For example, since the signal waveform is known, the normalized multi-stage Wiener filter coefficients corresponding to the signal subspace can be directly obtained using the Simplified Multi-Stage Wiener Filter (SMSWF) method, i.e.:

[0118] (9)

[0119] In the above formula, Indicates taking Take the average of the samples. The specific form can be expressed as:

[0120] (10)

[0121] Step 3: It can be seen that the coefficients of the multi-stage Wiener filter are the actual steering vector. Using... Indicates the first One correction source carrier frequency , The corresponding normalized multi-stage Wiener filter coefficients The result obtained by dividing the corresponding elements, where This indicates that corresponding elements of the vectors are divided. It can be represented as:

[0122] (11)

[0123] It is not hard to see that The formal equivalent is a frequency of The error-inducing steering vector of the signal is usually... This is called the equivalent frequency.

[0124] equivalent frequency Corresponding equivalent wavelength It can be represented as:

[0125] (12)

[0126] Therefore, for convenience, we use the equivalent frequency. With equivalent wavelength Will It can be represented in the following form:

[0127] (13)

[0128] The corresponding ideal equivalent steering vector It can be represented as:

[0129] (14)

[0130] make The ratio of the corresponding elements in the actual steering vector to the ideal steering vector can be obtained from equations (14) and (11):

[0131] (15)

[0132] Taking the phase of equation (15), we get:

[0133] (16)

[0134] set up Then we can get:

[0135] (17)

[0136] The above expression can be rewritten in the following form:

[0137] (18)

[0138] In formula (18)

[0139] (19)

[0140] (20)

[0141] (twenty one)

[0142] Based on the least squares principle, the estimated values ​​of the array element position error parameters can be obtained as follows:

[0143] (twenty two)

[0144] Step 4: Due to noise, the obtained element position error still differs significantly from the actual value, but this difference is less than half a wavelength. The estimated position error is then used to update the theoretical position, employing normalized multi-stage Wiener filter coefficients at two frequencies. , The position and phase errors were calculated separately using the single-frequency method. The updated theoretical position... It can be represented as:

[0145] (twenty three)

[0146] Correspondingly, the remaining phase error

[0147] With carrier frequency For example, the updated ideal array steering vector can be expressed as:

[0148] (twenty four)

[0149] set up , They represent , The ratio of the corresponding elements in the actual steering vector to the ideal steering vector at two frequencies, i.e. , Correspondingly,

[0150] (25)

[0151] (26)

[0152] Due to phase error With time delay error Both only affect the phase of the steering vector, making the frequency , The total phase errors caused by the two are as follows: , :

[0153] (27)

[0154] (28)

[0155] Equations (25) and (26) can be reformulated as follows:

[0156] (29)

[0157] (30)

[0158] Taking the phase of (29) and (30) respectively, we get:

[0159] (31)

[0160] (32)

[0161] Following equations (17) to (22), the frequencies can be respectively determined. , Two types of positional errors were estimated:

[0162] (33)

[0163] (34)

[0164] The discrepancy between the two estimates lies in the difference in their noise levels. Averaging the two estimates yields a more accurate estimate of the remaining position error. :

[0165] (35)

[0166] Substituting equations (33) and (34) into equations (31) and (32) respectively, the total phase error corresponding to the two carrier frequencies can be calculated:

[0167] (36)

[0168] (37)

[0169] Then , Substituting into equations (27) and (28), we can obtain the estimated values ​​of the time delay error, respectively. With phase error estimate :

[0170] (38)

[0171] (39)

[0172] Total position error estimate It can be represented as:

[0173] (40)

[0174] This embodiment will be further illustrated with reference to experiments:

[0175] The experimental setup was as follows: the ideal array structure was a 10×10 half-wavelength uniform array, operating at 3 GHz, with an allowable frequency hopping interval of 300 MHz. The array element position errors were randomly distributed within the range of 0.2×(-1,1) m, the phase errors within the range of 20×(-1,1)°, and the time delay errors within the range of 100×(0,1) ps. The calibration used two carrier frequencies of 3 GHz and 2.7 GHz, with a calibration signal bandwidth of 20 MHz, a sampling frequency 10 times the bandwidth, a signal duration of 80 μs, and a signal-to-noise ratio of 20 dB. The signal sources were 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 existing methods and the method in this embodiment shows that existing methods cannot correct array errors. After correction, the maximum errors in array position, communication delay, and phase in this embodiment are 8.738 × 10⁻⁶. -5 m, 1.186 × 10 -12 s, 1.186×10 -12 s, 1.214°.

[0176] Example 2

[0177] See Figure 2 A dual-frequency bee colony array error multi-domain joint correction system includes:

[0178] The correction signal transmission module is used to obtain correction signals from multiple correction sources through time diversity. Each correction source transmits correction signals to the swarm array with a position error exceeding half a wavelength at two carrier frequencies.

[0179] The actual steering vector estimation module is used to estimate the actual steering vectors of the two carrier frequencies using the simplified SMSWF method.

[0180] The position error estimation module is used to calculate the position error based on the actual steering vectors of the two carrier frequencies and to obtain the estimated values ​​of the array element position error parameters by using the equivalent frequency method.

[0181] The estimation error completion correction module is used to update the array element position information using the estimated values ​​of the array element position error parameters, and then use the received signals of two carrier frequencies to estimate the position error, phase error and communication delay error respectively, so as to complete the joint error correction of the swarm array with position error exceeding half a wavelength.

[0182] Example 3

[0183] See Figure 3 An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the dual-frequency cellular array error multi-domain joint correction method.

[0184] Example 4

[0185] A computer-readable storage medium storing a computer program, which, when executed by a processor, describes a method for multi-domain joint correction of errors in a dual-frequency beehive array.

[0186] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, read-only optical discs, optical storage, etc.) containing computer-usable program code.

[0187] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0188] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0189] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the functions specified in one or more boxes. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for multi-domain joint correction of errors in dual-frequency bee colony arrays, characterized in that, Includes the following steps: The correction signals of multiple correction sources are obtained by time diversity, and each correction source transmits the correction signal to the swarm array with a position error of more than half a wavelength at two carrier frequencies. 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 values ​​of the array element position error parameters. After updating the array element position information using the estimated values ​​of the array element position error parameters, the position error, phase error, and communication delay error are estimated using the received signals of two carrier frequencies respectively, thus completing the joint error correction for the swarm array with a position error exceeding half a wavelength.

2. The method for multi-domain joint correction of errors in a dual-frequency bee colony array according to claim 1, characterized in that, The plurality of correction sources include correction sources placed in four different orientations in the far field of a swarm array with a position error exceeding half a wavelength. Phase error received The correction source signal is shown in the following formula: in, The first received phase error One correction source signal, For phase and communication delay error 3D diagonal matrix The matrix represents the position error of the array elements. for Gaussian white noise data vector; Let be the steering vector of the i-th signal source; This refers to the element positions of a bee colony array with a position error exceeding half a wavelength. For a bee colony array, the position error is greater than half a wavelength. The phase error of a bee colony array with a position error exceeding half a wavelength. The communication delay error of a swarm array with a position error exceeding half a wavelength; Indicates the total number of array elements; For the first The pitch angle of each correction source, For the first The azimuth angle of each correction source, For the first The transmitted signal of each calibration source; This is the first carrier frequency.

3. The method for multi-domain joint correction of errors in a dual-frequency bee colony array according to claim 2, characterized in that, The method of estimating the actual steering vectors of the two carrier frequencies using the simplified SMSWF method is as follows: the normalized multi-stage Wiener filter coefficients of the signal subspace are directly obtained using the simplified SMSWF method, and the multi-stage Wiener filter coefficients are used as the actual steering vectors.

4. The method for multi-domain joint correction of errors in a dual-frequency bee colony array according to claim 3, characterized in that, The estimated values ​​of the array element position error parameters are obtained by calculating the position error using the equivalent frequency method based on the actual steering vectors of the two carrier frequencies. The equivalent frequency and equivalent wavelength are used to represent the first... The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the first... The result of dividing the corresponding elements of the normalized multi-stage Wiener filter coefficients of the second carrier frequency of each correction source; Take the phase of the ratio of corresponding elements in the actual steering vector to the ideal steering vector; Based on the phase and the least squares principle, the estimated values ​​of the array element position error parameters are obtained.

5. The method for multi-domain joint correction of errors in a dual-frequency bee colony array according to claim 4, characterized in that, After updating the array element position information using the estimated values ​​of the array element position error parameters, the position error, phase error, and communication delay error are estimated using the received signals of the two carrier frequencies, specifically as follows: The theoretical position is updated using the estimated values ​​of array element position error parameters. The position error and phase error are calculated using the coefficients of a normalized multi-stage Wiener filter at two frequencies, respectively, according to the single-frequency method. For each of the two carrier frequencies, the ratio of the corresponding elements in the actual steering vector to the updated ideal steering vector is taken as the phase. Based on the phase and according to the least squares principle, two position error estimates are obtained from the two carrier frequencies. The average of the two position error estimates is taken to obtain the remaining position error estimate. The total phase error corresponding to the two carrier frequencies is obtained by using two position error estimates and phase calculation. The total phase error corresponding to the two carrier frequencies is combined with the preset total phase error under the two carrier frequencies to obtain the time delay error estimate and the phase error estimate. The total position error estimate is the sum of the element position error parameter estimates and the remaining position error estimates.

6. The method for multi-domain joint correction of errors in a dual-frequency bee colony array according to claim 5, characterized in that, The equivalent frequency and equivalent wavelength are used to represent the first... The normalized multi-stage Wiener filter coefficients of the first carrier frequency of the correction source and the first... The result of dividing the element-wise coefficients of the normalized multi-stage Wiener filter for the second carrier frequency of each correction source is shown below: in, express The result of dividing by corresponding elements Indicates the first First carrier frequency of the correction source The normalized multi-stage Wiener filter coefficients, Indicates the first Second carrier frequency of the correction source The normalized multi-stage Wiener filter coefficients, For equivalent frequency, Equivalent wavelength; The phase ratio of corresponding elements in the actual steering vector and the ideal steering vector is taken as follows: in, Represents the ideal equivalent steering vector. Indicates the actual steering vector and The ratio of corresponding elements in; express The phase; The estimated values ​​of the array element position error parameters are obtained based on the phase according to the least squares principle, as shown in the following formula: in, This represents the estimated value of the array element position error parameter.

7. The method for multi-domain joint correction of errors in a dual-frequency bee colony array according to claim 6, characterized in that, The theoretical position is updated using the estimated values ​​of the array element position error parameters, as shown in the following formula: The ratio of the corresponding elements in the actual steering vector to the updated ideal steering vector under the preset total phase error at two carrier frequencies is used to take the phase. Based on the phase and according to the least squares principle, two position error estimates are obtained from the two carrier frequencies, as shown in the following formula: The remaining position error estimate is obtained by averaging the two position error estimates, as 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 phase calculation, as shown in the following formula: The total position error estimate is the sum of the element position error parameter estimates and the remaining position error estimates, as shown in the following formula: in, Indicates the updated theoretical position. This is the estimated value of the total position error. This is the estimated value of the remaining position error. This indicates 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 preset total phase error, Indicates the second carrier frequency The preset total phase error; Indicates phase error, Indicates time delay error; express phase, express phase, This represents the total phase error of the first carrier frequency. This represents the total phase error of the second carrier frequency.

8. A dual-frequency bee colony array error multi-domain joint correction system, characterized in that, include: The correction signal transmission module is used to obtain correction signals from multiple correction sources through time diversity. Each correction source transmits correction signals to the swarm array with a position error exceeding half a wavelength at two carrier frequencies. The actual steering vector estimation module is used to estimate the actual steering vectors of the two carrier frequencies using the simplified SMSWF method. The position error estimation module is used to calculate the position error based on the actual steering vectors of the two carrier frequencies and to obtain the estimated values ​​of the array element position error parameters by using the equivalent frequency method. The estimation error correction module is used to update the array element position information using the estimated values ​​of the array element position error parameters, and then use the received signals of the two carrier frequencies to estimate the position error, phase error and communication delay error respectively, so as to complete the joint error correction of the swarm array with position error exceeding half a wavelength.

9. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the dual-frequency beehive array error multi-domain joint correction method as described in any one of claims 1-7.

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

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