A phase correction method based on polynomial fitting

Abstract

This invention discloses a phase correction method based on polynomial fitting, relating to the field of electromagnetic signal direction finding technology, comprising: S1: acquiring phase difference data at each frequency point based on a set frequency interval; S2: transforming the phase difference data and estimating the phase difference value; S3: filtering data and removing invalid data; S4: determining whether the data acquired for this correction is valid; if valid, fitting the data based on polynomial fitting; otherwise, reporting the acquired data as invalid; S5: performing polynomial fitting based on the valid data, calculating polynomial coefficients, and obtaining polynomial parameters; S6: sending the polynomial parameters to an FPGA to reconstruct phase difference data at arbitrary frequencies for compensation. This invention can calculate correction data at arbitrary frequencies, improving correction accuracy, reducing correction time, and reducing storage usage.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic signal direction finding technology, and in particular to a phase correction method based on polynomial fitting. Background Technology

[0002] There are five common methods for electromagnetic signal direction finding: interferometer method, amplitude comparison method, spatial spectrum estimation method, Doppler method, and time difference of arrival method. Because the interferometer method offers advantages such as high sensitivity and high accuracy in direction finding, it is widely used in fields such as electronic countermeasures and radar.

[0003] Based on the direction finding principle of phase interferometer, such as Figure 5 As shown, the antenna element spacing is d, and the signal incident angle is θ. Due to the order in which the electromagnetic wave signal arrives at the antenna elements, the signal received by the left element is delayed by τ = l / c compared to the signal received by the right element, where c is the speed of light. This results in a phase lag between the signals received by the left element and the right element. Where f is the frequency of the electromagnetic wave signal. When performing direction finding based on a phase interferometer, for a system with a fixed and uniformly distributed antenna element spacing l, the phase difference between the two array elements and the signal frequency satisfy a linear relationship. However, in actual direction finding systems, due to individual differences in antennas, mutual coupling effects between antennas, temperature changes, and other reasons, there will be phase inconsistencies, i.e., phase deviations, between array element channels, which will affect the direction finding accuracy. Therefore, effective correction methods are needed to improve the direction finding performance.

[0004] For broadband direction finding systems, traditional phase correction methods typically involve first acquiring phase difference correction data for a subset of frequencies, then sending the corresponding correction data to a hardware FPGA (Field-Programmable Gate Array). Based on the theoretically linear relationship between phase difference Δφ and signal frequency f, the FPGA uses the phase difference correction data from the subset of frequencies for linear interpolation to calculate the correction data for other frequencies, thereby compensating for channel phase deviations and reducing phase inconsistencies. The specific interpolation method is as follows:

[0005]

[0006] Where (x0,y0) is the starting (frequency point, phase difference) correction data, (x1,y1) is the ending (frequency point, phase difference) correction data, and x∈(x0,x1).

[0007] The above method has the following problems:

[0008] The lack of judgment on the validity of the collected data means that if the corrected frequency point is invalid but is still used, it will directly affect the direction finding accuracy of the interpolated frequency point; in addition, the validity of this correction cannot be judged.

[0009] Due to multi-level reflections and antenna coupling in the link, the phase difference and frequency are not strictly linearly related, but fluctuate and glitches exist. Linear interpolation methods cannot capture this characteristic well.

[0010] The calibration time and the number of initial calibration frequency points are strongly positively correlated. Furthermore, as the number of data acquisitions increases, the calibration data sent to the FPGA will increase, thus occupying more FPGA storage space. Summary of the Invention

[0011] To address the aforementioned issues, this invention provides a phase correction method based on polynomial fitting. Without affecting the use of the broadband direction-finding system of the phase interferometer, it models the relationship between phase difference correction data and frequency points using polynomial fitting based on a limited amount of correction data, thus better characterizing features such as fluctuations and glitches. Through data filtering, outlier data is removed, and the confidence level of the correction is provided, enabling the assessment of its effectiveness. The polynomial fitting method can calculate correction data at any frequency point, reducing correction time. Furthermore, by distributing polynomial parameters instead of distributing correction data from multiple frequency points, storage requirements are reduced.

[0012] This invention provides a phase correction method based on polynomial fitting, the specific technical solution of which is as follows:

[0013] S1: Collect phase difference data at each frequency point based on the set frequency interval;

[0014] S2: Transform the phase difference data and estimate the phase difference value;

[0015] S3: Perform data filtering to remove invalid data;

[0016] S4: Determine whether the data collected for this correction is valid. If it is valid, then use the data based on the polynomial fitting; otherwise, report the data collected for this correction as invalid.

[0017] S5: Perform polynomial fitting based on valid data, calculate polynomial coefficients, and obtain polynomial parameters;

[0018] S6: Send the polynomial parameters to the FPGA to reconstruct phase difference data at arbitrary frequencies for compensation.

[0019] Furthermore, based on the number N of phase difference data flips... 翻转 The phase difference data is divided into N 翻转 +1 paragraph.

[0020] Furthermore, the acquired phase difference data is traversed, and the phase difference data is transformed by identifying the flip points of the phase difference data, as follows:

[0021] Obtain the current frequency and corresponding phase difference data. And the next frequency point and the corresponding phase difference correction data Determine the flipping status of the phase difference data;

[0022] Based on the aforementioned flipping situation, the next phase difference data is transformed accordingly until all phase difference data has been traversed.

[0023] Furthermore, in traversing the phase difference data, starting from the completion of the transformation process of the second segment of phase difference data, after completing the transformation process of each segment of phase difference data, the latest phase difference value is calculated until the traversal is completed, and the smallest phase difference value is taken as the estimated value of the phase difference value.

[0024] Furthermore, the phase difference filtering is specifically as follows:

[0025] Get the current data to be filtered The data to be filtered in the previous batch Perform the following calculations:

[0026]

[0027] If the result is If the data falls within the specified range, the current data to be filtered is considered valid; otherwise, it is considered invalid.

[0028] Among them, f 间隔 The frequency difference between the current data and the next data point. T is the estimated value of the phase difference. 抖动 The threshold is used to characterize the range of phase difference jitter.

[0029] Furthermore, in step S3, before the phase difference value filtering, amplitude frequency filtering is also included, and the amplitude frequency filtering is as follows:

[0030] Acquire the actual frequency of each frequency point and the amplitude of each array element collected during calibration;

[0031] Calculate the difference between the known true frequency of the system signal source and the actual frequency of each frequency point collected during calibration, and determine whether it is less than the set first threshold.

[0032] If the difference is less than the set first threshold, the amplitude of any array element is greater than the set second threshold, and the amplitude difference between any two array elements is less than the set third threshold, then the data is determined to be valid and the data to be filtered is obtained; otherwise, the data is invalid.

[0033] Furthermore, the specific process for determining whether the data collected in this correction is valid is as follows:

[0034] Obtain the proportion of valid data in the data collected for this calibration.

[0035] If the proportion of valid data in the data collected for this correction is not less than the valid threshold, and the number of valid data is greater than 1, then the data collected for this correction is valid.

[0036] Furthermore, in step S5, the specific process for obtaining the polynomial parameters is as follows:

[0037] Obtain valid correction data and the number of valid data points, and perform fitting based on a polynomial, which is expressed as follows:

[0038]

[0039] Where y represents the effective phase difference data, x represents the effective frequency point data, and a n The coefficients represent the fitting coefficients, where n∈[0,p];

[0040] The polynomial parameter a is obtained by solving the problem using the least squares method.

[0041] Furthermore, based on the number of valid data N 筛选有效 Using N p Fitting with a polynomial of degree N or degree 1, where N p >1;

[0042] If [N] 筛选有效 >(N p +1)], then use N p Fitting with a polynomial of degree 1;

[0043] If (N) 筛选有效 ≥2) and N 筛选有效 ≤(N p If +1), then a first-order polynomial is used for fitting.

[0044] Furthermore, in step S6, the specific formula for reconstructing the phase difference correction data at arbitrary frequencies is as follows:

[0045]

[0046] Where, f = (1 f 1 f 2 … f p ) 1×(p+1) , Here, p represents the polynomial parameter and the degree of the polynomial.

[0047] The beneficial effects of this invention are as follows:

[0048] This invention employs a polynomial fitting method to better model the relationship between phase difference correction data and frequency, closely reflecting the actual situation of the system and possessing universality, while also improving calibration accuracy. Compared to traditional methods, the polynomial fitting method reduces the number of frequency points that need to be collected, thereby reducing calibration time. Furthermore, this method only requires sending the polynomial coefficients to the FPGA for application, reducing the storage space required.

[0049] The method filters out invalid data through amplitude-frequency filtering and phase difference filtering. At the same time, by statistically analyzing the number of valid and invalid points, the confidence level of the current correction can be obtained, thereby improving the accuracy of the correction data and enhancing the stability and robustness of the correction. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the overall process of the method.

[0051] Figure 2 This is a schematic diagram of the data processing flow.

[0052] Figure 3 This is a graph showing the relationship between phase difference data and frequency before transformation.

[0053] Figure 4 This is a graph showing the relationship between the transformed phase difference data and the frequency.

[0054] Figure 5 This is a schematic diagram of a two-element antenna phase interference model. Detailed Implementation

[0055] The technical solutions in the embodiments of the present invention are clearly and completely described in the following description. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0056] In the description of the embodiments of the present invention, it should be noted that the indicated orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of the invention is conventionally placed during use, or the orientation or positional relationship in which those skilled in the art conventionally understand it during use. This is only for the convenience of describing the present invention and simplifying the description, and is not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of the present invention. Furthermore, the terms "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0057] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0058] Example 1

[0059] Embodiment 1 of the present invention discloses a phase correction method based on polynomial fitting, such as... Figure 1 As shown, the specific steps are as follows:

[0060] S1: Based on the set frequency interval, collect the phase difference data of each frequency point to form correction data (frequency point, phase difference).

[0061] like Figure 3 As shown, since the phase output value range of the signal phase detector is (0, 2π), when the signal frequency changes continuously, it may exceed the phase detection range, which will cause the phase difference data to flip, and the phase difference correction data and frequency will show a segmented relationship.

[0062] In this embodiment, the number of times the phase difference data is flipped, N, is based on... 翻转 The correction data is divided into (N) 翻转 +1) segment, i.e. Figure 3 There are 3 correction data segments.

[0063] like Figure 2 As shown, the data processing flow for polynomial fitting is as follows:

[0064] S2: Transform the phase difference data and estimate the phase difference value;

[0065] Because the phase difference data of nearby frequency points fluctuates too much during the flip, directly using the initial correction data for polynomial fitting has poor results and requires a high order (high complexity). Therefore, it is necessary to identify the flip point and transform the phase difference data.

[0066] In this embodiment, by traversing the collected phase difference data and identifying the flip points of the phase difference data, the phase difference data is transformed, including:

[0067] Obtain the current frequency and corresponding phase difference data. And the next frequency point and the corresponding phase difference correction data Determine the flipping status of the phase difference data;

[0068] Based on the aforementioned flipping situation, the next phase difference data is transformed accordingly until all phase difference data has been traversed.

[0069] In this embodiment, f is also estimated during the traversal of phase difference data. 间隔 The existing phase difference values ​​are calculated starting from the completion of the transformation process of the second segment of phase difference data. After each segment of phase difference data is transformed, the latest phase difference value is calculated until the traversal is completed. The smallest phase difference value is taken as the estimated phase difference value, which is used for phase difference value filtering.

[0070] Specifically, according to We can obtain:

[0071]

[0072] Where f2 > f1 (unit: 1MHz), These are the phase difference data at frequency f2. It is the phase difference data at frequency f1; when l is constant, the same frequency interval has the same phase difference value.

[0073] Therefore, in order to identify the flip point, in this embodiment, it is assumed that the number of points in each segment of correction data is at least T. 翻转点数 That is, the maximum phase difference between two adjacent frequency points is Only then can we determine whether the data has been flipped.

[0074] Record the current data Data with the next shot

[0075] when Recorded as TJ 翻转大到小 ;

[0076] when Recorded as TJ 翻转大到小 ;

[0077] Where T 未翻转 The threshold for counting unflipped items;

[0078] Let the threshold for segment counting be T. 段数 The phase difference of the data in this correction is 1. It is initialized to 2π, and the unflipped number N is... 未翻转 Set to 0, segment number N 段数 Set to 0, toggle the start flag F 翻转开始 If false, flip time marker F 翻转时刻 It is false; the latest flip time is f. now The previous flip time was f. Last .

[0079] Iterate through the collected phase difference data and identify the flip points;

[0080] If TJ翻转大到小 Then the start flag F will be flipped. 翻转开始 Set to true and perform correction on the next beat data. Transformation processing; transforming the unflipped number N 未翻转 Set to 0; simultaneously determine the flip time flag F. 翻转时刻 Is it false? If it is false, then set the current frequency f. now The frequency f assigned to the previous frequency point Last and the current frequency f now Update to the next frequency point at frequency f (i+1) At the same time, the flip time flag F 翻转时刻 Set to true;

[0081] If TJ 翻转小到大 Then the start flag F will be flipped. 翻转开始 Set to false, unflipped number N 未翻转 Set to 0;

[0082] If no flip occurs, meaning the phase difference data does not satisfy TH... 翻转大到小 Not satisfied with TH 翻转小到大 Then determine the start of the flip flag F. 翻转开始 If true, then adjust the correction data for the next beat. The transformation process, and the unflipped number N 未翻转 Increment the count by 1; otherwise, adjust the correction data for the next beat. Transformation processing;

[0083] Then determine N 未翻转 Is it equal to T? 未翻转 If they are equal, it means that the correction data transformation for that segment is complete, then the segment number N is... 段数 Increment the counter by 1, and flip the start flag F. 翻转开始 Set to false, unflipped number N 未翻转 Set to 0, flip time flag F 翻转时刻 Set as false;

[0084] Then determine N 段数 Does N satisfy? 段数 ≤T 段数 And N 段数 ≥2, if satisfied, then based on the latest flip time f now and the previous flip time f Last Calculate the latest phase difference value:

[0085]

[0086] If they are not equal, continue to traverse the correction data and perform transformation processing;

[0087] The relationship between the transformed phase difference data and frequency, such as Figure 4 As shown.

[0088] After traversing all the correction data, determine the start of the flip flag F. 翻转开始 Is it true? If true, then reduce the number of segments N. 段数 Increment the counter by 1, and determine N. 段数 Does N satisfy? 段数 ≤T 段数 And N 段数 ≥2, if satisfied, then use f now Assignment f Last Update f now f ( i +1) And calculate the latest phase difference value.

[0089] The smallest phase difference value in the above process is taken as the estimated phase difference value.

[0090] S3: Perform data filtering to remove invalid data;

[0091] The collected correction data may be invalid for various reasons. If it is used forcibly, it will directly affect the final calculated phase difference correction data, thus affecting the correction accuracy. Therefore, it is necessary to screen the data.

[0092] In this embodiment, filtering is performed based on the phase difference value, as detailed below:

[0093] Get the current data to be filtered The data to be filtered in the previous batch Perform the following calculations:

[0094]

[0095] If the result is If the data is within the specified range, then the data to be filtered is valid; otherwise, it is invalid. In this step, if only one filtering is performed based on the phase difference, then the data to be filtered is the data after the above transformation process.

[0096] Among them, f 间隔 For current data Data with the next shot The frequency difference, i.e., f (i+1) -f i =f 间隔 , T is the estimated value of the phase difference. 抖动 The threshold is used to characterize the range of phase difference jitter.

[0097] S4: Determine whether the data collected for this correction is valid. If it is valid, then use the data based on the polynomial fitting; otherwise, report the data collected for this correction as invalid.

[0098] The specific process is as follows:

[0099] Based on the above screening process, the number N of invalid correction data in this correction data is obtained. 筛选无效 The number of effective correction data N 筛选有效 Obtain the proportion of valid data in the data collected for this calibration:

[0100]

[0101] If the proportion of valid data in the data collected during this correction is not less than the valid threshold, and the number of valid data is greater than 1, then the condition is satisfied. If the data is correct, the correction is valid; otherwise, the correction is invalid.

[0102] S5: Perform polynomial fitting based on valid data, calculate polynomial coefficients, and obtain polynomial parameters;

[0103] In this embodiment, a polynomial is used. To fit and correct the data (frequency points, phase differences); where y represents the effective phase difference data, x represents the effective frequency point data, and a n The coefficients represent the fitting coefficients, where n∈[0,p];

[0104] After the above steps, the number N of valid correction data is obtained. 筛选有效 and correction data Solving using the least squares method, we obtain:

[0105] a=(X T X) -1 X T Y

[0106] Among them, matrix

[0107] In this embodiment, based on the number of valid data N 筛选有效 Using N p Fitting with a polynomial of degree N or degree 1, where N p >1;

[0108] If [N] 筛选有效 >(N p +1)], then use N p Fitting with a polynomial of degree 1;

[0109] If (N) 筛选有效 ≥2) and N 筛选有效≤(N p If +1), then a first-order polynomial is used for fitting.

[0110] S6: Send the polynomial parameters to the FPGA to reconstruct phase difference data at arbitrary frequencies for compensation.

[0111] FPGA applicable formulas Reconstruct phase difference data at arbitrary frequencies and compensate for phase inconsistencies between channels;

[0112] Where, f = (1 f 1 f 2 … f p ) 1×(p+1) , For a polynomial of degree p, where p represents the degree of the polynomial.

[0113] Example 2

[0114] Embodiment 2 of the present invention discloses a phase correction method based on polynomial fitting, such as... Figure 1 As shown, the specific steps are as follows:

[0115] S1: Based on the set frequency interval, collect the phase difference data of each frequency point to form correction data (frequency point, phase difference).

[0116] In this embodiment, a typical 4-baseline phase interferometer direction finding system is used, according to the frequency interval f. 间隔 Taking 60MHz acquisition and correction data as an example, we will set the threshold T for the number of points in each segment to determine whether the data is flipped. 翻转点数 The threshold for unflipped counts is 10. 未翻转 The threshold for segment counting is 5. 段数 Assuming the four channels of the 4-baseline phase interferometer direction finding system are A, B, C, and D, the correction data between channels A and B are shown in Table 1 below.

[0117] Table 1: Calibration data between channels A and B;

[0118]

[0119]

[0120] The meanings of the symbols in the table are as follows:

[0121] Phi AB Phase difference between antenna elements A and B;

[0122] Pa A The amplitude of antenna element A;

[0123] Pa B: Amplitude of antenna element B;

[0124] Pa C The amplitude of antenna array element C;

[0125] Pa D The amplitude of antenna element D;

[0126] like Figure 3 As shown, since the phase output value range of the signal phase detector is (0, 2π), when the signal frequency changes continuously, it may exceed the phase detection range, which will cause the phase difference data to flip, and the phase difference correction data and frequency will show a segmented relationship.

[0127] In this embodiment, the number of times the phase difference data is flipped, N, is based on... 翻转 The correction data is divided into (N) 翻转 +1) segment, i.e. Figure 3 There are 3 correction data segments.

[0128] like Figure 2 As shown, the data processing flow for polynomial fitting is as follows:

[0129] S2: Transform the phase difference data and estimate the phase difference value;

[0130] Because the phase difference data of nearby frequency points fluctuates too much during the flip, directly using the initial correction data for polynomial fitting has poor results and requires a high order (high complexity). Therefore, it is necessary to identify the flip point and transform the phase difference data.

[0131] In this embodiment, by traversing the collected phase difference data and identifying the flip points of the phase difference data, the phase difference data is transformed, including:

[0132] Obtain the current frequency and corresponding phase difference data. And the next frequency point and the corresponding phase difference correction data Determine the flipping status of the phase difference data;

[0133] Based on the aforementioned flipping situation, the next phase difference data is transformed accordingly until all phase difference data has been traversed.

[0134] In this embodiment, f is also estimated during the traversal of phase difference data. 间隔 The existing phase difference values ​​are calculated starting from the completion of the transformation process of the second segment of phase difference data. After each segment of phase difference data is transformed, the latest phase difference value is calculated until the traversal is completed. The smallest phase difference value is taken as the estimated phase difference value, which is used for phase difference value filtering.

[0135] Specifically, according to We can obtain:

[0136]

[0137] Where f2 > f1 (unit: 1MHz), These are the phase difference data at frequency f2. It is the phase difference data at frequency f1; when l is constant, the same frequency interval has the same phase difference value.

[0138] Therefore, in order to identify the flip point, in this embodiment, it is assumed that the number of points in each segment of correction data is at least T. 翻转点数 That is, the maximum phase difference between two adjacent frequency points is Only then can we determine whether the data has been flipped.

[0139] Record the current data Data with the next shot

[0140] when Recorded as TJ 翻转大到小 ;

[0141] when Recorded as TJ 翻转大到小 ;

[0142] Where T 未翻转 The threshold for counting unflipped items;

[0143] Let the threshold for segment counting be T. 段数 The phase difference of the data in this correction is 1. It is initialized to 2π, and the unflipped number N is... 未翻转 Set to 0, segment number N 段数 Set to 0, toggle the start flag F 翻转开始 If false, flip time marker F 翻转时刻 It is false; the latest flip time is f. now The previous flip time was f. Last .

[0144] Iterate through the collected phase difference data and identify the flip points;

[0145] If TJ 翻转大到小 Then the start flag F will be flipped. 翻转开始 Set to true and perform correction on the next beat data. Transformation processing; transforming the unflipped number N 未翻转 Set to 0; simultaneously determine the flip time flag F. 翻转时刻 Is it false? If it is false, then set the current frequency f. now The frequency f assigned to the previous frequency point Last and the current frequency f nowUpdate to the next frequency point at frequency f (i+1) At the same time, the flip time flag F 翻转时刻 Set to true;

[0146] If TJ 翻转小到大 Then the start flag F will be flipped. 翻转开始 Set to false, unflipped number N 未翻转 Set to 0;

[0147] If no flip occurs, meaning the phase difference data does not satisfy TJ 翻转大到小 Not satisfied with TJ 翻转小到大 Then determine the start of the flip flag F. 翻转开始 If true, then adjust the correction data for the next beat. The transformation process, and the unflipped number N 未翻转 Increment the count by 1; otherwise, adjust the correction data for the next beat. Transformation processing;

[0148] Then determine N 未翻转 Is it equal to T? 未翻转 If they are equal, it means that the correction data transformation for that segment is complete, then the segment number N is... 段数 Increment the counter by 1, and flip the start flag F. 翻转开始 Set to false, unflipped number N 未翻转 Set to 0, flip time flag F 翻转时刻 Set as false;

[0149] Then determine N 段数 Does N satisfy? 段数 ≤T 段数 And N 段数 ≥2, if satisfied, according to the latest flip time f now and the previous flip time f Last Calculate the latest phase difference value:

[0150]

[0151] If they are not equal, continue to traverse the correction data and perform transformation processing;

[0152] The relationship between the transformed phase difference data and frequency, such as Figure 4 As shown.

[0153] After traversing all the correction data, determine the start of the flip flag F. 翻转开始 Is it true? If true, then reduce the number of segments N. 段数 Increment the counter by 1, and determine N. 段数 Does N satisfy? 段数 ≤T 段数 And N 段数 ≥2, if satisfied, then use f nowAssignment f Last Update f now f (i+1) And calculate the latest phase difference value.

[0154] The smallest phase difference value in the above process is taken as the estimated phase difference value.

[0155] Based on the data described above in this embodiment, the estimated phase difference value is...

[0156] The corrected data after data transformation is shown in Table 2 below:

[0157] Table 2: Correction data between transformed channels A and B;

[0158]

[0159]

[0160] The symbols in the table have the following meanings:

[0161] Ph i ′ AB S3: Phase difference between A and B after transformation. S4: Perform data filtering to remove invalid data.

[0162] The collected correction data may be invalid for various reasons. If it is used forcibly, it will directly affect the final calculated phase difference correction data, thus affecting the correction accuracy. Therefore, it is necessary to screen the data.

[0163] In this embodiment, data filtering is first performed using amplitude-frequency filtering, and the specific process is as follows:

[0164] Obtain the actual frequency f of each frequency point collected during calibration. a and the amplitude PA of each array element i i ;

[0165] Calculate the known true frequency f of the system signal source. r The actual frequency f of each frequency point collected during calibration a The difference is used to determine whether it is less than a set first threshold T. f ;

[0166] If the difference is less than the set first threshold T f Furthermore, the amplitude of the array element is greater than the set second threshold. The amplitude difference between any two array elements is less than the set third threshold. If the data is deemed valid, the data to be filtered is obtained; otherwise, the data is invalid.

[0167] That is, satisfy When the data is valid, N 阵元 This indicates the total number of array elements.

[0168] After amplitude-frequency filtering, the effective data obtained after amplitude-frequency filtering is further filtered by phase difference filtering, as follows:

[0169] Get the current data to be filtered The data to be filtered in the previous batch Perform the following calculations:

[0170]

[0171] If the result is If the data is within the specified range, then the data to be filtered is valid; otherwise, it is invalid. In this step, if only one filtering is performed based on the phase difference, then the data to be filtered is the data after the above transformation process.

[0172] Among them, f 间隔 For current data Data with the next shot The frequency difference, i.e., f (i+1) -f i =f 间隔 , T is the estimated value of the phase difference. 抖动 The threshold is used to characterize the range of phase difference jitter.

[0173] Specifically, the current data can be obtained by traversing the correction data. Data with the next shot like but The initial valid data is stored in a new array during the traversal, which is the data to be filtered. Alternatively, all correction data can be traversed directly to perform amplitude and frequency filtering and phase difference filtering. In other words, invalid data can be removed during the traversal. The specific traversal logic is not specifically limited here.

[0174] Based on the data described above in this embodiment, this embodiment sets a threshold T for the difference between the actual frequency and the true frequency. f For 3MHz, the single correction amplitude threshold T PA_ 1 is 50, and the correction amplitude difference threshold T PA_ 2 is 30, the jitter threshold T when filtering phase difference values. 抖动 The value is 1.

[0175] After filtering the data using the above steps, we can conclude that:

[0176] The actual frequency of the 10920MHz calibration point in Table 2 above is 10930MHz, and the difference of 10MHz exceeds the threshold T. f The data does not meet the amplitude-frequency filtering requirements and is therefore invalid.

[0177] In Table 2 above, at the correction frequency of 12840MHz, the amplitude difference between antenna element A and element D exceeds the threshold T. PA_ 2. Data that does not meet the amplitude-frequency filtering requirements is invalid.

[0178] The phase difference between the calibration frequency of 11820MHz and the calibration frequency of 11760MHz in Table 2 above is... Data that does not meet the phase difference filtering requirements is invalid.

[0179] The filtered valid data is shown in Table 3 below;

[0180] Table 3: Valid data after filtering;

[0181]

[0182]

[0183] S4: Determine whether the data collected for this correction is valid. If it is valid, then use the data based on the polynomial fitting; otherwise, report the data collected for this correction as invalid.

[0184] The specific process is as follows:

[0185] Based on the above screening process, the number N of invalid correction data in this correction data is obtained. 筛选无效 The number of effective correction data N 筛选有效 Obtain the proportion of valid data in the data collected for this calibration:

[0186]

[0187] If the proportion of valid data in the data collected during this correction is not less than the valid threshold, and the number of valid data is greater than 1, then the condition is satisfied. If the data is correct, the correction is valid; otherwise, the correction is invalid.

[0188] Specifically, based on the above data, the number of invalid data points N 筛选无效 =3, number of valid data points N 筛选有效 =40;

[0189] In this embodiment, a threshold T is set to determine whether the current correction is effective. 本次有效 If the value is 0.8, then:

[0190]

[0191] S5: Perform polynomial fitting based on valid data, calculate polynomial coefficients, and obtain polynomial parameters;

[0192] In this embodiment, a polynomial is used. To fit and correct the data (frequency points, phase differences); where y represents the effective phase difference data, x represents the effective frequency point data, and a n The coefficients represent the fitting coefficients, where n∈[0,p];

[0193] After the above steps, the number of valid correction data points M is obtained. 筛选有效 and correction data Solving using the least squares method, we obtain:

[0194] a=(X T X) -1 X T Y

[0195] Among them, matrix

[0196] In this embodiment, based on the number of valid data N 筛选有效 Using N p Fitting with a polynomial of degree N or degree 1, where N p >1;

[0197] If [N] 筛选有效 >(N p +1)], then use N p Fitting with a polynomial of degree 1;

[0198] If (N) 筛选有效 ≥2) and N 筛选有效 ≤(N p If +1), then a first-order polynomial is used for fitting.

[0199] In this embodiment, N is set to be used. p If we fit the equation to a 5th-degree polynomial, then we have:

[0200] N 筛选有效 =40>(N p +2)

[0201] Use f a and Phi′ AB The polynomial fitting parameters can be calculated.

[0202] S6: Send the polynomial parameters to the FPGA to reconstruct phase difference data at arbitrary frequencies for compensation.

[0203] The fitting parameters obtained in step S5 are sent to the FPGA, which can then apply the following formula:

[0204] Phi′ AB =f×a

[0205] The phase difference correction data at any frequency point is recovered, thereby compensating for the phase deviation, where f = (1 / f) 1 f 2 f 3 f 4 f 5 ) 1×(5+1) , .

[0206] Based on Phi′ AB =f×a, reconstruct the phase difference data of the frequency points between 11000MHz and 12000MHz according to the 20M step, as shown in Table 4 below;

[0207] Table 4: Phase difference data of frequencies between 11000MHz and 12000MHz reconstructed using a 20MHz step.

[0208]

[0209]

[0210] As shown in the table above, the phase difference at any frequency point can be recovered by using polynomial fitting through the above processing method, and the system's requirements for correction data are met.

[0211] In addition, by increasing the frequency step of the acquisition frequency point (from 20MHz to 60MHz), the correction rate was improved, and by storing polynomial fitting parameters instead of storing correction data for each frequency point, the storage footprint of the FPGA was reduced.

[0212] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A phase correction method based on polynomial fitting, characterized in that, include: S1: Collect phase difference data at each frequency point based on the set frequency interval; S2: Transform the phase difference data and estimate the phase difference value; By traversing the collected phase difference data and identifying the flip points of the phase difference data, the phase difference data is transformed, as follows: Obtain the current frequency and corresponding phase difference data. And the next frequency point and the corresponding phase difference correction data Determine the flipping status of the phase difference data; Based on the aforementioned flipping situation, the next phase difference data is transformed accordingly until all phase difference data has been traversed. In traversing the phase difference data, starting from the completion of the transformation process of the second segment of phase difference data, after each segment of phase difference data transformation process is completed, the latest phase difference value is calculated until the traversal is completed, and the smallest phase difference value is taken as the estimated value of the phase difference value. S3: Perform data filtering to remove invalid data; Data filtering is performed using phase difference values, as detailed below: Get the current data to be filtered The data to be filtered in the previous batch Perform the following calculations: If the result is If the data falls within the specified range, the current data to be filtered is considered valid; otherwise, it is considered invalid. in, The frequency difference between the current data and the next data point. This is an estimate of the phase difference. A threshold characterizing the range of phase difference jitter; Before phase difference filtering, amplitude frequency filtering is also included, which is specifically as follows: Acquire the actual frequency of each frequency point and the amplitude of each array element collected during calibration; Calculate the difference between the known true frequency of the system signal source and the actual frequency of each frequency point collected during calibration, and determine whether it is less than the set first threshold. If the difference is less than the set first threshold, the amplitude of any array element is greater than the set second threshold, and the amplitude difference between any two array elements is less than the set third threshold, then the data is determined to be valid and the data to be filtered is obtained; otherwise, the data is invalid. S4: Determine whether the data collected for this correction is valid. If it is valid, then use the data based on the polynomial fitting; otherwise, report the data collected for this correction as invalid. S5: Perform polynomial fitting based on valid data, calculate polynomial coefficients, and obtain polynomial parameters; S6: Send the polynomial parameters to the FPGA to reconstruct phase difference data at arbitrary frequencies for compensation.

2. The phase correction method based on polynomial fitting according to claim 1, characterized in that, The number of times the phase difference data is flipped The phase difference data is divided into +1 paragraph.

3. The phase correction method based on polynomial fitting according to claim 1, characterized in that, The specific process for determining whether the data collected in this correction is valid is as follows: Obtain the proportion of valid data in the data collected for this calibration. If the proportion of valid data in the data collected for this correction is not less than the valid threshold, and the number of valid data is greater than 1, then the data collected for this correction is valid.

4. The phase correction method based on polynomial fitting according to claim 1, characterized in that, In step S5, the process of obtaining the polynomial parameters is as follows: Obtain valid correction data and the number of valid data points, and perform fitting based on a polynomial, which is expressed as follows: in, y This represents the effective phase difference data. x Indicates valid frequency point data. Represents the fitting coefficient. ; Solving using the least squares method yields the polynomial parameters. .

5. The phase correction method based on polynomial fitting according to claim 4, characterized in that, Based on the number of valid data ,use Fitting with either a first-order polynomial or a second-order polynomial, where ; like Then use Fitting with a polynomial of degree 1; like and If so, then a first-order polynomial is used for fitting.

6. The phase correction method based on polynomial fitting according to claim 1, characterized in that, In step S6, the reconstructing of phase difference correction data at arbitrary frequencies is specifically achieved using the following formula: in, , For polynomial parameters, p This indicates the degree of the polynomial.

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