A signal sorting method based on improved square sinusoidal interpolation

Abstract

This invention discloses a signal sorting method based on improved sine interpolation, comprising: constructing an arrival time model of a mixed pulse sequence, converting the arrival time model of the mixed pulse sequence into a discrete signal; calculating the difference interval sequence of the discrete signal according to an initial difference series, and clustering and correcting the difference interval sequence to obtain a corrected difference interval sequence; calculating the sine interpolation function of the corrected difference interval sequence, and calculating the Fourier transform result of the sine interpolation function of the corrected difference interval sequence; calculating the detection threshold corresponding to different difference intervals, and using the threshold criterion to select the value of the pulse repetition interval estimated in this round according to the detection threshold and the Fourier transform result; separating the pulse sequence corresponding to the value of the pulse repetition interval estimated in this round from the mixed pulse sequence, and performing the next round of pulse sequence sorting of the mixed pulse sequence according to a preset sorting judgment condition.

Description

Technical Field

[0001] This invention belongs to the field of signal sorting in Electronic Support Measures (ESM), and in particular relates to a signal sorting method based on improved square sine interpolation (SSI). Background Technology

[0002] An ESM (Electronic Signal Sorting) system is a device that uses passive reception and signal processing techniques to measure radar radiation source parameters and identify the attributes of the radiation sources. Radar signal sorting is a key issue for ESM systems. In complex electromagnetic environments, the signals received by the receiver are mixed pulse streams containing multiple electromagnetic signals from different radars. Only by identifying different radar radiation sources from the received signals can effective countermeasures be taken.

[0003] With the rapid development of radar technology, various functions and new radar systems are widely used, leading to increasingly complex electromagnetic environments. On one hand, this complex environment results in signals intercepted by receivers being densely and randomly mixed in time, spectrum, and space, with signal density exceeding one million pulses per second, causing mutual interference between multiple radar signals. On the other hand, to protect their own radar, advanced radar systems employ anti-interference techniques such as low probability of intercept (LPI) signals. Combined with receiver limitations, this results in severe pulse loss in the intercepted signals. Simultaneously, quantization errors, measurement noise, and human intervention can cause significant PRI (Pulse Repetition Interval) jitter in the received radar pulse sequence. Therefore, the mixed pulse stream intercepted by the receiver is a hybrid radar signal characterized by dense and randomly mixed time, spectrum, and space, accompanied by interference and loss, making radar signal sorting extremely challenging.

[0004] There are many existing radar signal sorting algorithms, and the SSI-based sorting algorithm is one of the important ones. The SSI-based sorting algorithm extracts the periodic components of the mixed pulse stream using the Fast Fourier Transform (FFT) algorithm, which has the advantages of good harmonic suppression performance and high computational efficiency. Furthermore, since the Fourier Transform is a global transform, it is less affected by random interference pulses and pulse missingness. However, the SSI-based sorting algorithm is sensitive to PRI jitter. When the pulse stream intercepted by the receiver has significant PRI jitter or contains jittered PRI signals, the algorithm cannot complete the sorting. Additionally, when the mixed pulse stream contains multiple radar signals arriving simultaneously, the algorithm is prone to misidentification, leading to sorting failure. Summary of the Invention

[0005] In view of the problems in the prior art, the present invention provides a signal sorting method based on improved square sinusoidal difference, which aims to solve at least one of the above problems.

[0006] According to an embodiment of the present invention, a signal sorting method based on improved square sinusoidal interpolation is provided, comprising:

[0007] Construct an arrival time model for a mixed pulse sequence, and then convert the arrival time model of the mixed pulse sequence into a discrete signal;

[0008] Based on the initial difference series, the difference interval sequence of the discrete signal is calculated, and the difference interval sequence is clustered and corrected to obtain the corrected difference interval sequence. Here, the difference series represents the number of pulses in the discrete signal that make the difference interval, and the difference interval sequence has multiple different difference intervals.

[0009] Calculate the square sinusoidal interpolation function of the corrected difference interval sequence, and calculate the Fourier transform result of the square sinusoidal interpolation function of the corrected difference interval sequence;

[0010] Calculate the detection thresholds corresponding to different difference intervals, and based on the detection thresholds and Fourier transform results, use the threshold criterion to select the value of the estimated pulse repetition interval for this round;

[0011] The pulse sequence corresponding to the estimated pulse repetition interval value in this round is separated from the mixed pulse sequence, and the next round of pulse sequence sorting is carried out according to the preset sorting judgment conditions.

[0012] According to an embodiment of the present invention, the arrival time model of the above-mentioned mixed pulse sequence is composed of the superposition of the arrival time model with a fixed pulse repetition interval and the arrival time model with a jittery pulse repetition interval.

[0013] According to an embodiment of the present invention, the above-described method of calculating the difference interval sequence of a discrete signal based on an initial difference series, and clustering and correcting the difference interval sequence to obtain a corrected difference interval sequence includes:

[0014] Based on the initial difference series, calculate the difference interval sequence of the discrete signal, use the first element of the difference interval sequence to initialize the first clustered subclass and the cluster center of the first clustered subclass, and initialize the element count variable;

[0015] Based on the element count variable, the elements to be clustered in the difference interval sequence are obtained, the clustering distance between the element to be clustered and the cluster center of the first clustered subclass is calculated, and the minimum clustering distance is obtained.

[0016] If the minimum clustering distance is less than the preset clustering distance threshold, update the subclass after the first cluster, the cluster center of the subclass after the first cluster, and the number of elements included in the subclass after the first cluster. The preset clustering distance threshold is determined based on the jitter rate of the pulse repetition interval of the mixed pulse sequence.

[0017] If the minimum clustering distance is greater than or equal to the preset clustering distance threshold, create a new sub-cluster, update the cluster center of the new sub-cluster and the number of elements included in the new sub-cluster, and update the element count variable.

[0018] If the updated element count variable is less than the preset value, the cluster distance calculation operation is performed again, where the preset value is determined based on the number of pulses of the discrete signal;

[0019] If the updated element count variable is greater than or equal to the preset value, the clustering of the difference interval sequence is completed, the difference interval sequence clustering result is obtained, and the difference interval sequence is corrected according to the difference interval sequence clustering result to obtain the corrected difference interval sequence.

[0020] According to an embodiment of the present invention, the above-described calculation of the square sinusoidal interpolation function of the corrected difference interval sequence and the calculation of the Fourier transform result of the square sinusoidal interpolation function of the corrected difference interval sequence include:

[0021] Calculate the square sinusoidal interpolation function for different difference intervals in the corrected difference interval sequence;

[0022] The sinusoidal interpolation function of the corrected difference interval sequence is obtained based on the sinusoidal interpolation function of different difference intervals;

[0023] Calculate the Fourier transform of the square sinusoidal interpolation function of the corrected difference interval sequence.

[0024] According to an embodiment of the present invention, the above-mentioned calculation of the detection thresholds corresponding to different difference intervals, and the selection of the estimated pulse repetition interval for this round based on the detection thresholds and Fourier transform results using the threshold criterion, includes:

[0025] Calculate the Fourier transform of the square sinusoidal interpolation function corresponding to different difference intervals, and calculate the single-sided spectral amplitude value corresponding to different difference intervals based on the Fourier transform.

[0026] Obtain the number of pulses corresponding to different difference intervals within a preset observation time;

[0027] Based on the number of pulses and the amplitude value of the single-sided spectrum, the detection threshold corresponding to different difference intervals is calculated;

[0028] The detection threshold and the Fourier transform results are compared, and based on the comparison results, the value of the estimated pulse repetition interval for this round is selected using the threshold criterion.

[0029] According to an embodiment of the present invention, the above-mentioned comparison of the detection threshold and the Fourier transform result, and the selection of the estimated pulse repetition interval for this round based on the comparison result using the threshold criterion, includes:

[0030] If the comparison result shows that only one Fourier transform result corresponds to a spectral value that exceeds the detection threshold, the period corresponding to the spectral value is used as the value of the pulse repetition interval estimated in this round.

[0031] If the comparison results show that the spectral values ​​corresponding to multiple Fourier transform results exceed the detection threshold, the period corresponding to the largest spectral value is selected as the value of the pulse repetition interval estimated in this round.

[0032] According to an embodiment of the present invention, the above-mentioned separation of the pulse sequence corresponding to the value of the pulse repetition interval estimated in this round from the mixed pulse sequence, and the sorting of the next round of pulse sequences of the mixed pulse sequence according to the preset sorting judgment conditions, includes:

[0033] The search interval coefficient, pulse count variable, and reference pulse count variable are initialized to preset values. The upper limit and lower limit of the search error are determined based on the jitter rate and error noise of the pulse repetition interval of the mixed pulse sequence. The reference pulse is initialized using the discrete signal and the reference pulse count variable.

[0034] The upper limit and lower limit of the pulse search range are calculated based on the interval coefficient, the upper limit of the search error, the lower limit of the search error, the reference pulse, and the value of the pulse repetition interval estimated in this round.

[0035] By using the upper limit of the pulse search range, the lower limit of the pulse search range, and the discrete signal, the single pulse search result is calculated to obtain the set of pulses to be selected;

[0036] If there is only one pulse in the candidate pulse set, update the value of the pulse repetition interval and the pulse count variable estimated in this round, update the search interval coefficient to the preset value, update the reference pulse using the pulses in the candidate pulse set, and re-perform the pulse search range calculation operation and the candidate pulse set acquisition operation.

[0037] If there are multiple pulses in the candidate pulse set, select one pulse that makes the interval between adjacent pulses closest to the value of the pulse repetition interval estimated in this round, update the value of the pulse repetition interval estimated in this round and the pulse count variable, update the search interval coefficient to the preset value, update the reference pulse using the selected pulse, and re-perform the pulse search range calculation operation and the candidate pulse set acquisition operation.

[0038] Based on the preset sorting criteria, the next round of pulse sequence sorting of the mixed pulse sequence is carried out.

[0039] According to an embodiment of the present invention, the process of separating the pulse sequence corresponding to the estimated pulse repetition interval value in this round from the mixed pulse sequence, and performing the next round of pulse sequence sorting of the mixed pulse sequence according to a preset sorting judgment condition, further includes:

[0040] Obtain the maximum value of the discrete signal, and then calculate the result by comparing the maximum value of the discrete signal with the upper limit of the search error.

[0041] If the upper limit of the search range is greater than the calculation result, a comparison operation is performed between the pulse count variable and the pulse quantity threshold.

[0042] According to an embodiment of the present invention, the process of separating the pulse sequence corresponding to the estimated pulse repetition interval value in this round from the mixed pulse sequence, and performing the next round of pulse sequence sorting of the mixed pulse sequence according to a preset sorting judgment condition, further includes:

[0043] If there are no pulses in the candidate pulse set, update the search interval coefficient and re-perform the pulse search range calculation and candidate pulse set acquisition operations.

[0044] According to an embodiment of the present invention, the above-mentioned sorting of the next round of pulse sequences of the mixed pulse sequence according to the preset sorting judgment conditions includes:

[0045] If the pulse count variable is greater than the pulse number threshold, the sorting of the mixed pulse sequence ends, where the pulse number threshold represents the number of pulse sequences in the mixed pulse sequence;

[0046] If the pulse count variable is less than or equal to the pulse number threshold, update the reference pulse count variable and perform the next round of pulse sequence sorting for the mixed pulse sequence;

[0047] The difference between the number of pulses in the discrete signal and the pulse count threshold is calculated. If the updated reference pulse count variable is greater than the difference, the sorting of the mixed pulse sequence ends.

[0048] If the updated reference pulse count variable is less than or equal to the difference, the reference pulse is updated using the updated reference pulse count variable and the discrete signal, and the pulse count variable and the search interval coefficient are updated to the preset value.

[0049] This invention proposes a signal sorting algorithm based on an improved SSI (Signal Sine Interpolation). This algorithm uses an improved square sinusoidal interpolation method to improve the sorting accuracy of jitter signals. In addition, a threshold criterion is proposed to suppress the mutual interference of multi-pulse sequences, solving the problems existing in the prior art. This is of great significance for improving the function and performance of ESM (Electronic Counter Measures) and ECM (Electronic Counter Measures). Attached Figure Description

[0050] Figure 1 This is a flowchart of a signal sorting method based on improved square sinusoidal difference according to an embodiment of the present invention;

[0051] Figure 2 This is a flowchart illustrating the process of obtaining the corrected difference interval sequence according to an embodiment of the present invention;

[0052] Figure 3 This is a flowchart illustrating the process of obtaining the estimated pulse repetition interval value for this round according to an embodiment of the present invention;

[0053] Figure 4 This is a flowchart illustrating how, according to an embodiment of the present invention, a pulse sequence corresponding to the value of the pulse repetition interval estimated in this round is separated from a mixed pulse sequence;

[0054] Figure 5 This is a flowchart illustrating the sorting of the next round of pulse sequences in a mixed pulse sequence according to preset sorting judgment conditions, based on an embodiment of the present invention.

[0055] Figure 6 This is a flowchart of a signal sorting method based on improved square sinusoidal output value according to another embodiment of the present invention;

[0056] Figure 7 The first round of sorting results is shown in the image below;

[0057] Figure 8 The second round of sorting results is shown in the image below;

[0058] Figure 9 The third round of sorting results is shown in the image below;

[0059] Figure 10 The fourth round of sorting results is shown in the image below;

[0060] Figure 11 The results of the fifth round of sorting are shown in the figure. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0062] SSI-based sorting algorithms are effective signal sorting algorithms that can suppress harmonics, adapt well to pulse loss and interference pulses, and have high computational efficiency. However, these algorithms also have drawbacks. SSI-based sorting algorithms are sensitive to PRI jitter; furthermore, misidentification can occur when multiple pulse sequences are mixed. To address these issues, this invention proposes a signal sorting algorithm based on improved SSI.

[0063] Figure 1 This is a flowchart of a signal sorting method based on improved square sinusoidal difference according to an embodiment of the present invention.

[0064] like Figure 1 As shown, the above signal sorting method based on the improved square sinusoidal difference includes operations S110 to S150.

[0065] In operation S110, an arrival time model of the mixed pulse sequence is constructed, and the arrival time model of the mixed pulse sequence is converted into a discrete signal.

[0066] Assume t n Let n be the pulse arrival time (TOA), n = 1, 2, ..., N, where N is the number of pulses. The pulse arrival times can be represented by a set, as shown in formula (1):

[0067] T = [t1, t2, ..., t N ] T (1).

[0068] According to an embodiment of the present invention, the arrival time model of the above-mentioned mixed pulse sequence is composed of the superposition of the arrival time model with a fixed pulse repetition interval and the arrival time model with a jittery pulse repetition interval.

[0069] The PRI value of the arrival time model with the fixed pulse repetition interval described above is a constant, and the model can be expressed by formula (2):

[0070] t n+1 =t n +q+t noise (2),

[0071] Where q represents the value of PRI, t noise This indicates noise error.

[0072] The arrival time model of the jitter pulse repetition interval described above has a PRI value that varies randomly within a fixed range, the range of which is determined by the jitter rate. Assuming the center value of the fixed range is q, the jitter rate is δ, and q(n) represents the actual PRI value, then q(n)∈[(1-δ)q,(1+δ)q], the arrival time model of the jitter pulse repetition interval can be expressed by formula (3):

[0073] t n+1 =t n +q(n)+t noise (3).

[0074] For hybrid radar signals, the TOA (Time of Arrival) model is a superposition of the TOA model with the fixed pulse repetition interval and the TOA model with the jitter pulse repetition interval. Furthermore, considering pulse loss and interference signals, the TOA model for hybrid radar signals can be expressed as formula (5):

[0075]

[0076] Where K represents the number of radars, T i Let i∈[1,K], representing the TOA model of the i-th radar; T mi T represents the set of missing pulses from the i-th radar; j This represents a set of interference pulses.

[0077] According to formula (4), the arrival time model of the above mixed pulse sequence can be converted into a discrete signal.

[0078] x[n]=t n ,t n ∈T,n∈[1,N] (5),

[0079] Where T represents the set of received signals TOA.

[0080] In operation S120, the difference interval sequence of the discrete signal is calculated based on the initial difference level, and the difference interval sequence is clustered and corrected to obtain the corrected difference interval sequence. Here, the difference level represents the number of pulses in the discrete signal that are being differentiated, and the difference interval sequence has multiple different difference intervals.

[0081] The difference interval sequence is related to the difference series, which represents the number of pulse sequences that are interspersed between two discrete signals. For example, when the difference series c = 1, the first-level difference interval sequence of the discrete signal is calculated to obtain the first-level difference interval sequence set.

[0082] Figure 2 This is a flowchart illustrating the process of obtaining the corrected difference interval sequence according to an embodiment of the present invention.

[0083] like Figure 2 As shown, based on the initial difference series, the difference interval sequence of the discrete signal is calculated, and the difference interval sequence is clustered and corrected to obtain the corrected difference interval sequence, including operations S210 to S260.

[0084] In operation S210, the difference interval sequence of the discrete signal is calculated based on the initial difference series. The first element of the difference interval sequence is used to initialize the first sub-cluster after clustering and the cluster center of the first sub-cluster after clustering. The element count variable is initialized, where the element count variable is used to represent the position of the element in the difference sequence. For example, when the element count variable is 2, it represents the second element of the difference interval sequence.

[0085] According to formula (6), the difference interval sequence is calculated:

[0086] DS = x[1+c:N] - x[1:Nc] (6),

[0087] For formula (6), when c = 1, DS = {DS(1),DS(2),…DS(N-1)}, where DS(1) = {x[2]-x[1],x[3]-x[2],…,x[N]-x[N-1]}, and DS represents the c-th level difference sequence of the discrete signal x[N].

[0088] The initial cluster subclasses and their cluster centers are determined as follows:

[0089] Cluster initialization: C1 = {DS(1)}, c1 = DS(1), j = 2, M = 1, j represents the element count variable, that is, the initial cluster subclasses and the cluster centers of the initial cluster subclasses are initialized using the first element in the difference interval sequence set, where C i c represents the i-th subclass after clustering; i The cluster center of the i-th subclass is represented by m. i M represents the number of elements in the i-th subclass; M represents the number of subclasses.

[0090] In operation S220, based on the element count variable, the elements to be clustered in the difference interval sequence are obtained, the cluster distance between the elements to be clustered and the cluster centers of the first clustered subclass is calculated, and the minimum cluster distance is obtained.

[0091] The distance between the inter-cluster difference interval and the cluster center is calculated using formula (7):

[0092]

[0093] Where zk∈[1,M], [,zkm]∈min(Dc), zkm represents the position of the minimum value of vector Dc, and zk represents the number of subclasses.

[0094] In operation S230, when the minimum clustering distance is less than the preset clustering distance threshold, update the first subclass after clustering, the clustering center of the first subclass after clustering, and the number of elements included in the first subclass after clustering, where the preset clustering distance threshold is determined according to the jitter rate of the pulse repetition interval of the mixed pulse sequence.

[0095] That is, if Dc(zkm) < Jc, then update subclass C as shown in formula (8): zkm Update:

[0096]

[0097] At the same time, j = j + 1, and perform operation S250.

[0098] The above preset distance threshold Jc is determined according to the jitter rate of the pulse repetition interval of the mixed pulse sequence.

[0099] In operation S240, when the minimum clustering distance is greater than or equal to the preset clustering distance threshold, create a new subclass after clustering, update the clustering center of the new subclass after clustering and the number of elements included in the new subclass after clustering, and update the element count variable.

[0100] That is, if Dc(zkm) ≥ Jc, then create a new subclass according to formula (9) and update the subclass number:

[0101]

[0102] At the same time, j = j + 1, and perform operation S250.

[0103] In operation S250, when the updated element count variable is less than the preset value, recalculate the clustering distance operation, where the preset value is determined according to the number of pulses of the discrete signal.

[0104] When j ≤ N - 1, it means that there are still unclustered difference interval sequences in the difference interval sequence set. If j > N - 1, then perform operation S260.

[0105] In operation S260, when the updated element count variable is greater than or equal to the preset value, complete the clustering of the difference interval sequence, obtain the clustering result of the difference interval sequence, and correct the difference interval sequence according to the clustering result of the difference interval sequence to obtain the corrected difference interval sequence.

[0106] The correction result of the difference interval sequence set is represented as DS.

[0107] In operation S130, calculate the square sine interpolation function of the corrected difference interval sequence, and calculate the Fourier transform result of the square sine interpolation function of the corrected difference interval sequence.

[0108] According to an embodiment of the present invention, the above-mentioned calculation of the sinusoidal interpolation function of the corrected difference interval sequence and the calculation of the Fourier transform result of the sinusoidal interpolation function of the corrected difference interval sequence include: calculating the sinusoidal interpolation function of different difference intervals in the corrected difference interval sequence; obtaining the sinusoidal difference function of the corrected difference interval sequence based on the sinusoidal interpolation function of different difference intervals; and calculating the Fourier transform result of the sinusoidal interpolation function of the corrected difference interval sequence.

[0109] The sine interpolation function s for the i-th difference interval is calculated according to formula (10). i (t):

[0110]

[0111] According to formula (11), calculate the sinusoidal interpolation function s(t) of the set of difference interval sequences:

[0112]

[0113] Calculate the Fourier transform of the square sinusoidal interpolation function s(t).

[0114] In operation S140, the detection thresholds corresponding to different difference intervals are calculated, and based on the detection thresholds and Fourier transform results, the values ​​of the estimated pulse repetition intervals for this round are selected using the threshold criterion.

[0115] Calculate the detection threshold of the improved square sinusoidal interpolation method. Compare the spectral values ​​corresponding to different PRI (Pulse Repetition Interval) in operation S130 with the detection threshold. Use the threshold criterion to select the estimated PRI for this round. If no PRI meets the threshold criterion, update the preset difference level, i.e., c = c + 1, and repeat operation S120 to operation S140. Otherwise, continue with the subsequent operation S150.

[0116] Figure 3 This is a flowchart illustrating the process of obtaining the estimated pulse repetition interval value for this round according to an embodiment of the present invention.

[0117] like Figure 3 As shown, the above calculation of the detection threshold of the sine interpolation function, and the selection of the estimated pulse repetition interval value for this round based on the detection threshold and the Fourier transform result, includes operations S310 to S340.

[0118] In operation S310, the Fourier transform of the sine interpolation function corresponding to different difference intervals is calculated, and the single-sided spectrum amplitude value corresponding to different difference intervals is calculated based on the Fourier transform.

[0119] According to formula (13), calculate s i The Fourier transform of (t) is given by...

[0120]

[0121] Calculate the single-sided spectral amplitude value according to formula (14):

[0122]

[0123] In operation S320, the number of pulses corresponding to different difference intervals within a preset observation time is obtained.

[0124] Calculate the number of difference interval sequences DS(i) within the observation time. When the number of pulses within the observation time is sufficiently large, and these pulses are generated simultaneously by multiple radiation sources, the difference interval between adjacent pulses can be treated as a random event, i.e., the arrival time of the pulse is designated as the Possion point. Assume the observation time is t. N The total number of pulses is N, the number of difference levels is c, and the number of difference intervals DS(i) within the observation time is expressed by formula (15):

[0125] numDS_i=(Nc)e -λDS(i) (15),

[0126] Where λ=N / t N .

[0127] When operating S330, the detection threshold corresponding to different difference intervals is calculated based on the number of pulses and the amplitude value of the single-sided spectrum.

[0128] According to formula (16), calculate the spectral threshold (detection threshold) of the Fourier transform of the square sinusoidal interpolation function s(t):

[0129] TH SW =αDS(i) 2 (Nc)e -λDS(i) / x[N]+W N (16),

[0130] Wherein, α is an adjustable parameter determined by the pulse loss rate; W N This represents the minimum detection threshold, used to suppress noise and cross-interference between pulse sequences.

[0131] In operation S340, the detection threshold and the Fourier transform result are compared, and based on the comparison result, the value of the estimated pulse repetition interval for this round is selected using the threshold criterion.

[0132] The above-mentioned comparison of the detection threshold and the Fourier transform result, and the selection of the pulse repetition interval value for this round based on the comparison result using the threshold criterion, includes: if the comparison result shows that only one Fourier transform result corresponds to a spectral value that exceeds the detection threshold, the period corresponding to the spectral value is taken as the pulse repetition interval value for this round; if the comparison result shows that multiple Fourier transform results correspond to spectral values ​​that exceed the detection threshold, the period corresponding to the largest spectral value is selected as the pulse repetition interval value for this round.

[0133] The result of the Fourier transform of s(t) is compared with the detection threshold. If only one spectral value exceeds the detection threshold, the period corresponding to that spectral value is the estimated PRI value. If multiple spectral values ​​exceed the detection threshold, the period corresponding to the largest spectral value is selected as the estimated PRI value.

[0134] In operation S150, the pulse sequence corresponding to the value of the pulse repetition interval estimated in this round is separated from the mixed pulse sequence, and the next round of pulse sequence sorting is performed according to the preset sorting judgment conditions.

[0135] Based on the PRI value determined in operation S140, operation S150 completes the separation of the pulse sequence corresponding to this PRI value. In the proposed sequence retrieval algorithm, the estimated PRI value is used as the initial PRI value. The PRI value is updated once for each separated pulse until the pulse sequence separation is complete.

[0136] Figure 4 This is a flowchart illustrating how, according to an embodiment of the present invention, a pulse sequence corresponding to the value of the pulse repetition interval estimated in this round is separated from a mixed pulse sequence.

[0137] like Figure 4 As shown, the pulse sequence corresponding to the value of the pulse repetition interval estimated in this round is separated from the mixed pulse sequence, and the next round of pulse sequence sorting operation of the mixed pulse sequence is performed according to the preset sorting judgment conditions, including operation S410 to operation S460.

[0138] In operation S410, the search interval coefficient, pulse count variable, and reference pulse count variable are initialized to preset values. The upper limit and lower limit of the search error are determined based on the jitter rate and error noise of the pulse repetition interval of the mixed pulse sequence. The reference pulse is initialized using the discrete signal and the reference pulse count variable.

[0139] The search interval coefficient sck represents the number of pulse sequences that are separated between the two pulse sequences being searched during each search process. For example, for the pulse sequences x[3] and x[1] that are searched, the search interval coefficient sck = 1.

[0140] Operation S410 is used to initialize parameters used in the separation process, such as the upper limit of error k. max Error lower limit k min The counting variable tt = 1 and the search interval coefficient sck = 1 are used for pulse counting. The reference pulse sequence toan = x[i].

[0141] In operation S420, the upper limit of the pulse search range and the lower limit of the pulse search range are calculated based on the interval coefficient, the upper limit of the search error, the lower limit of the search error, the reference pulse, and the value of the pulse repetition interval estimated in this round.

[0142] According to formula (17), the upper limit and lower limit of the pulse search are obtained:

[0143]

[0144] Where pri represents the estimated pulse repetition interval for this round.

[0145] According to an embodiment of the present invention, the maximum value of the discrete signal is obtained, and the maximum value of the discrete signal is calculated with the upper limit of the search error to obtain the calculation result; if the upper limit of the search range is greater than the calculation result, a comparison operation is performed between the pulse count variable and the pulse quantity threshold. That is:

[0146] TOA max >max(s)*k max If the condition is met, proceed with operation S460; otherwise, proceed with operation S430.

[0147] In operation S430, the upper limit of the pulse search range, the lower limit of the pulse search range, and the discrete signal are used to calculate the single pulse search result and obtain the set of pulses to be selected.

[0148] According to formula (18), calculate the single pulse search result:

[0149] cnn = find((x>TOA) min )&(x≤TOA max )) (18),

[0150] Wherein, cnn represents the position of the element in the discrete signal x[n] that satisfies the search condition.

[0151] According to an embodiment of the present invention, if there are no pulses in the candidate pulse set, the search interval coefficient is updated, and the pulse search range calculation operation and the candidate pulse set acquisition operation are performed again.

[0152] That is, if length(cnn) = 0, then sck = sck + 1, and proceed to operation S420; if

[0153] If length(cnn) = 1, then proceed to operation S440; otherwise, proceed to operation S450.

[0154] In operation S440, if there is only one pulse in the candidate pulse set, update the value of the pulse repetition interval and the pulse count variable estimated in this round, update the search interval coefficient to the preset value, update the reference pulse using the pulses in the candidate pulse set, and re-perform the pulse search range calculation operation and the candidate pulse set acquisition operation.

[0155] According to formula (19), update the value of the estimated pulse repetition interval for this round:

[0156]

[0157] And update the parameters in the relevant separation process, i.e., tt = tt + 1, toan = x[cnn], sck = 1, and then switch to operation S420.

[0158] In operation S450, if there are multiple pulses in the candidate pulse set, select one pulse that makes the interval between adjacent pulses closest to the value of the pulse repetition interval estimated in this round, update the value of the pulse repetition interval estimated in this round and the pulse count variable, update the search interval coefficient to the preset value, update the reference pulse using the selected pulse, and re-perform the pulse search range calculation operation and the candidate pulse set acquisition operation.

[0159] Since multiple pulses satisfy the condition, one pulse is selected such that the interval between adjacent pulses is closest to the value of the pulse repetition interval estimated in this round. Then, the value of the pulse repetition interval estimated in this round is updated according to formula (20):

[0160]

[0161] Where s(tpnum) represents the arrival time of the next separated pulse; and update the parameters in the relevant separation process, i.e. tt=tt+1, toan=x[cnn], sck=1, and then switch to operation S420.

[0162] When operating S460, the next round of pulse sequence sorting of the mixed pulse sequence is carried out according to the preset sorting judgment conditions.

[0163] Figure 5 This is a flowchart illustrating the sorting of the next round of pulse sequences in a mixed pulse sequence according to preset sorting judgment conditions, based on an embodiment of the present invention.

[0164] like Figure 5 As shown, the sorting of the next round of pulse sequences of the mixed pulse sequence according to the preset sorting judgment conditions includes operations S510 to S540.

[0165] In operation S510, if the pulse count variable is greater than the pulse number threshold, the sorting of the mixed pulse sequence ends, where the pulse number threshold represents the number of pulse sequences in the mixed pulse sequence.

[0166] In operation S520, if the pulse count variable is less than or equal to the pulse number threshold, the reference pulse count variable is updated, and the next round of pulse sequence sorting of the mixed pulse sequence is performed.

[0167] In operation S530, the difference between the number of pulses of the discrete signal and the pulse number threshold is calculated. If the updated reference pulse count variable is greater than the difference, the sorting of the mixed pulse sequence ends.

[0168] In operation S540, if the updated reference pulse count variable is less than or equal to the difference, the reference pulse is updated using the updated reference pulse count variable and the discrete signal, and the pulse count variable and the search interval coefficient are updated to the preset value.

[0169] Based on the PRI estimated in operation S140, the pulse sequence corresponding to that PRI is separated. If the pulse sequence is successfully separated, it is determined whether the number of remaining pulses exceeds the sorting threshold. If the number of remaining pulses exceeds the sorting threshold, c=1, and the process returns to operation S120 to start the next round of sorting; if the number of remaining pulses is less than the sorting threshold, the sorting ends.

[0170] If pulse sequence separation fails, adjust the difference level, c = c + 1. If the difference level exceeds the difference level threshold, the sorting ends; if the difference level is less than the difference level threshold, proceed to operation S120 to continue the current round of sorting.

[0171] If tt > TE, pulse sequence separation ends, where TE represents the threshold number of pulses in the pulse sequence; otherwise, i = i + 1. If i > length(x) - TE, pulse sequence separation ends. Otherwise, tt = tt + 1, toan = x[cnn], sck = 1, and proceed to operation S420.

[0172] This invention proposes a signal sorting algorithm based on an improved SSI (Signal Sine Interpolation). This algorithm uses an improved square sinusoidal interpolation method to improve the sorting accuracy of jitter signals. In addition, a threshold criterion is proposed to suppress the mutual interference of multi-pulse sequences, solving the problems existing in the prior art. This is of great significance for improving the function and performance of ESM (Electronic Counter Measures) and ECM (Electronic Counter Measures).

[0173] To better illustrate the advantages of the method provided by the present invention, another embodiment of the present invention will be described below in conjunction with... Figures 5-10 Tables 1 and 2 provide a further detailed explanation of the signal sorting method based on the improved square sinusoidal difference provided by the present invention.

[0174] Figure 6 This is a flowchart of a signal sorting method based on improved square sinusoidal output value according to another embodiment of the present invention.

[0175] like Figure 6 As shown, the above method includes steps 1 to 5.

[0176] Step 1: Construct a TOA (Time of Arrival) model for the mixed pulse sequence and convert the TOA model into a discrete signal.

[0177] Step 2: Calculate the c-th level difference sequence of the discrete signal and perform cluster correction on the difference sequence to overcome the influence of PRI jitter, and initialize c=1.

[0178] Step 3: Calculate the sine square interpolation function of the difference sequence obtained in Step 2, and calculate the FFT (Fast Fourier Transform) of the sine square interpolation function.

[0179] Step 4: Calculate the detection threshold of the SSI algorithm, and use the proposed threshold criterion to screen out the estimated PRI in this round to suppress the mutual interference of multi-pulse sequences; if no PRI meets the threshold criterion, c = c + 1, and return to step 2; otherwise, continue to step 5.

[0180] Step 5: Based on the PRI estimated in Step 4, complete the separation of the pulse sequence corresponding to the PRI. If the pulse sequence is successfully separated, determine whether the number of remaining pulses exceeds the sorting threshold; if the number of remaining pulses exceeds the sorting threshold, then c=1, return to Step 2, and start the next round of sorting; if the number of remaining pulses is less than the sorting threshold, then the sorting ends.

[0181] If pulse sequence separation fails, adjust the difference level, c = c + 1. If the difference level exceeds the difference level threshold, the sorting ends; if the difference level is less than the difference level threshold, go to step 2 and continue the current round of sorting.

[0182] Figures 7 to 11 To improve the simulation results of the SSI algorithm for sorting pulse streams.

[0183] Figure 7 The first round of sorting results is shown in the image, designed to improve the algorithm.

[0184] Figure 8 The results of the second round of sorting were shown in the image, which was designed to improve the algorithm.

[0185] Figure 9The results of the third round of sorting are shown in the figure.

[0186] Figure 10 The results of the fourth round of sorting are shown in the figure.

[0187] Figure 11 The results of the fifth round of sorting are shown in the figure.

[0188] To verify the effectiveness of this invention, the following simulations were performed. The main simulation parameters are shown in Table 1, and the simulation results are as follows: Figures 7-11 As shown. This sorting process consists of five rounds, as follows: Figures 7-11 As shown in the figure. In the first round of sorting, PRI1 = 105 is the estimated PRI result; in the second round, PRI2 = 235.7 is the estimated PRI result; in the third round, PRI3 = 322 is the estimated PRI result; in the fourth round, PRI4 = 555.4 is the estimated PRI result; and in the fifth round, PRI5 = 5885.6 is the estimated PRI result. Simulation results show that, even with pulse loss in the pulse stream, the improved SSI algorithm can successfully sort jittery signals with high PRI value estimation accuracy.

[0189] Table 1. Parameter Table for Mixed Pulse Sequence

[0190]

[0191] Table 2 Simulation results under different parameter conditions

[0192]

[0193] To further verify the effectiveness of the improved sine interpolation algorithm, simulations were conducted under different PRI jitter rates and the number of radiation sources. The simulation results are shown in Table 2. The simulation results show that even with a PRI jitter rate of +15% and a pulse loss rate of 5%, the algorithm can still successfully sort five radar radiation sources.

[0194] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A signal sorting method based on improved sinusoidal interpolation, comprising: constructing a time-of-arrival model of a mixed pulse sequence, and converting the time-of-arrival model of the mixed pulse sequence into a discrete signal; calculating a difference interval sequence of the discrete signal according to an initial difference series, and clustering and correcting the difference interval sequence to obtain a corrected difference interval sequence, including: calculating the difference interval sequence of the discrete signal according to the initial difference series, initializing a first clustered subclass and a cluster center of the first clustered subclass by using a first element of the difference interval sequence, and initializing an element count variable; obtaining an element to be clustered in the difference interval sequence according to the element count variable, calculating a clustering distance between the element to be clustered and the cluster center of the first clustered subclass, and obtaining a minimum clustering distance; in a case where the minimum clustering distance is less than a preset clustering distance threshold, updating the first clustered subclass, the cluster center of the first clustered subclass, and a number of elements included in the first clustered subclass, wherein the preset clustering distance threshold is determined according to a jitter rate of a pulse repetition interval of the mixed pulse sequence; in a case where the minimum clustering distance is greater than or equal to the preset clustering distance threshold, creating a new clustered subclass, updating a cluster center of the new clustered subclass, a number of elements included in the new clustered subclass, and the element count variable; in a case where an updated element count variable is less than a preset value, re-performing a clustering distance calculation operation, wherein the preset value is determined according to a pulse number of the discrete signal; in a case where the updated element count variable is greater than or equal to the preset value, completing clustering of the difference interval sequence to obtain a difference interval sequence clustering result, and correcting the difference interval sequence according to the difference interval sequence clustering result to obtain the corrected difference interval sequence, wherein the difference series represents a pulse number of a difference interval of the discrete signal, and the difference interval sequence has a plurality of different difference intervals; calculating a sinusoidal interpolation function of the corrected difference interval sequence, and calculating a Fourier transform result of the sinusoidal interpolation function of the corrected difference interval sequence; calculating a detection threshold corresponding to each different difference interval, and using a threshold criterion to filter out a value of a pulse repetition interval estimated in a current round according to the detection threshold and the Fourier transform result; separating a pulse sequence corresponding to the value of the pulse repetition interval estimated in the current round from the mixed pulse sequence, and performing sorting of a pulse sequence in a next round of the mixed pulse sequence according to a preset sorting judgment condition.

2. The method of claim 1, wherein, The time-of-arrival model of the mixed pulse sequence is composed of a time-of-arrival model of a fixed pulse repetition interval and a time-of-arrival model of a jittered pulse repetition interval.

3. The method of claim 1, wherein, The calculating of the sinusoidal interpolation function of the corrected difference interval sequence and the calculating of the Fourier transform result of the sinusoidal interpolation function of the corrected difference interval sequence include: calculating a square-sine interpolation function of different difference intervals in the corrected difference interval sequence; obtaining a square-sine difference function of the corrected difference interval sequence according to the square-sine interpolation function of the different difference intervals; calculating a Fourier transform result of the square-sine interpolation function of the corrected difference interval sequence.

4. The method of claim 1, wherein, calculating a detection threshold corresponding to different difference intervals, and filtering out a value of the estimated pulse repetition interval in the current round according to the detection threshold and the Fourier transform result by using a threshold criterion includes: calculating a Fourier transform of the square-sine interpolation function corresponding to different difference intervals, and calculating a one-sided spectrum amplitude value corresponding to the different difference intervals according to the Fourier transform; obtaining a pulse quantity corresponding to different difference intervals within a preset observation time; calculating a detection threshold corresponding to the different difference intervals according to the pulse quantity and the one-sided spectrum amplitude value; comparing the detection threshold and the Fourier transform result, and filtering out a value of the estimated pulse repetition interval in the current round according to a comparison result by using the threshold criterion.

5. The method of claim 4, wherein, comparing the detection threshold and the Fourier transform result, and filtering out a value of the estimated pulse repetition interval in the current round according to a comparison result by using the threshold criterion includes: in a case where the comparison result is that only one spectrum value corresponding to the Fourier transform result exceeds the detection threshold, taking a period corresponding to the spectrum value as the value of the estimated pulse repetition interval in the current round; in a case where the comparison result is that there are multiple spectrum values corresponding to the Fourier transform result exceeding the detection threshold, selecting a period corresponding to a maximum spectrum value as the value of the estimated pulse repetition interval in the current round.

6. The method of claim 1, wherein, separating a pulse sequence corresponding to the value of the estimated pulse repetition interval in the current round from the mixed pulse sequence, and performing sorting of a pulse sequence in a next round of the mixed pulse sequence according to a preset sorting judgment condition includes: initializing a search interval coefficient, a pulse count variable and a reference pulse count variable to preset values, determining an upper search error limit and a lower search error limit according to a jitter rate of a pulse repetition interval of the mixed pulse sequence and error noise, and initializing a reference pulse by using the discrete signal and the reference pulse count variable; calculating an upper pulse search range limit and a lower pulse search range limit according to the interval coefficient, the upper search error limit, the lower search error limit, the reference pulse and the value of the estimated pulse repetition interval in the current round; calculating a pulse single search result by using the upper pulse search range limit, the lower pulse search range limit and the discrete signal, to obtain a pulse candidate set; in a case where the pulse candidate set has only one pulse, updating the value of the estimated pulse repetition interval in the current round and the pulse count variable, updating the search interval coefficient to the preset value, updating the reference pulse by using the pulse in the pulse candidate set, and re-performing a pulse search range calculation operation and a pulse candidate set obtaining operation; In a case where the candidate pulse set contains multiple pulses, one pulse is selected, which makes the interval between adjacent pulses closest to the value of the current estimated pulse repetition interval, the value of the current estimated pulse repetition interval and the pulse count variable are updated, the search interval coefficient is updated to the preset value, the reference pulse is updated using the selected pulse, and the pulse search range calculation operation and the candidate pulse set acquisition operation are performed again; According to a preset sorting judgment condition, the next round of pulse sequence sorting of the mixed pulse sequence is performed.

7. The method of claim 6, further comprising: obtaining a maximum value of the discrete signal, and performing an operation between the maximum value of the discrete signal and the upper limit of the search error to obtain an operation result; in a case where the upper limit of the search range is greater than the operation result, performing the pulse count variable and pulse quantity threshold comparison operation.

8. The method of claim 6, further comprising: in a case where the candidate pulse set contains no pulse, updating the search interval coefficient, and performing the pulse search range calculation operation and the candidate pulse set acquisition operation again.

9. The method of claim 6, wherein, According to a preset sorting judgment condition, the next round of pulse sequence sorting of the mixed pulse sequence is performed, including: in a case where the pulse count variable is greater than the pulse quantity threshold, ending the sorting of the mixed pulse sequence, wherein the pulse quantity threshold represents the number of pulse sequences in the mixed pulse sequence; in a case where the pulse count variable is less than or equal to the pulse quantity threshold, updating the reference pulse count variable, and performing the next round of pulse sequence sorting of the mixed pulse sequence; performing a difference operation between the number of pulses of the discrete signal and the pulse quantity threshold, in a case where the updated reference pulse count variable is greater than the difference value, ending the sorting of the mixed pulse sequence; in a case where the updated reference pulse count variable is less than or equal to the difference value, updating the reference pulse using the updated reference pulse count variable and the discrete signal, and updating the pulse count variable and the search interval coefficient to the preset value.

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