MFR waveform unit extraction method based on step-by-step variable threshold isolation forest

Abstract

The present invention provides a MFR waveform unit extraction method based on step-by-step variable threshold isolation forest. First, the received multifunctional radar pulse signal is tested for leaky pulses and pseudo pulses. After obtaining the first-order differential data of the pulse parameters, the waveform unit start pulse is searched using the step-by-step variable threshold isolation forest algorithm to complete the task of unsupervised extraction of waveform units. Theoretical analysis and simulation experiments show that the method of the present invention can complete the extraction of waveform units with almost no prior knowledge, and at the same time has strong robustness and low computational complexity.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to an MFR waveform unit extraction method based on step-by-step variable threshold isolation forest. Background Art

[0002] Multi-Function Radar (MFR) is an advanced radar system. It is widely deployed and applied because of its multiple capabilities such as search, interception, tracking, distance detection and guidance. It is a large-scale dynamic system that combines the powerful data processing of computers and the beam control capabilities of phased array antennas. Analyzing intercepted radar signals through electronic reconnaissance is an important way to obtain electronic intelligence and electromagnetic situation. With the large-scale application of MFR, MFR working mode recognition has become an important part of modern electronic reconnaissance systems. Effective analysis and identification of MFR radiation source signals can provide important technical support for target threat level judgment. Its level determines the effectiveness of important military activities such as electronic intelligence reconnaissance, electronic countermeasures and fire guidance.

[0003] In order to effectively characterize the system state of MFR and describe the dynamic law of MFR radiation source signal, many literatures have tried to establish MFR signal model concisely and efficiently. Some literatures have equated MFR to finite state machine and used Hidden Markov Model (HMM) to directly model the pulse train. This method uses the timing characteristics between pulse signals and provides a new idea for describing MFR signals. However, it has a large amount of calculation and it is difficult to effectively characterize the operation law of MFR. On this basis, some literatures have constructed and improved the syntactic model, equating MFR signal to a language that conforms to certain grammatical rules, and describing MFR signal from three levels: radar word, radar phrase and radar sentence. The concept of radar word corresponds to the waveform unit of MFR signal, which is the bottom layer of syntactic model. The accuracy and completeness of its extraction directly affect the subsequent analysis of radar phrase and radar sentence. Therefore, the research on MFR waveform unit extraction is of great significance.

[0004] At present, there are some research results on the problem of MFR waveform unit extraction at home and abroad. Some literature uses recurrent neural network (RNN) to extract waveform units from noisy MFR signals, and then uses dynamic time warping algorithm (DTW) to identify MFR working mode based on prior knowledge; some literature proposes a "radar word" extraction algorithm based on three-level matching for the problem of waveform unit extraction, which solves the problem that the previous waveform unit extraction algorithm is sensitive to pulse parameters, and this method is easy to implement in engineering; some literature proposes an improved event-driven radar word extraction method, but this method cannot be applied to the case of small fluctuations in pulse parameters. In addition, the above methods are all based on waveform unit extraction under the framework of supervised learning. It is necessary to obtain prior knowledge such as MFR working mode and signal structure in advance to build a "radar word" template library before extracting waveform units from the received pulse. Considering the non-cooperativeness of target identification and the harshness of the scene in practical applications, this requirement is basically difficult to meet in the field of electronic reconnaissance. Therefore, Reference 1 (Ma Shuang, Liu Zheng, Jiang Wenli. Multifunctional radar pulse train analysis method based on amplitude change point detection [J]. Journal of Electronics, 2013, 41(7):6.) studied the pulse amplitude mutation caused by radar beam pointing switching, and proposed a waveform unit extraction method based on the cyclic binary algorithm based on this feature; Reference 2 (Yang Liu, Zhu Weigang, Lv Shouye, et al. Waveform unit extraction method for non-cooperative multifunctional radar [J]. Systems Engineering and Electronics, 2021, 43(10):8.) studied the change law of multifunctional radar signal pulse parameters and used the DA-DBSCAN algorithm to complete the waveform unit extraction. The above methods complete the waveform unit extraction task based on the characteristics of the radar signal itself, which fits the actual application scenario, but Reference 1 has problems such as poor robustness and Reference 2 has high computational complexity. Summary of the invention

[0005] In order to solve the problem of waveform unit extraction of MFR radiation source under non-cooperative conditions, the present invention proposes a MFR waveform unit extraction method based on step-by-step variable threshold isolation forest based on the syntactic model.

[0006] The present invention provides a MFR waveform unit extraction method based on step-by-step variable threshold isolation forest, comprising:

[0007] Step 1: Each pulse in the received deinterleaved pulse train p is described using three pulse parameters: PRI, RF and PW; where p = {p1, p2, p3…, p n}, p i represents the i-th pulse, i = 1, 2, ..., n; PRI represents the pulse repetition interval, RF represents the radio frequency, and PW represents the pulse width;

[0008] Step 2: Detect whether there are leaking pulses and / or false pulses in the pulse train p and perform corresponding processing;

[0009] Step 3: performing first-order difference processing on the pulse parameters of all pulses in the pulse train p to obtain a difference set {△PRI, △RF, △PW} of adjacent pulse parameters, and forming a data set D according to the difference set {△PRI, △RF, △PW};

[0010] Step 4: Using the isolation forest to construct a waveform unit extraction model based on the dataset D;

[0011] Step 5: Using the waveform unit extraction model to obtain an anomaly score corresponding to each pulse data point in the data set D;

[0012] Step 6: Preset a threshold ε, remove sample points with abnormal scores greater than the threshold ε from the data set D, and put them into the waveform unit starting pulse data set W f In the above example, the removed data set is used as the new data set D;

[0013] Step 7: Repeat steps 4 to 6 until all newly calculated abnormal scores do not exceed the threshold ε or the maximum search number r is reached, and then the search process of the waveform unit starting pulse is terminated. At this time, the waveform unit starting pulse data set W f One start pulse in the waveform corresponds to one MFR waveform unit.

[0014] Furthermore, step 1 specifically includes:

[0015] According to formula (1), each pulse is described by three pulse parameters: PRI, RF and PW:

[0016]

[0017] Among them, x 1i 、x 2i 、x 3i Represent pulse p i PRI, RF and PW.

[0018] Furthermore, step 2 specifically includes:

[0019] If p i With p i-1 If the time satisfies formula (2), then p i With p i-1 There is a leakage pulse between p i With p i-1 Add a pulse p in the middle i-1Pulses with the same RF and PW parameters and updating pulse position information;

[0020]

[0021] If p i If formula (3) is satisfied, then p i For a pseudo pulse, i Delete and update pulse position information from pulse train p;

[0022]

[0023] Wherein, τ represents the matching threshold adjustment parameter, 0<τ<1.

[0024] Furthermore, step 3 specifically includes:

[0025] According to formula (4), the difference set of adjacent pulse parameters is obtained:

[0026]

[0027] Furthermore, step 4 specifically includes:

[0028] Step 4.1: Build the dataset

[0029] Step 4.2: Preset the number of isolated trees t and the number of subsamples of a single isolated tree ψ;

[0030] Step 4.3: From the given dataset Randomly select ψ sample points from to form a new data set D′, and put D′ into the root node of the isolated tree to be trained;

[0031] Step 4.4: Randomly specify a dimension q from the three dimensions of the sample set in the current node data set D′ k A separation point e is randomly generated in the equation, satisfying:

[0032] min(x ji ,j=q,x ji ∈D′ k ) <e<max(x ji ,j=q,x ji ∈D′ k ) (5)

[0033] Among them, D′ k represents the kth data set generated in the process of segmenting the data set D′;

[0034] Step 4.5: Cut the separation point e to generate a hyperplane in the feature space of the selected dimension q, dividing the sample points in the current node into two sub-nodes: xji <The sample points of e are placed in the left child node, x ji >The sample points of x>e are placed in the right child node;

[0035] Step 4.6: Recursively execute Step 4.4 and Step 4.5 until all leaf nodes have only one sample point, or when the current isolation tree reaches the preset height, then exit;

[0036] Step 4.7: Repeat Step 4.3 to Step 4.6 until all t isolation trees are generated.

[0037] Furthermore, Step 5 specifically includes:

[0038] Input all the pulse data points in the dataset D into the waveform unit extraction model composed of t isolation trees, and traverse all the isolation trees to obtain the anomaly score corresponding to each pulse data point; the anomaly score is calculated according to the formula shown in Formula (6):

[0039]

[0040] where, is the path length from the root node to the leaf node in each isolation tree; E(·) represents taking the mean; c(ψ) is the average value of the isolation tree path length when the number of samples is ψ.

[0041] Furthermore, calculate the average value c(ψ) according to Formula (7):

[0042]

[0043] where, H(ψ) = ln(ψ) + ξ, and ξ is the Euler constant.

[0044] Furthermore, and satisfy the relationship shown in Formula (8):

[0045]

[0046] Furthermore, the path length from the root node to the leaf node in each isolation tree should satisfy the condition shown in Formula (9):

[0047]

[0048] Furthermore, in Step 6, the calculation process of the threshold ε specifically includes:

[0049] According to the anomaly score sequence Construct the sequence S′ according to Formula (10):

[0050] S′={S,1-S} (10)

[0051] For the sequence S′, calculate its mean μ and variance σ according to formula (11): 2 :

[0052]

[0053] Where m represents the sequence number of the element in the sequence S′;

[0054] Calculate the threshold ε according to formula (12):

[0055] ε=u+3σ (12).

[0056] Beneficial effects of the present invention:

[0057] The MFR waveform unit extraction method based on step-by-step variable threshold isolation forest provided by the present invention can reduce the algorithm calculation complexity while accurately extracting the waveform unit starting pulse. According to the differences in the changes in the pulse train parameters within the MFR waveform unit and between the waveform units, the method uses the first-order difference value of the pulse parameter to describe the characteristics of the waveform unit switching, converts the waveform unit extraction problem into a binary classification problem of waveform unit starting pulse extraction, and introduces the isolation forest algorithm to search for the waveform unit starting pulse, effectively solving the high computational complexity problem of the traditional clustering-based search for starting pulse algorithms. Experiments show that the method of the present invention has good robustness when facing missed pulses, false pulses, and parameter errors, and at the same time, it has short computational time and excellent performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 One of the flow charts of the MFR waveform unit extraction method based on step-by-step variable threshold isolation forest provided in an embodiment of the present invention;

[0059] Figure 2 A second flow chart of the MFR waveform unit extraction method based on step-by-step variable threshold isolation forest provided in an embodiment of the present invention;

[0060] Figure 3 A joint distribution diagram of MFR pulse signals provided by an embodiment of the present invention;

[0061] Figure 4 A schematic diagram of a threshold value ε provided in an embodiment of the present invention;

[0062] Figure 5 The extraction performance of the method of the present invention and two comparison algorithms under different RDPs provided by the embodiments of the present invention;

[0063] Figure 6 The extraction performance of the method of the present invention and two comparative algorithms under different RFPs provided in the embodiments of the present invention;

[0064] Figure 7 The extraction performance of the method of the present invention and two comparative algorithms under different EDLs provided by the embodiments of the present invention;

[0065] Figure 8 The computational complexity of the method of the present invention and two comparison algorithms under different numbers of waveform units provided in the embodiments of the present invention. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the embodiment of the present invention will be clearly described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] The inventors analyzed the characteristics of MFR radiation source signals in existing literature and found that when the waveform unit is switched, the pulse parameters will change significantly. Based on this characteristic, the present invention selects three pulse-level characteristics with relatively small measurement errors, namely radio frequency (RF), pulse width (PW) and pulse repetition interval (PRI), to describe the MFR radiation source signal, and obtains its first-order differential data to construct a waveform unit extraction model, transforming the waveform unit extraction problem into a binary classification problem of waveform unit starting pulse extraction. Under this concept, Figure 1 As shown, an embodiment of the present invention provides a method for extracting MFR waveform units based on step-by-step variable threshold isolation forest, comprising the following steps:

[0068] S101: Each pulse in the received de-interleaved pulse train p is described using three pulse parameters: PRI, RF and PW; wherein p = {p1, p2, p3…, p n}, p i represents the i-th pulse, i = 1, 2, ..., n; PRI represents the pulse repetition interval, RF represents the radio frequency, and PW represents the pulse width;

[0069] Specifically, a pulse in this step is a radar word, which is proposed in the syntactic model constructed by Visnevski and Haykin, etc. The syntactic model will not be described here. In the syntactic model, the radar word is a pulse with a certain regularity and a limited number of sequential arrangements. It is the minimum overall structure for MFR to complete a single detection and corresponds one-to-one to the waveform unit emitted by the radar.

[0070] The present invention uses three pulse parameters, PRI, RF and PW, to describe the pulse because:

[0071] When it is necessary to perform a specific task in the target area, the multifunction radar will select the corresponding waveform in its own waveform library and transmit it to the target area. The waveforms corresponding to different tasks will have obvious changes in parameters such as radio frequency, pulse width, pulse repetition interval and pulse amplitude. Among them, the change in pulse amplitude is mainly due to the fact that the phased array antenna will cause the amplitude of the transmitted pulse to change significantly when the beam pointing is switched. However, in a real battlefield environment, a large amount of noise and interference will cause the characteristics of the reconnaissance receiver's detection data in the power dimension to have greater distortion than other non-power dimension characteristics, and the waveform unit switching moment is not a one-to-one correspondence with the MFR beam pointing switching moment. Therefore, it is difficult to correctly extract the waveform unit according to the change in pulse amplitude. In comparison, when the multifunction radar switches the waveform unit, although there is a lot of overlap in the RF, PW and PRI parameter ranges of different waveform units, it is found that the degree of parameter fluctuation between adjacent waveform units is greater than the degree of parameter fluctuation within a single waveform unit. And compared with the PA parameter, the measurement errors of the three parameters of RF, PW and PRI are often smaller. Therefore, the inventor creatively thought of realizing the extraction of the waveform unit of the multifunction radar according to the joint change law between the RF, PW and PRI parameters. Therefore, this step uses three parameters, RF, PW, and PRI, to describe each pulse.

[0072] On this basis, as an implementable method, in this embodiment, three pulse parameters of PRI, RF and PW are used to describe each pulse according to formula (1):

[0073]

[0074] Among them, x 1i 、x 2i 、x 3i Respectively represent pulse p i PRI, RF and PW.

[0075] S102: Detect whether there are leaking pulses and / or false pulses in the pulse train p and perform corresponding processing;

[0076] Specifically, when actually detecting and receiving radiation source signals, due to the limitations of the pulse deinterleaving algorithm, interference from complex electromagnetic environments, and non-cooperative reception and processing of the ESM (Electronic Support Measures) system, the pulse train p is prone to missing pulses and false pulses. Among the three pulse description parameters selected by the present invention, PRI is obtained based on the time interval between two adjacent pulses, which means that when missing pulses and false pulses appear in the received pulse train, PRI will be greatly affected. Therefore, for the accuracy of waveform unit extraction, it is necessary to perform parameter correction on these two erroneous pulse situations according to the actual situation of the multi-function radar.

[0077] As an implementable method, in this embodiment, the following method is used to detect whether there is a leakage pulse between two adjacent pulses, specifically:

[0078] If p i With p i-1 If the time satisfies formula (2), then p i With p i-1 There is a leakage pulse between p i With p i-1 Add a pulse p in the middle i-1 Pulses with the same RF and PW parameters and updating pulse position information;

[0079]

[0080] Specifically, for multi-function radar pulse signals, the fluctuation degree of the parameters of adjacent pulses within its waveform unit is relatively small. Generally speaking, in the case of parameter jitter, the change of its parameters will not exceed 30%. Therefore, if the PRI of a pulse suddenly changes drastically to approximately twice the PRI of the adjacent pulse, it can be considered that a leaked pulse has occurred; but in order to avoid misidentifying the PRI change of the starting pulse of the adjacent waveform unit as a leaked pulse, it is also necessary to compare the degree of change in the RF and PW parameters of the current pulse and the pulse at the previous moment to make a comprehensive judgment. Therefore, the above formula (2) includes the following two situations:

[0081] The first case: If x 1i ∈[2(1-τ)x 1(i-1) ,2(1+τ)x 1(i-1) ] and x 2i ∈[(1-τ)x 2(i-1) ,(1+τ)x 2(i-1) ], it is considered that p i With p i-1 There are leakage pulses between

[0082] The second case: x 1i ∈[2(1-τ)x 1(i-1),2(1+τ)x 1(i-1) ] and x 3i ∈[(1-τ)x 3(i-1) ,(1+τ)x 3(i-1) ], it is considered that p i With p i-1 There are leakage pulses in between.

[0083] As an implementable method, in this embodiment, the following method is used to detect whether each pulse is a pseudo leakage pulse, specifically:

[0084] If p i If formula (3) is satisfied, then p i For a pseudo pulse, i Delete and update pulse position information from pulse train p;

[0085]

[0086] Wherein, τ in formula (2) and formula (3) represents the matching threshold adjustment parameter, 0<τ<1.

[0087] Specifically, if the PRI changes dramatically, we can preliminarily add the two adjacent segments of significantly reduced PRI and compare them with the normal PRI. Then, we can make a comprehensive judgment based on the change degree of the current pulse and the previous pulse in RF and PW parameters. When the conditions shown in the three sub-formulas in formula (3) are met, it is considered that p i It is a false pulse.

[0088] S103: performing first-order difference processing on the pulse parameters of all pulses in the pulse train p to obtain a difference set {△PRI, △RF, △PW} of adjacent pulse parameters, and forming a data set D according to the difference set {△PRI, △RF, △PW};

[0089] Specifically, since the pulse parameters will change dramatically when adjacent waveform units are switched, this step measures the oscillation degree of the pulse parameter timing by performing first-order difference processing on the pulse parameters of all pulses. The specific form of the difference set of adjacent pulse parameters {△PRI, △RF, △PW} is shown in formula (4):

[0090]

[0091] In step S101, it is mentioned that when the multifunctional radar switches waveform units, although different waveform units have a lot of overlap in the RF, PW and PRI parameter ranges, research has found that the parameter fluctuation between adjacent waveform units is greater than the parameter fluctuation within a single waveform unit. Therefore, the inventors have come up with the idea of ​​extracting waveform units of the multifunctional radar based on the joint variation law between RF, PW and PRI parameters. In order to verify the effectiveness of this concept, the inventors have given the following Figure 3 The joint distribution of {△PRI,△RF,△PW} in the three-dimensional feature space shown in the figure needs to be labeled before obtaining the joint distribution. The labeling process is as follows: label = {l1,l2,l3,…,l n}Mark each pulse. If the pulse p i is the starting pulse of a waveform unit, then l i =1; otherwise l i = 0. After a multifunctional radar pulse signal is processed according to the method described in step S101 to step S103, Figure 3 The joint distribution shown. Figure 3 In the figure, the gray dots are the mapping of the waveform unit start pulse in the {△PRI,△RF,△PW} feature space, and the black dots are the mapping of the waveform unit non-start pulse in the {△PRI,△RF,△PW} feature space. Figure 3 It can be seen that: due to the relatively stable change of pulse parameters within a single waveform unit and the greater number of starting pulses than the waveform unit (the number of pulses in a single waveform unit ranges from a few to dozens), the black dots are concentrated and densely distributed in a small feature space close to the origin; while for the red dots corresponding to the starting pulses of the waveform unit, since the pulse parameters between adjacent waveform units change more dramatically, they are widely distributed in a large feature space far from the origin. Therefore, the starting pulses of the waveform unit can be screened out according to the distribution of pulse parameters in the three-dimensional feature space {△PRI,△RF,△PW}.

[0092] S104: using the data set D as an object and using the isolation forest to construct a waveform unit extraction model;

[0093] Specifically, the Isolation Forest algorithm (iForest) is an efficient abnormal data detection algorithm. In the prior art, it is mainly used in the fields of network security and financial security. In the Isolation Forest, the abnormal point data is defined as "points that are sparsely distributed and far away from the high-density area", which coincides with the joint distribution of the MFR waveform unit starting pulse in the {△PRI, △RF, △PW} feature space proposed in the present invention. Therefore, the present invention proposes to use the Isolation Forest to construct a waveform unit extraction model.

[0094] As an implementable method, this step specifically includes the following sub-steps:

[0095] S1041: Building a Dataset

[0096] Before constructing and training the waveform unit extraction model, a data set for model training should be prepared. In this implementation, the data set D is composed according to the difference set {△PRI, △RF, △PW}, specifically: data set

[0097] S1042: Preset the number of isolated trees t and the number of sub-samples of a single isolated tree ψ;

[0098] Specifically, the isolation forest is composed of multiple isolated trees (iTrees). Considering the extraction performance and computational complexity of the model, the number of isolated trees and the subsample trees of a single isolated tree can be pre-set as needed.

[0099] S1043: From the given data set Randomly select ψ sample points from to form a new data set D′, and put D′ into the root node of the isolated tree to be trained;

[0100] S1044: Randomly specify a dimension q from the three dimensions of the sample set in the current node data set D′ k A separation point e is randomly generated in the equation, satisfying:

[0101] min(x ji ,j=q,x ji ∈D′ k ) <e<max(x ji ,j=q,x ji ∈D′ k ) (5)

[0102] Among them, D′ k represents the kth data set generated in the process of segmenting the data set D′;

[0103] Specifically, the present invention uses three pulse parameters to describe each pulse, which means that each pulse has three dimensional features and q has three value cases, namely q = 1, 2, 3. Since the data set D' is continuously split from the root node during the whole process, a new smaller data set will be generated and continue to be split until the requirements of step S1046 are met. In order to distinguish the data sets in the splitting process, D' is used k It represents the node dataset that is currently to be split, and also represents the newly generated k-th dataset.

[0104] S1045: Cut the separation point e to generate a hyperplane in the feature space of the selected dimension q, and divide the sample points in the current node into two child nodes: x ji The sample points of <e are put into the left child node, x ji The sample points of >e are put into the right child node;

[0105] S1046: Recursively execute S1044 and S1045 until all leaf nodes have only one sample point, or when the current isolation tree reaches the preset height, then exit;

[0106] S1047: Repeat steps S1043 to S1046 until all t isolation trees are generated. Thus, the construction of the waveform unit extraction model based on the isolation forest is completed.

[0107] S105: Use the waveform unit extraction model to obtain the anomaly score corresponding to each pulse data point in the dataset D;

[0108] Specifically, after obtaining the waveform unit extraction model based on the isolation forest, input all the pulse data points in the dataset D into the isolation forest composed of all t isolation trees, and traverse all the isolation trees to obtain the anomaly score (Abnormal Score) corresponding to each pulse data point.

[0109] As an implementable manner, the anomaly score is calculated according to formula (6) as follows:

[0110]

[0111] where is the path length from the root node to the leaf node in each isolation tree; E(·) represents taking the mean value; c(ψ) is the average value of the isolation tree path lengths when the number of samples is ψ.

[0112] c(ψ) plays a role in normalization, and its calculation formula is as shown in formula (7):

[0113]

[0114] where H(ψ) = ln(ψ) + ξ, and ξ is the Euler constant.

[0115] and satisfy the relationship shown in formula (8):

[0116]

[0117] It should be noted that the data points corresponding to the start pulse of the waveform unit are far away from the high-density area, so its average height in the isolated forest is The data point corresponding to the non-waveform unit start pulse is smaller, so its abnormal score Since the present invention only cares about data points with shorter paths, the path length of a single isolated tree is limited as follows:

[0118]

[0119] By limiting the maximum path length of a single isolated tree to This can effectively reduce the amount of computation when training isolated trees.

[0120] S106: Preset a threshold ε, remove sample points with abnormal scores greater than the threshold ε from the data set D, and put them into the waveform unit starting pulse data set W f In the above example, the removed data set is used as the new data set D;

[0121] S107: Repeat steps S104 to S106 until all newly calculated abnormal scores do not exceed the threshold ε or the maximum search number r is reached, and then the search process for the waveform unit starting pulse is terminated. At this time, the waveform unit starting pulse data set W f One start pulse in the waveform corresponds to one MFR waveform unit.

[0122] Specifically, from the distribution of MFR pulse signals in the {△PRI,△RF,△PW} feature space, the isolation forest algorithm can complete the extraction of the waveform unit start pulse. However, the isolation forest algorithm is applied to the waveform unit extraction of multi-function radar, and there are still the following problems:

[0123] 1) The isolation forest algorithm requires that the proportion of abnormal data in the total sample volume is very small. If a large number of pulse first-order differential eigenvalues ​​are simultaneously input into the isolation forest to search for the pulse starting point, the data points corresponding to the waveform unit starting pulse will roughly account for 5%-10% of the total data volume (the number of pulses in a single waveform unit ranges from a few to dozens). This is contrary to the small proportion of abnormal data required by the isolation forest;

[0124] 2) For non-cooperative multi-function radar signals, since the receiver only has the parameter data of the pulse received this time, the exact proportion of the waveform unit start pulse is unknown, and the abnormal score threshold for distinguishing the waveform unit start pulse and non-start pulse cannot be determined.

[0125] In view of the above problems, combined with Figure 1 and Figure 2As shown, through step S106 and step S107, the isolation forest is constructed multiple times, and the waveform unit extraction is completed in multiple steps and with variable thresholds. After the complete isolation tree training and sample point abnormality score calculation process is completed, a threshold ε is preset to separate all abnormal scores. The sample points are removed from the data set D and put into the waveform unit start pulse data set Then the eliminated data set is used as the new data set D. The above process is repeated until all newly calculated abnormal scores do not exceed the threshold ε or the maximum search number r is reached, and the search for the start pulse of the entire waveform unit is terminated.

[0126] The setting of the threshold ε is determined according to the distribution of the abnormality scores of the current round. As an implementable method, the calculation process of the threshold ε specifically includes:

[0127] According to the abnormal score sequence Construct the sequence S′ according to formula (10):

[0128] S′={S,1-S} (10)

[0129] Understandably, since the maximum height of an isolated tree is limited to inside, so The values ​​of are concentrated in the interval [0.5,1].

[0130] For the sequence S′, calculate its mean μ and variance σ according to formula (11): 2 :

[0131]

[0132] Where m represents the sequence number of the element in the sequence S′;

[0133] like Figure 4 As shown, the score distribution of S′ is roughly fitted with a mean of μ and a variance of σ 2 Therefore, the threshold ε is calculated according to formula (12):

[0134] ε=u+3σ (12).

[0135] In addition, the present invention also defines the evaluation index of waveform unit extraction. The specifics are as follows:

[0136] (1) The extraction of waveform units by the method of the present invention is equivalent to the binary classification of waveform unit start pulses and non-start pulses. Therefore, the following evaluation indicators are defined: True Positive (TP), which indicates the samples that are waveform unit start pulses and are marked as start pulses; False Positive (FP), which indicates the samples that are waveform unit non-start pulses and are marked as start pulses; True Negative (TN), which indicates the samples that are waveform unit non-start pulses and are marked as non-start pulses; False Negative (FN), which indicates the samples that are waveform unit start pulses and are marked as non-start pulses.

[0137] The performance of the waveform unit extraction algorithm is measured using three indicators: True Positive Rate (TPR), False Positive Rate (FPR) and F-score. Their definitions are as follows:

[0138]

[0139]

[0140]

[0141] (2) The Isolation Forest Algorithm is an anomaly detection algorithm with linear time complexity. In order to evaluate the performance advantage of the method of the present invention in terms of time complexity, the computational complexity and time consumption under different sample numbers are analyzed and tested.

[0142] In order to further verify the feasibility and effectiveness of the method of the present invention, the present invention also provides the following simulation experiment: The experiment generates 40 kinds of waveform unit simulation data based on the waveform library of a two-dimensional phased array MFR given in document 2.

[0143] (I) Effectiveness analysis

[0144] First, the effectiveness of the method of the present invention is verified by comparing it with the unsupervised DBSCAN and DA-DBSCAN in document 2. Considering that the electronic reconnaissance aircraft is affected by the complex electromagnetic environment and equipment performance in the real environment, the actual detection pulse train will have leakage pulses, false pulses and parameter measurement errors. In order to verify the adaptability of different algorithms to the above three factors, the generated simulation pulse train is added with different degrees of leakage pulses, false pulses and parameter errors for simulation testing. The definitions of the pulse drop rate (Ratio of Dropped Pulses, RDP), the false pulse rate (Ratio of False Pulses, RFP) and the error deviation level (Error Deviation Level, EDL) are as follows:

[0145]

[0146]

[0147]

[0148] Where n is the pulse train p = {p1, p2, p3…, p n} contains the number of pulses, n drop is the number of randomly discarded pulses, n false is the number of false pulses mixed in, x pi ={x 1i ,x 2i ,x 3i} is the error-free pulse parameter data, ξ pi ={ξ 1i ,ξ 2i ,ξ 3i} is a random measurement error. The simulation conditions are as follows: 200 waveform units are randomly and uniformly selected from the waveform library in Table 1 to form a pulse train for testing. The values ​​of RDP, RFP and EDL are 0%-20%. The added pseudo pulses are two fixed-system radar signals, and the parameters are set to PRI1=1000us, RF1=3GHz, PW1=20us and PRI2=500us, RF2=4GHz, PW2=10us. Since the DBSCAN and DA-DBSCAN algorithms are clustered based on density, PRI, RF, and PW are clustered according to the values ​​of us, MHz, and us, and the clustering parameters Minpts=7 and Eps=3. The parameter settings of the method of the present invention are as follows: the leakage pulse pseudo pulse test parameter τ=0.15, the number of single tree training samples ψ is one tenth of the number of samples in the data set D, the number of isolated trees t=100, and the maximum number of searches is 10 times. The average results after 500 Monte Carlo tests are as follows. Figure 5 , 6, as shown in 7.

[0149] from Figure 5 and Figure 6 It can be seen that when facing different degrees of leakage pulses and false pulses, the method of the present invention can always maintain a high extraction true rate, but the cost is that the false positive rate will continue to rise. With the continuous increase of pulse loss rate and false pulse rate, the F-score of the method of the present invention no longer has an advantage over the other two algorithms. This is because the idea of ​​the method of the present invention is to realize the search of the waveform unit starting pulse based on isolation. When the probability of pulse sorting error continues to increase, a large number of abnormal PRI values ​​will appear, resulting in severe jitter of the △PRI of more adjacent pulses, which are thus determined by the method of the present invention as the waveform unit starting pulse; while for DBSCAN and DA-DBSCAN, as the leakage pulse and false pulse rate continue to increase, their false positive rate first increases sharply and then gradually decreases. This is due to the characteristic of judging whether the target pulse is the waveform unit starting pulse based on the size of the feature space density. When the probability of PRI abnormality is small, the distribution of the corresponding pulse sample points in the feature space is sparse, so it is judged as the waveform unit starting pulse; and when the probability of PRI abnormality is large, the distribution of the corresponding pulse sample points in the feature space is relatively dense, so it will not be mistakenly judged as the waveform unit starting pulse.

[0150] from Figure 7 It can be seen that when faced with different degrees of pulse parameter measurement errors, the strategies of the method of the present invention and the comparison algorithm are different. As the pulse parameter measurement error continues to increase, the true positive rate of the method of the present invention will decrease to a certain extent, but the false positive rate will always remain at a low level; while the false positive rates of DBSCAN and DA-DBSCAN involved in the comparison continue to increase with the increase of the error level, but their true positive rates are not significantly better than the method of the present invention, which leads to the gap between their F-score values ​​and the method of the present invention gradually increasing as the pulse parameter measurement error continues to increase.

[0151] In general, the method of the present invention has advantages over the comparison algorithm in waveform unit extraction performance. However, considering that the error level of real detection pulse sorting is generally low, the performance of waveform unit starting pulse extraction of the method of the present invention is significantly better than that of the comparison algorithm when facing missed pulses and false pulses. When the pulse parameter measurement error is large, the method of the present invention can also better balance the recall rate and precision rate, and has a more excellent performance.

[0152] (II) Real-time analysis

[0153] In a real battlefield environment, radar emitters can emit a large number of pulse signals in a short period of time, so the computational complexity of the waveform unit extraction algorithm is an important indicator to measure its performance. This section first analyzes the computational complexity of the above three algorithms theoretically, and conducts simulation experiments to statistically analyze the average time taken by the three algorithms to process different numbers of waveform units.

[0154] In order to conduct a theoretical analysis of the algorithm's computational complexity, we first clarify the following variables: m represents the number of waveform units in the test sequence; t represents the number of isolated trees; ψ represents the number of samples used to train a single tree; and r represents the maximum number of search rounds. The total number of pulses N in the test sequence is:

[0155]

[0156] (1) For the method of the present invention, its computational complexity T IF for:

[0157]

[0158] because And for all isolated trees Therefore:

[0159]

[0160] (2) For the DBSCAN algorithm, its computational complexity is T DB for:

[0161]

[0162] (3) For the DA-DBSCAN algorithm, its computational complexity is T DA for:

[0163]

[0164] Based on the waveform unit table in Reference 2, assuming that the average number of pulses of the waveform unit is 20, the number of isolated trees is t=100, the number of samples for training a single tree is ψ=0.1N, and the maximum number of searches is r=10, the above conditions are brought into the complexity calculation results, and the computational complexity comparison results of the three algorithms under different sample numbers can be obtained, as shown in the figure. Figure 8 shown.

[0165] Condition settings and Figure 8 When comparing the computational complexity, the present invention will conduct simulation experiments to calculate the average time consumption of the three algorithms under different numbers of waveform units. The experimental data was calculated and measured using matlab2020a on the i9-11900K+32G DDR memory+Windows10 platform. The results are shown in Table 1.

[0166] Table 1 Running time of each algorithm under different numbers of waveform units

[0167]

[0168] It can be seen from theoretical analysis and simulation experiments that the computational complexity of the method of the present invention is significantly reduced compared with the DBSCAN and DA-DBSCAN algorithms, especially when the number of waveform units is large, the advantage of real-time calculation is more obvious. In addition, the method of the present invention does not need to set hyperparameters manually, which reduces the problem of poor algorithm effect due to lack of experience. Therefore, considering that the recognition performance of the method of the present invention is not much different from that of the comparison algorithm and the advantages of the method of the present invention in computational complexity, the method of the present invention has better engineering application prospects and research value.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. The MFR waveform unit extraction method based on step-by-step variable threshold isolation forest is characterized by: include: Step 1: Each pulse in the received deinterleaved pulse train p is described using three pulse parameters: PRI, RF and PW; where p = {p1, p2, p3…, p n }, p i represents the i-th pulse, i = 1, 2, ..., n; PRI represents the pulse repetition interval, RF represents the radio frequency, and PW represents the pulse width; Step 2: Detect whether there are leaking pulses and / or false pulses in the pulse train p and perform corresponding processing; Step 3: performing first-order difference processing on the pulse parameters of all pulses in the pulse train p to obtain a difference set {△PRI, △RF, △PW} of adjacent pulse parameters, and forming a data set D according to the difference set {△PRI, △RF, △PW}; Step 4: Using the isolation forest to construct a waveform unit extraction model based on the dataset D; specifically including: Step 4.1: Build the dataset Indicates pulse p i and pulse p i-1 The difference of the three corresponding pulse parameters; among them, x1′ i , x2′ i and x3′ i Respectively represent the differences among PRI, RF and PW; Step 4.2: Preset the number of isolated trees t and the number of subsamples of a single isolated tree ψ; Step 4.3: From the given dataset Randomly select ψ sample points from to form a new data set D′, and put D′ into the root node of the isolated tree to be trained; Step 4.4: Randomly specify a dimension q from the three dimensions of the sample set in the current node data set D′ k A separation point e is randomly generated in the equation, satisfying: min(x ji ,j=q,x ji ∈D′ k )<e<max(x ji ,j=q,x ji ∈D′ k ) (5) Among them, D′ k represents the kth data set generated in the process of segmenting the data set D′; Step 4.5: Cut the separation point e to generate a hyperplane in the feature space of the selected dimension q, and divide the sample points in the current node into two child nodes: x ji The sample points of <e are placed in the left child node, x ji The sample points >e are placed in the right child node; Step 4.6: Recursively repeat steps 4.4 and 4.5 until all leaf nodes have only one sample point, or when the current isolated tree reaches the preset height, exit; Step 4.7: Repeat steps 4.3 to 4.6 until all t isolated trees are generated; Step 5: Use the waveform unit extraction model to obtain the anomaly score corresponding to each pulse data point in the data set D; specifically, input all pulse data points in the data set D into the waveform unit extraction model composed of t isolated trees, traverse all isolated trees, and obtain the anomaly score corresponding to each pulse data point; the anomaly score The calculation formula is shown in formula (6): in, yes The path length from the root node to the leaf node in each isolated tree; E(·) represents the mean; c(ψ) is the average value of the path length of the isolated tree when the number of samples is ψ; The average value c(ψ) is calculated according to formula (7): Where H(ψ)=ln(ψ)+ξ, ξ is the Euler constant; and The relationship between them satisfies the formula (8): The path length from the root node to the leaf node in each isolated tree should satisfy the condition shown in formula (9): Step 6: Preset a threshold ε, remove sample points with abnormal scores greater than the threshold ε from the data set D, and put them into the waveform unit starting pulse data set W f In the above example, the removed data set is used as the new data set D; Step 7: Repeat steps 4 to 6 until all newly calculated abnormal scores do not exceed the threshold ε or the maximum search number r is reached, and then the search process of the waveform unit starting pulse is terminated. At this time, the waveform unit starting pulse data set W f One start pulse in the waveform corresponds to one MFR waveform unit.

2. The MFR waveform unit extraction method based on step-by-step variable threshold isolation forest according to claim 1 is characterized in that: Step 1 specifically includes: According to formula (1), each pulse is described by three pulse parameters: PRI, RF and PW: Among them, x 1i 、x 2i 、x 3i Respectively represent pulse p i PRI, RF and PW.

3. The MFR waveform unit extraction method based on step-by-step variable threshold isolation forest according to claim 2 is characterized in that: Step 2 specifically includes: If p i With p i-1 If the time satisfies formula (2), then p i With p i-1 There is a leakage pulse between p i With p i-1 Add a pulse p in the middle i-1 Pulses with the same RF and PW parameters and updating pulse position information; If p i If formula (3) is satisfied, then p i For a pseudo pulse, i Delete and update pulse position information from pulse train p; Wherein, τ represents the matching threshold adjustment parameter, 0<τ<1.

4. The MFR waveform unit extraction method based on step-by-step variable threshold isolation forest according to claim 2, characterized in that: Step 3 specifically includes: According to formula (4), the difference set of adjacent pulse parameters is obtained:

5. The MFR waveform unit extraction method based on step-by-step variable threshold isolation forest according to claim 1, characterized in that: In step 6, the calculation process of the threshold ε specifically includes: According to the abnormal score sequence Construct the sequence S′ according to formula (10): S′={S,1-S} (10) For the sequence S′, calculate its mean μ and variance σ according to formula (11): 2 : Where m represents the sequence number of the element in the sequence S′; Calculate the threshold ε according to formula (12): ε=u+3σ (12).

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