CN107479051A - The Operating Modes of Multi-function Radar discrimination method of model is represented based on predicted state - Google Patents
The Operating Modes of Multi-function Radar discrimination method of model is represented based on predicted state Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/021—Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S2013/0236—Special technical features
- G01S2013/0272—Multifunction radar
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Abstract
The present invention relates to a kind of Operating Modes of Multi-function Radar discrimination method that model is represented based on predicted state：Step 1：Establish MFR PSR models；Step 2：Carry out PSR model trainings；Training radar word sequence S is pre-processed first with string processing instrument；Calculate noise threshold and filter out noise；Linearly independent vector is found, finally extracts core event set Q and landmark set L.Step 3：MFR mode of operation discriminations are carried out using the PSR models trained；Beneficial effects of the present invention：First, the present invention is studied for MFR mode of operations identification problem, and conventional HMM, model simple stronger to the sign ability of dynamical system are substituted using PSR models；Second, the MFR mode of operation recognition effects of the invention based on PSR models are much better than traditional HMM methods；3rd, the present invention there is very strong application prospect, make it possible deduction radar operation strategy, estimation potential threat, predict MFR behaviors.
Description
[ technical field ] A method for producing a semiconductor device
The invention belongs to the field of radar electronic warfare, particularly relates to a multifunctional radar working mode identification technology, and further provides a multifunctional radar working mode identification method based on a prediction state representation model aiming at intercepted multifunctional radar signals.
[ background of the invention ]
Due to the flexible working mode and agile waveform characteristics of the multifunctional radar (MFR), the multifunctional radar can execute the advantages of multiple functions in parallel, obtains increasingly wide deployment and application, and brings great challenges to battlefield environment reconnaissance and cognitive electronic warfare. Because the threat degree, the mission planning and the like of the MFR are closely related to the current working mode of the MFR, the internal state and the running rule of the system can be estimated only by accurately identifying the working mode of the MFR, and powerful information support is provided for threat assessment, behavior prediction, interference intelligent decision and the like of the MFR. The existing MFR operation mode recognition is mainly based on Hidden Markov Model (HMM) method, which has two main problems: one is to rely heavily on MFR priors and the second is that HMMs are not able to adequately describe the regularity characteristics that are usually present in MFR signals. In view of the complexity of the MFR signal, conventional HMM-based approaches have not effectively addressed the MFR operating mode recognition problem. The present invention introduces a stochastic dynamic system modeling approach to the analysis of the MFR signal, in combination with a multi-level model of the MFR signal, replacing the HMM with a Predictive State Representation (PSR) model. The PSR model has the advantage of being able to accurately describe unknown regularity features in the MFR signal and reduce the dependence on MFR priors. The invention provides a training and recognition algorithm aiming at a PSR (Power System model) of MFR (flow Rate) according to the specific characteristics of an MFR signal, and the algorithm is verified through simulation experiments.
[ summary of the invention ]
The invention aims to provide a multifunctional radar working pattern identification method based on a prediction state representation model, which realizes MFR working pattern identification by utilizing a PSR model.
In order to achieve the above object, the present invention provides a method for identifying a multi-functional radar working mode based on a prediction state representation model, which comprises the following steps:
the method comprises the following steps: establishing a PSR model of the MFR;
the PSR model of an uncontrolled system can be represented as a four-tuple < O, h, e, p (e | h) >:
o is an observation space, a limited discrete set containing all observation values, and an observation O belongs to O; h is experience and refers to an observation sequence starting from the initial moment and ending at the current moment; e is an event, refers to the observation sequence after the experience, e = o t+ 1 o t+2 8230and its preparation method. For a linear PSR model, if the probabilities of all events can be represented by a linear combination of a set of event probabilities, then the set of events is referred to as core events, Q = { Q = { Q } 1 ,q 2 ,…,q Q }; p (e | h) is the probability of occurrence of event e given experience h.
The MFR radar word sequence is represented by the PSR model:
let W be the finite set of all radar words, each radar phrase is formed by connecting n radar words in series, then the observation o at time t t For a short sequence of n radar words, h = o 1 o 2 …o t Observation space O = W n . So event e is the observation o of the current time t And the core event set Q is a radar phrase set in the working mode. Setting the number of register bits as m, the memory is a set of all suffixes with length not greater than m in hAnd (6) mixing.
Thus, the probability p (e | h) of occurrence of event e under the experience of h condition is:
p(e|h)＝p(e＝o t |h＝o 1 o 2 …o t-1 ) (1)
core event Q = { Q = 1 ,q 2 ,…,q |Q| The probability distribution of is:
p(Q|h)＝[p(q 1 |h),p(q 2 |h),…,p(q |Q| |h)] T (2)
by definition of Q, the probability of any observation occurring can be represented by a linear combination of p (Q | h), so there is m o So that
p(o|h)＝p T (Q|h)m o (3)
Order toWhen a new observation o is obtained, p (Q | h) will be updated as:
the conditional probabilities that occur above indicate different meanings: h and l both belong to experience, o and q both are events, when "|" is flanked by the same class of symbols, the conditional probability represents the observation probability, e.g., p (l | h) and p (o | q), and vice versa represents the transition probability, e.g., p (q | h).
Step two: carrying out PSR model training;
firstly, preprocessing a training radar word sequence S by using a character string processing tool; calculating a noise threshold value and filtering noise; and (5) searching for a linear independent vector, and finally extracting a core event set Q and a landmark set L.
Step three: performing MFR working mode identification by using the trained PSR model;
the key to the estimation of the MFR operating mode ML is the calculation of p (o | h). For the PSR model of either mode of operation, the probability of observing o under the condition of experiencing h is:
wherein p (q) j |l i ) Is an element in D. With the Viterbi algorithm or according to Hamming distance, will experience h t Match landmark set L, observe o t Matching with the core event set Q, respectively calculating p (l) of the current time i |h t ) And p (o) t |q j ). Since the observation o is only dependent on the current actual transmitted signal q, but not on the previous history h, p (o | q) can be considered 1 ,h)＝p(o|q 1 )。
Comparing the formulas (3) and (7) shows that:
m o ＝[p(o|q 1 ),p(o|q 2 ),…,p(o|q |Q| )] T (6)
further solving each core event in Q:
with the above results, an iterative algorithm for sequentially computing p (o | h) is given below:
step1: initialization
At initial time t =1,h 1 Phi, when p (Q | h) 1 ) Comprises the following steps:
p(Q|φ)＝[p(q 1 |φ),p(q 2 |φ),…,p(q |Q| |φ)] T (8)
wherein p (q) j I phi) can be obtained by summing the columns of D:
if the first observation is o 1 And then:
and (3) identification result:
step2: iteration
The updating process of p (Q | h) by equation (4) is:
therefore, it is
The ML estimate of the MFR operating mode at time t is then:
the PSR model training in the second step comprises the following specific steps:
step1: training sequence preprocessing
Firstly, preprocessing a training sequence and extracting statistical information of event transfer times.
Step2: calculating a noise threshold for memory and event frequency and filtering noise
The presence of erroneously extracted radar words in the sequence S results in a number of memory and events of small probability, comparable to the system noise. Here, combining the actual characteristics of the MFR radar word sequence, the noise threshold value of the frequency of memory and event occurrence is directly calculated, and the memory and event with low frequency are removed.
The noise threshold for vector a is:
wherein | a | purple ∞ Denotes the ∞ norm of vector a, n being the dimension of a, i.e. the number of events occurring in S, D [ a ] j ]Represents the element a j α is the confidence. By the event frequency vector c E (can pass through pair D) count Summed for each column) for example. Due to c E All the elements in the formula can be regarded as the results of Bernoulli test, so any element c thereof j Uniformly distributed according to two terms, and the mean value is the occurrence probability p of the event j ＝c j N, variance is p j (1-p j ) N, where the number of trials N is about the training sequence length | S |. D [ c ] j ]By the formula (5), can obtain
Vector c E Elements smaller than σ are all considered to be caused by noise, which can be found at D count With the corresponding column removed. Processing the memory in the same way, and then processing the final D count Normalizing each row to obtain an original system dynamic submatrix D after noise reduction treatment raw 。
Step3: extracting landmarks and core events
Setting the minimum length k of the landmark, and adopting the suffix-history algorithm to obtain the length k from D raw And extracting a landmark set L, extracting a core event set Q, and obtaining a reduced submatrix D = p (Q | L).
The beneficial effects of the invention mainly comprise:
firstly, the method is researched aiming at the recognition problem of the MFR working mode, and a PSR model is adopted to replace a conventional HMM, so that the dynamic system has stronger characterization capability and a concise model;
secondly, the MFR work mode recognition effect based on the PSR model is far better than that of the traditional HMM method;
thirdly, the method has a strong application prospect, and makes it possible to deduce the operation strategy of the radar, estimate potential threat and predict MFR behavior.
[ description of the drawings ]
Fig. 1 is a general flowchart of the PSR model-based multifunctional radar operating mode discrimination method of the present invention.
FIG. 2 is a flow chart of training sequence preprocessing algorithm based on AC automata, wherein S is a radar training sequence, W is a radar word set,for the set of pattern strings, β is the maximum memory length, γ is the core event length, k is the minimum landmark length, suffix (m) k Representing a memory of length no more than k in M, c (E | M) representing the number of occurrences of an event E following memory M, M representing a set of memories of length between k and β, E representing a set of events of length γ, M (n) representing a memory of length β ending with the nth radar word in S, E (n) representing an event ending with the nth radar word in S.
FIG. 3 is a flow chart of an algorithm for extracting landmarks and core events, where D raw Is the system matrix obtained in FIG. 2, M is D raw In the memory set, E is D raw Set of medium events, rank (X) is the rank of vector set X, M mi Represents M in M i Set of all memories for suffixes, D raw ({m i }) denotes D raw Neutralization memory { m i Rank of the corresponding row vector group, D L ({e j }) denotes D L Neutralization event set { e } j The rank of the corresponding column vector set, L is the landmark set, Q is the core event set, D is equal to p (ql), representing the extracted system dynamic submatrix.
Fig. 4 is a schematic MFR operating mode shift relationship.
Fig. 5 shows MFR operation pattern recognition results based on HMM and PSR models when vocabularies are known, where fig. 5 (a) shows MFR operation pattern recognition results based on HMM and fig. 5 (b) shows MFR operation pattern recognition results based on PSR.
Fig. 6 shows the result of MFR operation pattern recognition based on the PSR model under the vocabulary unknown condition.
[ detailed description ] A
The present invention is applicable to MFR operating mode discrimination. Fig. 1 is a schematic flow chart of the present invention, and the method proposed by the present invention is further explained below with reference to the accompanying drawings. The method comprises the following specific steps and effects:
the method comprises the following steps: establishing a PSR model of MFR;
since the reconnaissance system can only passively reconnoiter the radar signal, the generation of the radar word sequence is an uncontrolled process from the perspective of the reconnaissance party. The PSR model of an uncontrolled system can be represented as a four-tuple < O, h, e, p (e | h) >:
o is an observation space, a finite discrete set containing all observation values, and an observation O belongs to O; h is experience and refers to an observation sequence starting from the initial moment and ending at the current moment; e is an event, refers to the sequence of observations after the experience, e = o t+ 1 o t+2 8230and its preparation method. For a linear PSR model, if the probabilities of all Events can be represented by a linear combination of a set of event probabilities, then the set of Events is referred to as Core Events (Core Events), Q = { Q = { (Q) } 1 ,q 2 ,…,q |Q| }; p (e | h) is the probability of occurrence of event e given experience h.
The MFR radar word sequence is represented by the PSR model below:
let W be the finite set of all radar words, each radar phrase is formed by connecting n radar words in series, then the observation o at time t t Is a short sequence of n-word, h = o 1 o 2 …o t Observation space O = W n . The study here is to identify the problem, only concerning the status at the current moment, story piece e being the observation o at the current moment t And the core event set Q is a radar phrase set in the working mode. And setting the number of the register bits as m, memorizing the number as a set of all suffixes with the length not more than m in h.
Thus, the probability p (e | h) that event e occurs under the experience h condition is:
p(e|h)＝p(e＝o t |h＝o 1 o 2 …o t-1 ) (17)
core event Q = { Q = 1 ,q2,…,q |Q| The probability distribution of is:
p(Q|h)＝[p(q 1 |h),p(q 2 |h),…,p(q |Q| |h)] T (18)
by definition of Q, the probability of any observation occurring can be represented by a linear combination of p (Q | h), so there is m o So that
p(o|h)＝p T (Q|h)m o (19)
Order toWhen a new observation o is obtained, p (Q | h) will be updated as:
the conditional probabilities that occur above indicate different meanings: h and l both belong to experience, o and q both are events, when "|" is flanked by symbols of the same type, the conditional probability represents the observation probability, such as p (l | h) and p (o | q), and vice versa represents the transition probability, such as p (q | h).
Step two: training a PSR model;
firstly, preprocessing a training radar word sequence S by using a character string processing tool; calculating a noise threshold value and filtering noise; and (5) finding a linear independent vector, and finally extracting a core event set Q and a landmark set L.
Step1：Training sequence preprocessing
Firstly, preprocessing a training sequence and extracting statistical information of event transfer times. In the commonly used string algorithm, an AC Automaton (Aho-coral automation) has the advantage of being capable of multi-pattern string matching, so that this step is partially implemented based on the AC Automaton, and the process thereof is shown in fig. 2.
Step2: calculating noise thresholds for memory and event frequencies and filtering noise
The presence of erroneously extracted radar words in the sequence S results in a number of memory and events of small probability, comparable to the system noise. Here, combining the actual characteristics of the MFR radar word sequence, the noise threshold value of the frequency of memory and event occurrence is directly calculated, and the memory and event with low frequency are removed. This approach preserves useful information in the dynamic matrix of the system.
The noise threshold for vector a is:
wherein | | a | | calucity ∞ Denotes the ∞ norm of vector a, n being the dimension of a, i.e. the number of events occurring in S, D [ a j ]Represents the element a j α is the confidence. By the event frequency vector c E (can pass through pair D) count Summed for each column) for example. Due to c E All the elements in the test can be regarded as the results of Bernoulli test, so any element c of the test can be regarded as j Uniformly distributed according to two terms, and the mean value is the occurrence probability p of the event j ＝c j N, variance is p j (1-p j ) N, where the number of trials N is about the training sequence length | S |. D [ c ] is j ]Substitution into formula (5) to obtain
Vector c E Elements smaller than σ are all considered to be caused by noise, which can be found at D count The corresponding column in (1) is removed. Processing the memory in the same way, and processing the final D count Normalizing each row to obtain an original system dynamic submatrix D subjected to noise reduction treatment raw 。
Step3: extracting landmarks and core events
Setting a minimum length k of the landmark, from D using the suffix-history algorithm raw And extracting a landmark set L, then extracting a core event set Q, and obtaining a reduced-dimension submatrix D = p (Q | L).
When the vocabulary is unknown, the PSR model can be trained through the process shown in FIG. 3, and the HMM cannot be used, which represents the advantage of the PSR model over the HMM. If the vocabulary is known, the radar phrase can be directly used as the core event set Q, and the Viterbi algorithm is applied to convert the radar word sequence into the radar phrase sequence before step1, so that the operation amount can be reduced in the subsequent operation, and a better training effect can be achieved.
Step three: performing MFR working mode identification by using the trained PSR model;
the key to the estimation of the MFR operating mode ML is the calculation of p (o | h). For the PSR model of either mode of operation, the probability of observing o under the condition of experiencing h is:
wherein p (q) j |l i ) Is an element in D. With Viterbi algorithm or according to Hamming distance, will experience h t Matching with landmark set L, observe o t Matching with the core event set Q, respectively calculating p (l) of the current time i |h t ) And p (o) t |q j ). Since the observation o is only dependent on the current actual transmitted signal q, but not on the previous history h, it is possible to useConsider p (o | q) 1 ,h)＝p(o|q 1 )。
Comparing the formulas (3) and (7) shows that:
m o ＝[p(o|q 1 ),p(o|q 2 ),…,p(o|q Q )] T (24)
further solving each core event in Q:
using the above results, an iterative algorithm for sequentially calculating p (o | h) is given below:
step1: initialization
At initial time t =1,h 1 Phi, when p (Q | h) 1 ) Comprises the following steps:
p(Q|φ)＝[p(q 1 |φ),p(q 2 |φ),…,p(q |Q| |φ)] T (26)
wherein p (q) j I phi) can be obtained by summing the columns of D:
if the first observation is o 1 And then:
and (3) identification result:
step2: iteration
The updating process of p (Q | h) by equation (4) is:
therefore, it is
The ML estimate of the MFR operating mode at time t is then:
taking an MFR with five modes of search, capture, non-adaptive tracking, distance resolution, track and hold as an example, the transition relationship of each operating mode is shown in fig. 4, and a plurality of vocabularies are corresponding to each operating mode. FIG. 5 shows the MFR operating pattern recognition results of HMM and PSR models for the case where the vocabulary is known, and FIG. 5 (a) shows that the dotted line and the dotted line deviate from the solid line at many times, which indicates that the ML and MAP estimation results based on HMM are not ideal; (b) The middle dotted line coincides with the solid curve most of the time, and the dashed line almost completely coincides with the solid curve, indicating that both ML and MAP estimation performance based on the PSR model is better, and MAP is more optimal. Statistics on multiple simulation results show that for this set of training and test sequences, the average correct rates for the ML and MAP estimates based on HMM are 0.841 and 0.917, respectively, while the average correct rates for the ML and MAP estimates based on PSR models are 0.969 and 0.982, respectively. The above results all demonstrate that the PSR model works better for MFR operation mode identification. When the vocabulary is unknown, in this case, the MFR operation pattern recognition cannot be performed by using the HMM, the unknown core event length of the PSR model is set to 6 radar words, the maximum memory length is 8 radar words, and the minimum landmark is 6 radar words, as a result, as shown in fig. 6, the abscissa value of fig. 6 is the time expressed in units of events, and compared with fig. 5 (b), points deviating from the solid line and the dotted line in the graph are more, and the multiple simulation results are statistically obtained, and for this set of training and test sequences, the average accuracy rates estimated based on the ML and the MAP of the PSR model are 0.877 and 0.954, respectively. The recognition effect is inferior to the case where the vocabulary is known. Nevertheless, the PSR model achieves recognition of MFR operating modes using only training data, is free from vocabulary dependency, and maintains high recognition accuracy, and thus is more practical than the known case of vocabulary.
Claims (2)
1. A multifunctional radar working mode identification method based on a prediction state representation model is characterized in that: the method comprises the following steps:
the method comprises the following steps: establishing a PSR model of the MFR;
the PSR model of an uncontrolled system can be expressed as a quadruple < O, h, e, p (e | h) >:
o is an observation space, a finite discrete set containing all observation values, and an observation O belongs to O; h is experience and refers to an observation sequence starting from the initial moment and ending at the current moment; e is an event, refers to the observation sequence after the experience, e = o t+1 o t+2 8230for a linear PSR model, if the probabilities of all events can be represented by a linear combination of a set of event probabilities, then the set of events is said to be the core event, Q = { Q = 1 ,q 2 ,…,q Q }; p (e | h) is the probability of the occurrence of event e given the experience of h
The MFR radar word sequence is represented by the PSR model:
setting a limited set of all radar characters as W, each radar phrase is formed by connecting n radar characters in series, and observing o at the time t t For a short sequence of n radar words, h = o 1 o 2 …o t Observation space O = W n So event e is the observation o of the current time t If the number of register bits is set to m for the radar phrase set in the operating mode in the core event set Q, the set is memorized as a set of all suffixes with lengths not greater than m in h
Thus, the probability p (e | h) that event e occurs under the experience h condition is:
p(e|h)＝p(e＝o t |h＝o 1 o 2 …o t-1 ) (1)
core event Q = { Q = { Q } 1 ,q 2 ,…,q |Q| The probability distribution of is:
p(Q|h)＝[p(q 1 |h),p(q 2 |h),…,p(q |Q| |h)] T (2)
by definition of Q, the probability of any observation occurring can be represented by a linear combination of p (Q | h), so there is m o So that
p(o|h)＝p T (Q|h)m o (3)
Order toWhen a new observation o is obtained, p (qh) will be updated as:
the conditional probabilities that occur above indicate different meanings: h and l both belong to experience, o and q are events, when "|" is flanked by symbols of the same type, the conditional probability represents the observation probability, e.g., p (l | h) and p (o | q), and vice versa represents the transition probability, e.g., p (q | h)
Step two: carrying out PSR model training;
firstly, preprocessing a training radar word sequence S by using a character string processing tool; calculating a noise threshold value and filtering noise; finding out linear independent vector, and finally extracting core event set Q and landmark set L
Step three: performing MFR (flow Rate) working mode identification by using the trained PSR model;
the key to the estimation of the MFR operating mode ML is the calculation of p (o | h) for the PSR model of any operating mode, the probability that o is observed under the condition of h is:
wherein p (q) j |l i ) For elements in D, using the Viterbi algorithm or according to Hamming distance, will pass through h t Match landmark set L, observe o t Matching with the core event set Q, respectively calculating p (l) of the current time i |h t ) And p (o) t |q j ) Since the observation o is only dependent on the current actual transmitted signal q, but not on the previous history h, p (o | q) 1 ,h)＝p(o|q 1 )
Comparing the formulas (3) and (7) shows that:
m o ＝[p(o|q 1 ),p(o|q 2 ),…,p(o|q |Q| )] T (6)
further solving each core event in Q:
with the above results, an iterative algorithm for sequentially computing p (o | h) is given below:
step1: initialization
At an initial time t =1,h 1 Phi, when p (Q | h) 1 ) Comprises the following steps:
p(Q|φ)＝[p(q 1 |φ),p(q 2 |φ),…,p(q |Q| |φ)] T (8)
wherein p (q) j I phi) can be obtained by summing the columns of D:
if the first observation is o 1 Then:
and (3) identification result:
step2: iteration
The updating process of p (Q | h) by equation (4) is:
therefore, it is
The ML estimate of the MFR at time t for the operating mode is then:
2. the multifunctional radar operation mode identification method based on the prediction state representation model according to claim 1, wherein: the second step of carrying out PSR model training comprises the following specific steps:
step1: training sequence preprocessing
Firstly, preprocessing a training sequence and extracting statistical information of event transfer times
Step2: calculating a noise threshold for memory and event frequency and filtering noise
The error extraction of radar words in the sequence S causes a plurality of memories and events with small probability, which is equivalent to system noise, wherein the noise threshold value of the occurrence frequency of the memories and events is directly calculated by combining the actual characteristics of the MFR radar word sequence, and the memories and events with low frequency are removed
The noise threshold for vector a is:
wherein | a | purple ∞ Denotes the ∞ norm of vector a, n being the dimension of a, i.e. the number of events occurring in S, D [ a j ]Representing element a j With α as confidence and the event frequency vector c E (can pass through pair D) count Summed columns) due to c E All the elements in the test can be regarded as the results of Bernoulli test, so any element c of the test can be regarded as j All obey binomial distribution, and the mean value is the occurrence probability p of the event j ＝c j N, variance is p j (1-p j ) N, where the number of trials N is approximately the training sequence length | S |, and D [ c |) j ]By the formula (5), can obtain
Vector c E Elements smaller than σ are all considered to be caused by noise, which can be found at D count Removing corresponding row from the memory by the same method, and processing the final D count Normalizing each row to obtain the dynamic submatrix D of the original system after noise reduction treatment raw
Step3: extracting landmarks and core events
Setting the minimum length k of the landmark, and adopting the suffix-history algorithm to obtain the minimum length k from D raw And extracting a landmark set L, extracting a core event set Q, and obtaining a reduced submatrix D = p (Q | L).
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| CN114706055A (en) * | 2022-03-30 | 2022-07-05 | 中国人民解放军战略支援部队航天工程大学 | Radar word extraction method for unbalanced samples |
| CN114997326A (en) * | 2022-06-20 | 2022-09-02 | 电子科技大学 | Airborne radar working mode identification method based on multi-feature fusion |
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| CN114706055A (en) * | 2022-03-30 | 2022-07-05 | 中国人民解放军战略支援部队航天工程大学 | Radar word extraction method for unbalanced samples |
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| CN114997326B (en) * | 2022-06-20 | 2024-06-04 | 电子科技大学 | Airborne radar working mode identification method based on multi-feature fusion |
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