CN107390189A - Multifunction radar behavior identification and method for quick predicting under the conditions of low prior information - Google Patents
Multifunction radar behavior identification and method for quick predicting under the conditions of low prior information 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
- 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
- G01S7/38—Jamming means, e.g. producing false echoes
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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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Abstract
The present invention relates to the multifunction radar behavior identification under the conditions of a kind of low prior information and method for quick predicting, step 1：Establish MFR PSR models；Step 2：Carry out PSR model trainings；Step 3：Carry out MFR mode of operation identifications；Step 4：Carry out MFR signal fast predictions.Beneficial effects of the present invention：One, studied for MFR work identifications with forecasting problem, model simple stronger to the sign ability of dynamical system using PSR models；Two, compared with full probability method, institute's extracting method of the present invention will be better than the former in performance and efficiency, be highly suitable for the PSR models with high-dimensional MFR, can substitute the multi-step prediction that Total probability is used for MFR signals completely.Three, there is very strong application prospect, accurately MFR signal sequences can be predicted so that dynamic analysis MFR mode of operations and scheduling strategy are possibly realized, and the realization for adaption radar confrontation provides technical support.
Description
【Technical field】
The present invention relates to the multifunction radar behavior identification under the conditions of low prior information and method for quick predicting, belong to thunder
Up to electronic warfare field, and in particular to multifunction radar behavior identification and Predicting Technique, further for be to be directed in low elder generation
The method tested under information condition and multifunction radar behavior identification and prediction are realized under the scene higher to requirement of real-time.
【Background technology】
With the application of the technologies such as AESA, multifunction radar (Multi-function radar, MFR) has been sent out
Transform into for one kind there is multi-mode, multitask and highly intelligentized sensory perceptual system, show extremely strong flexibility and adaptively
Ability.Conventional electronic reconnaissance and radar electronic warfare technology often has some limitations when tackling MFR, and recognizes electronic warfare skill
Art can realize preferably confrontation effect according to Battle Field Electromagnetic using targetedly counter measure.At present in Radar emitter
The research in identification field has achieved many achievements, but its foothold is the identification to radiation source model or individual mostly.This
No doubt be a bit most valuable information for disturber, but to interfering well cluster it is even more important should be radar currently and not
The behavior come, including its mode of operation, waveform parameter, scheduling strategy etc., this is also exactly the object of cognition.Therefore, it is how right
MFR behaviors accurately identify and predict as urgent problem to be solved in cognition electronic warfare research.Due to MFR signals
Complexity, existing identification and Forecasting Methodology generally existing the problem of being not easy to practical application.Represented based on predicted state
The MFR model frameworks of (Predictive State Representation, PSR) have good performance, for work
Effect is significantly better than HMM during pattern-recognition.The present invention attempts the deficiency to existing algorithm on the basis of this model framework
Part is improved：The problem of being not easy to obtain first against part prior information, have studied independent of state transition probability
MFR mode of operation discrimination methods；Then for full probability method it is computationally intensive the problem of, using PSR itself prediction attribute,
It has studied the multistep method for quick predicting of MFR signals.
【The content of the invention】
It is an object of the invention to utilize PSR model realizations MFR work identification and prediction.In order to achieve the above object, originally
The multifunction radar behavior identification being related under the conditions of low prior information of invention and method for quick predicting, the technical scheme taken
It is as follows：
Step 1：Establish MFR PSR models；
The PSR models of uncontrolled system are represented by a four-tuple<O,h,e,p(e|h)>：
O is observation space, and a finite discrete set for including all observations, one is observed o ∈ O；H is experience, is referred to
Since initial time and terminate in the observation sequence at current time, h=o1o2…ot；E is event, refers to the observation after experience
Sequence, e=ot+1ot+2….For linear PSR models, if the probability of all events can be by linear group of one group of probability of happening
Close and represent, then this group of event is referred to as core event (Core Events), Q={ q1,q2,…,q|Q|}；P (e | h) it is given experience h
Under the conditions of event e occur probability；
MFR radar word sequences are represented with PSR models：
If the finite aggregate of whole radar words is W, each radar phrase is in series by n radar word, then t
Observe otFor the short sequence of a n radar word, observation space O=Wn；Event e is the observation o at current timet, core event
It is the radar phrase set under the mode of operation to collect Q；If register digit is m, then memory is little for all length in experience h
In the set of m suffix.
Therefore, the Probability p (e | h) for the part e that makes trouble being issued in experience h is：
P (e | h)=p (e=ot| h=o1o2…ot-1) (1)
Core event Q={ q1,q2,…,q|Q|Probability distribution be：
P (Q | h)=[p (q1|h),p(q2|h),…,p(q|Q||h)]T (2)
According to Q definition, the probability that any observation occurs can be represented by p (Q | h) linear combination, therefore m be presento
So that
P (o | h)=pT(Q|h)mo (3)
OrderAfter new observation o is obtained, and p (Q | h) it will be updated to：
Meaning represented by conditional probability appearing above is different：H and l belongs to undergo, and o and q are event,
When " | " both sides are same class symbol, conditional probability represents observation probability, and such as p (l | h) and p (o | q), on the contrary then expression is shifted
Probability, such as p (q | h).
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：Carry out MFR mode of operation identifications；
Predicted state distribution p (the o observed under the conditions of each mode of operation is calculated first with above-mentioned PSR modelst+1|ht, λ=
I), further estimate corresponding mode of operation posterior probability p (λ=i | ht)。
Step 4：Carry out MFR signal fast predictions.
Step1：Initialization, i.e. Single-step Prediction.According to the mode of operation probability distribution result being previously obtained,
Finally Single-step Prediction probability is obtained.
To each possible ot∈ O, have
Wherein p (ot+1|ht, λ=i) obtained by (14), p (λ=i | ht) obtained by (17).Therefore, Single-step Prediction MAP estimates
Counting result is：
Therefore for any mode of operation λ=i, can be obtained according to (5) and (9)
Step2：K step iteration predictions.By the prediction result obtained be used for next step prediction, then iteration this
Process is to required step number.
For the sequence of completed preceding k-1 steps prediction resultHave
So
Wherein, λ represents the mode of operation of t, is estimated by the experience before t, unrelated with observation thereafter, because
This is believed that
Due to
Therefore
Obtain
Iteration (26) to (32) this process is to required step number, you can realizes the multi-step prediction of MFR signals.
Beneficial effects of the present invention mainly include：
First, the present invention is studied for MFR work identifications with forecasting problem, using PSR models to dynamical system
Sign ability is stronger, model simple；
Second, the present invention is directed to the problem of Forecasting Methodology based on total probability formula is computationally intensive, proposes a kind of MFR letters
Number fast prediction algorithm.Compared with full probability method, institute's extracting method will be better than the former in performance and efficiency, very suitable
For the PSR models with high-dimensional MFR, the multi-step prediction that Total probability is used for MFR signals can be substituted completely.
3rd, the present invention has very strong application prospect, and accurately MFR signal sequences can be predicted so that
Dynamic analysis MFR mode of operations and scheduling strategy are possibly realized, so as to provide technology branch for the realization of adaption radar confrontation
Support.
【Brief description of the drawings】
Fig. 1 is the overview flow chart of the multifunction radar signal estimation method proposed by the invention based on PSR models.
Fig. 2 is MFR mode of operation transfer relationship schematic diagrames.
Fig. 3 (a)~Fig. 3 (d) is the MFR Working moulds based on grid wave filter (Grid-Filter) method and improved method
Formula identification figure.
Fig. 4 (a), Fig. 4 (b) are by related factor figure based on grid filtered method and improved method performance.
Fig. 5 (a), Fig. 5 (b) are the predictablity rate and computation complexity comparison diagram of full probability method and fast algorithm.
【Embodiment】
The present invention is applied to MFR signal estimations.Fig. 1 is the outline flowchart of the present invention, below in conjunction with the accompanying drawings, to this hair
Bright proposed method is further explained.The specific steps and effect of this method are as follows：
Step 1：Establish MFR PSR models；
Because reconnaissance system can only passively detect receipts radar signal, therefore from square degree is scouted, the generation of radar word sequence is one
Individual uncontrolled process.The PSR models of uncontrolled system are represented by a four-tuple<O,h,e,p(e|h)>：
O is observation space, and a finite discrete set for including all observations, one is observed o ∈ O；H is experience, is referred to
Since initial time and terminate in the observation sequence at current time, h=o1o2…ot；E is event, refers to the observation after experience
Sequence, e=ot+1ot+2….For linear PSR models, if the probability of all events can be by linear group of one group of probability of happening
Close and represent, then this group of event is referred to as core event (Core Events), Q={ q1,q2,…,qQ}；P (e | h) it is given experience h
Under the conditions of event e occur probability.
MFR radar word sequences are represented with PSR models below：
If the finite aggregate of whole radar words is W, each radar phrase is in series by n radar word, then t
Observe otFor the short sequence of a n radar word, observation space O=Wn.What is studied herein is identification problem, when being only concerned about current
The state at quarter, story part e are the observation o at current timet, core event set Q is the radar phrase set under the mode of operation.
If register digit is m, then memory is not more than the set of m suffix for all length in experience h.
Therefore, the Probability p (e | h) for the part e that makes trouble being issued in experience h is：
P (e | h)=p (e=ot| h=o1o2…ot-1) (5)
Core event Q={ q1,q2,…,q|Q|Probability distribution be：
P (Q | h)=[p (q1|h),p(q2|h),…,p(q|Q||h)]T (6)
According to Q definition, the probability that any observation occurs can be represented by p (Q | h) linear combination, therefore m be presento
So that
P (o | h)=pT(Q|h)mo (7)
OrderAfter new observation o is obtained, and p (Q | h) it will be updated to：
Meaning represented by conditional probability appearing above is different：H and l belongs to undergo, and o and q are event,
When " | " both sides are same class symbol, conditional probability represents observation probability, and such as p (l | h) and p (o | q), on the contrary then expression is shifted
Probability, such as p (q | h).
Step 2：PSR models are trained；
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.
Step1：Training sequence pre-processes
First, training sequence is pre-processed, extracts the statistical information of event transfer number.In conventional character string
In algorithm, AC automatic machines (Aho-Corasick Automaton) have can Multi-Pattern Matching advantage, this step part base
Realized in AC automatic machines.
Step2：Extract boundary mark and core event
The minimum length k of boundary mark is set, suffix-history algorithms will be used below from DrawIn extract landmark set
L, then extract core event set Q, and obtain the submatrix D=p after dimensionality reduction (Q | L).
Weight vector m is calculated belowo|λAnd MQo|λ：For each element in core event probability distribution p (Q | h, λ)
Wherein p (qj|li, h, λ) and it is element in D, and p (li|ht, λ) and using Hamming distances, h will be undergonetWith landmark set L
Match and be calculated.
For the PSR models under any one mode of operation λ, the probability that o is observed under conditions of h is undergone is：
Due to observe o Probability p (o | qj, h, λ) it is only related to current actual transmission signal q, with experience before this
H is unrelated, thus it is believed that p (o | qj, h, λ) and=p (o | qj,λ).It is therefore comprehensive (4) and (5),
P (o | h, λ)=pT(Q|h,λ)·[p(o|q1,λ),p(o|q2,λ),…,p(o|q|Q|,λ)]T (6)
(2) and (6) formula of contrast is understood：
mo|λ=[p (o | q1,λ),p(o|q2,λ),…,p(o|q|Q|,λ)|T (7)
Thus each core event in Q is tried to achieve：
Core event probability distribution will be updated to：
The PSR models Jing Guo pre-training are thus obtained, it estimates as follow-up MFR mode of operation probability distribution
The basis of meter and signal estimation algorithm.
Step 3：Carry out MFR mode of operation identifications；
Predicted state distribution p (the o observed under the conditions of each mode of operation is calculated first with above-mentioned PSR modelst+1|ht, λ=
I), further estimate corresponding mode of operation posterior probability p (λ=i | ht)。
First, the iterative algorithm of predicted state estimation is under each mode of operation：
Step1：Initialization
In initial time t=0 (h0=φ), have：
P (Q | φ, λ)=[p (q1|φ,λ),p(q2|φ,λ),…,p(q|Q||φ,λ)]T (10)
Wherein p (qj| φ, λ) it is prior probability, it can be obtained by renormalization of being summed to D each row：
For being observed o for the first time1, have：
Step2：Iteration
By (10) formula, p (Q | h, λ) renewal process is：
So
Formula (14) utilizes vectorial mot+1|λCore event set Q prediction probability weighting is corresponded to specific operation mode λ, is calculated
The probability of subsequent time observation, which reflects PSR essence, i.e., is represented using the probability distribution of future time instance state current
State.Below with this predicted state estimated result to the Posterior probability distribution p of each mode of operation (λ=i | ht) estimated
Meter.
Because posterior probability sum is 1, therefore only demand goes out the ratio of each mode of operation posterior probability, then passes through normalizing
Change.To any mode of operation λ=i：
It can be seen that (15) are a recursive forms, therefore by t recurrence to initial time, obtain：
P (the o at each of which momentτ|hτ-1, λ=i) calculated by (15), and denominator is unrelated with λ, can be offseted in normalization
Disappear.If setting initial operation mode probability to be evenly distributed, i.e. p (λ=i | φ)=1/ | λ |, then to the probability normalizing of each pattern
It can be obtained after change
It was found from above formula, the essence of the process is the predicted state p (o to all historical juncturesτ|hτ-1, λ=i) carry out
Accumulation.In view of the Markov property of MFR signal sequences, each state probability is only related to several nearest states, therefore only needs
The result of accumulation several times recently.For the PSR models with r bit registers, the state at nearest r moment can be remembered, then
Have：
So MFR is estimated as in the MAP of t mode of operation：
Step 4：Carry out MFR signal fast predictions.
The conventional prediction algorithm based on total probability formula of summary first：Using the multi-step prediction to t+k moment observations as
Example, t need to be considered to the probability of all possible observation combination between the t+k moment, then bring total probability formula calculating into.So k is walked
Prediction probability distribution expression formula be：
Further according to PSR models, to each possible ot+1ot+2…ot+κ-1Combination, has
Therefore
As can be seen that the prediction computing based on total probability formula needs the k-1 moment that looks to the future from the expression formula of (22)
Interior all possible observation combination.If observation space dimension is N, mode of operation kind number is | λ |, core event number is | Q |, entirely
The magnitude of probabilistic algorithm computation complexity be about o (| λ | | Q | Nk).It can be seen that the amount of calculation of full probability algorithm is with mould
The dimension N of type is exponentially increased, and will be formed so-called " dimension disaster ".
A kind of new thinking might as well be considered, the observation of every one-step prediction is considered as, it is known that being used to solve as input condition
Next step prediction probability, then progressively recursion to required prediction step number, it is possible to avoid the high calculating as caused by uncertainty
Amount.The flow of this fast prediction algorithm based on PSR is given below：
Step1：Initialization, i.e. Single-step Prediction.According to the mode of operation probability distribution result being previously obtained, obtain finally
Single-step Prediction probability.
To each possible ot∈ O, have
Wherein p (ot+1|ht, λ=i) obtained by (14), p (λ=i | ht) obtained by (17).Therefore, Single-step Prediction MAP estimates
Counting result is：
Therefore for any mode of operation λ=i, can be obtained according to (5) and (9)
Step2：K step iteration predictions.By the prediction result obtained be used for next step prediction, then iteration this
Process is to required step number.
For the sequence of completed preceding k-1 steps prediction resultHave
So
Wherein, λ represents the mode of operation of t, is estimated by the experience before t, unrelated with observation thereafter, because
This is believed that
Due to
Therefore
Obtain
Iteration (26) to (32) this process is to required step number, you can realizes the multi-step prediction of MFR signals.
By taking the MFR that one has five kinds of patterns such as search, capture, non-self-adapting tracking, Range resolution, tracking holding as an example,
As shown in Figure 2, some Phases are as shown in table 1 below corresponding to every kind of mode of operation for the transfer relationship of its each mode of operation.
Table 1
Below for ordinary circumstance, simulated conditions are set：Training sequence for every kind of mode of operation is 500 radars
Phrase, several radar phrases recycle according to some cycles, to simulate the regular feature of MFR signals；By wherein 10%
Radar word random replacement is the radar word of mistake, causes the error of radar word extraction to simulate complex environment.Cycle tests is a length of
500 radar phrases, simulate MFR and find target, confirmation, tracking, it is final lose with process, radar character error rate is similarly
0.1.Under setting herein, radar character library W={ a, b, c }, observation space O=W4, therefore N=34, core event number | Q | i.e. radar
Phrase number, it is 3 or 4 according to mode of operation, mode of operation species number | λ | it is 5.Below with training sequence to the every kind of work of MFR
The PSR models of pattern are trained, then based on the PSR models after pre-training, are carried algorithm using this paper and carried out MFR Working moulds
Formula recognizes and the prediction of signal.Emulated for the algorithm of mode of operation identification, wherein in the method based on grid wave filter
Mode of operation transition probability such as Fig. 3 values, accumulation step number is set to 6 in this paper innovatory algorithm.Fig. 3 (a) and Fig. 3 (b) difference tables
Show the MFR mode of operation Distribution estimation results of method and improved method based on grid wave filter, wherein the song respectively marked
Line represents different working modes.As seen from the figure, the maximum probability of each mode of operation of each moment illustrates two methods all close to 1
Recognition result is respectively provided with higher confidence level.Fig. 3 (c) and Fig. 3 (d) is the MFR mode of operation recognition results of two methods.Figure
Middle MAP estimated results overlap in the equal real work pattern of most time, illustrate that the recognition effect of two methods is preferable.Two methods
When MFR real work patterns be mainly reflected in place of performance difference changing：Based on grid wave filter in Fig. 3 (c)
Method can relatively rapidly identify the mode of operation after change, the wrong identification occurred once in a while, it may be possible to turned by priori
Moving probable error and radar character error rate ρ influences；And improved method in Fig. 3 (d), although accidental wrong identification situation is less,
But needing to postpone several radar phrase times could make a response to the change of mode of operation, time delay has with accumulation step number
Close.Emulated respectively below for the factor for influenceing two methods performance, make the transition probability based on grid filtered method be averaged
Error changes between 0~0.4, and the accumulative step number of innovatory algorithm makes ρ take multiple values from 1 to 12, as a result respectively such as Fig. 4 (a)
With Fig. 4 (b) Suo Shi.Fig. 4 (a) is to be become based on the mode of operation discrimination of grid filtered method with transition probability mean error
Change situation.As seen from the figure, as the increase of mode of operation transition probability error, recognition effect are gradually deteriorated.Fig. 4 (b) is improvement
The discrimination of method is with accumulation step number situation of change.It can be seen that with the increase of accumulation step number, recognition effect first improves again
It is deteriorated, and is optimal when accumulative step number is 5 or so.When this is due to that accumulation step number is few, because the information utilized is few, effect
Fruit is general；And if accumulation step number is excessive, when mode of operation changes, the hysteresis of recognition result change is obvious.Simultaneously can be with
See, ρ takes the Curves Recognition rate of different value to be sufficiently close in two figures, illustrates two kinds of algorithms to the radar word of error hiding not
Sensitivity, robustness are preferable.It was found from result above, two kinds of algorithms respectively have quality.Method based on grid wave filter can be compared with
The change of mode of operation is identified soon, but it is higher to the accuracy requirement of the mode of operation transition probability value of priori.Improvement side
Method is without this limitation, but the recognition result in operational mode change has certain delay, delay number and discrimination it is equal
It is relevant with the step number of accumulation.Under the conditions of the suitable accumulation step number of selection, the inventive method can reach good performance, and nothing
Mode of operation transition probability need to be utilized, low is required to prior information, is more convenient for applying.Especially to the timeliness of mode of operation identification
Under the less demanding scene of property, the advantage of this method will be apparent from.
Lower surface analysis prediction result comparable situation.Precision of prediction is weighed by index of the error sign ratio of multi-step prediction result,
Counted respectively in units of radar word and radar phrase, predictablity rate result is calculated with MFR actual transmissions alignment
As shown in Fig. 5 (a).Record and draw emulation used time logarithmic curve, theoretic complexity logarithmic curve is drawn, such as Fig. 5 (b)
It is shown.Fig. 5 (a) is that full probability method and the predictablity rate of this paper fast algorithms contrast.As seen from the figure, with prediction step number
Increase, forecasting accuracy is generally on a declining curve.The predictablity rate ratio represented in units of radar word is with method with thunder
It is higher for the result of unit up to phrase, because a radar phrase is made up of multiple radar words, only wherein all radars
The prediction of word is completely correct, and the prediction of the radar phrase is just judged to correctly, therefore this probability is relatively lower.It can see simultaneously
Arrive, although the approximation of fast algorithm simply full probability method, predictablity rate are not deteriorated not only, on the contrary in prediction step number
It is more excellent than full probability method effect when higher.Because what full probability method utilized is the sequence with probability distribution, and institute
There is probability to be all used, and the error of intermediate result will constantly be accumulated, thus as prediction step number increase, error are also rapid
Increase.Conversely, fast algorithm can then be put error caused by intermediate steps in time when asking MAP to estimate prediction result
Zero, therefore the performance of the prediction for higher-order is better than full probability method on the contrary.Fig. 5 (b) is that the emulation of two kinds of prediction algorithms is used
When and computation complexity contrast.As seen from the figure, the simulation time logarithmic curve near linear of full probability method, illustrates its emulation
Time is in approximate exponential increase with prediction step number；On the contrary, the simulation time logarithmic curve of fast prediction algorithm substantially remains in
One very little section, illustrate that simulation efficiency is higher and is hardly influenceed by prediction step number.In summary, it is quick in performance
Algorithm is better than full probability method, and is even more to be far superior to the latter in efficiency.So comprehensive two aspects, fast algorithm can be with complete
It is complete to substitute full probability method, for realizing the multi-step prediction to MFR signals.
Claims (2)
1. multifunction radar behavior identification and method for quick predicting under the conditions of a kind of low prior information, it is characterised in that：The party
Method comprises the following steps：
Step 1：Establish MFR PSR models；
The PSR models of uncontrolled system are represented by a four-tuple<O,h,e,p(e|h)>：
O is observation space, and a finite discrete set for including all observations, one is observed o ∈ O；H is experience, is referred to from first
Moment beginning starts and terminates in the observation sequence at current time, h=o1o2…ot；E is event, refers to the observation sequence after experience,
E=ot+1ot+2…；For linear PSR models, if the probability of all events can be represented by the linear combination of one group of probability of happening,
Then this group of event is referred to as core event (Core Events), Q={ q1,q2,…,q|Q|}；P (e | h) under given experience h
The probability that event e occurs；
MFR radar word sequences are represented with PSR models：
If the finite aggregate of whole radar words is W, each radar phrase is in series by n radar word, then the observation o of tt
For the short sequence of a n radar word, observation space O=Wn；Event e is the observation o at current timet, core event set Q is should
Radar phrase set under mode of operation；If register digit is m, then memory is not more than m suffix for all length in experience h
Set；
Therefore, the Probability p (e | h) for the part e that makes trouble being issued in experience h is：
P (e | h)=p (e=ot| h=o1o2…ot-1) (1)
Core event Q={ q1,q2,…,q|Q|Probability distribution be：
P (Q | h)=[p (q1|h),p(q2|h),…,p(q|Q||h)]T (2)
According to Q definition, the probability that any observation occurs can be represented by p (Q | h) linear combination, therefore m be presentoSo that
P (o | h)=pT(Q|h)mo (3)
OrderAfter new observation o is obtained, and p (Q | h) it will be updated to：
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Meaning represented by conditional probability appearing above is different：H and l belongs to undergo, and o and q are event, when " | "
When both sides are same class symbol, conditional probability represents observation probability, on the contrary then represent transition probability such as p (l | h) and p (o | q),
Such as p (q | h)；
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：Carry out MFR mode of operation identifications；
Predicted state distribution p (the o observed under the conditions of each mode of operation is calculated first with above-mentioned PSR modelst+1|ht, λ=i), then enter
The corresponding mode of operation of one step estimation posterior probability p (λ=i | ht)；
Step 4：Carry out MFR signal fast predictions.
2. multifunction radar behavior identification and method for quick predicting under the conditions of low prior information according to claim 1,
It is characterized in that：The step 4 carries out MFR signal fast predictions, and detailed process is as follows：
Step1：Initialization, i.e. Single-step Prediction；According to the mode of operation probability distribution result being previously obtained,
Finally Single-step Prediction probability is obtained；
To each possible ot∈ O, have
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<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>o</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>|</mo>
<mi>&lambda;</mi>
<mo>|</mo>
</mrow>
</munderover>
<mo>&lsqb;</mo>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>o</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>=</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
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<mi>i</mi>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>23</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein p (ot+1|ht, λ=i) obtained by (14), p (λ=i | ht) obtained by (17)；Therefore, Single-step Prediction MAP estimated results
For：
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<mrow>
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<mi>arg</mi>
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<mi>a</mi>
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<mo>&Element;</mo>
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</mrow>
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<mo>(</mo>
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<msub>
<mi>o</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>24</mn>
<mo>)</mo>
</mrow>
</mrow>
Therefore for any mode of operation λ=i, can be obtained according to (5) and (9)
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</mrow>
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<mfrac>
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</mrow>
</mfrac>
<mo>,</mo>
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<mo>,</mo>
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<mo>-</mo>
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</mrow>
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<mo>&CenterDot;</mo>
<msub>
<mi>m</mi>
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<mn>2</mn>
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<mo>-</mo>
<mo>-</mo>
<mrow>
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<mn>26</mn>
<mo>)</mo>
</mrow>
</mrow>
Step2：K step iteration predictions；The prediction result obtained is used for the prediction of next step, then iteration this process to be extremely
Required step number；
For the sequence of completed preceding k-1 steps prediction resultHave
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<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
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<mi>k</mi>
<mo>-</mo>
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</mrow>
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<mrow>
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</mover>
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</mrow>
</msub>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mn>...</mn>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mi>k</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mi>&lambda;</mi>
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</mrow>
<msub>
<mi>m</mi>
<mrow>
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</mover>
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</mrow>
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</mrow>
</msub>
</mrow>
</mfrac>
<mo>,</mo>
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<mn>2</mn>
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<mi>&lambda;</mi>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>27</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
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<mrow>
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<msub>
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</mrow>
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<msub>
<mi>h</mi>
<mi>t</mi>
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<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
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<mn>1</mn>
</mrow>
</msub>
<msub>
<mover>
<mi>o</mi>
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</mover>
<mrow>
<mi>t</mi>
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<mn>2</mn>
</mrow>
</msub>
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<msub>
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</mrow>
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</mrow>
</msub>
<msub>
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<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mn>...</mn>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
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<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
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</mrow>
<mo>&CenterDot;</mo>
<msub>
<mi>m</mi>
<mrow>
<msub>
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</mover>
<mrow>
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</mrow>
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</mrow>
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<mo>,</mo>
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<mo>-</mo>
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<mrow>
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<mn>28</mn>
<mo>)</mo>
</mrow>
</mrow>
So
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<mrow>
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<msub>
<mi>o</mi>
<mrow>
<mi>t</mi>
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</mrow>
</msub>
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<msub>
<mi>h</mi>
<mi>t</mi>
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<mrow>
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</msub>
<msub>
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<mo>^</mo>
</mover>
<mrow>
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</mrow>
</msub>
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<msub>
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<mo>^</mo>
</mover>
<mrow>
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<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>&lambda;</mi>
<mo>=</mo>
<mi>i</mi>
</mrow>
<mrow>
<mo>|</mo>
<mi>&lambda;</mi>
<mo>|</mo>
</mrow>
</munderover>
<mo>&lsqb;</mo>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>o</mi>
<mrow>
<mi>t</mi>
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<mi>k</mi>
</mrow>
</msub>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
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<mn>2</mn>
</mrow>
</msub>
<mn>...</mn>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<mi>&lambda;</mi>
<mo>=</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>p</mi>
<mrow>
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<mi>&lambda;</mi>
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<mi>i</mi>
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<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>...</mo>
<msub>
<mover>
<mi>o</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>29</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, λ represents the mode of operation of t, is estimated by the experience before t, unrelated with observation thereafter,
It can thus be assumed that
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</msub>
<mo>)</mo>
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<mn>30</mn>
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</mrow>
</mrow>
Due to
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Obtain
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<mi>O</mi>
</mrow>
</munder>
<mo>(</mo>
<mrow>
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<mrow>
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<mi>k</mi>
</mrow>
</msub>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
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</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>33</mn>
<mo>)</mo>
</mrow>
</mrow>
Iteration (26) to (32) this process is to required step number, you can realizes the multi-step prediction of MFR signals.
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