CN107171753A - Based on the wrong signal detecting method for determining multi-model hypothesis testing - Google Patents
Based on the wrong signal detecting method for determining multi-model hypothesis testing Download PDFInfo
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Abstract
The invention discloses a kind of based on the wrong signal detecting method for determining multi-model hypothesis testing, including step：First, for signal characteristic, no signal Models Sets is selected and have signal model collection, the original signal detection problem based on model is described as into binary composite hypothesis examines form；2nd, the likelihood of the Models Sets without signal is calculated；3rd, according to Multiple Models Algorithm, the likelihood for the Models Sets for having signal is calculated；4th, the Models Sets of no signal are calculated and has the likelihood of the M signal model of the Models Sets of signal；5th, calculate the test statistics of 2 SPRT decision-makings rule and obtain asymptotic optimality testing result with threshold comparison.The inventive method step is simple, and it is convenient to realize, solves the problems, such as that judgement error and dwell time are without the upper bound in existing method, the testing result with suitable average sample number and error probability can be obtained, and new thinking can be provided for the future development of etection theory, and it is practical, it is easy to promote the use of.
Description
Technical field
The invention belongs to signal detection technique field, and in particular to a kind of based on the wrong signal inspection for determining multi-model hypothesis testing
Survey method.
Background technology
Developing rapidly for communication theory, information theory, Computer Science and Technology and microelectric technique etc. has driven signal
Etection theory and technology are to interference environment is more complicated, signal form is diversified, the wider range of direction of application is developed, people
Very big lifting has been obtained to the understanding of features, the signal detection problem based on model has been widely present in electronic information system
System, biomedical engineering, Aerospace Engineering, pattern-recognition and the numerous areas such as automatically control, especially in cognitive radio frequency
Spectrum perception field has broad application prospects.In view of the particularity of the problem, the distributed architecture that its difficult point is the assumption that is different
It is possible with wrong fixed presence, it is embodied in the following aspects：
(1) under real conditions, the distribution of detected signal there may be the uncertain of structure and parameter, and for distribution
The uncertain situation of structure, current theoretical research is less；
(2) real signal model may not be in the Models Sets of multi-model process；
(3) actual signal is also not necessarily assuming that in collection.
Traditional solution is that it is described as into M members hypothesis testing [Leang C, Johnson D.On the
asymptotic of M-hypothesis Bayesian detection[J].IEEE Transactions on
Information Theory,1997,43(1):(Leang C, Johnson D.M members assume Bayesian detection to 280-282.
Gradation [J] .IEEE information theory transactions, 1997,43 (1):280-282.)] problem.However, this way has following two
Aspect is not enough：
(1) what traditional M member hypothesis testings were typically solved is classification or identification problem, however, the signal based on model
Test problems are intended to binary detection.Therefore, the description of M members hypothesis testing is not suitable for this problem in itself.
(2) traditional M members hypothesis testing do not consider typically it is wrong determine problem, and mistake is determined problem and often existed in actual conditions.
Moreover, because the wrong presence for determining problem, when solving the problems, such as the signal detection based on model with traditional M member hypothesis testing methods,
It is possible that judgement error.For example, observation signal has two kinds of possible distribution F11(z|x11) and F12(z|x12), they may
Belong to two kinds of different family of distributions, x1i(i=1,2) it is signal to be detected.The purpose of detection is to determine whether signal, rather than
Which kind of signal identification is.This problem is described as by traditional M member hypothesis testing methods：
If H0H can be defeated respectively11And H12, then M members hypothesis testing method judge no signal.However, being truly Ht:Z~
ft(z) any one rather than in three, HtH may be compared respectively11And H12Closer to H0, still, HtH may be compared0Closer to H11
And H12Combination, like this, it should be determined as there is signal.Now, M members hypothesis testing method causes judgement to be slipped up.
On the one hand, existing parameter and Nonparametric detection method seldom consider simultaneously different distributions structure and it is wrong determine problem this
Two big difficult points, so, they can not solve the problems, such as such signal detection based on model well；On the other hand, although existing
Document in also have for such test problems and dabble, but be only embodied in some concrete application examples, not
Provide detailed stationary singnal detection algorithm.Multi-model hypothesis testing method [Li XR.Multiple-model based on SPRT
estimation with variable structure---Part II:Model-set adaptation[J].IEEE
Transactions on Automatic Control,2000,45:2047-2060. (Li XR. variable structure multi-models are estimated
Meter --- Part II：Modelsde adaptation [J] .IEEE automatically controls transactions, 2000,45:2047-2060.)] although solving
The uncertain problem of distributed architecture or parameter, still, the mistake that it does not account for assuming are pledged love condition, it is thus possible to when stopping
Between without upper bound problem, this is intolerable in most of signal detection problem.In other words, the multi-model based on SPRT is false
If check algorithm may run in indefinite duration, especially (appoint in this when truly close to the point for being most difficult to judgement
One assumes all to be difficult to be rejected), to some problems, such case is probably catastrophic.
Therefore, for the deficiency of the existing signal detecting method based on model, propose that one kind can solve the problem that in existing method
Judgement error and dwell time are necessary based on the wrong signal detecting method for determining multi-model hypothesis testing without upper bound problem.
The content of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing a kind of based on wrong fixed
The signal detecting method of multi-model hypothesis testing, its method and step is simple, and it is convenient to realize, solves and error is adjudicated in existing method
With dwell time without upper bound problem, the testing result with suitable average sample number and error probability can be obtained, and can be inspection
Survey theoretical future development and new thinking is provided, it is practical, it is easy to promote the use of.
In order to solve the above technical problems, the technical solution adopted by the present invention is：One kind determines multi-model hypothesis testing based on mistake
Signal detecting method, it is characterised in that this method comprises the following steps：
Step 1: for signal characteristic, selecting no signal Models Sets and having signal model collection, by the original letter based on model
Number test problems are described as H0And H1Binary composite hypothesis examine form：
Wherein, xkSignal condition for the k moment is vectorial and is nxDimensional vector, zkSignal observation vector for the k moment and be nz
Dimensional vector, k is discrete-time variable, a be signal observation model andB be signal model andThe subscript j of element represents that subscripting j element is under the jurisdiction of in the subscript j and b of element in a
Models Sets Mj, j value is 0,1；The subscript (i) of the subscript (i) of element and element in b represents the element with subscript (i) in a
It is under the jurisdiction of Models Sets MjIn i-th of model, i ∈ { 1,2 ..., r }；One model m is expressed as (a, b), and definedFor the Models Sets without signal, definitionTo there is the Models Sets of signal, r is model
Collect M1In Number of Models and value be positive integer not less than 1；
Step 2: according to formulaCalculate the Models Sets M without signal0During from initial time to k
The joint likelihood at quarter, and according to formulaCalculate the Models Sets M without signal0On the side at k moment
Edge likelihood；Wherein, zkFor the signal observation vector sequence from initial time to the k moment and be k × nzObserving matrix is tieed up, s is true
Pattern, zk-1For the signal observation vector sequence from initial time to the k-1 moment and be (k-1) × nzTie up observing matrix,
Represent modelMatched with actual pattern s；
Step 3: according to Multiple Models Algorithm, calculating the Models Sets M for having signal1Likelihood；I-th in Multiple Models Algorithm
Model meets below equation：
Wherein, xk+1Signal condition for the k+1 moment is vectorial and is nxDimensional vector,For the n of i-th of model of k momentwDimension
Process noise andNormal DistributionRepresent that average isCovariance matrix is
Gaussian probability-density function,ForAverage,ForCovariance matrix；For the n of i-th of model of k momentv
Dimension measure noise andNormal DistributionRepresent that average isCovariance matrix is
Gaussian probability-density function,ForAverage,ForCovariance matrix；For the n of i-th of model of k momentx
×nxTie up state-transition matrix,For the n of i-th of model of k momentx×nwNoise gain matrix is tieed up,For i-th of mould of k moment
The n of typez×nxTie up measurement matrix；nx、nz、nwAnd nvValue be positive integer not less than 1；
WithSubscript (i) represent that the amount with subscript (i) is carved with the Models Sets M of signal when being under the jurisdiction of k1In i-th of model
According to formulaCalculate the Models Sets M for having signal1From initial time to the joint at k moment seemingly
So, and according to formulaCalculate the Models Sets M for having signal1
In the edge likelihood at k moment；Wherein,Represent modelMatched with actual pattern s；For modelIn the edge likelihood at k moment,To there is the Models Sets M of signal1In i-th of model prediction probability and
The single cycle of Multiple Models Algorithm is as follows：
Step 301, the filtering based on model：
Predicted state：
Predicted state variance：
Measurement residuals：
Residual covariance：
Filter gain：
State updates：
State variance updates：
Wherein,Represent in setting models collection M1In i-th of model k-1 moment status informations on the premise of to the k moment
The predicted state of information,Represent in setting models collection M1In i-th of model k moment status informations on the premise of to the k moment
The state of information updates,Represent the n of i-th of model of k-1 momentx×nxTie up state-transition matrix,Represent given
Models Sets M1In i-th of model k-1 moment status informations on the premise of the states of k-1 time informations is updated,Represent k-
The n of 1 i-th of moment modelx×nwNoise gain matrix is tieed up,ForAverage,For the n of i-th of model of k-1 momentw
Tie up process noise andNormal DistributionRepresent that average isCovariance matrix
ForGaussian probability-density function,ForAverage,ForCovariance matrix；Represent to cover half
Type collection M1In i-th of model k-1 moment status informations on the premise of to the variance matrix of the status predications of k time informations；Represent in setting models collection M1In i-th of model k-1 moment status informations on the premise of to the shapes of k-1 time informations
The variance matrix that state updates；Represent in setting models collection M1In i-th of model k moment status informations on the premise of to k when
Carve the variance matrix that the state of information updates；(·)TRepresenting matrix seeks transposition；Represent Models Sets M1In i-th of model in k
The measurement residuals at quarter；Represent Models Sets M1In i-th of model the k moment residual covariance matrix；Represent Models Sets M1
In i-th of model the k moment filter gain；
Step 302, model probability update：
Model likelihood：
Model probability：
Wherein,Represent Models Sets M1In edge likelihood of i-th of model at the k moment,Represent parameterIt is that 0, covariance matrix is to obey averageNormal distribution；Indicate the Models Sets M of signal1In i-th model
Update probability；C=1,2 ..., r,Indicate the Models Sets M of signal1In i-th of model prediction probability and Indicate the Models Sets M of signal1In c-th of model,Represent Models Sets M1
In c-th of model the k moment likelihood and Represent
ParameterIt is that 0, covariance matrix is to obey averageNormal distribution；
Step 303, estimation fusion：
Totally it is estimated as：
Overall estimate variance is：
Wherein,Indicate the Models Sets M of signal1The totality of state is estimated at the k moment,Represent in setting models
Collect M1In i-th of model k moment status informations on the premise of the states of k time informations is updated；Pk|kIndicate the mould of signal
Type collection M1In overall estimate variance matrix of the k moment to state,Represent in setting models collection M1In i-th of model the k moment
The variance matrix updated on the premise of status information to the state of k time informations；
Step 4: according to formulaCalculate the Models Sets M of no signal0And have signal
Models Sets M1In the M signal model at k momentEdge likelihoodWherein, α0=α and α1=β is required to meet wrong general
Rate constraint P { " H1”|H0}≤α,P{“H0”|H1}≤β,α+β≤1；For K-
L information；
Step 5: according to formulaCalculate the test statistics and and threshold comparison of 2-SPRT decision-makings rule
Obtain asymptotic optimality testing result；WhenWhen, select M1；WhenWhen, select M0；Otherwise, k value is set to add 1
And return to step two；Wherein, A0=α-1, A1=β-1, k0To examine initial time,For the Models Sets M of no signal0And have signal
Models Sets M1In the M signal model at κ momentEdge likelihood.
The above-mentioned signal detecting method that multi-model hypothesis testing is determined based on mistake, it is characterised in that：According to public affairs in step 2
FormulaCalculate the Models Sets M without signal0Joint likelihood when, zkFor white, formulaIt is converted intoWherein,For the Models Sets M without signal0At the edge at κ moment
Likelihood andzκSignal observation vector for the κ moment and be nzDimensional vector, zκ-1For from during starting
It is carved into the signal observation vector sequence at κ -1 moment and for (κ -1) × nzTie up observing matrix.
The above-mentioned signal detecting method that multi-model hypothesis testing is determined based on mistake, it is characterised in that：According to public affairs in step 3
FormulaCalculate the Models Sets M for having signal1Joint likelihood when, zkFor white, formula
It is converted intoWherein,To there is the Models Sets M of signal1The κ moment edge likelihood andzκSignal observation vector for the κ moment and be nzDimension
Vector, zκ-1For the signal observation vector sequence at -1 moment from initial time to κ and be (κ -1) × nzTie up observing matrix,For κ
The Models Sets M of Shi Keyou signals1In i-th of model,Represent modelMatched with actual pattern s,For modelEdge likelihood,To there is the Models Sets M of signal1In i-th of model prediction it is general
Rate and
The present invention has advantages below compared with prior art：
1st, method and step of the invention is simple, and it is convenient to realize.
2nd, it is of the present invention that multi-model hypothesis inspection is determined based on mistake compared with the existing signal detecting method based on model
The signal detecting method tested fundamentally solves existing method while consider the different and wrong presence for determining problem of distributed architecture
Middle judgement error and dwell time can obtain the detection knot with suitable average sample number and error probability without upper bound problem
Really, requirement can be met well.
3rd, method of the invention is general, and calculates simple, and new thinking can be provided for the future development of etection theory.
4th, the present invention's is practical, and using effect is good, is easy to promote the use of.
In summary, method and step of the invention is simple, and it is convenient to realize, solves judgement in existing method and slips up and stop
Time, without upper bound problem, can obtain the testing result with suitable average sample number and error probability, and can be etection theory
Future development new thinking is provided, it is practical, be easy to promote the use of.
Below by drawings and examples, technical scheme is described in further detail.
Brief description of the drawings
Fig. 1 is method flow block diagram of the invention.
Fig. 2 is cognitive radio frequency spectrum sensory perceptual system scene analysis figure in the embodiment of the present invention.
Fig. 3 is the present invention in the scene 1 of the embodiment of the present invention and the average sample of traditional signal detecting method based on model
This amount comparison diagram.
The decision-making of Fig. 4 signal detecting methods based on model for the present invention in the scene 1 of the embodiment of the present invention and tradition is just
True probability comparison diagram.
Fig. 5 is averaged for the present invention in the scene 2 of the embodiment of the present invention with signal detecting method of the tradition based on model
Sample size comparison diagram.
The decision-making of Fig. 6 signal detecting methods based on model for the present invention in the scene 2 of the embodiment of the present invention and tradition is just
True probability comparison diagram.
Embodiment
As shown in figure 1, the signal detecting method that multi-model hypothesis testing is determined based on mistake of the present invention, is comprised the following steps：
Step 1: for signal characteristic, selection no signal Models Sets and there is signal model collection (no signal Models Sets are usually
Average is 0 Gaussian Profile, has signal model collection to include various signal distributions forms), by the original signal detection based on model
Problem is described as H0And H1Binary composite hypothesis examine form：
Wherein, xkSignal condition for the k moment is vectorial and is nxDimensional vector, zkSignal observation vector for the k moment and be nz
Dimensional vector, k is discrete-time variable, a be signal observation model andB be signal model andThe subscript j of element represents that subscripting j element is under the jurisdiction of in the subscript j and b of element in a
Models Sets Mj, j value is 0,1；The subscript (i) of the subscript (i) of element and element in b represents the element with subscript (i) in a
It is under the jurisdiction of Models Sets MjIn i-th of model, i ∈ { 1,2 ..., r }；One model m is expressed as (a, b), and definedFor the Models Sets without signal, definitionTo there is the Models Sets of signal, r is model
Collect M1In Number of Models and value be positive integer not less than 1；Here, a model m be expressed as (a, b), it is necessary to note
Be, actual signal model not necessarily assuming that concentrate, so, this is that the mistake of a quasi-representative determines problem；
In the present embodiment, for the cognitive radio frequency spectrum sensory perceptual system in certain region, its scene analysis is as shown in Figure 2.Certain
Period, when perception user mandate frequency range interested is not taken by primary user, perceiving user can just be entered using the frequency range
Row communication；But the frequency range must periodically be detected by perceiving user, to be exited in time after primary user returns, it is to avoid to master
User interferes.In fig. 2, PU1 represents primary user's emitter, and PU2 represents primary user's receiver, and primary user's emitter has
Certain communication covered radius, is represented with Rc；And primary user's receiver normally receives for guarantee, it is also desirable to exempt to do with certain
Radius of protection is disturbed, is represented with Rp.When perception user is located at by the center of circle of primary emitter, Rc+Rp is within the scope of radius,
It could must be communicated when the frequency range is idle using it；And when beyond Rc+Rp scopes, the perception user in such as Fig. 2
SU3 and SU4, no matter now primary user whether take the frequency range, perceive user and may be by the frequency range and communicated.Even if production
Raw co-channel interference, interference level is also primary user's receiver acceptable.In summary, signal inspection of the present invention is illustrated
Survey method has the attribute that space-time is multiplexed.
For above concrete signal test problems, example signal Models Sets are selected as follows：
H0:Z~Ν (0,1) (no signal)
It is possible thereby to which original signal detection problem is described as into binary composite hypothesis check problem.For the sake of comprehensively, this
Example considers two kinds of conventional scenes：
Scene 1, actual signal are to determine：The average of actual signal changes to θ=1.5 (for example, just from θ=- 0.5 respectively
Beginning actual signal is z~Ν (- 0.5,1)), to detect Detection results of the present invention for signal.
Scene 2, actual signal are random：From H in single Monte Carlo0、H1Or Hm:Z~Ν (0.5,1) three
Assuming that in random selection one produce measurement, the prior probability each assumed is 1/3.Here, HmIt is used to indicate that mistake is asked surely
Topic.For H1, the present embodiment is according to mixed distribution z~η Ν (1,1)+(1- η) [Ν (2,1) of 0.4 Ν (1,1)+0.6] generations
Measurement sequence.For simplicity, the present embodiment is by η according to 0:0.1:1 (Matlab notations) changes, to characterize H1In distribution it is not true
It is qualitative, and assume that M signal model is a Gaussian Profile；
Step 2: according to formulaCalculate the Models Sets M without signal0During from initial time to k
The joint likelihood at quarter, and according to formulaCalculate the Models Sets M without signal0On the side at k moment
Edge likelihood；Wherein, zkFor the signal observation vector sequence from initial time to the k moment and be k × nzObserving matrix is tieed up, s is true
Pattern, zk-1For the signal observation vector sequence from initial time to the k-1 moment and be (k-1) × nzTie up observing matrix,
Represent modelMatched with actual pattern s；
In the present embodiment, according to formula in step 2Calculate the Models Sets M without signal0Connection
When closing likelihood, zkFor white (white), formulaIt is converted intoWherein,Not have
There is the Models Sets M of signal0The κ moment edge likelihood andzκFor the κ moment signal observe to
Amount and for nzDimensional vector, zκ-1For the signal observation vector sequence at -1 moment from initial time to κ and be (κ -1) × nzDimension observation square
Battle array.
Step 3: according to Multiple Models Algorithm, calculating the Models Sets M for having signal1Likelihood；I-th in Multiple Models Algorithm
Model meets below equation：
Wherein, xk+1Signal condition for the k+1 moment is vectorial and is nxDimensional vector,For the n of i-th of model of k momentwDimension
Process noise andNormal DistributionRepresent that average isCovariance matrix is
Gaussian probability-density function,ForAverage,ForCovariance matrix；For the n of i-th of model of k momentv
Dimension measure noise andNormal DistributionRepresent that average isCovariance matrix isGaussian probability-density function,ForAverage,ForCovariance matrix；For i-th of model of k moment
Nx×nxTie up state-transition matrix,For the n of i-th of model of k momentx×nwNoise gain matrix is tieed up,For the k moment i-th
The n of individual modelz×nxTie up measurement matrix；nx、nz、nwAnd nvValue be positive integer not less than 1；WithSubscript (i) represent that the amount with subscript (i) is carved with the Models Sets M of signal when being under the jurisdiction of k1
In i-th of model
According to formulaCalculate the Models Sets M for having signal1From initial time to the joint at k moment seemingly
So, and according to formulaCalculate the Models Sets M for having signal1
In the edge likelihood at k moment；Wherein,Represent modelMatched with actual pattern s；For mould
TypeIn the edge likelihood at k moment,To there is the Models Sets M of signal1In i-th of model prediction probability and
The single cycle of Multiple Models Algorithm is as follows：
Step 301, the filtering based on model：
Predicted state：
Predicted state variance：
Measurement residuals：
Residual covariance：
Filter gain：
State updates：
State variance updates：
Wherein,Represent in setting models collection M1In i-th of model k-1 moment status informations on the premise of to the k moment
The predicted state of information,Represent in setting models collection M1In i-th of model k moment status informations on the premise of to the k moment
The state of information updates,Represent the n of i-th of model of k-1 momentx×nxTie up state-transition matrix,Represent to cover half
Type collection M1In i-th of model k-1 moment status informations on the premise of the states of k-1 time informations is updated,Represent k-1
The n of i-th of model of momentx×nwNoise gain matrix is tieed up,ForAverage,For the n of i-th of model of k-1 momentw
Tie up process noise andNormal DistributionRepresent that average isCovariance matrix
ForGaussian probability-density function,ForAverage,ForCovariance matrix；Represent to cover half
Type collection M1In i-th of model k-1 moment status informations on the premise of to the variance matrix of the status predications of k time informations；Represent in setting models collection M1In i-th of model k-1 moment status informations on the premise of to the shapes of k-1 time informations
The variance matrix that state updates；Represent in setting models collection M1In i-th of model k moment status informations on the premise of to k when
Carve the variance matrix that the state of information updates；(·)TRepresenting matrix seeks transposition；Represent Models Sets M1In i-th of model in k
The measurement residuals at quarter；Represent Models Sets M1In i-th of model the k moment residual covariance matrix；Represent Models Sets M1
In i-th of model the k moment filter gain；
Step 302, model probability update：
Model likelihood：
Model probability：
Wherein,Represent Models Sets M1In edge likelihood of i-th of model at the k moment,Represent parameterIt is that 0, covariance matrix is to obey averageNormal distribution；Indicate the Models Sets M of signal1In i-th model
Update probability；C=1,2 ..., r,Indicate the Models Sets M of signal1In i-th of model prediction probability and Indicate the Models Sets M of signal1In c-th of model,Represent Models Sets M1
In c-th of model the k moment likelihood and Represent
ParameterIt is that 0, covariance matrix is to obey averageNormal distribution；
Step 303, estimation fusion：
Totally it is estimated as：
Overall estimate variance is：
Wherein,Indicate the Models Sets M of signal1The totality of state is estimated at the k moment,Represent in setting models
Collect M1In i-th of model k moment status informations on the premise of the states of k time informations is updated；Pk|kIndicate the mould of signal
Type collection M1In overall estimate variance matrix of the k moment to state,Represent in setting models collection M1In i-th of model the k moment
The variance matrix updated on the premise of status information to the state of k time informations；
In the present embodiment, according to formula in step 3Calculate the Models Sets M for having signal1Joint
During likelihood, zkFor white (white), formulaIt is converted intoWherein,To there is letter
Number Models Sets M1The κ moment edge likelihood and
zκSignal observation vector for the κ moment and be nzDimensional vector, zκ-1For the signal observation vector sequence at -1 moment from initial time to κ
And be (κ -1) × nzTie up observing matrix,The Models Sets M of signal is carved with during for κ1In i-th of model,Represent mould
TypeMatched with actual pattern s,For modelEdge likelihood,To there is the Models Sets of signal
M1In i-th of model prediction probability and
The concept of Models Sets likelihood can handle the problem of distributed architecture is different, and composite hypothesis can be changed into letter
It is single to assume；In order to obtain Models Sets likelihood, it is assumed that model is real according to probability match；That is, it is known that above simple
Assuming that under model be probably real probability distribution.
Step 4: according to formulaCalculate the Models Sets M of no signal0And have signal
Models Sets M1In the M signal model at k momentEdge likelihoodWherein, α0=α and α1=β is required to meet wrong general
Rate constraint P { " H1”|H0}≤α,P{“H0”|H1}≤β,α+β≤1；For K-
L information (Kullback-Leibler information)；K-L information refers to paper Kullback S, Leibler RA.On
information and sufficiency[J].The Annals of Mathematical Statistics,1951,55:
(Kullback S, Leibler RA. discuss information and adequacy [J] mathematical statistics annual reports, 1951,55 to 79-86.:79-86.)
In the present embodiment, the average θ of M signal model profile*As shown in table 1：
The average table of the M signal model profile of table 1
Step 5: according to formulaCalculate the test statistics and and threshold comparison of 2-SPRT decision-makings rule
Obtain asymptotic optimality testing result；WhenWhen, select M1；WhenWhen, select M0；Otherwise, k value is set to add
1 and return to step two；Wherein, A0=α-1, A1=β-1, k0To examine initial time,For the Models Sets M of no signal0And have letter
Number Models Sets M1In the M signal model at κ momentEdge likelihood.When it is implemented,According to formulaCalculating is obtained.
Comparison test statistic and threshold value are restrained using 2-SPRT decision-makings, you can obtain the testing result for having no signal, the knot
Fruit sample size used on the premise of error probability constraint is met is minimum.
In the present embodiment, Fig. 3, Fig. 4 and Fig. 5, Fig. 6 sets forth the present invention in two kinds of conventional scenes and exist with conventional method
5000 Monte Carlo experiments relatively under the correct probability of average sample number and decision-making.MMSPRT represents traditional based on SPRT
Multi-model hypothesis testing signal detecting method, 2-MMSPRT represent it is of the present invention based on mistake determine multi-model hypothesis testing
Signal detecting method.
It is clear that in scene 1, first, when truly close to the M signal model between two Models Sets, this
The Detection results for inventing the 2-MMSPRT signal detection algorithms being related to are better than MMSPRT, because its average sample number is small, and
And its error probability is close to 0.5.Therefore, 2-MMSPRT asymptotic optimal efficiency Worth Expecting, this exactly it to mistake determine problem
Meaning.It is worth noting that, in Fig. 4, a good inspection should have such curve：It is right on curve when θ is small
The value answered is also small；When θ=0.5, corresponding value is close to 0.5 on curve；When θ is big, corresponding value is also big on curve.Separately
Outside, when model does not have the traditional optimal effect of MMSPRT algorithms of mistake timing (for example, θ=0 or 1).Secondly, in different truths
Under, 2-MMSPRT has the average sample number more balanced than MMSPRT.Finally, they all receive from true that nearest vacation
If.We can see that, it is higher closer to the real received probability of signal model collection.
In scene 2, MMSPRT and 2-MMSPRT meet accuracy constraint, but no matter 2-MMSPRT is in average sample
Better than MMSPRT in amount or accuracy.Because 2-MMSPRT methods proposed by the present invention can handle and there is mistake and pledge love
The signal detection problem of shape, and MMSPRT can not.
From this it can be concluded that mistake of the present invention, which determines multi-model hypothesis testing signal detecting method, can solve biography
Judgement error and dwell time in signal detecting method of the system based on model obtain good detection performance without upper bound problem.
It is described above, only it is presently preferred embodiments of the present invention, not the present invention is imposed any restrictions, it is every according to the present invention
Any simple modification, change and equivalent structure change that technical spirit is made to above example, still fall within skill of the present invention
In the protection domain of art scheme.
Claims (3)
1. it is a kind of based on the wrong signal detecting method for determining multi-model hypothesis testing, it is characterised in that this method comprises the following steps：
Step 1: for signal characteristic, selecting no signal Models Sets and having signal model collection, the original signal based on model is examined
Survey problem is described as H0And H1Binary composite hypothesis examine form：
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Wherein, xkSignal condition for the k moment is vectorial and is nxDimensional vector, zkSignal observation vector for the k moment and be nzTie up to
Amount, k is discrete-time variable, a be signal observation model andB be signal model andThe subscript j of element represents that subscripting j element is under the jurisdiction of in the subscript j and b of element in a
Models Sets Mj, j value is 0,1；The subscript (i) of the subscript (i) of element and element in b represents the element with subscript (i) in a
It is under the jurisdiction of Models Sets MjIn i-th of model, i ∈ { 1,2 ..., r }；One model m is expressed as (a, b), and definedFor the Models Sets without signal, definitionTo there is the Models Sets of signal, r is model
Collect M1In Number of Models and value be positive integer not less than 1；
Step 2: according to formulaCalculate the Models Sets M without signal0From initial time to the k moment
Joint likelihood, and according to formulaCalculate the Models Sets M without signal0At the edge at k moment seemingly
So；Wherein, zkFor the signal observation vector sequence from initial time to the k moment and be k × nzObserving matrix is tieed up, s is true mould
Formula, zk-1For the signal observation vector sequence from initial time to the k-1 moment and be (k-1) × nzTie up observing matrix,Table
Representation modelMatched with actual pattern s；
Step 3: according to Multiple Models Algorithm, calculating the Models Sets M for having signal1Likelihood；I-th of model in Multiple Models Algorithm is expired
Sufficient below equation：
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Wherein, xk+1Signal condition for the k+1 moment is vectorial and is nxDimensional vector,For the n of i-th of model of k momentwDimension process
Noise andNormal DistributionRepresent that average isCovariance matrix isHeight
This probability density function,ForAverage,ForCovariance matrix；For the n of i-th of model of k momentvDimension amount
Survey noise andNormal DistributionRepresent that average isCovariance matrix isHeight
This probability density function,ForAverage,ForCovariance matrix；For the n of i-th of model of k momentx×nx
Tie up state-transition matrix,For the n of i-th of model of k momentx×nwNoise gain matrix is tieed up,For i-th of model of k moment
nz×nxTie up measurement matrix；nx、nz、nwAnd nvValue be positive integer not less than 1；With
Subscript (i) represent that the amount with subscript (i) is carved with the Models Sets M of signal when being under the jurisdiction of k1In i-th of modeli∈{1,
2,…,r}；
According to formulaCalculate the Models Sets M for having signal1From initial time to the joint likelihood at k moment, and
According to formulaCalculate the Models Sets M for having signal1In k
The edge likelihood at quarter；Wherein,Represent modelMatched with actual pattern s；For model
In the edge likelihood at k moment,To there is the Models Sets M of signal1In i-th of model prediction probability and
The single cycle of Multiple Models Algorithm is as follows：
Step 301, the filtering based on model：
Predicted state：
Predicted state variance：
Measurement residuals：
Residual covariance：
Filter gain：
State updates：
State variance updates：
Wherein,Represent in setting models collection M1In i-th of model k-1 moment status informations on the premise of to k time informations
Predicted state,Represent in setting models collection M1In i-th of model k moment status informations on the premise of to k time informations
State update,Represent the n of i-th of model of k-1 momentx×nxTie up state-transition matrix,Represent in setting models
Collect M1In i-th of model k-1 moment status informations on the premise of the states of k-1 time informations is updated,When representing k-1
Carve the n of i-th of modelx×nwNoise gain matrix is tieed up,ForAverage,For the n of i-th of model of k-1 momentwDimension
Process noise andNormal DistributionRepresent that average isCovariance matrix isGaussian probability-density function,ForAverage,ForCovariance matrix；Represent in setting models
Collect M1In i-th of model k-1 moment status informations on the premise of to the variance matrix of the status predications of k time informations；
Represent in setting models collection M1In i-th of model k-1 moment status informations on the premise of the states of k-1 time informations is updated
Variance matrix；Represent in setting models collection M1In i-th of model k moment status informations on the premise of to k time informations
State update variance matrix；(·)TRepresenting matrix seeks transposition；Represent Models Sets M1In i-th of model the k moment amount
Survey residual error；Represent Models Sets M1In i-th of model the k moment residual covariance matrix；Represent Models Sets M1In i-th
Filter gain of the individual model at the k moment；
Step 302, model probability update：
Model likelihood：
Model probability：
Wherein,Represent Models Sets M1In edge likelihood of i-th of model at the k moment,Represent parameterClothes
It is that 0, covariance matrix is from averageNormal distribution；Indicate the Models Sets M of signal1In i-th of model renewal it is general
Rate；C=1,2 ..., r,Indicate the Models Sets M of signal1In i-th of model prediction probability and Indicate the Models Sets M of signal1In c-th of model,Represent Models Sets M1
In c-th of model the k moment likelihood andTable
Show parameterIt is that 0, covariance matrix is to obey averageNormal distribution；
Step 303, estimation fusion：
Totally it is estimated as：
Overall estimate variance is：
Wherein,Indicate the Models Sets M of signal1The totality of state is estimated at the k moment,Represent in setting models collection M1In
The state of k time informations is updated on the premise of the k moment status informations of i-th of model；Pk|kIndicate the Models Sets M of signal1
In overall estimate variance matrix of the k moment to state,Represent in setting models collection M1In i-th model k moment state letter
The variance matrix updated on the premise of breath to the state of k time informations；
Step 4: according to formulaCalculate the Models Sets M of no signal0With the model for having signal
Collect M1In the M signal model at k momentEdge likelihoodWherein, α0=α and α1=β is required to meet error probability about
Beam P { " H1”|H0}≤α,P{“H0”|H1}≤β,α+β≤1；Believe for K-L
Breath；
Step 5: according to formulaCalculate the test statistics of 2-SPRT decision-makings rule and obtained with threshold comparison
Asymptotic optimality testing result；WhenWhen, select M1；WhenWhen, select M0；Otherwise, k value is set to add 1 simultaneously
Return to step two；Wherein, A0=α-1, A1=β-1, k0To examine initial time,For the Models Sets M of no signal0And have signal
Models Sets M1In the M signal model at κ momentEdge likelihood.
2. according to the signal detecting method that multi-model hypothesis testing is determined based on mistake described in claim 1, it is characterised in that：Step
According to formula in twoCalculate the Models Sets M without signal0Joint likelihood when, zkFor white, formulaIt is converted intoWherein,For the Models Sets M without signal0At the edge at κ moment
Likelihood andzκSignal observation vector for the κ moment and be nzDimensional vector, zκ-1For from during starting
It is carved into the signal observation vector sequence at κ -1 moment and for (κ -1) × nzTie up observing matrix.
3. according to the signal detecting method that multi-model hypothesis testing is determined based on mistake described in claim 1, it is characterised in that：Step
According to formula in threeCalculate the Models Sets M for having signal1Joint likelihood when, zkFor white, formulaIt is converted intoWherein,To there is the Models Sets M of signal1At the edge at κ moment seemingly
So andzκSignal observation vector for the κ moment and it is
nzDimensional vector, zκ-1For the signal observation vector sequence at -1 moment from initial time to κ and be (κ -1) × nzTie up observing matrix,The Models Sets M of signal is carved with during for κ1In i-th of model,Represent modelMatched with actual pattern s,For modelEdge likelihood,To there is the Models Sets M of signal1In i-th of model prediction it is general
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