CN106156496B - The maximum Likelihood of the sea clutter amplitude model parameter of inverse Gauss texture - Google Patents
The maximum Likelihood of the sea clutter amplitude model parameter of inverse Gauss texture Download PDFInfo
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Abstract
The invention discloses a kind of maximum Likelihoods of the sea clutter amplitude model parameter of inverse Gauss texture.Mainly solve the problems, such as that the prior art is inaccurate to sea clutter amplitude model parameter Estimation.Implementation step is：1) N number of clutter amplitude data are chosen, the moments estimation value of scale parameter and the moments estimation value of form parameter are calculated；2) probability density function of sea clutter Amplitude Distributed Model is utilized to calculate log-likelihood function；3) the two-parameter iterative formula of maximal possibility estimation is obtained using log-likelihood function；4) utilize 1) in two moments estimation values respectively as two parameters in maximal possibility estimation iterative initial value；5) maximum likelihood estimator of scale parameter is acquired according to two-parameter iterative formula iteration in 3)With the maximum likelihood estimator of form parameterIt is effective that the present invention can make full use of sample information to carry out the sea clutter Amplitude Distributed Model parameter based on inverse Gauss texture, accurately estimates, the target detection that can be used under sea clutter background.
Description
Technical field
The invention belongs to signal processing technology fields, and in particular to a kind of sea clutter Amplitude Distributed Model of inverse Gauss texture
Method for parameter estimation, the target detection that can be used under sea clutter background.
Background technology
Extra large surface is referred to as sea clutter or extra large surface echo to the back scattering of radar emission signal.Relative to land clutter or
The characteristic of meteorological clutter, sea clutter is much more complex and the presence of sea clutter to the target detection of radar, locating and tracking performance all
It will produce serious influence.Optimal objective detection method under sea clutter background depends on the model of sea clutter Amplitude Distributed Model
The Amplitude Distributed Model of parameter, sea clutter changes with the variation of radar resolution and sea situation, how to be effectively estimated go to sea it is miscellaneous
The model parameter of wave amplitude distributed model is the key that sea-surface target test problems.Under the conditions of low-resolution radar, multiple Gauss mould
Type simulation sea clutter can be distributed very well, the general Rayleigh distributed of amplitude of sea clutter.And in low incidence angle, high-resolution
Under the conditions of radar, due to the appearance of extra large spike, the amplitude distribution of sea clutter will appear long " hangover " compared with rayleigh distributed, sea
Clutter shows stronger non-Gaussian system.In this regard, being that gamma is distributed and the classics of inverse gamma distributions are miscellaneous compared to texture component
Wave pattern, a kind of texture component newly proposed in recent years are the Clutter Model of dead wind area, i.e., texture is dead wind area
Sea clutter amplitude model (Compound-Gaussian model with the inverse Gaussian texture) can be with
The preferably hangover characteristic of description clutter.Practicability based on the model in actually detected, corresponding adaptive targets
The research of detector also yields good result.Document " Adaptive Signal Detection in Compound-
The clutter suitable for inverse Gauss texture is proposed in Gaussian Clutter with Inverse Gaussian Texture "
Self-adapting signal detecting method.Wherein the structure of detector depends on form parameter and scale parameter in Clutter Model, because
This method of estimation for improving Model Parameter has very important significance to target detection tool.
For the sea clutter Amplitude Distributed Model parameter based on inverse Gauss texture, moments estimation method is common.Amplitude distribution
Square can be expressed as the nonlinear function of model parameter, therefore square can be utilized to calculate the form parameter and ruler of sea clutter model
Spend parameter.It has been achieved at present and carries out two-parameter estimation using the second moment and Fourth-order moment of clutter amplitude.But moment estimation method,
Required exponent number is high, the especially utilization wherein for amplitude Fourth-order moment, when sample size deficiency, the estimation essence of moment estimation method
Degree is very low, influences the realization of sea-surface target detection.
Invention content
It is an object of the invention to propose a kind of maximal possibility estimation of the sea clutter amplitude model parameter of inverse Gauss texture
Method, to improve in sample size data deficiencies, the estimation of sea clutter Amplitude Distributed Model form parameter and scale parameter is accurate
Degree.
To realize the above-mentioned technical purpose, technical scheme of the present invention includes the following steps：
(1) the sea clutter data R based on inverse Gauss texture is generated by emulation, it includes only clutter data to be chosen from R
Range cell chooses N number of clutter amplitude data in total：x1,x2,...,xn,....,xN, using the clutter amplitude data, according to
Moment estimation method obtains the moments estimation value of the scale parameter of sea clutter data RWith the moments estimation value of form parameter
(2) using the probability density function f (r, μ, β) of the sea clutter Amplitude Distributed Model based on inverse Gauss texture, N is calculated
A sea clutter model amplitude r1,r2,...,rn,....,rNLog-likelihood function Ψ (r1,r2,...,rn,....,rN|μ,β)：
Wherein,Indicate that iteration intermediate variable, μ indicate the scale parameter of the Amplitude Distributed Model,
β indicates that the form parameter of the Amplitude Distributed Model, r indicate sea clutter amplitude, rnIndicate n-th of sea clutter range value, n=1,
2 ..., N, N indicate sea clutter data amount check；
(3) N number of sea clutter model amplitude r is calculated1,r2,...,rn,....,rNLog-likelihood function Ψ (r1,r2,...,
rn,....,rN| μ, β) partial derivative about form parameter μ and scale parameter β, and it is 0 to enable it：
Obtain two-parameter iterative formula of the maximal possibility estimation about scale parameter μ and form parameter β：
Wherein,Indicate kth time iteration intermediate variable,Indicate scale ginseng
Several kth time iterative values,Indicate the kth time iterative value of form parameter,Indicate -1 iterative value of kth of scale parameter,Indicate -1 iterative value of kth of form parameter, rnIndicate n-th of sea clutter range value；
(4) the moments estimation value of the scale parameter of sea clutter data R is utilizedWith the moments estimation value of form parameterPoint
Iterative initial value not as maximal possibility estimation mesoscale parameterWith the iterative initial value of form parameter
(5) according to the two-parameter iterative formula of the maximal possibility estimation in step (3), to scale parameter μ and form parameter β
It is iterated, until iterations reach maximum iteration L=100, stopping iteration acquiring the scale ginseng of sea clutter data R
Several maximum likelihood estimatorsWith the maximum likelihood estimator of form parameter
Compared with the prior art, the present invention has the following advantages：
1) present invention makes log-likelihood function obtain pole in the method by scale parameter and form parameter iterative numerical
Big value, is compared with high order method, especially in sample number deficiency, error smaller, and obtained form parameter and scale parameter
It is more accurate.
2) it is iterated using the two-parameter iterative formula of maximal possibility estimation due to the present invention, with moment estimation method phase
Than present invention calculating is simpler, and it is short to solve the time；
Description of the drawings
Fig. 1 is the implementation flow chart of the present invention；
When Fig. 2 is scale parameter μ=1, with the sea clutter width based on inverse Gauss texture of the invention obtained with existing method
Spend the RMSE root-mean-square error result figures of distributed model form parameter estimation；
When Fig. 3 is scale parameter μ=10, with the sea clutter width based on inverse Gauss texture of the invention obtained with existing method
Spend the RMSE root-mean-square error result figures of distributed model form parameter estimation；
The sea clutter width based on inverse Gauss texture obtained with the present invention and existing method when Fig. 4 is form parameter β=0.5
Spend the RMSE root-mean-square error result figures of distributed model scale parameter estimation；
When Fig. 5 is form parameter β=10, with the sea clutter width based on inverse Gauss texture of the invention obtained with existing method
Spend the RMSE root-mean-square error result figures of distributed model scale parameter estimation.
Specific implementation mode
The invention will be further described below in conjunction with the accompanying drawings：
The present invention estimates the scale parameter of the sea clutter Amplitude Distributed Model based on inverse Gauss texture using moment estimation method
MeterEstimate with form parameterRespectively as the iterative initial value of scale parameterWith the iterative initial value of form parameter
It is iterated according to the two-parameter iterative formula of maximal possibility estimation, finally obtains the maximum likelihood estimator of scale parameterWith
The maximum likelihood estimator of form parameter
Referring to Fig.1, steps are as follows for realization of the invention：
Step 1, N number of clutter amplitude data are chosen：x1,x2,...,xn,....,xN, calculate the scale ginseng of sea clutter data R
Several moments estimation valuesWith the moments estimation value of form parameter
In the prior art, the method for calculating the estimated value of the scale parameter of sea clutter data R and the estimated value of form parameter
Typically moment estimation method is shown in Ollila E, Tyler D E, Koivunen V, et al.. " Compound gaussian
clutter modeling with an inverse gaussian texture distribution[J]”.IEEE
Signal Processing Letters,2012,19(12):876-879, this example also use existing moment estimation method,
Steps are as follows：
(1.1) the sea clutter data R based on inverse Gauss texture is generated by emulation, it includes only clutter data to be chosen from R
Range cell, choose N number of clutter amplitude data in total：x1,x2,...,xn,....,xN, xnIndicate n-th of clutter amplitude number
According to n=1,2 ..., N；
(1.2) clutter amplitude data x is utilized1,x2,...,xn,....,xN, the second moment for calculating sea clutter data R estimates
EvaluationWith Fourth-order moment estimated value
(1.2) according to the second moment estimated value of sea clutter data RWith Fourth-order moment estimated valueCalculate sea clutter data R
Scale parameter moments estimation valueWith the moments estimation value of form parameter
Step 2, the probability density function f (r, μ, β) of the sea clutter Amplitude Distributed Model based on inverse Gauss texture, meter are utilized
Calculate N number of sea clutter model amplitude r1,r2,...,rn,....,rNLog-likelihood function Ψ (r1,r2,...,rn,....,rN|μ,
β)。
(2.1) N number of sea clutter model amplitude r is calculated separately1,r2,...,rn,....,rNProbability density function f (rn,μ,
β)：
Wherein, μ indicates that the scale parameter of the Amplitude Distributed Model, β indicate the form parameter of the Amplitude Distributed Model, rnTable
Show n-th of sea clutter model amplitude, n=1,2 ..., N；
(2.2) N number of sea clutter model amplitude r is calculated1,r2,...,rn,....,rNProbability density function f (rn, μ, β)
Product obtains likelihood function Ω (r1,r2,...,rn,....,rN|μ,β)：
Wherein, μ indicates that the scale parameter of the Amplitude Distributed Model, β indicate the form parameter of the Amplitude Distributed Model, rn, n
=1,2 ..., N indicates that n-th of sea clutter model amplitude, N indicate sea clutter data amount check；
(2.3) by likelihood function Ω (r1,r2,...,rn,....,rN| μ, β) logarithm is taken, obtain log-likelihood function Ψ
(r1,r2,...,rn,....,rN|μ,β)：
Wherein,Indicate iteration intermediate variable, rnIndicate n-th of sea clutter model amplitude, μ tables
Show that the scale parameter of the Amplitude Distributed Model, β indicate the form parameter of the Amplitude Distributed Model.
Step 3, N number of sea clutter model amplitude r is utilized1,r2,...,rn,....,rNLog-likelihood function Ψ (r1,
r2,...,rn,....,rN| μ, β), the two-parameter iteration for obtaining maximal possibility estimation about scale parameter μ and form parameter β is public
Formula；
(3.1) log-likelihood function Ψ (r are calculated separately1,r2,...,rn,....,rN| μ, β) about form parameter μ and ruler
The partial derivative of parameter beta is spent, and it is 0 to enable it,
It obtains two-parameter being most worth formula：
Wherein,Indicate that iteration intermediate variable, μ indicate the scale parameter of the Amplitude Distributed Model,
β indicates the form parameter of the Amplitude Distributed Model, rnIndicate that n-th of sea clutter model amplitude, n=1,2 ..., N, N indicate sea
Clutter data number；
(3.2) most it is worth formula using two-parameter in step (3.1), obtains the two-parameter iterative formula of maximal possibility estimation such as
Under：
Wherein,Indicate kth time iteration intermediate variable,Indicate scale parameter
Kth time iterative value,Indicate the kth time iterative value of form parameter,Indicate -1 iterative value of kth of scale parameter,
Indicate -1 iterative value of kth of form parameter, rnIndicate n-th of sea clutter model amplitude.
Step 4, the moments estimation value of the scale parameter of sea clutter data R is utilizedWith the moments estimation value of form parameterRespectively as the iterative initial value of maximal possibility estimation mesoscale parameterWith the iterative initial value of form parameter
Step 5, according to the two-parameter iterative formula of the maximal possibility estimation in step (3.2), to scale parameter μ and shape
Parameter beta is iterated, and acquires the maximum likelihood estimator of the scale parameter of sea clutter data RWith form parameter it is maximum seemingly
Right estimated value
(5.1) as k=n, n indicates nth iteration, utilizes N number of clutter amplitude data in step (1)：x1,x2,...,
xn,....,xN, according to the two-parameter iterative formula of maximal possibility estimation, obtain the kth time iterative value of scale parameterShape
The kth time iterative value of parameter
Wherein,Indicate kth time iteration intermediate variable value,Indicate scale parameter
- 1 iterative value of kth,Indicate -1 iterative value of kth of form parameter, xnIndicate n-th of clutter amplitude data, n=1,
2 ..., N, N indicate sea clutter data amount check；
(5.2) k=n+1 is enabled, step (5.1) is repeated, until k gets maximum iteration L=100, stops iteration,
Obtain the maximum likelihood estimator of the scale parameter of sea clutter data RWith the maximum likelihood estimator of form parameter
The effect of the present invention is described further with reference to emulation experiment.
1. simulation parameter
The sea clutter data used in emulation experiment are the inverse Gauss data texturings that random simulation generates in MATLAB and equal
Value is 0, the multiple Gauss speckle data that variance is 1, sample data volume N=10000.
2. emulation experiment content
The method of the present invention is respectively adopted in emulation experiment and moment estimation method obtains the sea clutter width based on inverse Gauss texture
The effect of two kinds of methods of estimation is compared in the estimation for spending distributed model parameter by the analysis of root-mean-square error checking R MSE methods.
Square error checking R MSE values are smaller, and specification error is smaller, and parameter Estimation is more accurate.
Emulation experiment 1
It is μ=1 to take scale parameter, and form parameter is β from 0.1 to 20, is divided into 0.1 inverse Gauss grain distribution generation
Sea clutter data, are respectively adopted the present invention on this basis and moments estimation method acquires form parameter estimated value, iteration of the present invention time
Number 100 times, experiment number 104It is secondary, the RMSE root-mean-square error curves of its form parameter estimated value are drawn, as shown in Fig. 2, Fig. 2
Horizontal axis indicates that form parameter true value, the longitudinal axis indicate RMSE root-mean-square errors.
From figure 2 it can be seen that compared with moment estimation method, the method for the present invention has the estimation of form parameter smaller
Error.
Emulation experiment 2
It is μ=10 to take scale parameter, and form parameter is β from 0.1 to 20, is divided into 0.1 inverse Gauss grain distribution generation
Sea clutter data, be respectively adopted on this basis the present invention and moments estimation method acquire form parameter estimated value, iteration of the present invention
Number 100 times, experiment number 104It is secondary, the RMSE root-mean-square error curves of its form parameter estimated value are drawn, as shown in figure 3, figure
3 horizontal axis indicate that form parameter true value, the longitudinal axis indicate its RMSE root-mean-square error.
From figure 3, it can be seen that compared with moment estimation method, the method for the present invention has the estimation of form parameter smaller
Error.Contrast simulation experiment 1, it is also found that the change of the scale parameter of clutter amplitude has little influence on form parameter estimation
Error.
Emulation experiment 3
It is β=0.5 to take form parameter, and scale parameter μ is divided into 0.1 inverse Gauss grain distribution generation from 0.1 to 20
Sea clutter data, are respectively adopted the present invention on this basis and moments estimation method acquires scale parameter estimated value, iteration of the present invention time
Number 100 times, experiment number 104It is secondary, the RMSE root-mean-square error curves of its scale parameter estimated value are drawn, as shown in figure 4, Fig. 4
Horizontal axis indicates that scale parameter true value, the longitudinal axis indicate its RMSE root-mean-square error.
Figure 4, it is seen that the method for the present invention is almost consistent to the estimation of form parameter and moments estimation, all there is very little
Error.The RMSE root-mean-square error curves of scale parameter estimated value are almost horizontal simultaneously, illustrate that its error is joined with scale
Several changes is unrelated.
Emulation experiment 4
It is β=10 to take form parameter, and scale parameter is μ from 0.1 to 20, is divided into 0.1 inverse Gauss grain distribution generation
Sea clutter data, be respectively adopted on this basis the present invention and moments estimation method acquire scale parameter estimated value, iteration of the present invention
Number 100 times, experiment number 104It is secondary, the RMSE root-mean-square error curves of its scale parameter estimated value are drawn, as shown in figure 5, figure
5 horizontal axis indicate that scale parameter true value, the longitudinal axis indicate its RMSE root-mean-square error.
From figure 5 it can be seen that the method for the present invention is slightly more better than moments estimation to the estimation of scale parameter, with very little
Error.
In conclusion the maximum likelihood of the sea clutter Amplitude Distributed Model parameter proposed by the present invention based on inverse Gauss texture
Method of estimation can make full use of sample information in data volume deficiency, estimation performance be improved, to sea clutter complex Gaussian width
It spends distributed model parameter and carries out more effective, more accurately estimation.
Claims (5)
1. a kind of maximum Likelihood of the sea clutter amplitude model parameter of inverse Gauss texture, which is characterized in that including：
(1) the sea clutter data R based on inverse Gauss texture is generated by emulation, the distance for only including clutter data is chosen from R
Unit chooses N number of clutter amplitude data in total：x1,x2,...,xn,....,xN, using the clutter amplitude data, estimated according to square
Meter method obtains the moments estimation value of the scale parameter of sea clutter data RWith the moments estimation value of form parameter
(2) using the probability density function f (r, μ, β) of the sea clutter Amplitude Distributed Model based on inverse Gauss texture, N number of sea is calculated
Clutter Model amplitude r1,r2,...,rn,....,rNLog-likelihood function Ψ (r1,r2,...,rn,....,rN|μ,β)：
Wherein,Indicate that iteration intermediate variable, μ indicate that the scale parameter of the Amplitude Distributed Model, β indicate
The form parameter of the Amplitude Distributed Model, r indicate sea clutter amplitude, rnIndicate n-th of sea clutter model amplitude, n=1,
2 ..., N, N indicate sea clutter data amount check；
(3) N number of sea clutter model amplitude r is calculated1,r2,...,rn,....,rNLog-likelihood function Ψ (r1,r2,...,
rn,....,rN| μ, β) partial derivative about form parameter μ and scale parameter β, and it is 0 to enable it：
Obtain two-parameter iterative formula of the maximal possibility estimation about scale parameter μ and form parameter β：
Wherein,Indicate kth time iteration intermediate variable,Indicate scale parameter
Kth time iterative value,Indicate the kth time iterative value of form parameter,Indicate -1 iterative value of kth of scale parameter,
Indicate -1 iterative value of kth of form parameter, rnIndicate n-th of sea clutter model amplitude；
(4) the moments estimation value of the scale parameter of sea clutter data R is utilizedWith the moments estimation value of form parameterMake respectively
For the iterative initial value of maximal possibility estimation mesoscale parameterWith the iterative initial value of form parameter
(5) according to the two-parameter iterative formula of the maximal possibility estimation in step (3), scale parameter μ and form parameter β are carried out
Iteration, until iterations reach maximum iteration L=100, stopping iteration acquiring the scale parameter of sea clutter data R
Maximum likelihood estimatorWith the maximum likelihood estimator of form parameter
2. obtaining the scale of sea clutter data R according to moment estimation method in the method as described in claim 1, wherein step (1)
The moments estimation value of parameterWith the moments estimation value of form parameter
Wherein,Indicate the second order moments estimation of sea clutter data R,Indicate sea clutter data R
Quadravalence moments estimation, xnIndicate that n-th of clutter amplitude data, n=1,2 ..., N, N indicate sea clutter data amount check.
3. utilizing the sea clutter amplitude distribution mould based on inverse Gauss texture in the method as described in claim 1, wherein step (2)
The probability density function f (r, μ, β) of type calculates N number of sea clutter model amplitude r1,r2,...,rn,....,rNLog-likelihood letter
Number Ψ (r1,r2,...,rn,....,rN| μ, β), it carries out as follows：
2a) calculate separately N number of sea clutter model amplitude r1,r2,...,rn,....,rNProbability density function f (rn,μ,β)：
Wherein, μ indicates that the scale parameter of the Amplitude Distributed Model, β indicate the form parameter of the Amplitude Distributed Model, rnIndicate n-th
A sea clutter model amplitude, n=1,2 ..., N；
2b) calculate N number of sea clutter model amplitude r1,r2,...,rn,....,rNProbability density function f (rn, μ, β) product,
Obtain likelihood function Ω (r1,r2,...,rn,....,rN|μ,β)：
2c) by likelihood function Ω (r1,r2,...,rn,....,rN| μ, β) logarithm is taken, obtain log-likelihood function Ψ (r1,
r2,...,rn,....,rN|μ,β)：
Wherein,Indicate iteration intermediate variable.
4. utilizing N number of sea clutter model amplitude r in the method as described in claim 1, wherein step (3)1,r2,...,
rn,....,rNLog-likelihood function Ψ (r1,r2,...,rn,....,rN| μ, β), it obtains maximal possibility estimation and joins about scale
The two-parameter iterative formula of number μ and form parameter β, carries out as follows：
3a) calculate separately log-likelihood function Ψ (r1,r2,...,rn,....,rN| μ, β) about form parameter μ and scale parameter β
Partial derivative, and it is 0 to enable it, obtains two-parameter being most worth formula：
Wherein,Indicate that iteration intermediate variable, μ indicate that the scale parameter of the Amplitude Distributed Model, β indicate
The form parameter of the Amplitude Distributed Model, rnIndicate that n-th of sea clutter model amplitude, N indicate sea clutter data amount check；
3b) utilize step 3a) in it is two-parameter be most worth formula, obtain the two-parameter iterative formula of maximal possibility estimation：
Wherein,Indicate kth time iteration intermediate variable,Indicate the kth time of scale parameter
Iterative value,Indicate the kth time iterative value of form parameter,Indicate -1 iterative value of kth of scale parameter,Indicate shape
- 1 iterative value of kth of shape parameter.
5. according to the two-parameter of the maximal possibility estimation in step (3) in the method as described in claim 1, wherein step (5)
Iterative formula is iterated scale parameter μ and form parameter β, and the maximum likelihood for acquiring the scale parameter of sea clutter data R is estimated
EvaluationWith the maximum likelihood estimator of form parameterIt carries out as follows：
5a) as k=n, n indicates nth iteration, utilizes N number of clutter amplitude data in step (1)：x1,x2,...,xn,....,
xN, according to the two-parameter iterative formula of maximal possibility estimation, obtain the kth time iterative value of scale parameterThe kth of form parameter
Secondary iterative value
Wherein,Indicate kth time iteration intermediate variable value,Indicate the of scale parameter
K-1 iterative value,Indicate -1 iterative value of kth of form parameter, xnIndicate n-th of clutter amplitude data, n=1,
2 ..., N, N indicate sea clutter data amount check；
K=n+1 5b) is enabled, step 5a is repeated), until k gets maximum iteration L=100, it is miscellaneous to obtain sea for stopping iteration
Wave number according to the scale parameter of R maximum likelihood estimatorWith the maximum likelihood estimator of form parameter
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