CN113640763A - Estimation method of lognormal texture sea clutter amplitude distribution shape parameters based on fractional order moment - Google Patents
Estimation method of lognormal texture sea clutter amplitude distribution shape parameters based on fractional order moment Download PDFInfo
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Abstract
The invention relates to the technical field of radar signal processing, in particular to a fractional order moment-based method for estimating the shape parameter of amplitude distribution of lognormal texture sea clutter, which adopts the negative fractional order moment and the positive fractional order moment of the amplitude of a sea clutter sample, reduces the calculation complexity and improves the estimation precision of the shape parameter compared with the existing estimation method based on zlogz and the estimation method based on the high order moment, and further obtains the logarithm normal texture sea clutter amplitude distribution shape parameter estimation value by the method
The method is more accurate in the value of the detection statistic in the radar target detection method obtained by the radar target detection method, so that the detection performance of the radar target is further improved.
Description
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a method for estimating distribution shape parameters of lognormal texture sea clutter amplitude based on fractional order moment.
Background
The sea surveillance radar inevitably receives, in operation, backscattered signals of electromagnetic waves transmitted by the sea surface to the radar, which are commonly referred to as sea clutter. The radar target detection method in the sea clutter background is usually related to the shape parameter of the sea clutter amplitude distribution, so in order to better detect the radar target, the shape parameter of the sea clutter amplitude distribution must be accurately estimated. When the radar resolution unit length is much larger than the wavelength of the swell or the ground-scraping angle observed by the radar is larger than 10 degrees, a Gaussian model can be used for modeling the sea clutter. However, as the radar resolution increases or the observed ground angle decreases, the sea clutter will appear significantly non-gaussian, and the gaussian model will be severely mismatched. At present, a model capable of effectively modeling non-Gaussian sea clutter is a composite Gaussian model, the model is based on a sea clutter physical formation mechanism, and theoretical verification and experimental inspection are carried out. The complex gaussian model describes the sea clutter by using the product of the slowly varying texture component and the rapidly varying speckle component. The speckle component of sea clutter is an electromagnetic wave speckle component caused by small-scale capillary waves on the sea surface, which is a complex gaussian random variable obeying zero-mean unit power. The texture component of the sea clutter is generated by large-scale gravity waves of the sea clutter, and is a random variable. The amplitude characteristic of the composite gaussian sea clutter is determined by the probability density function of the texture component. Under the composite Gaussian model, according to the probability density function of the texture component and the speckle component, the amplitude distribution of the sea clutter can be obtained based on a total probability formula. The texture component of the sea clutter is modeled as a random variable obeying gamma distribution, and K distribution which is widely used in the field of radar target detection and used for describing the amplitude of the sea clutter can be obtained. However, as radar resolution increases, the K-distribution has not been able to accurately describe non-gaussian sea clutter. To more accurately model the amplitude of non-Gaussian sea clutter, a lognormal texture complex Gaussian distribution is proposed. The lognormal texture composite gaussian distribution models the texture component of the sea clutter using lognormal distribution, which is more suitable for describing the amplitude characteristics of non-gaussian sea clutter than K distribution.
The shape parameters contained in the lognormal texture complex gaussian distribution control the non-gaussian nature of sea clutter: the larger the shape parameter is, the more serious the non-gaussian property of the sea clutter is; the smaller the shape parameter, the weaker the non-gaussian nature of the sea clutter. The shape parameter occurs in a radar target detection method under a lognormal texture sea clutter background, so the shape parameter must be estimated by using sea clutter data received by a radar before detecting a target. At present, the estimation methods of the lognormal texture sea clutter amplitude distribution shape parameters include a high-order moment estimation method and a zlogz method, and the estimation methods are shown in documents of I.Chalabi and A.Mezache, Estimators of compound Gaussian distributor with log-normal texture, Remote Sensing Letters, vol.10, No.7, pp.709-716, Jul.2019, doi:10.1080/2150704X.2019.1601275. However, when the sea clutter is not gaussian (i.e. when the shape parameter is large), the estimation error of the amplitude distribution shape parameter estimation method of the lognormal texture sea clutter based on zlogz is too large, which affects the detection performance of the radar target under the background of the lognormal texture sea clutter.
Disclosure of Invention
The invention aims to solve the technical problem that the existing lognormal texture sea clutter amplitude distribution shape parameter estimation method is insufficient in precision, and provides a shape parameter estimation method of lognormal texture sea clutter amplitude distribution based on fractional order moment aiming at the defects in the prior art so as to improve the estimation precision of shape parameters in the lognormal texture sea clutter amplitude distribution.
The technical problem solved by the invention can be realized by adopting the following technical scheme:
the method for estimating the distribution shape parameters of the amplitude of the sea clutter based on the lognormal texture of the fractional order moment comprises the following steps
S1: calculating n-order theoretical moment m of lognormal texture sea clutter amplitude distributionnWherein m represents the theoretical moment of the sea clutter amplitude distribution, and n represents the order of the sea clutter amplitude distribution moment;
s2: according to the n-order theoretical moment m obtained in S1nDeducing a mathematical equation of a lognormal texture sea clutter amplitude distribution shape parameter gamma based on the fractional order moment;
s3: selecting N sea clutter amplitude samples from sea clutter data received by a radar, and respectively calculating statistical moments of the N sea clutter amplitude samples based on fractional order;
s4: substituting the fractional order statistical moment obtained in the step S3 into the mathematical equation in the step S2 to obtain the lognormal texture sea clutter based on the fractional order momentEstimation of amplitude profile shape parameters
S5: according to the obtained lognormal texture sea clutter amplitude distribution shape parameter estimation value based on fractional order moment
The parameter estimation value is applied to a radar target detection method under a lognormal texture sea clutter background, and test statistics of the radar target detection method is calculated and used for improving detection performance of the radar target.
Further, the mathematical equation of the shape parameter γ of the distribution of the amplitude of the sea clutter based on the lognormal texture of the fractional order moment in S2 is obtained by derivation
And
and (3) a mathematical equation of a shape parameter gamma of the amplitude distribution of the time lognormal texture sea clutter.
Further, the step of calculating the fractional order-based statistical moments of the N sea clutter amplitude samples in S3 is to calculate the N sea clutter amplitude samples based on
Order sum
Statistical moments of order
And
further, the nth order theoretical moment m of the log-normal texture sea clutter amplitude distribution is calculated in S1nThe method also comprises the following steps:
s01: calculating a lognormal texture sea clutter amplitude distribution probability density function f (r) according to the following formula:
wherein r represents the amplitude of the sea clutter, τ represents the texture component of the sea clutter, γ represents the shape parameter of the amplitude distribution of the lognormal texture sea clutter, δ represents the scale parameter of the amplitude distribution of the lognormal texture sea clutter, and ln (·) represents a natural logarithm function; e.g. of the type(·)Representing a natural exponential function;
s02: calculating the n-order theoretical moment m of the lognormal texture sea clutter amplitude distribution according to the lognormal texture sea clutter amplitude distribution probability density function f (r) obtained in the S01nThe calculation formula is as follows:
where E (-) represents the statistical averaging and Γ (-) represents the gamma function.
Further, the derivation in S2 is based on fractional order moment
And
the mathematical equation of the shape parameter gamma of the distribution of the amplitude of the time lognormal texture sea clutter comprises the following methods:
s001: n-order theoretical moment m of sea clutter amplitude distribution using lognormal texturenTo obtain
The equation for the order moment is as follows:
s002: n-order theoretical moment m of sea clutter amplitude distribution using lognormal texturenTo obtain
The equation for the order moment is as follows:
s003: and solving a mathematical equation of a lognormal texture sea clutter amplitude distribution shape parameter gamma based on the fractional order moment by using the equations in S001 and S002, wherein the mathematical equation comprises the following steps:
further, the N sea clutter amplitude samples in S3 are r1,r2,...,rNRespectively calculating N sea clutter amplitude samples r1,r2,...,rNIs/are as follows
Order sum
Statistical moments of order
And
wherein N represents the number of sea clutter samples, and r represents the amplitude of the sea clutter; the calculation formula is as follows:
further, in the step S4, the order is
Is taken as
Is taken as
Will be provided with
And
substituting into the mathematical equation in S2 to obtain the estimation value of the distribution shape parameter of the amplitude of the lognormal texture sea clutter based on the fractional order moment
The formula is as follows:
the invention has the beneficial effects that:
compared with the prior art, the method for estimating the shape parameter of the lognormal texture sea clutter amplitude distribution based on the fractional order moment adopts the negative fractional order moment and the positive fractional order moment of the sea clutter sample amplitude, reduces the calculation complexity and improves the estimation precision of the shape parameter compared with the existing estimation method based on zlogz and the estimation method based on the high order moment, and further obtains the shape parameter estimation value of the lognormal texture sea clutter amplitude distribution by the method
The method is more accurate in the value of the detection statistic in the radar target detection method obtained by the radar target detection method, so that the detection performance of the radar target is further improved.
Drawings
The invention is further illustrated with reference to the following figures and examples.
Fig. 1 is a schematic flow chart of the implementation of the invention.
FIG. 2 is a diagram of a relative root mean square error curve of the lognormal texture sea clutter amplitude distribution shape parameter estimation obtained by the present invention and the existing method.
Detailed Description
In the following, a scheme of the method for estimating the shape parameter of the sea clutter amplitude distribution based on the lognormal texture with fractional order moments according to the present invention will be described in detail through several specific embodiments.
It should be noted that the same symbols are used to represent the same meanings in all the formulas of the present invention.
Wherein m represents the theoretical moment of the sea clutter amplitude distribution;
n represents the order of the sea clutter amplitude distribution moment;
r represents the amplitude of the sea clutter;
τ represents the texture component of the sea clutter;
gamma represents the shape parameter of the amplitude distribution of the lognormal texture sea clutter;
δ represents a scale parameter of the lognormal texture sea clutter amplitude distribution.
Referring to fig. 1, the invention relates to a method for estimating the distribution shape parameters of the amplitude of the lognormal texture sea clutter based on fractional order moment, which comprises the following steps
S1: calculating n-order theoretical moment m of lognormal texture sea clutter amplitude distributionn；
Calculating n-order theoretical moment m of lognormal texture sea clutter amplitude distributionnThe method specifically comprises the following steps:
s01: calculating a lognormal texture sea clutter amplitude distribution probability density function f (r) according to a lognormal distribution probability density function obeyed by a texture component tau of the sea clutter and a conditional Rayleigh distribution probability density function obeyed by a sea clutter amplitude r, wherein the calculation formula is as follows:
wherein ln (·) represents a natural logarithmic function; e.g. of the type(·)Representing a natural exponential function;
s02: calculating the n-order theoretical moment m of the lognormal texture sea clutter amplitude distribution according to the lognormal texture sea clutter amplitude distribution probability density function f (r) obtained in the S01nThe calculation formula is as follows:
wherein, E (-) represents the statistical average, and Γ (-) represents the gamma function;
s2: according to the n-order theoretical moment m obtained in S1nDeducing a mathematical equation of a lognormal texture sea clutter amplitude distribution shape parameter gamma based on the fractional order moment;
further, in the step S2, the mathematical equation of the lognormal texture sea clutter amplitude distribution shape parameter γ based on the fractional order moment is obtained by derivation
And
a mathematical equation of a time lognormal texture sea clutter amplitude distribution shape parameter gamma;
further, derived to obtain
And
the mathematical equation of the shape parameter gamma of the distribution of the amplitude of the time lognormal texture sea clutter comprises the following methods:
s001: n-order theoretical moment m of sea clutter amplitude distribution using lognormal texturenTo obtain
The equation for the order moment is as follows:
s002: n-order theoretical moment m of sea clutter amplitude distribution using lognormal texturenTo obtain
The equation for the order moment is as follows:
s003: and solving a mathematical equation of a lognormal texture sea clutter amplitude distribution shape parameter gamma based on the fractional order moment by using the equations in S001 and S002, wherein the mathematical equation comprises the following steps:
s3: selecting N sea clutter amplitude samples from sea clutter data received by a radar, and respectively calculating statistical moments of the N sea clutter amplitude samples based on fractional order;
further, the N sea clutter amplitude samples in S3 are r1,r2,...,rN。
Furthermore, N sea clutter amplitude samples r are respectively selected from the sea clutter data received by the radar1,r2,...,rNThe acquisition method comprises the following steps:
a1, representing echo data received after a radar transmits pulse signals to the sea surface as a three-dimensional matrix Z, wherein Z is a P multiplied by L multiplied by Q three-dimensional matrix, P represents the azimuth number of the echo data matrix, L represents the distance unit number of the echo data matrix, and Q represents the pulse number of the echo data matrix;
a2 at echo numberSelecting a sea clutter data area G from a matrix Z, wherein G is a three-dimensional matrix P multiplied by L multiplied by Q, P is more than or equal to 1 and less than or equal to P, and L is more than or equal to 1 and less than or equal to L, and the amplitude of the sea clutter data contained in G is represented as r1,r2,...,rN，N＝p×l×Q；
A3 calculating N sea clutter amplitude samples r respectively1,r2,...,rNIs/are as follows
Order sum
Statistical moments of order
And
wherein N represents the number of sea clutter samples, and r represents the amplitude of the sea clutter;
the formula is as follows:
s4: substituting the fractional order statistical moment obtained in the step S3 into the mathematical equation in the step S2 to obtain an estimated value of the log-normal texture sea clutter amplitude distribution shape parameter based on the fractional order moment
Further, in S4 is order
Is taken as
Is taken as
Will be provided with
And
substituting into the mathematical equation of the shape parameter gamma in S2, namely formula 5, to obtain the estimation value of the shape parameter of the lognormal texture sea clutter amplitude distribution based on the fractional order moment
The formula is as follows:
s5: according to the obtained lognormal texture sea clutter amplitude distribution shape parameter estimation value based on fractional order moment
The parameter estimation value is applied to a radar target detection method under a lognormal texture sea clutter background, and test statistics of the radar target detection method is calculated and used for improving detection performance of the radar target.
The radar target detection method is as follows:
the obtained lognormal texture sea clutter amplitude distribution shape parameter estimation value based on the fractional order moment
Introducing the equation to obtain test statistic of radar target detection method, and obtaining lognormal texture sea clutter amplitude distribution shape parameter estimation value obtained by the method
The method is more accurate in test statistic obtained by the method applied to radar target detection, and therefore the detection performance of the radar target is further improved.
The effect of the present invention will be further explained with the simulation experiment.
1. Simulation parameters
And simulating lognormal texture sea clutter amplitude samples by utilizing matlab software, namely selecting N sea clutter amplitude samples, setting experimental simulation parameters as sample number N being 10000, setting scale parameter delta being 1, increasing shape parameter gamma from 0.1 to 10, and increasing the step length to 0.1. The number of independent simulation experiments under each shape parameter was set to 10000. The Error of the shape parameter estimation is estimated by using a Relative Root Mean Square Error (RRMSE) with a calculation formula of RRMSE
2. Content of simulation experiment
In a simulation experiment, a high-order moment estimation method, a zlogz estimation method and the estimation method are used for estimating the shape parameters of the sea clutter data respectively, and an RRMSE curve graph of an estimation result is drawn.
The experimental result is shown in fig. 2, wherein the horizontal axis represents the true shape parameter γ of the sea clutter data, and the vertical axis represents the RRMSE corresponding to the estimation result. In fig. 2, the "- -" marked curve represents the RRMSE curve corresponding to the high-order moment estimation method, the "- - -" marked curve represents the RRMSE curve corresponding to the zlogz estimation method, and the "-" marked curve represents the RRMSE curve corresponding to the invention.
It can be seen from fig. 2 that the RRMSE of the present invention is smaller than the high-order moment estimation method and zlogz estimation method when the shape parameter is greater than 2.5. The larger the shape parameter is, the stronger the non-gaussian property of the sea clutter is, and the result of fig. 2 shows that the estimation error of the shape parameter of the invention is smaller than that of the existing method under the non-gaussian sea clutter environment.
In summary, the invention provides a lognormal texture sea clutter amplitude distribution shape parameter estimation method based on fractional order moment, and the method has high estimation precision on shape parameters under the non-Gaussian sea clutter background.
Therefore, the lognormal texture sea clutter amplitude distribution shape parameter estimation value with high estimation precision obtained by the invention
The method is applied to radar target detection under the background of the lognormal texture sea clutter, and the detection performance of the radar target is improved.
While the embodiments of the present invention have been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art, and the scope of the present invention is within the scope of the claims.
Technical solutions between various embodiments may be combined with each other, but must be realized by those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination should not be considered to exist, and is not within the protection scope of the present invention.
Claims (7)
1. The method for estimating the distribution shape parameters of the lognormal texture sea clutter amplitude based on the fractional order moment is characterized by comprising the following steps of: comprises the following steps
S1: calculating n-order theoretical moment m of lognormal texture sea clutter amplitude distributionnWherein m represents the theoretical moment of the sea clutter amplitude distribution, and n represents the order of the sea clutter amplitude distribution moment;
s2: according to the n-order theoretical moment m obtained in S1nDeducing a mathematical equation of a lognormal texture sea clutter amplitude distribution shape parameter gamma based on the fractional order moment;
s3: selecting N sea clutter amplitude samples from sea clutter data received by a radar, and respectively calculating statistical moments of the N sea clutter amplitude samples based on fractional order;
s4: substituting the fractional order statistical moment obtained in the step S3 into the mathematical equation in the step S2 to obtain an estimated value of the log-normal texture sea clutter amplitude distribution shape parameter based on the fractional order moment
S5: according to the obtained lognormal texture sea clutter amplitude distribution shape parameter estimation value based on fractional order moment
The parameter estimation value is applied to a radar target detection method under a lognormal texture sea clutter background, and test statistics of the radar target detection method is calculated and used for improving detection performance of the radar target.
2. The method for estimating the shape parameter of the distribution of the lognormal texture sea clutter amplitude based on the fractional order moment as claimed in claim 1, wherein: the mathematical equation of the lognormal texture sea clutter amplitude distribution shape parameter gamma in the S2 based on the fractional order moment is obtained by derivation
And
and (3) a mathematical equation of a shape parameter gamma of the amplitude distribution of the time lognormal texture sea clutter.
3. The method for estimating the shape parameter of the distribution of the lognormal texture sea clutter amplitude based on the fractional order moment as claimed in claim 2, wherein: the step of S3 is that the fractional order-based statistical moments of the N sea clutter amplitude samples are respectively calculated
Order sum
Statistical moments of order
And
4. the method for estimating the shape parameter of the distribution of the lognormal texture sea clutter amplitude based on the fractional order moment as claimed in claim 1, wherein: in S1, an nth order theoretical moment m of the logarithmic normal texture sea clutter amplitude distribution is calculatednThe method also comprises the following steps:
s01: calculating a lognormal texture sea clutter amplitude distribution probability density function f (r) according to the following formula:
wherein r represents the amplitude of the sea clutter, τ represents the texture component of the sea clutter, γ represents the shape parameter of the amplitude distribution of the lognormal texture sea clutter, δ represents the scale parameter of the amplitude distribution of the lognormal texture sea clutter, and ln (·) represents a natural logarithm function; e.g. of the type(·)Representing natural exponential functions；
S02: calculating the n-order theoretical moment m of the lognormal texture sea clutter amplitude distribution according to the lognormal texture sea clutter amplitude distribution probability density function f (r) obtained in the S01nThe calculation formula is as follows:
where E (-) represents the statistical averaging and Γ (-) represents the gamma function.
5. The method for estimating the shape parameter of the distribution of the lognormal texture sea clutter amplitude based on the fractional order moment as claimed in claim 2, wherein: the derivation of S2 is based on fractional order moment
And
the mathematical equation of the shape parameter gamma of the distribution of the amplitude of the time lognormal texture sea clutter comprises the following methods:
s001: n-order theoretical moment m of sea clutter amplitude distribution using lognormal texturenTo obtain
The equation for the order moment is as follows:
s002: n-order theoretical moment m of sea clutter amplitude distribution using lognormal texturenTo obtain
The equation for the order moment is as follows:
s003: and solving a mathematical equation of a lognormal texture sea clutter amplitude distribution shape parameter gamma based on the fractional order moment by using the equations in S001 and S002, wherein the mathematical equation comprises the following steps:
6. the method according to claim 3, wherein the method comprises: the N sea clutter amplitude samples in the S3 are r1,r2,...,rNRespectively calculating N sea clutter amplitude samples r1,r2,...,rNIs/are as follows
Order sum
Statistical moments of order
And
wherein N represents the number of sea clutter samples, and r represents the amplitude of the sea clutter; the calculation formula is as follows:
7. the method according to claim 3, wherein the fractional order moment-based method for estimating the shape parameter of the amplitude distribution of the lognormal texture sea clutter is characterized in thatCharacterized in that: in the step S4, the order is
Is taken as
Is taken as
Will be provided with
And
substituting into the mathematical equation in S2 to obtain the estimation value of the distribution shape parameter of the amplitude of the lognormal texture sea clutter based on the fractional order moment
The formula is as follows:
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