Equivalent form parameter estimation method under CGIG + N background based on curve fitting

Abstract

The invention discloses an equivalent form parameter estimation method under a CGIG + N background based on curve fitting, and the method comprises the steps: obtaining a first cumulative distribution function according to a sea clutter model constructed by a CGIG, and obtaining a second cumulative distribution function according to a noisy sea clutter model constructed by the CGIG; substituting the equivalent scale parameter into the first cumulative distribution function to obtain a third cumulative distribution function; wherein the equivalent scale parameter is obtained according to clutter power and noise average power; a loss function obtained according to the second cumulative distribution function and the third cumulative distribution function is calculated for multiple times, and different shape parameters serve as input to obtain values of corresponding equivalent shape parameters; and obtaining a fitting expression of the equivalent shape parameters according to the values of the different shape parameters and the corresponding equivalent shape parameters. According to the method, the probability distribution characteristics of radar echoes are fully utilized, and equivalent shape parameters which are more effective than those in the prior art can be obtained on the aspects of middle and low noise-to-noise ratios and shape parameters.

Description

Technical Field

[0001] The present invention belongs to the field of sea clutter and noise processing, and particularly relates to an equivalent shape parameter estimation method in a CGIG+N background based on curve fitting. Background Art

[0002] Sea-surface radar target detection technology holds irreplaceable strategic significance in safeguarding national territorial waters, ensuring the development of marine resources, and promoting the marine economy. It serves as a core safeguard for territorial sovereignty and national defense security, a technological underpinning for marine resource development, infrastructure for the Maritime Silk Road Economic Belt, and a key component of the marine environmental disaster early warning system. In the military, it plays a vital role in enhancing all-weather surveillance capabilities, situational awareness of distant sea operations, and anti-stealth and anti-interference capabilities. In the civilian sector, it is widely used in ship scheduling and maintenance, as well as in early warning of dangerous incidents.

[0003] The performance of sea radar target detection is affected by the accuracy of sea clutter modeling and the choice of detector. Therefore, accurately modeling sea clutter and selecting the most appropriate detector are crucial. Under high-resolution and low-angle observation, sea clutter deviates significantly from the complex Gaussian model. To better fit the tail of high-resolution sea clutter distribution, four complex Gaussian models are commonly used to describe high-resolution radar sea clutter echoes: the K distribution, the generalized Pareto distribution, the CGIG (Compound Gaussian model with Inverse-Gaussian texture) distribution, and the lognormal distribution. A series of optimal or near-optimal detectors have been proposed for different distributions, such as the optimal detector and near-optimal detector for K-distributed clutter, and the generalized likelihood ratio linear threshold detector for the CGIG distribution.

[0004] However, the above detectors are all detectors under pure clutter background. When the noise power is high, if a composite Gaussian model is used to describe the model of composite Gaussian distribution sea clutter plus noise background, the reduction of parameters will inevitably lead to information loss in the model description, and effective equivalent shape parameters cannot be obtained. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides an equivalent parameter estimation method in the CGIG+N background based on curve fitting.

[0006] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] In a first aspect, the present invention provides a method for estimating equivalent form parameters in a CGIG+N context based on curve fitting, the method comprising:

[0008] Construct sea clutter model and noise sea clutter model according to CGIG;

[0009] obtaining a first cumulative distribution function according to the sea clutter model, and obtaining a second cumulative distribution function according to the noisy sea clutter model;

[0010] Substituting the equivalent scale parameter into the first cumulative distribution function to obtain a third cumulative distribution function; wherein the equivalent scale parameter is obtained according to the clutter power and the noise average power;

[0011] Obtaining a loss function according to the second cumulative distribution function and the third cumulative distribution function;

[0012] The loss function is calculated multiple times, and different shape parameters are used as input to obtain corresponding equivalent shape parameter values;

[0013] A fitting expression of the equivalent shape parameter is obtained according to the different shape parameters and the corresponding equivalent shape parameter values.

[0014] Optionally, obtaining a first cumulative distribution function according to the sea clutter model includes:

[0015] obtaining a first intensity probability density according to the sea clutter model;

[0016] Obtaining a first intensity probability density under CGIG distribution according to the first intensity probability density;

[0017] The first cumulative distribution function is obtained according to the first intensity probability density under the CGIG distribution.

[0018] Optionally, obtaining a second cumulative distribution function according to the noisy sea clutter model includes:

[0019] Obtaining a second intensity probability density according to the noisy sea clutter model;

[0020] Obtaining a second intensity probability density under CGIG distribution according to the second intensity probability density;

[0021] The second cumulative distribution function is obtained according to the second intensity probability density under the CGIG distribution.

[0022] Optionally, the first cumulative distribution function is expressed as follows:

[0023]

[0024] Among them, F CGIG(I; b, υ) represents the first cumulative distribution function of the inverse Gaussian distribution when the clutter intensity I obeys the clutter power b and the shape parameter υ, e is the natural exponential, and exp() is the exponential function.

[0025] Optionally, the second cumulative distribution function is expressed as follows:

[0026]

[0027] Among them, F CGIG+N (I;υ,b,σ 2 ) means that when the clutter intensity I obeys the clutter power b, shape parameter υ and noise average power σ 2 The second cumulative distribution function of the inverse Gaussian distribution in the case of p τ (τ) represents the probability density of the inverse Gaussian distribution corresponding to the texture component τ under noise conditions.

[0028] Optionally, the loss function is expressed as follows:

[0029]

[0030] in, Indicates that when the loss function W1(υ eff ) is minimum, the equivalent shape parameter υ eff The value of F CGIG (I;υ eff ,b eff ) indicates that when the clutter intensity I obeys the equivalent clutter power b eff and the equivalent shape parameter υ eff The third cumulative distribution function of the inverse Gaussian distribution in the case of .

[0031] Optionally, the equivalent clutter power is expressed as follows:

[0032]

[0033] Here, CNR stands for noise-canceling ratio.

[0034] Optionally, the fitting expression of the equivalent shape parameter is expressed as follows:

[0035]

[0036] The technical solutions provided by the embodiments of the present invention may have the following beneficial effects:

[0037] In the above technical solution, the present invention constructs a sea clutter model and a noisy sea clutter model based on CGIG, fully utilizing the probability distribution characteristics of radar echoes, and can obtain equivalent shape parameters that are more effective than the existing technology in terms of medium and low noise-clutter ratios and shape parameters.

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of an equivalent parameter estimation method based on curve fitting in a CGIG+N context provided by an embodiment of the present invention;

[0040] Figure 2 1 is a schematic diagram comparing the KS distances of a moment estimation method provided by an embodiment of the present invention and a curve fitting method of the present invention;

[0041] Figure 3 3 is a schematic diagram comparing the KL divergence of a moment estimation method provided by an embodiment of the present invention and the curve fitting method of the present invention. DETAILED DESCRIPTION

[0042] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0043] Figure 1 FIG. 1 is a flow chart of an equivalent parameter estimation method based on curve fitting in the CGIG+N context provided by an embodiment of the present invention. Figure 1 As shown, the method may include the following steps:

[0044] S101. Construct a sea clutter model and a noisy sea clutter model according to CGIG.

[0045] It can be understood that in the composite Gaussian model, sea clutter can be expressed as the product of two independent random variables, so the sea clutter model can be expressed as:

[0046]

[0047] Where τ represents the texture component and u is a speckle component that obeys a complex Gaussian distribution with zero mean and variance 1.

[0048] When the noise cannot be ignored, the radar echo can be expressed as the sum of sea clutter and noise in a composite Gaussian model. Therefore, the noisy sea clutter model can be expressed as:

[0049]

[0050] Where c' represents the noisy sea clutter model and n is the radar thermal noise.

[0051] S102: Obtain a first cumulative distribution function according to a sea clutter model, and obtain a second cumulative distribution function according to a noisy sea clutter model.

[0052] Optionally, S102 may include:

[0053] Obtaining the first intensity probability density according to the sea clutter model;

[0054] According to the first intensity probability density, the first intensity probability density under the CGIG distribution is obtained;

[0055] The first cumulative distribution function is obtained according to the first intensity probability density under the CGIG distribution.

[0056] It can be understood that the clutter intensity is I = |c| 2 According to the total probability formula, the probability density of clutter intensity is:

[0057]

[0058] When the texture component τ is constant, the sea clutter model follows a complex Gaussian distribution with zero mean and variance τ. The intensity I follows an exponential distribution. Its texture component τ follows a two-parameter inverse Gaussian distribution, which can be expressed as follows:

[0059]

[0060] Where b is the scale parameter (also the clutter power), and υ is the shape parameter. Based on the probability density of the clutter intensity and integrating τ, the first intensity probability density under the CGIG distribution can be obtained as:

[0061]

[0062] Integrating the first intensity probability density under the CGIG distribution, the first cumulative distribution function is expressed as follows:

[0063]

[0064] Among them, F CGIG (I; b, υ) represents the first cumulative distribution function of the inverse Gaussian distribution when the clutter intensity I obeys the clutter power b and the shape parameter υ, e is the natural exponential, and exp() is the exponential function.

[0065] Optionally, S102 may further include:

[0066] Obtaining a second intensity probability density according to a noisy sea clutter model;

[0067] Obtaining the second intensity probability density under the CGIG distribution according to the second intensity probability density;

[0068] A second cumulative distribution function is obtained according to the second intensity probability density under the CGIG distribution.

[0069] It can be understood that, referring to the above steps, the probability density of the clutter intensity in the noisy sea clutter model is:

[0070]

[0071] When the texture component τ is constant, the noise sea clutter model obeys zero mean and the variance is τ+σ 2 The intensity I follows an exponential distribution. Its texture component τ follows a two-parameter inverse Gaussian distribution, expressed as follows:

[0072]

[0073] Among them, σ 2 is the average power of the noise. According to the probability density of the clutter intensity and integrating τ, the second intensity probability density under the CGIG distribution can be obtained as:

[0074]

[0075] Integrating the second intensity probability density under the CGIG distribution, the first cumulative distribution function is expressed as follows:

[0076]

[0077] Among them, F CGIG+N (I;υ,b,σ 2 ) means that when the clutter intensity I obeys the clutter power b, shape parameter υ and noise average power σ 2 The second cumulative distribution function of the inverse Gaussian distribution in the case of p τ (τ) represents the probability density of the inverse Gaussian distribution corresponding to the texture component τ under noise conditions.

[0078] S103 , substituting the equivalent scale parameter into the first cumulative distribution function to obtain a third cumulative distribution function; wherein the equivalent scale parameter is obtained according to the clutter power and the noise average power.

[0079] S104: Obtain a loss function according to the second cumulative distribution function and the third cumulative distribution function.

[0080] It is understandable that the Wasserstein distance, also known as the Earth Mover's distance, is a measure of the difference between two probability distributions. It reflects the minimum amount of work required to transform one distribution into another, that is, the minimum average distance required to transform distribution P into distribution Q.

[0081] For the first intensity probability density f CGIG and the second intensity probability density f CGIG+N , which corresponds to the first cumulative distribution function F CGIG and the first cumulative distribution function F CGIG+N, then their Wasserstein distance is defined as:

[0082]

[0083] Compared with KL divergence (relative entropy), Wasserstein distance can provide smoother results for parameter updates of optimization algorithms, but the computational cost will be higher. Therefore, KS distance and KL divergence can also be used instead of Wasserstein distance.

[0084] The sea clutter model is used to describe the noisy sea clutter model, that is, a dual-parameter composite Gaussian model containing shape parameters and scale parameters is used to describe the model containing shape parameters, scale parameters, and noise power. Since the scale parameter b in the above form is the clutter power, the clutter-to-noise ratio CNR can be obtained from the physical meaning as b / σ 2 , the equivalent scale parameter can be expressed as:

[0085]

[0086] Equivalent shape parameter υ eff It is expressed as a functional relationship between shape parameter υ and noise ratio CNR:

[0087] υ eff =f(υ,CNR);

[0088] Define Wasserstein distance as the loss function and use the optimization algorithm to minimize the loss function. The loss function is expressed as follows:

[0089]

[0090] in, Indicates that when the loss function W1(υ eff ) is minimum, the equivalent shape parameter υ eff The value of F CGIG (I;υ eff ,b eff ) indicates that when the clutter intensity I obeys the equivalent clutter power b eff and the equivalent shape parameter υ eff The third cumulative distribution function of the inverse Gaussian distribution in the case of . The equivalent scale parameter b eff Given the given condition, find the equivalent shape parameter υ that minimizes the difference between the sea clutter model and the noisy sea clutter model eff .

[0091] The equivalent clutter power is expressed as follows:

[0092]

[0093] Here, CNR stands for noise-canceling ratio.

[0094] S105. Calculate the loss function multiple times, and use different shape parameters as input to obtain corresponding equivalent shape parameter values.

[0095] S106 , obtaining a fitting expression of the equivalent shape parameter according to different shape parameters and corresponding equivalent shape parameter values.

[0096] It can be understood that by using Matlab to calculate multiple times, a series of equivalent shape parameters υ are obtained. eff The fitting expression of the equivalent shape parameter is expressed as follows with the shape parameter υ and the noise-to-noise ratio CNR:

[0097]

[0098] This expression satisfies the basic conditions that the equivalent shape parameter is consistent with the shape parameter and the equivalent scale parameter is the same as the scale parameter when the noise power is 0.

[0099] The CGIG probability density function f of equivalent shape parameter and equivalent scale parameter is obtained CGIG (I;υ eff ,b eff ) and the cumulative distribution function F CGIG (I;υ eff ,b eff ), and calculate the KS distance and KL divergence with the noisy sea clutter model:

[0100]

[0101] To verify its effect, it is compared with the moment estimation method. eff and the equivalent scale parameter b′ eff The form is:

[0102]

[0103] The same method is used to calculate the KS distance and KL divergence of the sea clutter model and the noisy sea clutter model.

[0104] Comparing the KS distance and KL divergence of the two methods, it is found that the KS distance and KL divergence of the present invention are smaller. Figure 2 : is a schematic diagram comparing the KS distance of a moment estimation method provided by an embodiment of the present invention and the curve fitting method of the present invention, Figure 3 : is a KL divergence comparison diagram of a moment estimation method provided by an embodiment of the present invention and a curve fitting method of the present invention, such as Figure 2 and Figure 3As shown, it is explained that the CGIG distribution calculated by the equivalent shape parameters obtained by the present invention is closer to the distribution of CGIG plus noise than the moment estimation.

[0105] In the above technical solution, the present invention constructs a sea clutter model and a noisy sea clutter model based on CGIG, fully utilizing the probability distribution characteristics of radar echoes, and can obtain equivalent shape parameters that are more effective than the existing technology in terms of medium and low noise-clutter ratios and shape parameters.

[0106] It should be noted that the terms "first," "second," and the like are used to distinguish similar objects and are not necessarily used to describe a particular order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in sequences other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0107] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0108] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the drawings and the disclosure. In the description of the present invention, the word "comprising" does not exclude other components or steps, "one" or "an" does not exclude multiple situations, and "multiple" means two or more, unless otherwise clearly and specifically defined. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

Claims

1. A method for estimating equivalent parameters in the CGIG+N context based on curve fitting, characterized in that: The method comprises: Construct sea clutter model and noise sea clutter model according to CGIG; obtaining a first cumulative distribution function according to the sea clutter model, and obtaining a second cumulative distribution function according to the noisy sea clutter model; Substituting the equivalent scale parameter into the first cumulative distribution function to obtain a third cumulative distribution function; wherein the equivalent scale parameter is obtained according to the clutter power and the noise average power; Obtaining a loss function according to the second cumulative distribution function and the third cumulative distribution function; The loss function is calculated multiple times, and different shape parameters are used as input to obtain corresponding equivalent shape parameter values; A fitting expression of the equivalent shape parameter is obtained according to the different shape parameters and the corresponding equivalent shape parameter values.

2. The method for estimating equivalent parameters based on curve fitting in the CGIG+N context according to claim 1, characterized in that: The obtaining a first cumulative distribution function according to the sea clutter model includes: obtaining a first intensity probability density according to the sea clutter model; Obtaining a first intensity probability density under CGIG distribution according to the first intensity probability density; The first cumulative distribution function is obtained according to the first intensity probability density under the CGIG distribution.

3. The method for estimating equivalent parameters based on curve fitting in the CGIG+N context according to claim 1, characterized in that: The obtaining a second cumulative distribution function according to the noisy sea clutter model includes: Obtaining a second intensity probability density according to the noisy sea clutter model; Obtaining a second intensity probability density under CGIG distribution according to the second intensity probability density; The second cumulative distribution function is obtained according to the second intensity probability density under the CGIG distribution.

4. The method for estimating equivalent form parameters based on curve fitting in the CGIG+N context according to claim 1, characterized in that: The first cumulative distribution function is expressed as follows: Among them, F CGIG (I; b, υ) represents the first cumulative distribution function of the inverse Gaussian distribution when the clutter intensity I obeys the clutter power b and the shape parameter υ, e is the natural exponential, and exp() is the exponential function.

5. The method for estimating equivalent parameters based on curve fitting in the CGIG+N context according to claim 4, characterized in that: The second cumulative distribution function is expressed as follows: Among them, F CGIG+N (I;υ,b,σ 2 ) means that when the clutter intensity I obeys the clutter power b, shape parameter υ and noise average power σ 2 The second cumulative distribution function of the inverse Gaussian distribution in the case of p τ (τ) represents the probability density of the inverse Gaussian distribution corresponding to the texture component τ under noise conditions.

6. The method for estimating equivalent form parameters based on curve fitting in the CGIG+N context according to claim 5, characterized in that: The loss function is expressed as follows: in, Indicates that when the loss function W1(υ eff ) is minimum, the equivalent shape parameter υ eff The value of F CGIG (I;υ eff ,b eff ) indicates that when the clutter intensity I obeys the equivalent clutter power b eff and the equivalent shape parameter υ eff The third cumulative distribution function of the inverse Gaussian distribution in the case of .

7. The method for estimating equivalent form parameters based on curve fitting in the CGIG+N context according to claim 6, characterized in that: The equivalent clutter power is expressed as follows: Here, CNR stands for noise-canceling ratio.

8. The method for estimating equivalent parameters based on curve fitting in the CGIG+N context according to claim 7, characterized in that: The fitting expression of the equivalent shape parameter is expressed as follows:

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