Marine reverberation probability density model based on maximum entropy principle
By adopting the Gaussian-Laplace distribution model based on the maximum entropy principle in marine reverb modeling, the problem of poor robustness of existing models in time-varying environments is solved, and more accurate reverb modeling and lower KL divergence values are achieved.
Patent Information
- Application Number
- CN202411848287.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-16
- Publication Date
- 2025-04-22
AI Technical Summary
The existing marine reverberation probability density models are poorly robust in time-varying environments, making it difficult to accurately model reverberation.
The Gaussian-Laplace distribution model based on the maximum entropy principle is used to model ocean reverbs. This model describes the probability density of reverbs through a linear combination of the Gaussian distribution model and the pollution distribution model, combined with the maximum entropy principle.
The model remains robust in time-varying environments, with lower overall KL divergence values, which are close to the real reverb model, improving the accuracy of reverb modeling.
Smart Images
Figure CN119862364A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of ocean reverberation probability density, and in particular to an ocean reverberation probability density model based on the maximum entropy principle. Background Art
[0002] Ocean reverberation refers to the background noise generated by reflection and scattering of scatterers (such as suspended particles, organisms, etc.) on the seabed, sea surface, and inside the water body when sound waves propagate in the marine environment. It has a significant impact on active sonar systems (which emit sound waves and receive echoes to detect targets) because reverberation mixes with useful signals from the target, thereby reducing the ability to detect targets. The probability density model of ocean reverberation describes the statistical distribution characteristics of reverberation intensity over time or space. Accurate probability density modeling of reverberation is the key to detecting weak signals in the context of ocean reverberation. The reverberation probability density models currently used mainly include Gaussian distribution model, mixed Gaussian distribution model, symmetric α-stable distribution model, etc.
[0003] However, reverberation is a time-varying signal with uncertainty in its probability density. It is difficult to always accurately model reverberation using the above model, and model mismatch may occur, that is, the robustness of the model is poor. Summary of the invention
[0004] The present invention aims to provide an ocean reverberation probability density model based on the maximum entropy principle, and adopts a new probability density model to model reverberation, which not only conforms to the reverberation probability density characteristics, but also maintains robustness in a time-varying environment. Solve the problems in the background technology.
[0005] In order to achieve the above object, the present invention provides the following technical solutions:
[0006] A probability density model of ocean reverberation based on the maximum entropy principle, the expression of the model is:
[0007]
[0008] Among them, ε is the pollution coefficient, σ 2 is the variance of Gaussian distribution, and b is the shape parameter of Laplace distribution.
[0009] Furthermore, the model is formed by a linear combination of the probability density function of the Gaussian distribution model and the probability density function of the pollution distribution model, and the expression of the linear combination is:
[0010] f g-w (x) = (1-ε)f g (x)+εf w (x)
[0011] Among them, f g(x) = is the probability density function of the Gaussian distribution model, f w (x) is the probability density function line of the pollution distribution model.
[0012] Furthermore, the probability density function line expression of the Gaussian distribution model is:
[0013]
[0014] Among them, σ 2 is the variance of Gaussian distribution;
[0015] The probability density function line expression of the pollution distribution model is:
[0016]
[0017] Where b is the shape parameter of the Laplace distribution.
[0018] The beneficial effects of the technical solution are:
[0019] The ocean reverberation probability density model based on the maximum entropy principle of the present invention is based on the maximum entropy principle and adopts a new probability density model to model the reverberation. The probability density model not only conforms to the reverberation probability density characteristics, but also has a lower overall KL divergence value than the Gaussian distribution model, the mixed Gaussian distribution model and the symmetric α-stable distribution model. That is, the ocean reverberation probability density model proposed by the present invention is close to the real reverberation model and is more robust. BRIEF DESCRIPTION OF THE DRAWINGS
[0020] Figure 1 This is a schematic diagram of the Gaussian-contamination distribution model process in Example 1 of the present invention;
[0021] Figure 2 This is a flow chart of parameter estimation using the EM algorithm in Example 1 of the present invention;
[0022] Figure 3 This is a KL divergence comparison diagram of reverberation modeling using a Gaussian distribution model, a mixed Gaussian distribution model (GMM), a symmetric α-stable distribution model (SαS), and a Gaussian-Laplace distribution model (GL) in the test examples of the present invention. DETAILED DESCRIPTION
[0023] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:
[0024] Example 1
[0025] A probability density model of ocean reverberation based on the maximum entropy principle is expressed as:
[0026]
[0027] Among them, ε is the pollution coefficient, σ 2 is the variance of Gaussian distribution, and b is the shape parameter of Laplace distribution.
[0028] The derivation process of the model is as follows:
[0029] S1. First, the Gaussian-contamination distribution model is used to model the reverberation, such as Figure 1 As shown, ε in the figure is called the contamination coefficient. It can be seen that the Gaussian-contamination distribution model is a linear combination of the Gaussian distribution model and a contamination distribution model. The probability density function expression of the Gaussian-contamination distribution model is:
[0030] f g-w (x) = (1-ε)f g (x)+εf w (x) (1)
[0031] in, The mean is 0 and the variance is σ 2 The probability density function of the Gaussian distribution model, f w (x) is the probability density function of pollution distribution;
[0032] S2. Probability density function f for the pollution distribution model w (x), whose information entropy is defined as
[0033] H(f w )=-∫f w (x)log f w (x)dx (2)
[0034] In the constraint f w When the mean value of (x) is 0, the pollution distribution model with maximum entropy is the Laplace distribution model, and its probability density function f L The expression of (x) is:
[0035]
[0036] Where b is the shape parameter of the Laplace distribution;
[0037] Therefore, the pollution distribution model is taken as the Laplace distribution model. At this time, the Gaussian-pollution distribution model is the Gaussian-Laplace distribution model, and its probability density function f g-L (x) is:
[0038]
[0039] The EM algorithm flow chart is as follows: Figure 2 As shown. The Gaussian-Laplace distribution model involves three parameters, namely the contamination coefficient ε, the Gaussian distribution variance σ2 And the shape parameter b of the Laplace distribution. The probability density parameter group of the Gaussian-Laplace distribution model is g = [ε,σ 2 ,b] T , let the reverberation data to be modeled be u n (n=1,...,N), and the EM algorithm is used for parameter estimation.
[0040]
[0041]
[0042]
[0043] Test Example 1
[0044] When performing probability density modeling on reverberation, the difference between the true probability density model of the reverberation and the modeling model can be measured by KL divergence. The smaller the KL divergence value, the smaller the difference between the modeling model and the true model. Let p(x) and q(x) be two probability density models, where p(x) represents the true probability density model and q(x) represents the modeling model. The KL divergence is defined as:
[0045]
[0046] For a 4-second long ocean reverberation data, Gaussian distribution model, mixed Gaussian distribution model (GMM), symmetric α-stable distribution model (SαS) and Gaussian-Laplace distribution model (GL) were used to model each time. The data length of each modeling was 0.2 seconds, the modeling step was 0.1 seconds, and a total of 40 models were built. The KL divergence comparison results are shown in the figure. Figure 3 shown.
[0047] In summary, when modeling ocean reverberation, the Gaussian-Laplace distribution model proposed in the present invention has a lower overall KL divergence value than the Gaussian distribution model, the mixed Gaussian distribution model and the symmetric α-stable distribution model, that is, the modeling model proposed in the present invention is closer to the real reverberation model and is more robust.
[0048] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the technical solution of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.
Claims
1. A probability density model of ocean reverberation based on the maximum entropy principle, characterized in that: The expression of the model is: Among them, ε is the pollution coefficient, σ 2 is the variance of Gaussian distribution, and b is the shape parameter of Laplace distribution.
2. The ocean reverberation probability density model based on the maximum entropy principle according to claim 1, characterized in that: The model is formed by a linear combination of the probability density function of the Gaussian distribution model and the probability density function of the pollution distribution model, and the expression of the linear combination is: f g-w (x)=(1-ε)f g (x)+εf w (x) Among them, f g (x) is the probability density function of the Gaussian distribution model, f w (x) is the probability density function line of the pollution distribution model, and ε is the pollution coefficient.
3. The ocean reverberation probability density model based on the maximum entropy principle according to claim 2, characterized in that: The probability density function line expression of the Gaussian distribution model is: Among them, σ 2 is the variance of Gaussian distribution; The probability density function line expression of the pollution distribution model is: Where b is the shape parameter of the Laplace distribution.