A method for estimating statistical characteristic parameters of sound pressure of ice-source noise

Abstract

A method for estimating the statistical characteristic parameters of ice-source noise sound pressure belongs to the field of underwater acoustic signal processing technology. The statistical characteristic parameters include a characteristic exponent α, a scale parameter γ, a skew parameter β, and a location parameter δ. The method includes: 1) basic theoretical analysis of the α-stable distribution; 2) estimation of the scale parameter γ; 3) calculation of the characteristic function point ω; 4) estimation of the characteristic exponent α; 5) estimation of the skew parameter β; and 6) estimation of the location parameter δ. A statistical characteristic parameter estimation method model is constructed based on the α-stable distribution theory to achieve rapid estimation of the four statistical characteristic parameters of ice-source noise sound pressure with non-stationary and impulsive characteristics. The value of the second characteristic function point is determined by the estimated result of the scale parameter. The skew parameter is estimated by selecting different estimation formulas based on the size of the characteristic exponent. This method is applicable to both skewed and symmetric α-stable distributions, has high estimation accuracy, and does not require a quantile table, making the calculation simple.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic signal processing, and in particular relates to a method for estimating statistical characteristic parameters of sound pressure of ice source noise. Background Art

[0002] In recent decades, as global climate warms, Arctic sea ice coverage, thickness, structure and other characteristics have undergone tremendous changes. [1-3] These changes have a profound impact on the characteristics of ice-source noise. [4-5] Ice-source noise is generated by sea ice cracking, collision, squeezing, heaving, friction, melting, ice ridge formation, collision and friction of granular snow on the rough sea ice surface under the action of wind, relative movement of floating ice, and even waves hitting the sea ice. [6-9] . In general open sea areas, wind and wave noise and ship noise are the most common, persistent and best noise sources in the ocean, and the two dominate the marine environmental noise. However, in the Arctic Ocean, the presence of sea ice isolates the noise generated by the interaction of wind and waves on the ocean surface, and significantly reduces other shipping noise except icebreakers. Ice-source noise has become the main source of Arctic marine environmental noise. For sonar and other hydroacoustic equipment, ice-source noise has become one of the main background interferences. In the prediction of sonar range or the design of signal processing solutions, it is required to predict the "signal-to-noise ratio" and to fully understand the spatiotemporal statistical characteristics of the noise field. Therefore, establishing a statistical model of ice-source noise, estimating the statistical characteristic parameters of ice-source noise, and studying and mastering the statistical characteristics of ice-source noise are of great significance to improving the detection performance of sonar and other hydroacoustic equipment when working in ice areas.

[0003] Ice-source noise often contains a large number of transient signals. In the time domain, its amplitude (sound pressure) often increases suddenly, and it has non-stationary and impulse characteristics. [5-13] Therefore, ice source noise does not obey Gaussian distribution like general wind and wave ocean environmental noise, but has non-Gaussian distribution. [6] In traditional underwater acoustic signal processing, in order to simplify the implementation and analysis of the detection system, it is often assumed that the noise obeys Gaussian distribution. According to the central limit theorem, this assumption is reasonable.

[14] However, due to factors such as sea ice conditions, sea surface wind speed, snow accumulation, and air temperature, the non-Gaussian statistical characteristics of ice-source noise will increase the false alarm probability of the detection method based on the Gaussian distribution ocean environmental noise model, and the detection performance will be significantly deteriorated. [15-16] .

[0004] In practical underwater acoustic signal processing, it is often necessary to estimate the statistical characteristic parameters of ice source noise. Currently, the more commonly used parameter estimation methods are the characteristic function method.

[17] , Maximum Likelihood Method

[18] , Quantile method

[19] , Fractional Lower-Order Moment Method

[20] and logarithmic moment method

[21] The characteristic function method and maximum likelihood method offer high computational accuracy but require a large computational workload. The quantile method requires a table lookup based on the five sample quantiles, resulting in relatively poor estimation accuracy and a large computational workload. Furthermore, the characteristic function method also requires a quantile table lookup. The location parameters of the fractional lower-order moment method and the logarithmic moment method are both assumed to be the mean of the random variable, and no estimator exists. These methods are primarily used for estimating parameters of symmetric α-stable distributions.

[0005] References:

[0006] [1] Cavalieri DJ, Parkinson C L. Arctic sea ice variability and trends, 1979-2010. The Cryosphere, 2012; 6(4): 881-889.

[0007] [2] Kwok R. Arctic sea ice thickness, volume, and multiyear ice coverage: losses and coupled variability (1958-2018). Environ. Res. Lett., 2018; 13(10): 105005.

[0008] [3] Li Qihu, Huang Haining, Yin Li, et al. New progress and new trends in Arctic hydroacoustics research. Acta Acoustics, 2018; 43(4): 420-431.

[0009] [4] Ozanich E, Gerstoft P, Worcester PF, et al. Eastern Arctic ambientnoise on a drifting vertical array. J. Acoust. Soc. Am., 2017; 142(4): 1997-2006.

[0010] [5] Kinda GB, Simard Y, Gervaise C, et al. Under-ice ambient noise in Eastern Beaufort Sea, Canadian Arctic, and its relation to environmental forcing. J. Acoust. Soc. Am., 2013; 134(1): 77-87.

[0011] [6]Milne A R,Ganton J H.Ambient Noise under Arctic-SeaIce.J.Acoust.Soc.Am.,1964;36(5):855-863。

[0012] [7]Greening M V,Zakarauskas P.Pressure ridging spectrum level and aproposed origin of the infrasonic peak in arctic ambient noisespectra.J.Acoust.Soc.Am.,1994;95(2):791-797。

[0013] [8]Kinda G B,Simard Y,Gervaise C,et al.Arctic underwater noisetransientsfrom sea ice deformation:Characteristics,annual time series,andforcing in Beaufort Sea.J.Acoust.Soc.Am.,2015;138(4):2034-2045。

[0014] [9]Wen H,Yang Y,Ruan H,et al.Nearfield measurements of ice meltingnoise in the central Arctic Ocean in summer.Polar Science,2020;24:100528。

[0015]

[10] Han,D.G.,Joo,J.,Son,W.,Cho,K.H.,Choi,J.W.,Yang,E.J.,Kim,J.H.,KangS.H.,La,H.S.Effects of geophony and anthrophony on the underwater acousticenvironment in the East Siberian Sea,Arctic Ocean.Geophysical ResearchLetters,2021,48:e2021GL093097。

[0016]

[11] Han,

[0017]

[12] Roth, EH, Hildebrand, JA, Wiggins, SM, Ross, D. Underwater ambientnoise on the Chukchi Sea continental slope from 2006-2009. J. Acoust. Soc. Am., 2012, 131(1), 104-110.

[0018]

[13] Zakarauskas, P., Parfitt, CJ, Thorleifson, JM Automatic extraction of spring time Arctic ambient noise transients. J. Acoust. Soc. Am., 1991, 90(1), 470-474.

[0019]

[14] Song Guoli, Guo Xinyi, Ma Li. Study on the model of non-Gaussian ocean ambient noise with deterministic kurtosis. Acta Acoustics, 2019, 44(05): 887-896.

[0020]

[15] Seo, JS, Cho, SJ, Feher K. Impact of Non-Gaussian Impulsive Noiseon the Performance of High-Level QAM. IEEE Trans. Electromagn. Compat., 1989, 31(2): 177-180.

[0021]

[16] Izzo,L.,Paura,L..Error Probability for Fading CPSK Signals inGaussian and Impulsive Atmospheric Noise Environments.IEEE Transactions onAerospace and Electronic Systems,1981,AES-17(5):719-722。

[0022]

[17] Koutrouvelis I A.Regression-Type Estimation of the Parameters ofStable Laws.J.Acoust.Soc.Am.,1980;75(372):918-928。

[0023]

[18] Bodenschatz J S,Nikias C L.Maximum-likelihood symmetricα-stableparameter estimation.Signal Process.,1999;47(5):1382-1384。

[0024]

[19] McCulloch J H.Simple consistent estimators of stable distributionparameters.Communications in Statistics-Simulation and Computation,1966;15(4):1109-1136。

[0025]

[20] Shao M,Nikias C L.Signal Processing with Fractional Lower OrderMoments:Stable Processes and Their Applications.P.IEEE,1993;81(7):986-1010。

[0026]

[21] Tsihrintzis GA, Nikias C L. Fast estimation of the parameters of alpha-stable impulsive interference. Signal Process., 1996; 44(6): 1492-1503. Summary of the Invention

[0027] The purpose of the present invention is to address the above-mentioned problems existing in the prior art and provide a method for estimating the statistical characteristic parameters of ice source noise sound pressure, which has high estimation accuracy, simple calculation and small amount of computation, and can realize rapid and real-time estimation of the statistical characteristic parameters of ice source noise sound pressure.

[0028] The present invention constructs a statistical characteristic parameter estimation method model based on the α-stable distribution theory to achieve rapid estimation of four statistical characteristic parameters of ice source noise sound pressure with non-stationary and impulse characteristics. The four statistical characteristic parameters are characteristic exponent α, scale parameter γ, skew parameter β and position parameter δ; the estimation formula of skew parameter β is selected according to the size of characteristic exponent α.

[0029] The method for estimating the statistical characteristic parameters of ice source noise sound pressure described in the present invention specifically comprises the following steps:

[0030] 1) Basic Theoretical Analysis of α-Stable Distribution: The definition and expression of the characteristic function of a random variable X that obeys the α-stable distribution are given, and the basic properties of the α-stable distribution are discussed and analyzed based on the expression;

[0031] 2) Estimation of the scale parameter γ: Based on the basic theory of α-stable distribution, the estimation formula of the scale parameter γ is derived. The scale parameter of the ice-source noise pressure is estimated based on the measured ice-source noise data.

[0032] 3) Calculation of characteristic function point ω: The characteristic function points include the first characteristic function point (ω = 1) and the second characteristic function point (ω = ω0). The first characteristic function point is a deterministic characteristic function point, and the value of the second characteristic function point ω0 is determined by the estimation result of the scale parameter;

[0033] 4) Estimation of characteristic index α: After the scale parameter γ and the second characteristic function point ω0 are determined, the characteristic index α is estimated according to the estimation formula;

[0034] 5) Estimation of skewness parameter β: The joint estimation method is used for estimation, and different skewness parameter β estimation formulas are selected according to the size of the characteristic exponent α;

[0035] 6) Estimation of position parameter δ: Based on the above parameter estimation, the position parameter δ is calculated according to the derived estimation formula.

[0036] In step 1), the basic theoretical analysis of the stable distribution of the characteristic index α is to provide the definition and expression of the characteristic function of the random variable X that obeys the α stable distribution, and discuss and analyze the basic properties of the α stable distribution based on the expression; the characteristic function of the random variable X that obeys the α stable distribution is defined as:

[0037]

[0038] Where sign(ω) is the sign function, α is the characteristic exponent, β is the skew parameter, γ is the scale parameter, and δ is the location parameter. The α-stable distribution is uniquely determined by the four parameters α, β, γ, and δ.

[0039] From formula (1), we can get the absolute value characteristic function of the α-stable distribution random variable X:

[0040]

[0041] In the formula, the characteristic function point ω has two values, ω=1 and ω=ω0.

[0042] In step 2), the estimation of the scale parameter γ is to substitute the first characteristic function point ω=1 into formula (2), and the estimated value of the scale parameter γ is:

[0043]

[0044] Where x i is the specific numerical sequence of the random variable X.

[0045] In step 3), the characteristic function points include a first characteristic function point and a second characteristic function point; wherein ω=1 is a deterministic characteristic function point, i.e., the first characteristic function point; the second characteristic function point is the characteristic function point of ω=ω0; according to the solution of the relevant nonlinear equation, ω0 has two roots within the value range (0<ω0<0.5 and ω0>1) to be selected, and needs to be selected according to the size of the scale parameter γ; the specific steps may be:

[0046] According to the absolute value characteristic function of Gaussian distribution and the absolute value characteristic function e of the Cauchy distribution -γω The distance between them changes with ω, and the conversion relationship between ω and γ is established as follows:

[0047]

[0048] The value of the second characteristic function point ω0 can be determined as the solution of the above nonlinear equation; Equation (4) has two roots, with value ranges of 0<ω0<0.5 and ω0>1, representing the maximum and minimum distances between the absolute value characteristic function of the Gaussian distribution and the absolute value characteristic function of the Cauchy distribution, respectively.

[0049] In step 4), the characteristic index α is estimated by substituting the scale parameter γ and the second characteristic function point ω0 into formula (2), and the estimated value of the characteristic index α can be obtained as follows:

[0050]

[0051] in:

[0052]

[0053] In step 5), the estimation of the skew parameter β is performed using a joint estimation method. Different estimation formulas are selected according to the size of the characteristic index. When 1 < α ≤ 1.8, the parameter estimation method under the condition of ω0 > 1 is adopted, that is, formula (8); when 1.8 < α ≤ 2, a new β value estimation method is adopted, that is, formula (10). The specific steps are as follows:

[0054] When 1<α≤1.8, since ln y=ln|y|+j(arg y+2kπ), we can take the logarithm of equation (1) and obtain:

[0055]

[0056] Substituting ω = 1 and ω = ω0 into the imaginary part of Equation (7), we can obtain the estimated value of the skew parameter β:

[0057]

[0058] When 1.8<α≤2, the estimation formula of the skew parameter β is:

[0059]

[0060] in, I(·) is an indicator function, ε n is a threshold parameter, ε n >0.

[0061] In step 6), the estimation of the position parameter δ may be performed by the following steps:

[0062] Substituting ω = 1 and ω = ω0 into the imaginary part of Equation (7), we can obtain the estimated value of the location parameter δ:

[0063]

[0064] The present invention constructs a statistical characteristic parameter estimation method model based on the α-stable distribution theory, realizing the rapid estimation of four statistical characteristic parameters of ice-source noise sound pressure with non-stationary and impulse characteristics. These four statistical characteristic parameters are the characteristic exponent α, the scale parameter γ, the skew parameter β, and the position parameter δ. The selection of the value of the second characteristic function point needs to be determined based on the estimation result of the scale parameter. The estimation of the skew parameter requires the selection of different estimation formulas based on the size of the characteristic exponent.

[0065] Compared with the prior art, the present invention has the following advantages:

[0066] (1) This method is applicable to both skewed α-stable distribution and symmetric α-stable distribution. It has high estimation accuracy and is simple to calculate without looking up the quantile table.

[0067] (2) According to the size of the scale parameter γ, the root of the second characteristic function point ω0 is selected, which can significantly improve the estimation accuracy of the statistical characteristic parameters.

[0068] (3) In view of the problem that the estimation accuracy of the skew parameter β decreases when 1.8<α≤2, a new method for estimating β is introduced. Different estimation methods are used according to the value of α to improve the estimation accuracy of β. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 are the standard errors and means of the four statistical characteristic parameters obtained by numerical simulation. The initial conditions of the simulation are α∈(1,2], β=0.5, γ=0.001, δ=0.0002.

[0070] Figure 2 are the standard errors and means of the four statistical characteristic parameters obtained from the numerical simulation. The initial conditions of the simulation are α = 1.5, β = 0.5, γ∈[0.00001, 2], δ = 0.0002.

[0071] Figure 3 The time domain diagram and statistical characteristic distribution diagram of ice source noise during the freezing period.

[0072] Figure 4 The time domain diagram and statistical characteristic distribution diagram of ice source noise during the ice-covered period.

[0073] Figure 5 The time domain diagram and statistical characteristic distribution diagram of ice source noise during ice melting. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will be further described in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. On the contrary, the present invention encompasses any substitutions, modifications, equivalent methods and solutions made within the spirit and scope of the present invention as defined by the claims. Furthermore, in order to provide the public with a better understanding of the present invention, some specific details are described in detail in the following detailed description of the present invention. Those skilled in the art can fully understand the present invention without the description of these details.

[0075] The α-stable distribution is the only distribution that satisfies the generalized central limit theorem, which states that for an infinite number of independent and identically distributed random variables with potentially infinite variances, their sum will tend to a stable distribution. The characteristic function of a random variable X that obeys an α-stable distribution is defined as:

[0076]

[0077] Where sign(ω) is the sign function. As can be seen, the α-stable distribution is uniquely determined by four parameters: α, β, γ, and δ. α is the characteristic exponent, β is the skew parameter, γ is the scale parameter, and δ is the location parameter.

[0078] From formula (1), we can see that the absolute value characteristic function of the α-stable distribution random variable X is:

[0079]

[0080] Substituting the first characteristic function point ω = 1 into equation (2), we can get the estimated value of the scale parameter γ:

[0081]

[0082] According to the absolute value characteristic function of Gaussian distribution and the absolute value characteristic function e of the Cauchy distribution -γω The distance between them changes with ω, and the conversion relationship between ω and γ can be established as follows:

[0083]

[0084] The value of the second characteristic function point ω0 can be determined as the solution to the above nonlinear equation. Equation (4) has two roots, with value ranges of 0<ω0<0.5 and ω0>1, representing the maximum and minimum distances between the absolute value characteristic function of the Gaussian distribution and the absolute value characteristic function of the Cauchy distribution, respectively. Regarding the value range of the root of ω0, numerical simulation and measured data verification show that when 0.00006≤γ≤0.4, it is necessary to select a root within the range of ω0>1; when 0.4<γ≤2, it is necessary to select a root within the range of 0<ω0<0.5.

[0085] When the estimated value γ and the second characteristic function point ω0 are both known, substituting them into formula (2) can obtain the estimated value of the characteristic index α, which is:

[0086]

[0087] in:

[0088]

[0089] Since ln y = ln|y| + j(arg y + 2kπ), taking the logarithm of equation (1) yields:

[0090]

[0091] Substituting ω = 1 and ω = ω0 into the imaginary part of Equation (7), we can obtain the estimated values ​​of the skew parameter β and the location parameter δ, where the skew parameter β is:

[0092]

[0093] If only formula (8) is used to estimate β, the estimation accuracy will decrease when α approaches 2. Simulation results show that: although the β estimation error when ω0>1 is smaller than the β estimation error when 0<ω0<0.5 in the entire α range, when α>1.8, the estimation error when ω0>1 increases abnormally with the increase of α value, and its value is greater than 1. At this time, the estimation accuracy of parameter β decreases. To solve this problem, a new method of skew parameter estimation is used to estimate the β value, and its estimation formula is:

[0094]

[0095] in, I(·) is an indicator function, ε n is a threshold parameter, ε n >0.

[0096] In summary, for the β estimate, a joint estimation method is needed, that is, when 1<α≤1.8, the parameter estimation method under the condition of ω0>1 is adopted, that is, formula (8); when 1.8<α≤2, the new β value estimation method is adopted, that is, formula (9).

[0097] As mentioned above, substituting ω = 1 and ω = ω0 into the imaginary part of equation (7) yields an estimate of the location parameter δ:

[0098]

[0099] The principle of the present invention is given below:

[0100] 1. The basic theory of α-stable distribution is the theoretical foundation of this paper and represents a development and advancement based on this basic theory. This paper defines and expresses the characteristic function of a random variable X that follows an α-stable distribution. Based on this expression, the basic properties of the α-stable distribution are discussed and analyzed.

[0101] 2. The scale parameter γ, also known as the coefficient of dispersion or dispersion, describes the degree to which a stable distribution random variable deviates from the mean or median. This parameter is estimated based on the basic theory of the α-stable distribution, deriving a formula for its estimation. This is then used to estimate the scale parameter of the ice-source noise pressure using measured ice-source noise data.

[0102] 3. The calculation of the characteristic function point ω is based on the properties of the absolute value characteristic function and the logarithmic characteristic function. There are two characteristic function points in total, of which ω = 1 is the deterministic characteristic function point, also known as the first characteristic function point. The second characteristic function point, ω = ω0, is mainly calculated. Based on the solution of the relevant nonlinear equation, ω0 has two optional roots within the value range (0 < ω0 < 0.5 and ω0 > 1). The selection needs to be based on the size of the scale parameter γ, otherwise the parameter estimation accuracy will be seriously affected.

[0103] 4. The characteristic exponent α determines the strength of the impulsive characteristics of the estimated data and the thickness of the probability density function's tail. Smaller α values ​​indicate stronger impulsive characteristics and thicker tails in the probability density function, indicating a greater likelihood that the random variable X will deviate from its central position. α is estimated using the relevant estimation formula after the scale parameter γ and the second characteristic function point ω0 are determined.

[0104] 5. The skew parameter β determines the degree of skewness of the distribution. This parameter is estimated based on the previously described parameter estimates, using the derived estimation formula. However, when 1.8 < α ≤ 2, the estimation accuracy of β decreases, necessitating the introduction of a new method for estimating the skew parameter β.

[0105] 6. The location parameter δ determines the location of the peak of the probability density function of the α-stable distribution and represents the mean or median of the α-stable distribution. This parameter is also estimated based on the above parameter estimates and calculated according to the derived estimation formula.

[0106] Figure 1 and 2 The numerical simulation results of the method shown in the present invention are given. Figure 1 , assuming β = 0.5, γ = 0.001, δ = 0.0002, and α varies within the range of greater than 1 and less than or equal to 2, the standard errors and means of the four statistical characteristic parameters obtained by numerical simulation of this method. In order to solve the problem that the estimation accuracy decreases when α is close to 2, a new β value estimation method is used for simulation. Figure 2 , assuming α = 1.5, β = 0.5, δ = 0.0002, and γ varies within the range of greater than or equal to 0.00001 and less than or equal to 2, the standard errors and means of the four statistical characteristic parameters obtained by numerical simulation of this method.

[0107] The simulation results show that:

[0108] (1) When γ = 0.001, the parameter estimation method under the condition of 0 < ω0 < 0.5 shows good performance only when α is close to 2; while the parameter estimation method under the condition of ω0 > 1 can show good performance in the entire α range. For the β estimate, a joint estimation method is required, that is, when 1 < α ≤ 1.8, the parameter estimation method under the condition of ω0 > 1 is used; when 1.8 < α ≤ 2, the new β value estimation method is used.

[0109] (2) In the range of 0.00006≤γ≤0.4, when the second characteristic function point ω0>1, the estimation performance of each parameter is better and the error is smaller; in the range of 0.4<γ≤2, when the second characteristic function point 0<ω0<0.5, the estimation performance of each parameter is better and the error is smaller.

[0110] Figure 3 The time domain diagram and statistical characteristic distribution diagram of ice source noise during the freezing period (19:00, November 8, 2018) are given. The figure shows a comparison of the estimation effects when different ω0 values ​​are selected (i.e., ω0 is in the range of 0<ω0<0.5 and ω0>1, respectively), and the final optimal estimation results of the four statistical characteristic parameters are given in the upper right corner of the figure.

[0111] Figure 4 A temporal plot of ice-source noise and its statistical characteristics during the ice-covered period (at 06:00 on April 22, 2019) are presented. The figure also compares the estimation results for different values ​​of ω0 (i.e., ω0 within the ranges of 0 < ω0 < 0.5 and ω0 > 1). The final optimal estimation results for the four statistical characteristic parameters are shown in the upper right corner of the figure.

[0112] Figure 5 A time-domain plot of ice-source noise and its statistical characteristics during the ice melt period (at 1:00 AM on July 7, 2019) are presented. The figure also compares the estimation results for different values ​​of ω0 (i.e., ω0 within the ranges of 0 < ω0 < 0.5 and ω0 > 1). The final optimal estimation results for the four statistical characteristic parameters are shown in the upper right corner of the figure.

[0113] Figures 3 to 5 The statistical characteristic parameter estimation results of the measured ice source noise sound pressure under different sea ice conditions are given. Figure 1 and 2 The relevant conclusions of numerical simulation are verified, which also shows the applicability and effectiveness of the method shown in the present invention in estimating the statistical characteristic parameters of ice source noise sound pressure.

[0114] The present invention constructs a statistical characteristic parameter estimation method model based on the theory of α-stable distribution. It estimates the statistical characteristic parameters of ice-source noise sound pressure through processes such as scale parameter estimation, calculation of characteristic function point values, characteristic index estimation, skew parameter estimation, and position parameter estimation. The present invention can promptly adjust the selection of characteristic function point values ​​based on the size of the scale parameter and the skew parameter estimation method based on the size of the characteristic index, thereby improving parameter estimation accuracy and exhibiting good adaptability. Experiments have shown that compared with existing ice-source noise statistical characteristic parameter estimation methods, the present invention eliminates the need for quantile table lookup, offers simple calculations, rapid speed, and high parameter estimation accuracy.

[0115] The above embodiments are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent of the present invention.

Claims

1. A method for estimating the statistical characteristic parameters of ice source noise sound pressure, characterized in that Based on the α-stable distribution theory, a statistical characteristic parameter estimation method model is constructed to achieve rapid estimation of four statistical characteristic parameters of the sound pressure of ice-source noise with non-stationary and impulsive characteristics. The four statistical characteristic parameters are the characteristic exponent α, the scale parameter γ, the skew parameter β, and the location parameter δ. The method specifically comprises the following steps: 1) Basic Theoretical Analysis of α-Stable Distribution: The definition and expression of the characteristic function of a random variable X that obeys the α-stable distribution are given, and the basic properties of the α-stable distribution are discussed and analyzed based on the expression; 2) Estimation of the scale parameter γ: Based on the basic theory of α-stable distribution, the estimation formula of the scale parameter γ is derived. The scale parameter of the ice-source noise pressure is estimated based on the measured ice-source noise data. 3) Calculation of characteristic function point ω: The characteristic function points include the first characteristic function point ω = 1 and the second characteristic function point ω = ω0. The first characteristic function point is a deterministic characteristic function point, and the value of the second characteristic function point ω0 is determined by the estimation result of the scale parameter; 4) Estimation of characteristic index α: After the scale parameter γ and the second characteristic function point ω0 are determined, the characteristic index α is estimated according to the estimation formula; 5) Estimation of skewness parameter β: The joint estimation method is used for estimation, and different skewness parameter β estimation formulas are selected according to the size of the characteristic exponent α; The estimation of the skew parameter β is performed using a joint estimation method. Different estimation formulas are selected according to the size of the characteristic index. When 1<α≤1.8, the parameter estimation method under the condition of ω0>1 is adopted, that is, formula (8); when 1.8<α≤2, a new β value estimation method is adopted, that is, formula (10). The specific steps are as follows: When 1<α≤1.8, since lny=ln|y|+j(argy+2kπ), taking the logarithm of equation (1) yields: Substituting ω = 1 and ω = ω0 into the imaginary part of Equation (7), we obtain the estimated value of the skew parameter β: When 1.8<α≤2, the estimation formula of the skew parameter β is: in, I(·) is an indicator function, ε n is a threshold parameter, ε n >0; 6) Estimation of position parameter δ: Based on the above parameter estimation, the position parameter δ is calculated according to the derived estimation formula.

2. The method for estimating the statistical characteristic parameters of ice source noise sound pressure according to claim 1, characterized in that In step 1), the characteristic function of the random variable X that obeys the α-stable distribution is defined as: Where sign(ω) is the sign function, α is the characteristic index, β is the skew parameter, γ is the scale parameter, and δ is the location parameter; the characteristic index α is a stable distribution uniquely determined by the four parameters α, β, γ, and δ; From formula (1), the absolute value characteristic function of the α-stable distribution random variable X is: In the formula, the characteristic function point ω has two values, ω=1 and ω=ω0, namely the first characteristic function point and the second characteristic function point.

3. The method for estimating statistical characteristic parameters of ice source noise sound pressure according to claim 1, characterized in that In step 2), the estimation of the scale parameter γ is to substitute the first characteristic function point ω=1 into formula (2), and the estimated value of the scale parameter γ is: Where x i is the specific numerical sequence of the random variable X.

4. The method for estimating statistical characteristic parameters of ice source noise sound pressure according to claim 1, characterized in that In step 3), the characteristic function points include a first characteristic function point and a second characteristic function point; wherein ω=1 is a deterministic characteristic function point, i.e., the first characteristic function point; The second characteristic function point is the characteristic function point of ω=ω0; according to the solution of the relevant nonlinear equation, ω0 has two roots in the value range 0<ω0<0.5 and ω0>1 to choose from, which is selected according to the size of the scale parameter γ.

5. The method for estimating the statistical characteristic parameters of ice source noise sound pressure according to claim 1, characterized in that In step 3), the calculation of the second characteristic function point ω=ω0 is performed in the following steps: According to the absolute value characteristic function of Gaussian distribution and the absolute value characteristic function e of the Cauchy distribution -γω The distance between them changes with ω, and the conversion relationship between the characteristic function point ω and the scale parameter γ is established as follows: The value of the second characteristic function point ω0 is determined as the solution of the above nonlinear equation; Equation (4) has two roots, with values ​​ranging from 0 < ω0 < 0.5 and ω0 > 1, which represent the maximum and minimum distances between the absolute value characteristic function of the Gaussian distribution and the absolute value characteristic function of the Cauchy distribution, respectively.

6. The method for estimating the statistical characteristic parameters of ice source noise sound pressure according to claim 1, characterized in that In step 4), the characteristic index α is estimated by substituting the scale parameter γ and the second characteristic function point ω0 into formula (2) to obtain the estimated value of the characteristic index α, which is: in:

7. The method for estimating statistical characteristic parameters of ice source noise sound pressure according to claim 1, characterized in that In step 6), the estimation of the position parameter δ is carried out in the following steps: Substituting ω = 1 and ω = ω0 into the imaginary part of Equation (7), we obtain the estimated value of the location parameter δ:

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