Sea clutter feature description method and parameter correction method thereof

Abstract

The present application relates to a kind of sea clutter characteristic description method and its parameter correction method, by proposing the description function of multiple characteristics of sea clutter, and the parameter in description function is corrected, the purpose that can be described the characteristics of sea clutter using small amount of parameter information is realized, to reduce the storage cost of sea clutter.First, by amplitude distribution description function, time correlation description function, space correlation description function to represent the actual characteristics of sea clutter;Then, utilize the improved Adam algorithm to correct the parameters in these functions, realize the accurate description of sea clutter characteristics;Finally, by small amount of parameter information, the characteristics of actual sea clutter can be represented, and the storage cost of sea clutter is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar digital signal processing, in particular to a sea clutter feature description method and a parameter correction method thereof. BACKGROUND

[0002] The target detection of a guidance detection radar in a sea scene is greatly affected by sea clutter. Influenced by waves, sea winds, tides and other factors, it is difficult to accurately model the sea clutter, and a large amount of sea clutter measured data needs to be statistically analyzed to obtain the accurate features of the sea clutter. However, the amount of sea clutter measured data is huge, occupying a large amount of storage space, and if the newly collected sea clutter data cannot be processed in time, important information may be lost during storage, causing serious waste of resources. Therefore, there is an urgent need for a solution that can effectively record the features of the sea clutter and save storage costs.

[0003] The features of the sea clutter mainly include amplitude distribution and correlation characteristics. Early sea clutter amplitude distribution, such as Rayleigh distribution, lognormal distribution and Weibull distribution, only describes the mathematical statistical characteristics of the sea clutter, mainly applicable to single-pulse detection with low radar resolution, the structure is relatively simple, and the physical mechanism is not considered, such as patent CN201410487752.5 "Radar sea clutter adaptive suppression processing method based on parameter selection", patent CN201710206425.1 "Estimation method of quantile point of sea clutter amplitude lognormal distribution parameters". Then, a more accurate composite Gaussian distribution model is proposed to describe the sea clutter, including K distribution amplitude with texture obeying Gamma distribution, generalized Pareto distribution with texture obeying inverse Gamma distribution, and IG-CG distribution with texture obeying inverse Gaussian distribution, such as patent CN201610536574.X "Parameter estimation range expansion method of sea clutter Pareto distribution model", patent CN201810360487.2 "Simulation method of high-resolution sea clutter". The correlation characteristics of the sea clutter include time correlation and spatial correlation, and the time correlation of the sea clutter can be used to reflect the fluctuation characteristics of the clutter. The clutter power spectrum is usually used to describe it, such as patent CN202110668819.5 "Sea clutter parameter estimation method, system, device and storage medium". The spatial correlation of the sea clutter reflects the correlation characteristics between the clutters in adjacent distance units, which is generally described by an exponential decay model, such as patent CN201410523229.3 "Simulation method and system of radar sea clutter". The radar echo has I (in-phase component) and Q (quadrature component) two channels, which are expressed in complex form. The existing literature mostly uses the absolute value method of complex numbers to calculate the correlation characteristics of the sea clutter, and few models use complex form to describe the correlation characteristics of the sea clutter, ignoring the internal phase characteristics of the signal.

[0004] At present, the description function of sea clutter time correlation and space correlation mainly adopts expert experience to set model parameters, which is difficult to adapt to the accurate description of sea clutter correlation characteristics under complex sea conditions. In the parameter determination of the sea clutter amplitude distribution model, the method of moment (MOM) and the iterative maximum likelihood (IML) method are mainly used. When dealing with sea clutter data with heavy tail phenomenon, these methods are often sensitive to abnormal samples and difficult to ensure the accuracy of parameter estimation of the amplitude distribution model. Therefore, there is a lack of a parameter correction method that can adapt to various characteristic description functions of sea clutter. SUMMARY

[0005] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a sea clutter characteristic description method and a parameter correction method. The method represents the actual characteristics of sea clutter through the amplitude distribution target function, the time correlation target function and the space correlation target function, and uses the improved Adam algorithm to correct the parameters in these functions to realize accurate description of the characteristics of sea clutter. Finally, the characteristics of actual sea clutter can be represented by a small amount of parameter information, reducing the storage cost of sea clutter.

[0006] The technical scheme adopted by the present application to achieve the above technical purpose is: a sea clutter characteristic description method, which is composed of an amplitude distribution target function for describing the amplitude distribution of sea clutter, a time correlation target function for describing the time correlation of sea clutter and a space correlation target function for describing the space correlation of sea clutter. The formula of the amplitude distribution target function is:

[0007]

[0008] In the formula, v represents the shape parameter of the sea clutter amplitude distribution, b represents the scale parameter of the sea clutter amplitude distribution, H is the sequence length of the sampling sequence of sea clutter echoes, i represents the i-th sea clutter amplitude in the H sea clutter amplitudes, and the amplitude of sea clutter satisfies z1<z2<…<z N ;f g (z i ) represents the measured probability density when the amplitude of sea clutter is z i ; f1(z i ; v, b) represents the amplitude distribution probability density function obtained according to the CG-IG distribution when the amplitude of sea clutter is z i .

[0009] The formula of the time correlation target function is:

[0010]

[0011] where m is the number of time interval, M is the number of samples, f2(m; σ time ,ω d ) is the time correlation function of sea clutter, R t (m) is the time correlation function of samples.

[0012] The formula of the space correlation target function is:

[0013]

[0014] where n is the number of distance unit, N is the number of samples, f3(n; σ space ) is the space correlation function of sea clutter, R s (n) is the measured probability density.

[0015] As an optimization scheme of the above sea clutter characteristic description method, the expression of f1(z i ; v, b) is:

[0016]

[0017] where F is an operation substitute symbol.

[0018] As another optimization scheme of the above sea clutter characteristic description method, the expression of the time correlation function f2(m; σ time ,ω d ) of sea clutter is:

[0019] f2(m; σ time ,ω d ) = exp(-σ time m + jω d m)

[0020] where σ time is a parameter for determining the strength of time correlation, exp is the base of natural logarithm, ω d is a parameter for determining the periodicity of the correlation function, and its value is [0, 2π], which is related to the central Doppler shift of the clutter; m represents the number of time interval of radar pulses.

[0021] As another optimization scheme of the above sea clutter characteristic description method, the expression of the time correlation function R t (m) of samples is:

[0022]

[0023] In the formula, n is the number of interval distance units, N represents the number of distance units in the sample, m is the number of interval pulses, M represents the number of pulses in the sample, ii represents the ii-th pulse, and x n (ii) represents the nth distance unit x n The intensity in the echo of the iith pulse.

[0024] As another optimization scheme for the above-mentioned sea clutter characteristic description method, the spatial correlation description function of the sea clutter is f3(n; σ). space The expression for ) is:

[0025] f3(n;σ space )=exp(-(σ space gn) 2 )

[0026] In the formula, σ space The parameter that determines the strength of spatial correlation is n, which represents the distance interval.

[0027] As another optimization scheme for the above-mentioned sea clutter characteristic description method, the measured probability density R s The expression for (n) is:

[0028]

[0029] In the formula, m is the number of interval pulses, M represents the number of pulses in the sample, n is the number of interval distance units, N represents the number of distance units in the sample, jj represents the jj-th distance unit, and y m (jj) represents a certain pulse y m The intensity at the jj-th distance unit.

[0030] The parameter correction method in the above-mentioned sea clutter characteristic description method uses the improved Adam algorithm to find the minimum value of the parameters in the amplitude distribution objective function, the time correlation objective function and the spatial correlation objective function respectively, so as to obtain the optimal value of the parameters in each objective function;

[0031] The rules for the improved Adam algorithm are as follows:

[0032]

[0033] Among them, X t =[x t-1 ,x t-2 ,…x t-k …,x t-K [] represents the vector consisting of the parameters that need to be corrected in the t-th iteration; x t-k Let g be the k-th parameter that needs to be corrected in the t-th iteration; ▽f(g) is the formula for calculating the gradient; g tis the gradient vector in the tth iteration; g t-k is the gradient vector g t is the kth element in is the gradient vector g t is the normalized vector; η is the learning rate; t and t+1 represent the tth and (t+1)th iterations, respectively; β1 and β2 are the decay rates of the estimated first and second moments, which are 0.9 and 0.999, respectively, and are used for bias correction, respectively, and represent the tth power of β1 and β2; is a constant to avoid division by zero, which is 10 -8 .

[0034] As an optimization scheme of the above-mentioned parameter correction method in the sea clutter characteristic description method, when the improved Adam algorithm is used to minimize the amplitude distribution target function, x t =[v t ,b t ] is a vector composed of the shape parameter v and the scale parameter b in the tth iteration which need to be corrected, and the initial parameter value of the improved Adam algorithm is obtained by moment estimation to obtain the estimated value (v1, b1) of the shape parameter and the scale parameter of the CG-IG distribution.

[0035] As another optimization scheme of the above-mentioned parameter correction method in the sea clutter characteristic description method, when the improved Adam algorithm is used to minimize the time correlation target function, x t =[σ time ,ω d ] is a vector composed of σ time and ω d in the tth iteration which need to be corrected, and the initial parameter value of the improved Adam algorithm is 0.

[0036] As another optimization scheme of the above-mentioned parameter correction method in the sea clutter characteristic description method, when the improved Adam algorithm is used to minimize the spatial correlation target function, since only one parameter σ space_t needs to be evaluated, the normalized gradient fails, and the improved Adam algorithm will degenerate into the Adam algorithm, x t =[σ space_t ] is a vector composed of the parameter σ space_t in the tth iteration which need to be corrected in the spatial correlation target function, and the initial value is 0.

[0037] The method of the application mainly determines the parameter values in various characteristic description functions of sea clutter by solving the sea clutter amplitude distribution target function, the sea clutter time correlation target function and the sea clutter spatial correlation target function.

[0038] Compared with the prior art, the present application has the following beneficial effects:

[0039] 1) The present application provides a sea clutter feature description method, which characterizes the actual features of sea clutter through amplitude distribution objective function, time correlation objective function and space correlation objective function, and then uses the improved Adam algorithm to correct the parameters in the objective function, so as to realize accurate description of the features of sea clutter. Finally, the features of actual sea clutter can be represented by a small amount of parameter information, reducing the storage cost of sea clutter;

[0040] 2) Compared with the traditional method of using power spectrum to describe time correlation, the present application uses a complex form of time correlation objective function, which can more accurately describe the time correlation features of radar signals, and has the advantages of fewer parameters, better fitting effect, higher efficiency and better compliance with the actual form of radar signals (radar signals are often described in complex form), and simulation examples verify that the function has good fitting effect;

[0041] 3) Compared with the traditional method of using exponential function to describe space correlation, the space correlation objective function proposed by the present application can more accurately describe the space correlation features of radar signals, and has the advantages of fewer parameters, better fitting effect and higher efficiency, and simulation examples verify that the present application has good fitting effect;

[0042] 4) Since the partial derivative values of different parameters in the objective function in the solution space are not fixed, and even the partial derivative values are abnormally large or small, the existing Adam algorithm has the problem of inconsistent and unstable gradient scale in the update step, in order to solve this problem, the present application proposes an improved Adam algorithm, which normalizes the partial derivative values by dividing the partial derivative values of each parameter by the square root of all parameters, which reduces the difference in parameter updating and ensures that all parameters are updated with consistent scale. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 Comparison chart of amplitude distribution description function in comparative experiment;

[0044] Figure 2 Comparison chart of time correlation description function in comparative experiment;

[0045] Figure 3 Comparison chart of space correlation description function in comparative experiment. DETAILED DESCRIPTION

[0046] The present application will be further described in connection with specific embodiments. The parts not described in the present application are known or should be known to those skilled in the art or are prior art.

[0047] Embodiment 1

[0048] A sea clutter characteristic description method, which is composed of an amplitude distribution objective function describing sea clutter amplitude distribution, a time correlation objective function describing sea clutter time correlation and a space correlation objective function describing sea clutter space correlation, the formula of the amplitude distribution objective function is:

[0049]

[0050] In the formula, v represents a shape parameter of sea clutter amplitude distribution, b represents a scale parameter of sea clutter amplitude distribution, H is the sequence length of a sampling sequence of sea clutter echo, i represents the i-th sea clutter amplitude in H sea clutter amplitudes, the amplitudes of sea clutter satisfy z1<z2<…<z N ;f g (z i ) represents the measured probability density when the amplitude of sea clutter is z i ; f1(z i ; v, b) represents the amplitude distribution probability density function obtained according to the CG-IG distribution when the amplitude of sea clutter is z i ;

[0051] The expression of f1(z i ; v, b) is:

[0052]

[0053] In the formula, F is an operation substitution symbol;

[0054] The formula of the time correlation objective function is:

[0055]

[0056] In the formula, m is the number of interval pulses, M represents the number of pulse samples, f2(m; σ time , ω d ) is a time correlation description function of sea clutter, R t (m) is a time correlation function of samples;

[0057] The expression of the time correlation description function f2(m; σ time , ω d ) is:

[0058] f2(m; σ time , ω d ) = exp(-σtime m+jω d m)

[0059] where σ time is a parameter determining the strength of the time correlation, exp is the base of natural logarithm, ω d is a parameter determining the periodicity of the correlation function, and its value is in the range of [0, 2π], which is related to the Doppler shift of the clutter center; m represents the number of time intervals of the radar pulse.

[0060] The expression of the time correlation function R t (m) is:

[0061]

[0062] where n is the number of interval distance units, N represents the number of distance units of the sample, m is the number of interval pulses, M represents the number of pulses of the sample, ii represents the ith pulse, x n (ii) represents the intensity in the echo of the ith pulse in the nth distance unit; n

[0063] The formula of the spatial correlation target function is:

[0064]

[0065] where n is the number of interval distance units, N represents the number of distance units of the sample, f3(n; σ space ) is the spatial correlation description function of the sea clutter, R s (n) is the measured probability density;

[0066] The expression of the spatial correlation description function f3(n; σ space ) is:

[0067] f3(n; σ space ) = exp(-(σ space gn) 2 )

[0068] where σ space is a parameter determining the strength of the spatial correlation, and n represents the distance interval number;

[0069] The expression of the measured probability density R s (n) is:

[0070]

[0071] where m is the number of interval pulses, M represents the number of pulses of the sample, n is the number of interval distance units, N represents the number of distance units of the sample, jj represents the jth distance unit, and y​m (jj) represents a certain pulse y m Intensity on the jjth distance cell.

[0072] Example 2

[0073] The parameter modification method in the sea clutter feature description method of Example 1 uses the improved Adam algorithm to find the minimum value of the parameters in the amplitude distribution objective function, the time correlation objective function and the spatial correlation objective function, respectively, so as to obtain the optimal value of the parameters in each objective function.

[0074] The rules of the improved Adam algorithm are as follows:

[0075]

[0076] Where X t =[x t-1 ,x t-2 ,…x t-k …,x t-K ] represents a vector composed of parameters to be modified in the tth iteration; x t-k is the kth parameter to be modified in the tth iteration;▽f(g) is the formula for calculating the gradient; g t is the gradient vector in the tth iteration; g t-k is the kth element in the gradient vector g t ; is the normalized vector of the gradient vector g t ; η is the learning rate; t and t+1 represent the tth and (t+1)th iterations, respectively; β1 and β2 are the decay rates of the estimated first and second moments, taking values of 0.9 and 0.999, and respectively, which are used for bias correction, representing the tth power of β1 and β2; is a constant to avoid division by zero, taking a value of 10 -8 .

[0077] When the improved Adam algorithm is used to find the minimum value of the amplitude distribution objective function, the specific operation rules are as follows:

[0078]

[0079] At this time, x t =[v t ,b t ] is a vector composed of the shape parameter v and the scale parameter b to be modified in the tth iteration, and the initial parameter value of the improved Adam algorithm is the estimated value of the shape parameter and the scale parameter of the CG-IG distribution obtained by moment estimation (v1, b1);

[0080] When using the improved Adam algorithm to minimize the time-dependent objective function, the specific calculation rules are as follows:

[0081]

[0082]

[0083] At this time, x t ′=[σ time ,ω d ] represents the σ in the time-dependent function that needs to be corrected in the t-th iteration. time and ω d The vector is composed of two parameters, both of which are initially set to 0 in the improved Adam algorithm.

[0084] When using the improved Adam algorithm to minimize the spatial correlation objective function, since only one parameter σ needs to be adjusted... space_t Therefore, the normalized gradient fails, and the improved Adam algorithm degenerates into the original Adam algorithm, with the specific computational rules as follows:

[0085]

[0086] At this time, σ space_t is the parameter that determines the strength of spatial correlation in the spatial correlation objective function that needs to be corrected in the t-th iteration, and its initial value is 0.

[0087] To verify the present invention, the following comparative experiments were conducted:

[0088] The data used were echo data of LFM transmitted signals from the data file "20210106155330_01_staring" in the first phase of 2020 of the "Radar Observation Data Sharing Program (SDRDSP)". A 500×500 matrix was extracted as a sample (the matrix ranges from 2001 to 2500 in the time dimension and from 2001 to 2500 in the range dimension). The number of data extracted for both the time correlation function and the spatial correlation function was 40 (m=40, n=40).

[0089] The parameters in the amplitude distribution description function, time correlation description function, and spatial correlation description function of this invention are corrected using the parameter correction method of this invention. The three corrected functions are then compared with the three description functions obtained by existing methods and the curves of measured sea clutter data. The comparison results are shown in the appendix. Figure 1 Appendix Figure 2 and attached Figure 3 ;

[0090] Appendix Figure 1The three curves shown are the amplitude distribution description function after correction by the parameter correction method of the present invention, the amplitude distribution description function obtained by the existing moment estimation method, and the measured sea clutter amplitude distribution, respectively. As can be seen from the figure, the parameter correction method of the present invention can effectively correct the parameters in the CG-IG distribution, improve the fitting effect of the CG-IG distribution to the sea clutter amplitude distribution, and the CG-IG distribution after correction by the present invention has a better fitting effect than the traditional moment estimation method.

[0091] Appendix Figure 2 The three types of curves shown are the time correlation description function after correction by the parameter correction method of the present invention, the time correlation description function corresponding to the existing Gaussian power spectrum after correction by the parameter correction method of the present invention, and the time correlation function of the measured sea clutter.

[0092] The source of the time correlation describing function corresponding to the existing Gaussian power spectrum is:

[0093] The time correlation of sea clutter is commonly described by the power spectrum, with the Gaussian power spectrum being the most prevalent. Taking the inverse Fourier transform of the power spectrum yields the time correlation function of sea clutter. The time correlation function obtained by taking the Fourier transform of the Gaussian power spectrum can then be simplified as follows:

[0094] f2′(m;σ t ′ ime ,ω d ′)=exp(-σ t ′ ime m 2 +jω d ′m)

[0095] Where, σ t ′ ime ω′ is the parameter in the describing function that determines the strength of the time correlation. d The parameter in this describing function determines the periodicity of the related function; m represents the number of time intervals.

[0096] The parameter correction method of this invention is used to correct the parameters in the function, and its curve is... Figure 2 The time correlation describing function corresponding to the corrected Gaussian power spectrum;

[0097] from Figure 2 As can be seen, the time correlation description function of the present invention can more accurately describe the time correlation characteristics of radar signals and has a better fitting effect compared with the traditional power spectrum method.

[0098] Appendix Figure 3Three types of curves shown in the figure are the spatial correlation description function after correction by the parameter correction method of the application, the spatial correlation function in the form of existing exponential decay after correction by the parameter correction method of the application and the spatial correlation function of the actually measured sea clutter;

[0099] The spatial correlation function in the form of existing exponential decay is from:

[0100] The spatial correlation of sea clutter is generally described by an exponential decay model, and the spatial correlation function in the form of existing exponential decay model is as follows:

[0101] f3'(n;σ s ′ pace )=exp(-σ s ′ pace gn)

[0102] Wherein, σ s ′ pace The parameter in the description function that determines the strength of spatial correlation is n, which represents the distance interval number;

[0103] The parameter in the function is corrected by the parameter correction method of the application, and the curve is the spatial correlation function in the form of corrected exponential decay in Figure 3

[0104] As can be seen from Figure 3 , the spatial correlation description function of the application can more accurately describe the spatial correlation characteristics of the radar signal, and has a better fitting effect than the traditional exponential decay model.​

Claims

1. A sea clutter characterization method, the characterization method consisting of an amplitude distribution objective function describing an amplitude distribution of the sea clutter, a time correlation objective function describing a time correlation of the sea clutter, and a spatial correlation objective function describing a spatial correlation of the sea clutter, characterized in that: A formula of the amplitude distribution target function is: In the formula, v represents a shape parameter of the sea clutter amplitude distribution, b represents a scale parameter of the sea clutter amplitude distribution, H is a sequence length of a sampling sequence of sea clutter echo, i represents an i-th sea clutter amplitude in H sea clutter amplitudes, the sea clutter amplitudes satisfy z1 N ; g (z i ) represents a measured probability density when the sea clutter amplitude is z i ; f1(z i ; v, b) represents a probability density function of the amplitude distribution obtained according to the CG-IG distribution when the sea clutter amplitude is z i ; A formula of the time correlation target function is: where m is the number of the interval pulse, M represents the number of pulses of the sample, f2(m;σ time ,ω d ) is the time correlation function of the sea clutter, R t (m) is the time correlation function of the sample; The time dependence of the sea clutter is described by the expression of the function f2(m;σ time ,ω d ) f2(m; σ time , ω d ) = exp(-σ time m + jω d m); where σ time is a parameter determining the strength of the time correlation, which takes values in [0, 1], exp is the base of the natural logarithm, ω d is a parameter determining the periodicity of the correlation function, which takes values in [0, 2π] and is related to the Doppler shift of the clutter center; m is the number of the interval pulses; The time correlation function R of the sample t The expression of (m) is where n is the number of range bins, N represents the number of range bins of the sample, m is the number of pulses, M represents the number of pulses of the sample, ii represents the ith pulse, x n (ii) represents the nth range bin x n the intensity in the echo of the ith pulse. A formula of the space correlation target function is: where n is the number of interval units, N represents the number of interval units of the sample, f3(n;σ space ) is a spatial correlation description function of the sea clutter, and R s (n) is a spatial correlation function of the sample. The spatial correlation of the sea clutter is described by the function f3(n;σ space The expression of the function f3(n;σ f3(n; σ space ) = exp(-(σ space ·n) 2 ); where σ space is a parameter that determines the strength of spatial correlation, and n represents the number of distance intervals. The spatial correlation function R of the sample s The expression of (n) is: where m is the number of the interval pulses, M represents the number of pulses of the sample, n is the number of the interval distance units, N represents the number of distance units of the sample, jj represents the jjth distance unit, y m (jj) represents the intensity on the jjth distance unit of the jth pulse y m distance unit.

2. A sea clutter characterization method as claimed in claim 1, characterized in that: The f1(z i The expression of v, b) is: In the formula, F is an operation substitute symbol.

3. The method of claim 1 or 2, wherein the method of correction of parameters in the sea scatter feature description method is characterized by: An improved Adam algorithm is used to find minimum values of parameters in the amplitude distribution target function, the time correlation target function and the space correlation target function, so as to obtain optimal values of the parameters in the target functions; Rules of the improved Adam algorithm are as follows: where X t = [x t-1 , x t-2 ,..., x t-k ,..., x t-K ] represents a vector composed of parameters to be corrected in the tth iteration; x t-k is the kth parameter to be corrected in the tth iteration; is a formula for calculating a gradient; g t is a gradient vector in the tth iteration; g t-k is the kth element of the gradient vector g t in the tth iteration; is a normalized vector of the gradient vector g t ; η is a learning rate; t and t+1 represent the tth and (t+1)th iterations, respectively; β1 and β2 are decay rates for estimating a first moment and a second moment, and take values of 0.9 and 0.999, respectively, and are used for bias correction, and represent powers of β1 and β2, respectively; ∈ is a constant for avoiding division by zero, and takes a value of 10 -8 .

4. The method of claim 3, wherein the parameters are modified according to the sea state. When the improved Adam algorithm is used to minimize the amplitude distribution objective function, x t = [v t , b t ] is a vector composed of the shape parameter v and the scale parameter b to be corrected in the tth iteration, and the initial parameter value of the improved Adam algorithm is the estimate (v1, b1) of the shape parameter and the scale parameter of the CG-IG distribution obtained by the matrix estimation.

5. The method of claim 3, wherein the parameters are modified according to the sea state. X t = [σ time , ω d ] is a vector composed of σ time and ω d in the time-dependent function to be corrected in the tth iteration, and the initial parameter values of the two parameters in the improved Adam algorithm are both 0.

6. The method of claim 3, wherein the parameters are modified according to the sea state. When the improved Adam algorithm is used to minimize the spatial correlation objective function, since only one parameter σ space_t needs to be evaluated, the normalized gradient fails, at this time, X t = [σ space_t ] is the parameter σ space_t in the spatial correlation objective function that needs to be corrected in the tth iteration, and its initial value is 0.

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