An Optimal Selection Method for Statistical Distribution Models of Sea Clutter Simulation for CFAR Detection

Abstract

The present invention discloses a method for optimizing a statistical distribution model of sea clutter simulation for CFAR detection, belonging to the technical field of sea clutter simulation, and specifically including the following steps: S1, select measured sea clutter data and estimate the parameters of the statistical distribution model; S2, adopt the integral goodness-of-fit test, calculate the integral goodness-of-fit test statistic of each statistical distribution model, and optimize the statistical distribution model that best fits the selected data according to the decision criterion; S3, calculate the spatial and temporal correlation lengths of the intensity of the selected data and generate a two-dimensional autocorrelation matrix; S4, adopt the memory nonlinear transformation method to simulate and generate a spatio-temporally correlated sea clutter sequence driven by the measured statistical parametric model for training the CFAR detector. The present invention adopts the above method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection, optimizes the statistical distribution model with a detection threshold slightly higher than the measured data, and is used to generate a spatio-temporally correlated sea clutter sequence, improving the accuracy and robustness of the CFAR detector.

Description

Technical Field

[0001] The present invention relates to the technical field of sea clutter simulation, and in particular to a method for optimizing a statistical distribution model of sea clutter simulation for CFAR detection. Background Art

[0002] The electromagnetic wave emitted by the radar is reflected and refracted by the sea surface and the target and then captured by the radar receiver again, obtaining the echo signal jointly generated by the target and the sea surface. At this time, the echo signal generated by the sea surface is an interference signal to the target echo, generally referred to as sea clutter. Statistically, sea clutter has the characteristics of non-uniformity, non-stationarity, and non-Gaussianity, and it is difficult to describe with a simple mathematical and physical model. In order to detect whether there is a sea surface target in the scene under the interference of strong sea clutter, a large number of non-coherent, coherent, and feature detectors have been designed and applied. The CFAR detector is a widely used non-coherent detector, which mainly constructs a detection threshold based on the difference between the target echo and the sea clutter in the intensity domain and combines the intensity statistical distribution characteristics of the sea clutter to realize the detection of sea surface targets. In order to train and test the performance of the CFAR detector, conducting sea clutter measurement experiments including cooperative targets is an efficient, accurate, and widely used research method. However, due to the limited amount of sea clutter data measured by the radar, it is often necessary to generate more spatio-temporally correlated sea clutter intensity sequences based on the measured data for training and testing.

[0003] The statistical distribution characteristics of sea clutter intensity vary significantly under different radar and environmental parameters. Therefore, it is very necessary to select the distribution that best fits the measured data under different measurement conditions. Only when the statistical distribution model accurately fits the probability density function (PDF) of the measured sea clutter, especially in the tail region, can the simulation data generated by it be used for the performance evaluation of CFAR detectors.The goodness-of-fit (GoF) test is a relatively general method for selecting an optimal statistical distribution model. However, for GoF test statistics defined based on distance or square, such as the root mean square error (see reference [1] Xue J, Xu S, Liu J, et al. Model for non-Gaussian sea clutter amplitudes using generalized inverse Gaussian texture [J]. IEEE Geoscience and Remote Sensing Letters, 2018, 16(6): 892-896.), the chi-square test statistic (see reference [2] Huang P, Zou Z, Xia X G, et al. A statistical model based on modified generalized-K distribution for sea clutter [J]. IEEE Geoscience and Remote Sensing Letters, 2021, 19: 1-5.), the modified chi-square test statistic (see reference [3] Antipov I. Statistical analysis of northern Australian coastline sea clutter data [R]. Technical Report DSTO-TR-1236, 2001.), the Bhattacharyya distance (see reference [4] Angelliaume S, Rosenberg L, Ritchie M. Modeling the amplitude distribution of radar sea clutter [J]. Remote Sensing, 2019, 11(3): 319.), and the Kolmogorov-Smirnov distance (see reference [5] Massey Jr F J. The Kolmogorov-Smirnov test for goodness of fit [J]. Journal of the American statistical Association, 1951, 46(253): 68-78.), their results are positive in any case and cannot characterize the magnitude relationship between the detection thresholds of different statistical distribution models and the measured results under the same false alarm rate (FAR).When the detection threshold of the statistical distribution model is lower than the measured data, the performance of the CFAR detector will decrease significantly; on the other hand, if the detection threshold of the statistical distribution model is greater than the measured result, its impact on the performance of the CFAR detector is relatively small. Summary of the Invention

[0004] The object of the present invention is to provide a method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection, aiming at the sea clutter simulation for CFAR detection, to select a statistical distribution model that best fits the tail region of the complementary cumulative distribution function of the measured data and has a detection threshold slightly greater than the measured result, and use this statistical distribution model to generate a spatio-temporally correlated sea clutter sequence for training the CFAR detector, aiming to improve the accuracy and robustness of the CFAR detector.

[0005] To achieve the above object, the present invention provides a method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection, including the following steps:

[0006] S1. Select the measured sea clutter data and estimate the parameters of Weibull, lognormal, K, Pareto and other statistical distribution models;

[0007] S2. Adopt the integral goodness-of-fit (IGoF) test, calculate the IGoF test statistic of each statistical distribution model at a set false alarm rate (FAR) respectively, and select the statistical distribution model that fits the measured data well under this environment and radar conditions according to the decision criterion;

[0008] S3. Calculate the spatial and temporal correlation lengths of the sea clutter intensity of the selected measured data, and generate a two-dimensional intensity autocorrelation matrix according to the set simulation parameters;

[0009] S4. Adopt the memory nonlinear transformation method (MNLT) to simulate and generate a spatio-temporally correlated sea clutter sequence driven by the measured statistical parametric model for training the CFAR (constant false alarm rate) detector.

[0010] Preferably, the parameter estimation of the statistical distribution model in step S1 is specifically:

[0011] Select the actually measured sea clutter data and read the following measurement parameters:

[0012] The number of distance sampling points P of the measurement data;

[0013] The number of pulses Q of the measurement data;

[0014] The pulse repetition frequency (PRF) of the measurement radar The unit is Hz;

[0015] The analog / digital (A / D) sampling rate of the measurement radar The unit is Hz;

[0016] Measure the grazing angle of the radar The unit is degree (°);

[0017] Measure the bandwidth B of the radar transmitted signal, and the unit is Hz;

[0018] Measure the polarization mode of the radar;

[0019] Measure the meteorological and hydrological data such as sea state level, wind speed, wind direction, significant wave height (SWH), wave direction, etc. during measurement.

[0020] Preferably, determine the selection range of the optimal statistical distribution model. Without loss of generality, the present invention uses Weibull and lognormal distributions as representatives of non-Gaussian statistical distribution models, and K and Pareto distributions as representatives of dual-scale models based on texture and speckle components;

[0021] The probability density function (PDF) of the Weibull distribution model is

[0022]

[0023] where z is the sea clutter intensity; β and α are the shape and scale parameters of the Weibull distribution model respectively;

[0024] Its cumulative distribution function (CDF) is

[0025]

[0026] The parameter estimation formulas of the Weibull distribution are respectively

[0027]

[0028] where E[·] represents the mathematical expectation of the variable; Z is the observed random variable of the sea clutter intensity;

[0029] The PDF of the lognormal distribution model is

[0030]

[0031] where s and σ m are the variance and median of ln(z) following a normal distribution respectively;

[0032] Its CDF is

[0033]

[0034] where erf(·) is the error function, and its expression is

[0035]

[0036] The parameters of the lognormal distribution are estimated by the second moment method, and the estimation formulas are respectively

[0037]

[0038] The PDF of the K-distribution model is

[0039]

[0040] where K v-1 (·) is the modified Bessel function of the second kind of order v - 1; Γ(·) is the gamma function; v and b are the shape and scale parameters of the K-distribution respectively;

[0041] Its CDF is

[0042]

[0043] The parameter estimation formulas of the K-distribution are respectively

[0044]

[0045] The PDF of the Pareto distribution model is

[0046]

[0047] where a and b are the shape and scale parameters of the Pareto distribution model respectively;

[0048] Its CDF is

[0049]

[0050] The estimation formulas of the parameters of the Pareto distribution model are respectively

[0051]

[0052] Preferably, the integral goodness-of-fit test in step S2 is specifically as follows:

[0053] The complementary cumulative distribution function (CCDF) is defined as the difference between 1 and the CDF, that is, CCDF = 1 - CDF. When using the integral definition of the GoF test statistic, the integral interval should be the tail region where the intensity exceeds the detection threshold. Therefore, the definition of the IGoF test statistic is

[0054]

[0055] where F(x) is the cumulative distribution function of the statistical distribution model; 1 - F(x) represents the complementary cumulative distribution function of the statistical distribution model; is the cumulative distribution function of the measured data; represents the complementary cumulative distribution function of the measured data; represents the detection threshold of the measured data;

[0056] Equation (18) integrates the CCDF instead of the PDF to avoid the sharp oscillation of the PDF of the measurement data due to too small data volume, which will affect the integration result. It can be seen from Equation (18) that as the CCDF of the statistical distribution model fits closer and closer to the measurement result, the area of the region enclosed by the two becomes smaller accordingly, and the absolute value of the IGoF test statistic also becomes smaller. At the same FAR, if the detection threshold of the statistical distribution model is less than the result of the measurement data, then is less than F(x), and the IGoF test statistic is negative; on the other hand, if the detection threshold of the statistical distribution model is greater than the measured result, the IGoF test statistic is positive.

[0057] In summary, the criterion for determining the optimal distribution is the statistical distribution model with the smallest absolute value.

[0058] Preferably, the generation of the two-dimensional autocorrelation matrix in step S3 is specifically as follows:

[0059] For the measured sea clutter intensity data H, it is a P×Q order matrix, one dimension is the distance, that is, the fast time of the radar; the other dimension is the pulse, that is, the slow time of the radar; in the distance dimension, the ground distance interval between two adjacent distance units is

[0060]

[0061] where c is the propagation speed of electromagnetic waves in vacuum, is the analog / digital sampling rate of the measurement radar; is the grazing angle of the measurement radar;

[0062] The unnormalized spatial autocorrelation function in the distance dimension is

[0063]

[0064] where the superscript * represents the complex conjugate. For the intensity data, H * = H;

[0065] Normalize the spatial autocorrelation function so that the autocorrelation function value at zero lag is equal to 1, which is

[0066]

[0067] The spatial correlation length is defined as the distance when it is less than one over the natural logarithm for the first time in the interval of [0, P-1], and 1≤a≤P-1, there is

[0068]

[0069] The space-related length is

[0070] l r = a·Δr M (23)

[0071] In the pulse dimension, the time interval between two adjacent pulses is

[0072]

[0073] where is the pulse repetition frequency of the measurement radar;

[0074] The unnormalized time autocorrelation function in the pulse dimension is

[0075]

[0076] Normalize the time autocorrelation function so that the value of the autocorrelation function at zero lag is equal to 1, which is

[0077]

[0078] The time-related length is then defined as the distance at which it is first less than one over the natural logarithm within the interval [0, Q - 1], and 1 ≤ b ≤ Q - 1, there is

[0079]

[0080] The space-related length is

[0081] l t = b·Δt M (28)

[0082] According to the training requirements of the CFAR detector, the following simulation parameters are set:

[0083] Set the number of range samples M of the simulation data, and its value range is positive integers;

[0084] Set the number of pulses N of the simulation data, and its value range is positive integers;

[0085] Set the pulse repetition frequency (PRF) f of the radar of the simulation data p , whose unit is Hz and the value range is positive real numbers;

[0086] Set the A / D sampling rate F of the radar of the simulation data s , whose unit is Hz and the value range is positive real numbers;

[0087] Based on the above simulation parameters, let the spatio-temporal correlated sea clutter intensity sequence of the simulation be S, which is an M×N matrix;

[0088] In the range dimension, the ground range interval between two adjacent range cells of the simulation data is

[0089]

[0090] The spatial autocorrelation function of the simulated sea clutter intensity is modeled as an exponential decay function, which is

[0091]

[0092] In the pulse dimension, the time interval between two adjacent pulses of the simulation data is

[0093]

[0094] Without loss of generality, assuming that the sea clutter Doppler spectrum is exponential, the temporal autocorrelation function of the simulated sea clutter intensity is modeled as

[0095]

[0096] The two-dimensional autocorrelation matrix is constructed using equations (30) and (32), and equations (29) and (31) are substituted into it to discretize it. Then, the two-dimensional autocorrelation matrix of the simulated sea clutter is modeled as

[0097]

[0098] Preferably, the generation of the spatio-temporal correlated sea clutter sequence driven by the measured statistical parametric model in step S4 is specifically as follows:

[0099] Generate a set of two-dimensional standard normal distribution random variables X with an M×N order, a mean of 0, and a variance of 1;

[0100] The standard normal distribution random variable X is transformed by MNLT to obtain a non-Gaussian distribution variable Y with a CDF of F dist (Y). The relationship between X and Y satisfies the equation

[0101]

[0102] where erfc(·) represents the complementary error function, and its expression is

[0103] erfc(x) = 1 - erf(x) (35)

[0104] Define Q dist as the inverse function of the CCDF of the non-Gaussian distribution model with a CDF of F dist (Y), which is

[0105]

[0106] Then the nonlinear mapping relationship between the non-Gaussian distribution variable Y and the standard normal distribution random variable X is expressed as

[0107]

[0108] The autocorrelation characteristic of the non-Gaussian distribution variable Y is

[0109]

[0110] where R G (m,n) represents the two-dimensional autocorrelation matrix of the standard normal distribution random variable X; H i (·) represents the Hermite polynomial, and its expression is

[0111]

[0112] The two-dimensional autocorrelation matrix of the non-Gaussian distribution variable Y is then expressed as

[0113]

[0114] Then, the two-dimensional autocorrelation matrix R G of the standard normal distribution random variable X is calculated using Equation (40) and Equation (38). The standard normal distribution random variable X is filtered using the Fourier synthesis (FS) method to make its two-dimensional autocorrelation matrix be R. Finally, the non-Gaussian distribution variable Y with the two-dimensional autocorrelation matrix being R is obtained using the mapping relationship of Equation (37); the nonlinear mapping relationships for different distributions are as follows respectively:

[0115] If the Weibull distribution model is the optimal distribution, the mapping relationship of Equation (37) is

[0116]

[0117] If the lognormal distribution model is the optimal distribution, the mapping relationship of Equation (37) is

[0118]

[0119] If the K distribution model is the optimal distribution, the mapping relationship of Equation (37) is completed in two steps. First, the nonlinear mapping relationship between the texture component obeying the negative exponential distribution and the standard normal is

[0120]

[0121] Second, on the basis of generating the texture component, the two-dimensional autocorrelation matrix of the speckle component changes to

[0122]

[0123] When generating the speckle component that follows the gamma distribution, the gamma distribution cumulative distribution function corresponding to the standard normal distribution random variable X is

[0124]

[0125] When the cumulative distribution function of the gamma distribution and the shape parameter v are known, the Newton method is used to calculate the inverse function of the incomplete gamma function with respect to the integration range [0, Y gamma , which is

[0126]

[0127] Multiply Y gamma by Equation (43) to obtain the mapping relationship between the random variable that follows the K distribution and the standard normal distribution

[0128]

[0129] If the Pareto distribution model is the optimal distribution, the mapping relationship of Equation (37) is

[0130]

[0131] In summary, the IGoF is used to optimize the statistical distribution model that most accurately fits the CCDF tail region of the measured sea clutter data, and the spatio-temporal correlated sea clutter sequence is generated using this statistical distribution model for training the CFAR detector.

[0132] Therefore, the present invention adopts the above-mentioned method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection, and has the following beneficial effects:

[0133] (1) It solves the problem that when optimizing the statistical distribution model in the prior art, most of the GoF test statistics defined by distance or square are used, and their results are positive in any case, and cannot characterize the magnitude relationship between the detection thresholds of different statistical distribution models and the measured results under the same FAR. The present invention uses integral to quantitatively analyze the deviation degree between the CCDF tail region of the statistical distribution model and the measured sea clutter data. The absolute value of the IGoF test statistic reflects the goodness of fit of the distribution to the tail region of the measurement data, and its positive and negative nature characterizes the magnitude relationship between the distribution and the measurement detection threshold, and has the ability to optimize the tail region slightly stronger than the statistical distribution model of the measurement data;

[0134] (2) Using MNLT, a spatio-temporal correlated sea clutter sequence driven by the measured statistical parametric model is simulated and generated. It has a fast operation speed, high fidelity, and the ability to generate simulation data with arbitrary PRF and A / D sampling rates, and can be effectively used for the performance evaluation of the CFAR detector.

[0135] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0136] Figure 1 It is a flowchart of a method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection according to the present invention;

[0137] Figure 2 It is a one-dimensional high-resolution range profile (HRRP) of the measured sea clutter in the Ku band of the present invention varying with time;

[0138] Figure 3 It is the sea clutter intensity data of simple, normal and difficult samples generated based on the measured data according to the present invention; among them, (a) is a schematic diagram of the sea clutter sequence generated by using the Weibull distribution; (b) is a schematic diagram of the sea clutter sequence generated by using the lognormal distribution; (c) is a schematic diagram of the sea clutter sequence generated by using the K distribution; (d) is a schematic diagram of the sea clutter sequence generated by using the Pareto distribution;

[0139] Figure 4 It is the statistical distribution characteristics of the sea clutter intensity data generated according to the present invention;

[0140] Figure 5 It is the two-dimensional correlation characteristics of the sea clutter intensity data generated according to the present invention, where (a) is the measured data; (b) is the sea clutter sequence generated by using the Pareto distribution. Detailed Embodiments

[0141] Embodiment

[0142] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0143] As Figure 1 shown, a method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection, which can optimize a statistical distribution model whose complementary cumulative distribution function (CCDF) trailing region is slightly stronger than the measured data, and use this distribution model to generate a space-time correlated sea clutter sequence to train a CFAR detector, includes the following steps:

[0144] S1. Select the measured sea clutter data and estimate the parameters of the Weibull, lognormal, K, Pareto, and other statistical distribution models, specifically as follows:

[0145] Select the actually measured sea clutter data and read the following measurement parameters:

[0146] The number of range samples P of the measurement data;

[0147] The number of pulses Q of the measurement data;

[0148] Of the measurement radar The unit is Hz;

[0149] The analog / digital (A / D) sampling rate of the measurement radar The unit is Hz;

[0150] The grazing angle of the measurement radar The unit is degrees (°);

[0151] The bandwidth B of the signal transmitted by the measurement radar, the unit is Hz;

[0152] The polarization mode of the measurement radar;

[0153] Meteorological and hydrological data such as the sea state level, wind speed, wind direction, significant wave height (SWH), wave direction, etc. during the measurement.

[0154] Determine the selection range of the optimal statistical distribution model. Without loss of generality, the present invention uses the Weibull and log-normal distributions as representatives of non-Gaussian statistical distribution models, and the K and Pareto distributions as representatives of the two-scale models based on texture and speckle components;

[0155] The PDF of the Weibull distribution model is

[0156]

[0157] where z is the sea clutter intensity; β and α are the shape and scale parameters of the Weibull distribution model, respectively;

[0158] Its CDF is

[0159]

[0160] The parameter estimation formulas of the Weibull distribution are respectively

[0161]

[0162] where E[·] represents the mathematical expectation of the variable; Z is the observed sea clutter intensity random variable;

[0163] The PDF of the log-normal distribution model is

[0164]

[0165] where s and σm They are the variance and median of ln(z) following a normal distribution, respectively;

[0166] Its CDF is

[0167]

[0168] where erf(·) is the error function, and its expression is

[0169]

[0170] The parameters of the log-normal distribution are estimated by the second moment method, and the estimation formulas are respectively

[0171]

[0172] The PDF of the K-distribution model is

[0173]

[0174] where K v-1 (·) is the modified Bessel function of the second kind of order v - 1; Γ(·) is the gamma function; v and b are the shape and scale parameters of the K-distribution, respectively;

[0175] Its CDF is

[0176]

[0177] The parameter estimation formulas of the K-distribution are respectively

[0178]

[0179]

[0180] The PDF of the Pareto distribution model is

[0181]

[0182] where a and b are the shape and scale parameters of the Pareto distribution model, respectively;

[0183] Its CDF is

[0184]

[0185] The estimation formulas of the parameters of the Pareto distribution model are respectively

[0186]

[0187] S2. Conduct the IGoF test, calculate the IGoF test statistic for each statistical distribution model at the set FAR, and select the statistical distribution model that fits the measured data well under this environment and radar conditions according to the decision criterion. The IGoF test is specifically as follows:

[0188] The complementary cumulative distribution function (CCDF) is defined as the difference between 1 and the CDF, i.e., CCDF = 1 - CDF. When using the integral to define the GoF test statistic, the integral interval should be the tail region where the intensity exceeds the detection threshold. Therefore, the definition of the IGoF test statistic is

[0189]

[0190] where F(x) is the cumulative distribution function of the statistical distribution model; 1 - F(x) represents the complementary cumulative distribution function of the statistical distribution model; is the cumulative distribution function of the measured data; represents the complementary cumulative distribution function of the measured data; represents the detection threshold of the measured data;

[0191] Equation (18) integrates the CCDF rather than the PDF to avoid the sharp oscillation of the measured data PDF caused by too small data volume, which may affect the integration result. It can be seen from Equation (18) that as the CCDF of the statistical distribution model fits closer and closer to the measurement result, the area of the region enclosed by the two becomes smaller accordingly, and the absolute value of the IGoF test statistic also becomes smaller. At the same FAR, if the detection threshold of the statistical distribution model is less than the result of the measured data, then is less than F(x), and the IGoF test statistic is negative; on the other hand, if the detection threshold of the statistical distribution model is greater than the measured result, the IGoF test statistic is positive.

[0192] In summary, the decision criterion for the optimal distribution is the statistical distribution model with the smallest positive value.

[0193] S3. Calculate the spatial and temporal correlation lengths of the selected measured data of the sea clutter intensity, and generate a two-dimensional intensity autocorrelation matrix according to the set simulation parameters, specifically as follows:

[0194] For the measured sea clutter intensity data H, which is a matrix of order P×Q, one dimension is the distance, i.e., the fast time of the radar; the other dimension is the pulse, i.e., the slow time of the radar. In the distance dimension, the ground distance interval between two adjacent distance units is

[0195]

[0196] where c is the propagation speed of electromagnetic waves in vacuum, is the analog / digital sampling rate of the measuring radar; To measure the grazing angle of the radar;

[0197] The unnormalized spatial autocorrelation function in the distance dimension is

[0198]

[0199] where the superscript * represents complex conjugate, and for intensity data, H * = H;

[0200] Normalize the spatial autocorrelation function so that the autocorrelation function value at zero lag is equal to 1, which is

[0201]

[0202] The spatial correlation length is then defined as the distance at which it is first less than one over the natural logarithm within the interval [0, P - 1], and 1 ≤ a ≤ P - 1, there is

[0203]

[0204] Then the spatial correlation length is

[0205] l r = a·Δr M (23)

[0206] In the pulse dimension, the time interval between two adjacent pulses is

[0207]

[0208] where, is the pulse repetition frequency of the measurement radar;

[0209] The unnormalized temporal autocorrelation function in the pulse dimension is

[0210]

[0211] Normalize the temporal autocorrelation function so that the autocorrelation function value at zero lag is equal to 1, which is

[0212]

[0213] The temporal correlation length is then defined as the distance at which it is first less than one over the natural logarithm within the interval [0, Q - 1], and 1 ≤ b ≤ Q - 1, there is

[0214]

[0215] Then the spatial correlation length is

[0216] l t = b·Δt M (28)

[0217] According to the training requirements of the CFAR detector, the following simulation parameters are set:

[0218] Set the number of range samples M of the simulation data, and its value range is a positive integer;

[0219] Set the number of pulses N of the simulation data, and its value range is a positive integer;

[0220] Set the pulse repetition frequency (PRF) f of the radar of the simulation data p , whose unit is Hz, and the value range is a positive real number;

[0221] Set the A / D sampling rate F of the radar of the simulation data s , whose unit is Hz, and the value range is a positive real number;

[0222] Based on the above simulation parameters, let the spatio-temporal correlation sea clutter intensity sequence of the simulation be S, which is an M×N order matrix;

[0223] In the range dimension, the ground range interval between two adjacent range cells of the simulation data is

[0224]

[0225] The spatial autocorrelation function of the simulated sea clutter intensity is modeled as an exponential decay function, which is

[0226]

[0227] In the pulse dimension, the time interval between two adjacent pulses of the simulation data is

[0228]

[0229] Without loss of generality, assuming that the sea clutter Doppler spectrum is exponential, the temporal autocorrelation function of the simulated sea clutter intensity is modeled as

[0230]

[0231] Use Equation (30) and Equation (32) to construct a two-dimensional autocorrelation matrix, and substitute Equation (29) and Equation (31) into it to discretize it. Then the two-dimensional autocorrelation matrix of the simulated sea clutter is modeled as

[0232]

[0233] S4. Use MNLT to simulate and generate a spatio-temporal correlated sea clutter sequence driven by an empirically measured statistical parametric model for training the CFAR detector. The generation of the spatio-temporal correlated sea clutter sequence driven by the empirically measured statistical parametric model is as follows:

[0234] Generate a set of two-dimensional standard normal distribution random variables X of order M×N with a mean of 0 and a variance of 1;

[0235] The standard normal distribution random variable X passes through MNLT to obtain a non-Gaussian distribution variable Y with a CDF of F dist (Y), and the relationship between x and Y satisfies the relational expression

[0236]

[0237] where erfc(·) represents the complementary error function, and its expression is

[0238] erfc(x) = 1 - erf(x) (35)

[0239] Define Q dist as the inverse function of the CCDF of the non-Gaussian distribution model with a CDF of F dist (Y), which is

[0240]

[0241] Then the non-linear mapping relationship between the non-Gaussian distribution variable Y and the standard normal distribution random variable X is expressed as

[0242]

[0243] The autocorrelation characteristic of the non-Gaussian distribution variable Y is

[0244]

[0245] where R G (m,n) represents the two-dimensional autocorrelation matrix of the standard normal distribution random variable X; H i (·) represents the Hermite polynomial, and its expression is

[0246]

[0247] The two-dimensional autocorrelation matrix of the non-Gaussian distribution variable Y is then expressed as

[0248]

[0249] Then use Equation (40) and Equation (38) to calculate the two-dimensional autocorrelation matrix R of the standard normal distribution random variable X G, the Fourier synthesis (FS) method is used to filter the standard normal distribution random variable X so that its two-dimensional autocorrelation matrix is R. Finally, the mapping relationship of Equation (37) is used to obtain the non-Gaussian distribution variable Y with the two-dimensional autocorrelation matrix R. The non-linear mapping relationships for different distributions are as follows:

[0250] If the Weibull distribution model is the optimal distribution, the mapping relationship of Equation (37) is

[0251]

[0252] If the lognormal distribution model is the optimal distribution, the mapping relationship of Equation (37) is

[0253]

[0254] If the K-distribution model is the optimal distribution, the mapping relationship of Equation (37) is completed in two steps. First, the non-linear mapping relationship between the texture component obeying the negative exponential distribution and the standard normal is

[0255]

[0256] Secondly, on the basis of generating the texture component, the two-dimensional autocorrelation matrix of the speckle component changes to

[0257]

[0258] When generating the speckle component obeying the gamma distribution, the gamma distribution cumulative distribution function corresponding to the standard normal distribution random variable X is

[0259]

[0260] When the cumulative distribution function of the gamma distribution and the shape parameter v are known, the Newton method is used to calculate the inverse function of the incomplete gamma function with respect to the integration range [0, Y gamma , which is

[0261]

[0262] Multiply Y gamma by Equation (43) to obtain the mapping relationship between the random variable obeying the K-distribution and the standard normal distribution

[0263]

[0264] If the Pareto distribution model is the optimal distribution, the mapping relationship of Equation (37) is

[0265]

[0266] Figure 2The HRRP of the measured sea clutter in the Ku band varying with time. The number of range sampling points P is 21, and the number of pulses Q is 2001; the is 2000 Hz, and the A / D sampling rate is 500 MHz, the grazing angle is 70°, the signal bandwidth B is 400 MHz, and the polarization mode is VV polarization; the sea state level during measurement is 3, the average wind speed is 5.72 m / s, the wind direction is 146.51°, the average SWH is 0.64 m, and the wave direction is 81.40°.

[0267] Figure 3 is based on Figure 2 the measured data in, and the space-time correlated sea clutter sequences generated by the Weibull, log-normal, K, and Pareto distributions respectively using this method. The number of range sampling points M of the simulation data is 41, and the number of pulses N is 4001; the PRF f p of the simulation data radar is 4000 Hz, and the A / D sampling rate F s is 1000 MHz. In the process of estimating the statistical distribution model parameters in step S1, the estimated values of the shape parameter β and scale parameter α of the Weibull distribution are 0.983 and 0.971 respectively; the estimated values of the parameters σ m and s of the log-normal distribution are 0.684 and 0.891 respectively; the estimated values of the shape parameter v and scale parameter b of the K distribution are 9.480 and 9.320 respectively; the estimated values of the shape parameter a and scale parameter b of the Pareto distribution are 11.480 and 10.659 respectively. In the process of the IGoF test in step S2, the FAR is set to 0.01, and the IGoF test statistics of the Weibull, log-normal, K, and Pareto distributions are -7.333×10 -3 , 10.333×10 -3 , -3.779×10 -3 and 1.521×10 -3 respectively. In the process of generating the two-dimensional autocorrelation matrix in step S3, the spatial and temporal correlation lengths are 1.754 m and 2.5 ms respectively.

[0268] Figure 4 is Figure 3 the sea clutter data generated by using four different statistical distribution models in, and Figure 2 the statistical distribution characteristics of the intensity of the measured data in. The horizontal axis is the mean-normalized intensity, and the vertical axis is the CCDF, using logarithmic coordinates. Different dashed lines give the fitting results of the four distributions to the CCDF of the measured data, and different shaped markers give the CCDF of the simulated sea clutter sequences using the four distributions. From Figure 4It can be seen that the fitting effects on the measured data from good to bad are K, Pareto, Weibull, and lognormal distributions in turn, which also correspond to the absolute values of the IGoF test statistics. The smaller the absolute value, the better the goodness of fit. However, the CCDF tail regions of the sea clutter sequences simulated by the Weibull and K distributions are lower than the measured data, and their IGoF test statistics are correspondingly negative. When training the CFAR detector with the data generated by these two distributions, the requirements for the CFAR detector are relatively loose, with fewer strong scatter points, which easily leads to a decline in the performance of the CFAR detector. On the other hand, the CCDF tail regions of the sea clutter data generated by the lognormal and Pareto distributions are stronger than the actual measurement data, and their IGoF test statistics are correspondingly positive. During training, the data generated by these two distributions are more stringent for the CFAR detector, and it is easier to obtain excellent detection performance. Among them, the optimal selection results of the statistical distribution model based on the IGoF test statistics show that the spatio-temporal correlated sea clutter sequence simulated by the Pareto distribution exhibits the best training performance under the selected environment and radar parameters.

[0269] Figure 5 The sea clutter data generated by using the Pareto distribution and Figure 2 the two-dimensional autocorrelation function of the intensity of the measured data in []. The horizontal axis is the pulse dimension, and the vertical axis is the range dimension. From Figure 5 it can be seen that the correlation characteristics of the simulated and measured sea clutter intensities are basically the same.

[0270] Therefore, the present invention adopts the above-mentioned method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection. The IGoF test statistic is defined by integration, and the statistical distribution model with a CCDF tail region slightly stronger than the measured result is optimized. A spatio-temporal correlated sea clutter sequence driven by the measured statistical parametric model is generated for training the CFAR detector, providing data support for the training and testing of the sea surface target detector.

[0271] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing the statistical distribution model of sea clutter simulation for CFAR detection, characterized in that It includes the following steps: S1. Select measured sea clutter data and estimate the parameters of Weibull, log-normal, K-distribution, Pareto and other statistical distribution models; S2. Adopt the integral goodness-of-fit test, calculate the integral goodness-of-fit test statistic of each statistical distribution model under the set false alarm probability respectively, and select the statistical distribution model that best fits the measured data under the environmental and radar conditions according to the decision criterion; S3. Calculate the spatial and temporal correlation lengths of the sea clutter intensity of the selected measured data, and generate a two-dimensional autocorrelation matrix of the intensity according to the set simulation parameters; S4. Adopt the memory nonlinear transformation method to simulate and generate a spatio-temporal correlated sea clutter sequence driven by the measured statistical parametric model for training the CFAR detector; The integral goodness-of-fit test in step S2 is specifically as follows: The complementary cumulative distribution function is defined as the difference between 1 and the cumulative distribution function. When using the integral to define the test statistic, the integral interval should be the tail region where the intensity exceeds the detection threshold. Therefore, the definition of the integral goodness-of-fit test statistic is （18） Among them, is the cumulative distribution function of the statistical distribution model; represents the complementary cumulative distribution function of the statistical distribution model; is the cumulative distribution function of the measured data; represents the complementary cumulative distribution function of the measured data; represents the detection threshold of the measured data; The generation of the spatio-temporal correlated sea clutter sequence driven by the measured statistical parametric model in step S4 is specifically as follows: Generate a set of two-dimensional standard normal distribution random variables with a mean of 0 and a variance of 1 ; Standard normal distribution random variable The cumulative integral function obtained by the memory non-linear transformation method is Non-Gaussian distribution variable , and Satisfy the relational expression between （34） Among them, represents the complementary error function, and its expression is （35）。 2. The preferred method for a sea clutter simulation statistical distribution model for CFAR detection according to claim 1, wherein The parameter estimation of the statistical distribution model in step S1 is specifically as follows: Select the actually measured sea clutter data and read the following measurement parameters: Distance sampling points of measurement data ; The number of pulses of the measurement data ; Pulse repetition frequency of the measuring radar , in Hz; Analog / Digital Sampling Rate of the Measuring Radar , in Hz; Glancing angle of the measuring radar , in degrees; Measure the bandwidth of the radar transmitted signal , in Hz; The polarization mode of the measuring radar; The sea state level, wind speed, wind direction, significant wave height, wave direction and other meteorological and hydrological data during measurement.

3. A method for optimizing a statistical distribution model of sea clutter simulation for CFAR detection according to claim 2, characterized in that, Determine the selection range of the statistical distribution model. Use Weibull and log-normal distributions as representatives of non-Gaussian statistical distribution models, and use K-distribution and Pareto distribution as representatives of dual-scale models based on texture and speckle components; The probability density function of the Weibull distribution model is （1） Among them, is the sea clutter intensity; and are the shape and scale parameters of the Weibull distribution model, respectively; Its cumulative distribution function is （2） The parameter estimation formulas of the Weibull distribution are respectively （3） （4） Among them, represents the mathematical expectation of a variable; is the observed sea clutter intensity random variable; The probability density function of the log-normal distribution model is （5） Among them, and are respectively the variance and median that follow a normal distribution; Its cumulative distribution function is （6） where erf( ) is the error function, and its expression is （7） The parameters of the log-normal distribution are estimated by the second moment, and the estimation formulas are respectively （8） （9） The probability density function of the K-distribution model is （10） Among them, is the second-kind modified order Bessel function; is the gamma function; and are the shape and scale parameters of the K-distribution, respectively; Its cumulative distribution function is （11） The parameter estimation formulas of the K-distribution are respectively （12） （13） The probability density function of the Pareto distribution model is （14） Among them, and are the shape and scale parameters of the Pareto distribution model, respectively; Its cumulative distribution function is （15） The estimation formulas of the parameters of the Pareto distribution model are respectively （16） （17）。 4. A method for optimizing a statistical distribution model of sea clutter simulation for CFAR detection according to claim 3, characterized in that, The generation of the two-dimensional autocorrelation matrix in step S3 is specifically as follows: For measuring the sea clutter intensity data H, it is a matrix of order , one dimension is range and the other dimension is pulse; in the range dimension, the ground range interval between two adjacent range cells is （19） Among them, is the propagation speed of electromagnetic waves in vacuum, is the analog / digital sampling rate of the measurement radar; is the grazing angle of the measurement radar; The unnormalized spatial autocorrelation function in the range dimension is （20） where the superscript denotes complex conjugation, for intensity data ; Normalize the spatial autocorrelation function so that the autocorrelation function value at zero lag is equal to 1, which is （21） The space-related length is defined as within the distance when it is less than one over the natural logarithm for the first time within the interval of , and , there is （22） Then the spatial correlation length is （23） In the pulse dimension, the time interval between two adjacent pulses is （24） Among them, is the pulse repetition frequency of the measurement radar; The unnormalized temporal autocorrelation function in the pulse dimension is （25） Normalize the temporal autocorrelation function so that the autocorrelation function value at zero lag is equal to 1, which is （26） The time-related length is defined as at the distance when it is less than one over the natural logarithm for the first time within the interval of and there is （27） Then the spatial correlation length is （28） According to the training requirements of the CFAR detector, set the following simulation parameters: Set the number of distance sampling points for simulation data , and its value range is positive integers; Set the number of pulses of the simulation data , and its value range is positive integers; Set the pulse repetition frequency of the simulation data radar , with the unit of Hz and the value range being positive real numbers; Set the A / D sampling rate of the simulation data radar , with the unit of Hz and the value range being positive real numbers; Based on the above simulation parameters, let the space-time correlated sea clutter intensity sequence of the simulation be , which is order matrix; In the range dimension, the ground range interval between two adjacent range cells of the simulation data is （29） Model the spatial autocorrelation function of the simulated sea clutter intensity as an exponential decay function, which is （30） In the pulse dimension, the time interval between two adjacent pulses of the simulation data is （31） Assume that the sea clutter Doppler spectrum is exponential, then the temporal autocorrelation function of the simulated sea clutter intensity is modeled as （32） Construct a two-dimensional autocorrelation matrix using equations (30) and (32), and substitute equations (29) and (31) into it for discretization. Then, the two-dimensional autocorrelation matrix modeling of simulated sea clutter is （33）。 5. A method for optimizing a statistical distribution model of sea clutter simulation for CFAR detection according to claim 4, characterized in that, Step S4 further includes: Definition is the inverse function of the complementary cumulative distribution function of a non-Gaussian distribution model with the cumulative distribution function being and is （36） The non-Gaussian distribution variable and the standard normal distribution random variable The non-linear mapping relationship between them is expressed as （37） Non-Gaussian distribution variable has an autocorrelation characteristic of （38） Among them, represents the two-dimensional autocorrelation matrix of the standard normal distribution random variable ; represents the Hermite polynomial, and its expression is （39） Non-Gaussian distributed variable The two-dimensional autocorrelation matrix is expressed as （40） Then, the two-dimensional autocorrelation matrix of the standard normal distribution random variable is calculated using Equation (40) and Equation (38). The standard normal distribution random variable is filtered using the Fourier synthesis method to make its two-dimensional autocorrelation matrix , and finally, the non-Gaussian distribution variable with the two-dimensional autocorrelation matrix is obtained using the mapping relationship of Equation (37). The two-dimensional autocorrelation matrix is ; the non-linear mapping relationships for different distributions are as follows: The non-Gaussian distribution variable ; If the Weibull distribution model is the optimal distribution, the mapping relationship of equation (37) is （41） If the log-normal distribution model is the optimal distribution, the mapping relationship of equation (37) is （42） If the K-distribution model is the optimal distribution, the mapping relationship of equation (37) is completed in two steps. First, the non-linear mapping relationship between the texture component obeying the negative exponential distribution and the standard normal is （43） Secondly, based on the generated texture component, the two-dimensional autocorrelation matrix of the speckle component changes to （44） When generating the speckle component that follows the gamma distribution, the gamma distribution cumulative distribution function corresponding to the standard normal distribution random variable is （45） Given the cumulative distribution function and shape parameter of the known gamma distribution when using the Newton method with respect to the integration range [0, to calculate the inverse of the incomplete gamma function, it is （46） Multiply by Equation (43) to obtain the mapping relationship between the random variable subject to the K distribution and the standard normal distribution （47） If the Pareto distribution model is the optimal distribution, the mapping relationship of equation (37) is （48）。

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