A radar target constant false alarm rate detection method based on stationary Gaussian process

Abstract

The application discloses a radar target constant false alarm detection method based on a stationary Gaussian process, which comprises the following steps: dividing echo data received by a radar system, determining a to-be-detected unit Z0 and surrounding reference units Z1, Z2,..., Z N , constructing a decision rule of a basic constant false alarm detection method and a decision rule of a stationary Gaussian process constant false alarm detection method; constructing a posterior distribution of the to-be-detected unit z0 after no clutter and after adding clutters according to a Gaussian process regression method; perfecting the decision rule of the stationary Gaussian process constant false alarm detection method, calculating a detection threshold of a false alarm probability, and judging whether a target exists at the to-be-detected unit z0. Compared with a traditional constant false alarm detection method, the application has better detection performance, performs better in an interference environment and a non-central chi-square clutter for an extended target, and the detector has a constant false alarm characteristic, and the false alarm control ability is more stable compared with other detectors.

Description

Technical Field

[0001] This invention belongs to the field of radar target detection technology, and specifically relates to a constant false alarm rate (CFAR) detection method for radar targets based on a stationary Gaussian process. Background Technology

[0002] In modern radar systems, constant false alarm rate (CFAR) detection is frequently used for adaptive target detection in unknown and non-stationary environments. CFAR methods estimate the background noise parameters of reference cells surrounding the target cell as its own background noise parameters, and then determine whether a target exists in the target cell. Commonly used CFAR methods include cell-averaged CFAR (CA-CFAR) and ordered statistical CFAR (OS-CFAR). However, CA-CFAR detectors suffer from performance degradation due to target obstruction and non-uniform clutter conditions. Introducing Bayesian methods into CFAR results in Bayesian CFAR. Bayesian CFAR detectors can obtain the Bayesian posterior distribution of the target cell through Bayesian inference. It exhibits better detection performance when the statistical data of the target cell and its neighboring cells are considered as a joint distribution.

[0003] With the development of radar technology, modern radars have achieved high range resolution. Target echoes may be distributed across multiple range cells, forming range-spread targets. Because some of the target's energy is dispersed into the reference cell, generating interfering targets, the detector's performance is severely degraded. Bayesian CFAR can be used in this situation. For interfering targets in clutter, Bayesian CFAR compensates for the interfering targets by modeling a distribution, and then eliminates them by constructing a posterior distribution. However, Bayesian CFAR requires the number of interfering targets to be determined in advance; otherwise, its detection performance cannot be determined, making it difficult to apply in practical scenarios. The universality of stationary Gaussian processes and the unrestricted correlation of statistical data in Gaussian process regression methods can be set arbitrarily. Summary of the Invention

[0004] In view of this, the present invention proposes a radar target constant false alarm detection method based on a stationary Gaussian process, comprising the following steps:

[0005] S1. Divide the echo data received by the radar system to determine the target element Z0 and the surrounding reference elements Z1, Z2, ..., Zn. N And construct the decision rules for the basic constant false alarm rate (CFAR) detection method;

[0006] S2. Construct the posterior distribution of the unit z0 to be tested using the Gaussian process regression method;

[0007] S3. Based on the decision rules of the basic constant false alarm rate (CFAR) detection method constructed in step S1, construct the decision rules of the CFAR detection method for a stationary Gaussian process.

[0008] S4. Based on the posterior distribution of the unit z0 under test constructed in step S2, clutter is added, and the posterior distribution of the unit z0 under test is constructed according to the Gaussian process regression method.

[0009] S5. Improve the decision rules of the constant false alarm detection method for stationary Gaussian process in step S3, and calculate the detection threshold of false alarm probability according to the method in step S4. Determine whether there is a target at the target unit z0 by the improved decision rules of the constant false alarm detection method for stationary Gaussian process and the detection threshold of false alarm probability.

[0010] Furthermore, step S1 specifically includes:

[0011] H0 is a null hypothesis that there is no target in the cell under test, and H1 is a hypothesis that the cell under test contains a target embedded in clutter. The cell under test is transmitted through a function g(Z1, Z2, ..., Zn) acting on the statistics of the reference cell. N A single measurement of the clutter level is generated, which is then multiplied by a threshold factor ∝, if and only if Z0 exceeds ∝·g(Z1, Z2, ..., Z). N When H0 is selected, the decision rule is to reject H0 to determine whether there is an interesting target. The decision rule is expressed as follows:

[0012]

[0013] Wherein, the threshold factor ∝ is determined by the false alarm probability P fa The expectation is determined by T, which is the detection threshold, i.e., ∝·g(Z1, Z2, ..., Z). N Z0 greater than T indicates the presence of a target (H1), while Z0 less than T indicates the absence of a target (H0).

[0014] False alarm probability P fa The representation is as follows:

[0015]

[0016] Where: false alarm probability P fa When there is no target (H0), the probability that the test unit z0 > T is judged as having a target is Z0 = z0, and f(z0|H0) represents the probability density function of the test unit z0 when there is no target.

[0017] P fa The expectation is expressed as follows:

[0018]

[0019] Where E[·] is the expectation operator, and the reference unit statistics Z1, Z2, ..., Zn are given. N If it is irrelevant, then the detection method is considered to have constant false alarm rate (CFAR) characteristics.

[0020] Furthermore, step S2 specifically includes:

[0021] A Gaussian process is determined by the mean function and covariance function shown in Equation 4:

[0022]

[0023] Where the input r = [r1, r2, ..., r N ] T , r represents the radar range set, k(r) i r j The definition of ) is as follows:

[0024]

[0025] Where: l is the prior scale parameter, θ 2 μ and μ are hyperparameters;

[0026] The models of the unit under test and the reference unit are as follows:

[0027] z = μ z +e, e~N(0, θ) 2 (6)

[0028] Where z is a noisy sample and e is the noise model;

[0029] The prior distribution of sample z is as follows:

[0030] y~N(μ z , K+θ 2 I n )_____________(7)

[0031] The joint distribution of samples z and z0 is as follows:

[0032]

[0033] Where: K(r, r) = K n =(k ij Let be an n×n symmetric positive definite covariance matrix, with matrix elements k. ij =k(r i r j ) is used to measure r i and r j The correlation between them; K(r, r0) = K(r0, r) T Let r be the n×1 covariance matrix between the test point r0 and the input r; k(r0, r0) is the covariance of the test point r0 itself; I n It is an n-dimensional identity matrix; μ zμ0 represents the mean of sample z, and μ0 is the mean of the unit z0 to be tested.

[0034] The posterior distribution of the unit z0 to be tested is as follows:

[0035]

[0036] in:

[0037] m0=K(r0,r)·[K(r,r)+θ 2 I n ] -1 z+μ0 (10)

[0038]

[0039] m0, Let r0 be the mean and variance of the unit z0 to be tested corresponding to the test point r0.

[0040] Furthermore, step S3 specifically includes:

[0041] Design a stationary Gaussian process constant false alarm rate detector with the following decision rule:

[0042]

[0043] Where: τ is the detection threshold, which is determined by formula (13);

[0044] According to formula (12), P fa The expression (2) can be written as formula (13):

[0045]

[0046] Where: f(z|z1,z2,...,z) N P(·) represents the probability density function of the unit to be tested, and P(·) represents the probability.

[0047] Construct a decision rule to manage false alarm rules, transforming formula (12) into formula (14):

[0048]

[0049] Where: P fa (τ) represents the probability of a false alarm detected. The statistic T acting on the reference cell and the test cell z0 indicate that expression (14) has constant false alarm characteristics.

[0050] Furthermore, step S4 specifically includes:

[0051] The clutter random variable at a distance r from the radar is:

[0052] X(r) =I (r) +jQ (r) (15)

[0053] in:

[0054]

[0055]

[0056] I (r) and Q (r) They are X (r) The real and imaginary components, I (r) and Q (r) It is a Gaussian distribution with different mean values;

[0057] For expression (15), when m1≠0 and m2≠0, the output of the square law detector is a non-central chi-square distribution; when m1=m2=0, the output of the square law detector is an exponential distribution, and the non-central chi-square distribution is as follows:

[0058]

[0059] in, I0(·) is the first-order zero-order modified Bessel function. Replacing m1 and m2 with expression (10), we obtain the noncentrality parameter λ as follows:

[0060] λ(μ0, θ) 2 ,l)=(K(r,r0)′·K(r,r) -1 i+μ0) 2 +(K(r, r0)′·K(r, r) -1 q+μ0) 2 (19)

[0061] Where i and q are the reference samples of signals I and Q, respectively, and μ0 and θ 2 The scale parameter l is determined using the maximum likelihood method and is a priori parameter.

[0062] The probability density function of the multidimensional Gaussian distribution is as follows:

[0063]

[0064] Where: K is the covariance matrix, |·| is the determinant operator, N is the number of reference units, and its log-likelihood function is as follows:

[0065]

[0066] in:

[0067]

[0068] make Then θ 2 The estimated values ​​for μ are:

[0069]

[0070]

[0071] According to θ 2 and μ z The estimated value is k(r) i r j The value of ) is obtained, that is, K is obtained, and m0 is calculated. The value of z0 is obtained, which is the posterior distribution of the unit to be tested.

[0072] Furthermore, step S5 specifically includes:

[0073] The false alarm probability P of the test cell z0 FA as follows:

[0074]

[0075] Where: P(·) is the probability. It is a chi-square distribution with 2+2j degrees of freedom. It is a cumulative function of a non-central chi-square distribution; z1, ..., z N Let z represent the reference cell, and z represent the element in the sample.

[0076] Based on the integration of expression (20), the decision rule for the constant false alarm rate (CFAR) detection method of a stationary Gaussian process with non-central chi-square clutter and a known scale parameter l is as follows:

[0077]

[0078] Among them, P FA (z0, λ) is the detection threshold, when P fa (τ)<P FA When (z0, λ), it is assumed that there is no target at z0 of the unit under test; otherwise, it is assumed that there is a target at z0 of the unit under test.

[0079] Define the element to be tested z0, and the surrounding reference elements z1, ..., z2. N The number of reference units N, the preset prior scale parameter l, and the false alarm probability P fa The value;

[0080] Reference elements z1, ..., z N Divided into real parts Re(z1, ..., z) N ) and the imaginary part Im(z1, ..., z)N The posterior distribution of the real part Re(z0) of the test unit z0 is obtained by the Gaussian process regression method in step S2. The posterior distribution of the imaginary part Im(z0)

[0081] Solve for P using formula (25) FA :

[0082] Where ncx2cdf(·) represents the accumulation function of the noncentral chi-square distribution, 2 is the corresponding degree of freedom, and the noncentrality parameter is...

[0083] The presence of a target at position z0 of the unit to be measured is determined by formula (26). If P fa (τ)<P FA (z0, λ) indicates that there is no target at z0 of the unit under test; otherwise, there is a target at z0 of the unit under test.

[0084] The beneficial effects of the technical solution provided by this invention are:

[0085] (1) This method has better detection performance than the traditional constant false alarm rate detection method. It performs better in interference environment and non-central chi-square clutter for extended targets.

[0086] (2) The detector has constant false alarm characteristics, and its false alarm control capability is more stable compared with other detectors. Attached Figure Description

[0087] Figure 1 This is a flowchart of a radar target constant false alarm detection method based on a stationary Gaussian process according to the present invention;

[0088] Figure 2 This refers to the detection performance in this embodiment of the invention under the condition of a 10dB interfering target in the presence of exponentially distributed clutter.

[0089] Figure 3 This is the detection performance of the present invention in the case of a 10dB interfering target under non-central chi-square clutter.

[0090] Figure 4 This is the detection performance of the present invention in the case of two 10dB interfering targets under exponential clutter.

[0091] Figure 5 This describes the detection performance of two 10dB interfering targets under non-central chi-square clutter in this embodiment of the invention. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0093] refer to Figure 1 , Figure 1 This is a flowchart of a radar target constant false alarm rate (CFAR) detection method based on a stationary Gaussian process according to the present invention. The CFAR detection method based on a stationary Gaussian process according to an embodiment of the present invention includes the following steps:

[0094] S1. Divide the echo data received by the radar system to determine the target element Z0 and the surrounding reference elements Z1, Z2, ..., Zn. N And construct the decision rules for the basic constant false alarm rate (CFAR) detection method.

[0095] H0 is a null hypothesis that there is no target in the cell under test, and H1 is a hypothesis that the cell under test contains a target embedded in clutter. The cell under test is transmitted through a function g(Z1, Z2, ..., Zn) acting on the statistics of the reference cell. N A single measurement of the clutter level is generated, which is then multiplied by a threshold factor ∝, if and only if Z0 exceeds ∝·g(Z1, Z2, ..., Z). N When H0 is selected, the decision rule is to reject H0 to determine whether there is an interesting target. The decision rule is expressed as follows:

[0096]

[0097] Wherein, the threshold factor ∝ is determined by the false alarm probability P fa The expected value is determined by T, which is the detection threshold, i.e., ∝·g. Z0 greater than T indicates the presence of target H1, and less than T indicates the absence of target H0.

[0098] False alarm probability P fa The representation is as follows:

[0099]

[0100] Where: false alarm probability P fa When there is no target (H0), the probability that the test unit z0 > T is judged as having a target is Z0 = z0, and f(z0|H0) represents the probability density function of the test unit z0 having no target.

[0101] Since g(Z1, Z2, ..., Z) N ) is composed of reference unit statistics Z1, Z2, ..., Z N Constructed, so P fa It is also a random statistic, which changes with the reference unit statistics Z1, Z2, ..., Zn. N P changes with the changes faThe expectation is expressed as follows:

[0102]

[0103] Where E[·] is the expectation operator, and the reference unit statistics Z1, Z2, ..., Zn are given. N If it is irrelevant, then the detection method is considered to have constant false alarm rate (CFAR) characteristics.

[0104] S2. Construct the posterior distribution of the test unit z0 using the Gaussian process regression method. A stationary Gaussian process (sGP) is a set of random variables that all have a joint Gaussian distribution. It can be regarded as a function distribution, which we can use to estimate the distribution of the test unit Z0 = z0.

[0105] A Gaussian process is determined by the mean function and covariance function shown in Equation 4:

[0106]

[0107] Where the input r = [r1, r2, ..., r N ] T , r represents the radar range set, k(r) i r j The definition of ) is as follows:

[0108]

[0109] Where: l is the prior scale parameter, θ 2 μ and μ are hyperparameters;

[0110] The models of the unit under test and the reference unit are as follows:

[0111] z = μ z +e, e~N(0, θ) 2 (6)

[0112] Where z is a noisy sample, e is the noise model, and for simplicity of notation, the noise variance is also θ. 2 The reference unit z = [z(r1), z(r2), ..., z(r)] can be used. N )] T and its corresponding input r = [r1, r2, ..., r N ] T Given a sample, predict the result z0 = z(r0) for other test inputs r0.

[0113] The prior distribution of sample z is as follows:

[0114] y~N(μ z , K+θ 2 I n(7)

[0115] The joint distribution of samples z and z0 is as follows:

[0116]

[0117] Where: K(r, r) = K n =(k ij Let be an n×n symmetric positive definite covariance matrix, with matrix elements k. ij =k(r i r j ) is used to measure r i and r j The correlation between them; K(r, r0) = K(r0, r) T Let r be the n×1 covariance matrix between the test point r0 and the input r; k(r0, r0) is the covariance of the test point r0 itself; I n It is an n-dimensional identity matrix; μ z μ0 represents the mean of sample z, and μ0 is the mean of the unit z0 to be tested.

[0118] The posterior distribution of the unit z0 to be tested is as follows:

[0119]

[0120] in:

[0121] m0=K(r0,r)·[K(r,r)+θ 2 I n ] -1 z+μ0 (10)

[0122]

[0123] m0, Let r0 be the mean and variance of the unit z0 to be tested corresponding to the test point r0.

[0124] S3. Based on the decision rules of the basic constant false alarm rate (CFAR) detection method constructed in step S1, construct the decision rules of the CFAR detection method for a stationary Gaussian process.

[0125] Design a stationary Gaussian process constant false alarm rate detector (CFAR) that assumes the measured element and the reference element are coupled, non-independent, and identically distributed. In the coupled case, the reference elements Z1, Z2, ..., Z... N Determine the detection threshold τ, and compare the target unit Z0 with τ. If and only if Z0 exceeds τ, it is considered that a target may exist at the target unit Z0. The decision rule is as follows:

[0126]

[0127] Where: τ is the detection threshold, which is determined by formula (13);

[0128] According to formula (12), P fa The expression (2) can be written as formula (13):

[0129]

[0130] Where: f(z|z1,z2,...,z) N P(·) represents the probability density function of the unit to be tested, and P(·) represents the probability.

[0131] Construct a decision rule to manage false alarm rules, and set a preset false alarm probability P. fa (τ) and the false alarm probability P at the measured unit z0 fa (z0) is compared if and only if P fa (τ) exceeds P fa When (z0), it is assumed that there may be a target at z0 of the unit to be measured, and formula (12) is transformed into formula (14):

[0132]

[0133] Where: P fa (τ) represents the false alarm probability detected, which is generally a preset constant false alarm probability. The statistic T acting on the reference cell and the cell z0 under test indicate that expression (14) has constant false alarm characteristics.

[0134] S4. Based on the posterior distribution of the unit under test z0 constructed in step S2, clutter is added, and the posterior distribution of the unit under test z0 is constructed according to the Gaussian process regression method.

[0135] Assuming the background noise follows a non-zero mean Gaussian distribution in the complex domain, this means that the output of the square-law detector for the background noise is non-centrally distributed.

[0136] The clutter random variable at a distance r from the radar is:

[0137] X (r) =I (r) +jQ (r) (15)

[0138] in:

[0139]

[0140]

[0141] I (r) and Q (r) They are X (r) The real and imaginary components, I(r) and Q (r) It is a Gaussian distribution with different mean values; all random variables with parameter r are considered as stationary Gaussian processes.

[0142] For expression (15), when m1≠0 and m2≠0, the output of the square law detector is a non-central chi-square distribution; when m1=m2=0, the output of the square law detector is an exponential distribution, and the non-central chi-square distribution is as follows:

[0143]

[0144] in, I0(·) is the first-order zero-order modified Bessel function. Replacing m1 and m2 with expression (10), we obtain the noncentrality parameter λ as follows:

[0145] λ(μ0, θ) 2 ,l)=(K(r,r0)′·K(r,r) -1 i+μ0) 2 +(K(r, r0)′.K(r, r) -1 q+μ0) 2 (19)

[0146] Where i and q are the reference samples of signals I and Q, respectively, and μ0 and θ 2 The scale parameter l is determined using the maximum likelihood method and is a priori parameter.

[0147] The probability density function of the multidimensional Gaussian distribution is as follows:

[0148]

[0149] Where: K is the covariance matrix, |·| is the determinant operator, N is the number of reference units, and its log-likelihood function is as follows:

[0150]

[0151] in:

[0152]

[0153] make Then θ 2 and μ z The estimated value is:

[0154]

[0155]

[0156] According to θ 2 and μ zThe estimated value is k(r) i r j The value of ) is obtained, that is, K is obtained, and m0 is calculated. The value of z0 is obtained, which is the posterior distribution of the unit to be tested.

[0157] S5. Improve the decision rules of the constant false alarm detection method for stationary Gaussian process in step S3, and calculate the detection threshold of false alarm probability according to the method in step S4. Determine whether there is a target at the target unit z0 by the improved decision rules of the constant false alarm detection method for stationary Gaussian process and the detection threshold of false alarm probability.

[0158] Using reference cells as training data, the probability density function of the test cell z0 in the constant false alarm rate (CFAR) detection method for stationary Gaussian processes is predicted, that is, the false alarm probability P of the test cell z0 is predicted. FA The false alarm probability P of the unit under test z0 FA as follows:

[0159]

[0160] Where: P(·) is the probability. It is a chi-square distribution with 2+2j degrees of freedom. It is a cumulative function of a non-central chi-square distribution; z1, ..., z N Let z represent the reference unit, and z represent the element in the sample, which is used here to represent the unit to be tested, z0.

[0161] Based on the integration of expression (20), the decision rule for the constant false alarm detection method of a stationary Gaussian process with known scale parameter l and non-central chi-square clutter can be determined. At this time, the false alarm probability P at the measured cell z0 is P. FA (z0, λ) can be calculated. The decision rule for the constant false alarm rate (CFAR) detection method for a stationary Gaussian process with non-central chi-square clutter and a known scale parameter l is as follows:

[0162]

[0163] Among them, P FA (z0, λ) is the detection threshold obtained from the calculation, when P fa (τ)<P FA When (z0, λ), it is assumed that there is no target at z0 of the unit under test; otherwise, it is assumed that there is a target at z0 of the unit under test.

[0164] The steps to solve formula (26) are explained below:

[0165] Define the element to be tested z0, and the surrounding reference elements z1, ..., z2. N The number of reference units N, the preset prior scale parameter l, and the false alarm probability Pfa The value of .

[0166] Reference elements z1, ..., z N Divided into real parts Re(z1, ..., z) N ) and the imaginary part Im(z1, ..., z) N The posterior distribution of the real part Re(z0) of the test unit z0 is obtained by the Gaussian process regression method in step S2. The posterior distribution of the imaginary part Im(z0)

[0167] Solve for P using formula (25) FA :

[0168] Where ncx2cdf(·) represents the accumulation function of the noncentral chi-square distribution, 2 is the corresponding degree of freedom, and the noncentrality parameter is...

[0169] The presence of a target at position z0 of the unit to be measured is determined by formula (26). If P fa (τ)<P FA (z0, λ) indicates that there is no target at z0 of the unit under test; otherwise, there is a target at z0 of the unit under test.

[0170] In this embodiment, the scale parameter l = 0.2, the number of reference units N = 32, and the false alarm probability is set to P. fa =10 -4 The exponential and non-central chi-square distributions were used to simulate clutter, with mean μ0 of 0 and 1 respectively, and variance... The detection performance of CA-CFAR, OS-CFAR, and Bayesian CFAR is compared with that of stationary Gaussian process CFAR. The Monte Carlo method is used to simulate the detection performance of all CFAR detectors.

[0171] Under exponential clutter and non-central chi-square clutter conditions, one 10dB interference target and two 10dB interference targets were added to the reference cells, respectively. The four detectors mentioned above were used for detection, and their detection performance was compared. In the case of one interference target, the interference was placed in the 4th reference cell; in the case of two interference targets, the interference was placed in the 4th and 29th reference cells. For the Bayesian CFAR detector, the prior probabilities were taken as π⁴ = 1, π... i≠4 =0 and π i≠4，29 =0. The detection performance of the four CFAR detectors is as follows: Figure 2 , 3 As shown in Figures 4 and 5, Figure 2This describes the detection performance in this embodiment of the invention under the condition of an exponentially distributed cluttered environment with a 10dB interfering target. Figure 3 This is the detection performance of the present invention in the case of a 10dB interfering target under non-central chi-square clutter. Figure 4 This is the detection performance of the present invention in the case of two 10dB interfering targets under exponential clutter. Figure 5 This describes the detection performance of two 10dB interfering targets under non-central chi-square clutter in this embodiment of the invention.

[0172] from Figure 2 , 3 As shown in Figures 4 and 5, the stationary Gaussian process constant false alarm rate (sGP-CFAR) performs well in interference environments and in non-central chi-square clutter. It should be noted that Bayesian CFAR is optimized for interfering targets, resulting in greater detection loss in real-world scenarios. sGP-CFAR exhibits the best detection performance in non-central chi-square distributions, but the presence of strong or multiple interferences can overestimate the power of the clutter.

[0173] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A radar target constant false alarm rate (CFAR) detection method based on a stationary Gaussian process, characterized in that, Includes the following steps: S1. Divide the echo data received by the radar system to determine the unit under test. and surrounding reference units And construct the decision rules for the basic constant false alarm rate (CFAR) detection method; S2. Construct the test unit based on the Gaussian process regression method. The posterior distribution of; S3. Based on the decision rules of the basic constant false alarm rate (CFAR) detection method constructed in step S1, construct the decision rules of the CFAR detection method for a stationary Gaussian process. S4. Test unit constructed based on step S2 The posterior distribution is obtained, clutter is added, and the test cell is constructed according to the Gaussian process regression method. The posterior distribution of; S5. Improve the decision rules of the constant false alarm rate (CFAR) detection method for stationary Gaussian processes in step S3, and calculate the detection threshold of the false alarm probability according to the method in step S4. Use the improved decision rules of the constant CFAR detection method for stationary Gaussian processes and the detection threshold of the false alarm probability to determine the unit under test. Does the target exist at this location? Step S1 is as follows: It is a null hypothesis that there is no target in the unit under test. The assumption is that the cell under test contains a target embedded in clutter, and the cell under test is transmitted through a function acting on the statistics of the reference cell. A single measurement of the clutter level is generated, which is then multiplied by a threshold factor. If and only if Exceed At that time, I decided to refuse. To determine whether there exists an interesting target, the decision rule is expressed as follows: （1） Among them, threshold factor From the probability of false alarm Expectations determine The detection threshold is... , Z 0 greater than T This indicates the existence of a target, i.e. H 1, less than T Indicates no goal H 0; False alarm probability The representation is as follows: （2） Among them: false alarm probability It means having no goal. H At 0 o'clock, the unit under test z 0> T The probability of being judged as having a target. , This represents the test unit when there is no target. The probability density function; The expectation is expressed as follows: （3） in, For the expectation operator, and the reference cell statistic If irrelevant, the detection method is considered to have constant false alarm rate (CFAR) characteristics. Step S2 is as follows: A Gaussian process is determined by the mean function and covariance function shown in Equation 4: （4） Among them, input , This represents the radar's range set. The definition is as follows: （5） in: These are the prior scale parameters. and It's a hyperparameter; The models of the unit under test and the reference unit are as follows: （6） in: It is a noisy sample. e It is a noise model; sample The prior distribution is as follows: （7） sample and The joint distribution is as follows: （8） in: for A covariance matrix of order-order symmetric positive definiteness, matrix elements Used to measure and The correlation between them; For test points With input Between The order covariance matrix; For test points Its own covariance; for 3D identity matrix; Indicates sample z The mean, It is the unit under test z 0 is the mean of itself; Unit under test The posterior distribution is as follows: （9） in: （10） （11） ， For test points Corresponding unit under test The mean and variance; Step S3 is as follows: Design a stationary Gaussian process constant false alarm rate detector with the following decision rule: （12） in: The detection threshold is determined by formula (13); According to formula (12), The expression (2) can be written as formula (13): （13） in: This represents the probability density function of the unit under test. Represents probability; Construct a decision rule to manage false alarm rules, transforming formula (12) into formula (14): （14） in: The statistic representing the probability of a false alarm detected, applied to the reference cell. and the unit under test This indicates that expression (14) has constant false alarm rate (CFAR) characteristics; Step S4 is as follows: Stay away from radar r The clutter random variable at the location is: （15） in: （16） （17） and They are The real and imaginary components, and It is a Gaussian distribution with different mean values; For expression (15), when When the square-law detector outputs a non-central chi-square distribution, when... At that time, the output of the square-law detector follows an exponential distribution, while the non-central chi-square distribution is as follows: （18） in, , It is the first kind of zeroth-order modified Bessel function, replaced by expression (10). and The noncentrality parameter was obtained. as follows: （19） in and Signals I and Q Reference sample, The scale parameter is determined using the maximum likelihood method. It is a prior parameter; The probability density function of the multidimensional Gaussian distribution is as follows: （20） in: For determinant operators, N The log-likelihood function for the number of reference units is as follows: （21） in: （22） make , ,but and The estimated value is: （23） （24） according to and The estimated value is The value is obtained, that is, the value of . Find ， The value of is obtained, that is, the value of the unit under test. The posterior distribution of; Step S5 is as follows: Unit under test False alarm probability as follows: （25） in: For probability, For having 2+2 j Chi-square distribution of degrees of freedom It is a cumulative function of a non-central chi-square distribution; z 1,…, z N Indicates the reference unit. z Represents the elements in the sample; Based on the integration of expression (25), for non-central chi-square clutter and known scale parameters The decision rules for the constant false alarm rate (CFAR) detection method for stationary Gaussian processes are as follows: （26） in, As the detection threshold, when At that time, it is considered that the unit under test The target does not exist at the location; otherwise, the unit to be tested is considered to be... There is a target; Determine the unit to be tested surrounding reference units Number of reference units N Preset prior scale parameters and false alarm probability The value; Reference unit Divided into real part and the virtual part The test units are obtained by the Gaussian process regression method in step S2. Real part posterior distribution and the virtual part posterior distribution ; Solve according to formula (25) : in, This represents the accumulation function of a non-central chi-square distribution, where 2 represents the corresponding degrees of freedom and the non-centrality parameter. ; Determine the unit to be tested using formula (26) Does the target exist at that location? The unit under test is considered to be The target does not exist at the location; otherwise, the unit to be tested is considered to be... There is a target.

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