Fully adaptive constant false alarm rate detection method for generalized clutter texture distribution

Abstract

The invention discloses a generalized clutter texture distribution-oriented extended target full-adaptive constant false alarm rate detection method, which belongs to the field of radar signal processing, and comprises the following steps of: constructing test statistics according to texture distribution knowledge, covariance matrix structure information, signal subspace and the like; establishing an interpolation function of a threshold offline by using a Monte Carlo method, and estimating a corresponding threshold quickly and precisely according to parameters of a probability density function of a texture component; in a radar target detection process, unknown parameters in texture distribution are estimated by using a second group of training data, a full-adaptive detector is constructed by combining an interpolation function of test statistics and a threshold, and the detector is ensured to have a constant false alarm rate property for the parameters of the texture distribution and the change of a clutter covariance matrix. Compared with a traditional radar target detection method, the cognitive ability of a radar system to a complex environment is remarkably improved, and the method has good engineering application value and popularization potential.

Description

Technical Field

[0001] The present invention belongs to the field of radar signal processing, and focuses on an extended target full adaptive constant false alarm rate detection method for generalized clutter texture distribution. In a complex clutter environment, the knowledge of texture distribution is used to improve the target detection performance, realize the adaptive estimation of unknown parameters in the texture distribution by the radar system, quickly adjust the detector and the threshold of the detector, and ensure that the detector has the property of constant false alarm rate (CFAR). Background Art

[0002] With the continuous development of radar technology, the resolution of radar is constantly improving, and the targets detected by radar often occupy multiple range cells, which are also called extended targets. Due to the uncertainty of the spatial frequency or Doppler frequency of the target, the steering vector is uncertain. To address this problem, a known signal subspace is used to constrain the steering vector, reducing the complexity of the detection problem while considering the uncertainty and improving the detection robustness of the detector for different targets. In summary, from the perspective of algorithm design, the detection algorithm for point targets can be regarded as a special case of the extended target detection algorithm; the detection algorithm assuming that the steering vector is deterministically known is a special case of the subspace signal detection algorithm.

[0003] With the improvement of radar resolution or under the surveillance condition of low grazing angle, the ground / sea echoes received by the radar no longer follow the central limit theorem, and the probability density function of the clutter echo amplitude shows the characteristic of long tails. Research shows that compared with the Gaussian distribution, the K distribution, t distribution, and Weibull distribution can better describe the statistical characteristics of the clutter echo. These non-Gaussian distributions can be uniformly modeled by the compound Gaussian distribution (family). The compound Gaussian (CG) distribution decomposes the clutter into the product of a "slowly varying" texture component and a "rapidly varying" speckle component. The speckle component follows a Gaussian distribution, while the texture component is a non-negative random variable. The covariance matrix of the speckle component determines the clutter spectrum characteristics, and the probability density function of the texture component determines the non-Gaussianity of the clutter. The generalized inverse Gaussian (GIG) distribution, as a modeling method for the texture component, has strong statistical description ability. The GIG includes three special cases: Gamma distribution texture (corresponding to K distribution clutter), inverse Gamma distribution texture (corresponding to t distribution clutter), and inverse Gaussian texture. Statistical analysis of radar measured data shows that compared with other texture distributions, the GIG distribution can more accurately describe the statistical characteristics of the texture component.

[0004] By researching relevant domestic and foreign literatures, when the type of known texture distribution is given, the false alarm probability of the detector depends on the unknown parameters in the texture distribution. In the published literature, these unknown parameters are obtained through methods such as empirical setting and statistical inference, and then directly substituted into the test statistic. However, none of the published detectors can guarantee the CFAR property under the change of the parameters of the texture distribution. In summary, in the field of radar signal processing, it is a difficulty that needs to be overcome in the engineering application of radar systems to improve the detection probability by using the knowledge of the clutter texture distribution in the environmental knowledge base and to ensure the CFAR property of the detector under the change of the parameters of the texture component probability density and the clutter covariance matrix. Summary of the Invention

[0005] The present invention designs a fully adaptive constant false alarm rate detection method, which has the following capabilities: 1) It can handle extended target detection; 2) It can handle the uncertainty problems of the spatial frequency and Doppler frequency of the target signal, showing high detection robustness; 3) For a complex and changing clutter environment, it can effectively estimate the unknown parameters of the clutter texture distribution to ensure a high detection probability; 4) It provides a two-dimensional interpolation technology, which adaptively adjusts the detector and the threshold of the detector according to the change of the clutter texture distribution, guarantees the CFAR property, improves the reliability of the radar system in a complex clutter environment, and meets the real-time calculation requirements of the radar system. The fully adaptive detection method proposed by the present invention is realized through the following technical solutions:

[0006] 1) For the target of interest, determine the signal subspace A according to the radar environmental knowledge base k ; Utilize the statistical distribution knowledge of the texture component, such as the Generalized Inverse Gaussian Distribution (GIG); Utilize the structural knowledge of the covariance matrix of the clutter, such as the widely symmetric structure (when the radar system uses a symmetrically spaced linear array and / or a symmetrically spaced pulse sequence, the special structure of the clutter covariance matrix); Under the selected detection criteria, such as the Generalized Likelihood Ratio Test (GLRT), Wald test, Gradient test, Durbin test or Rao test criteria, use a two-step strategy to establish the detector where X is the observation matrix (including the main data and the first set of training data), and θ is the unknown parameter in the probability density function of the texture component.

[0007] 2) According to the radar environmental knowledge base, determine the value range of the parameter θ, and select an interpolation point set {θ l} within the value range. For each θ l , obtain the empirical distribution of under the null hypothesis using the Monte Carlo method

[0008] According to the preset false alarm probability P fa , obtain the upper P fa quantile of the empirical distribution That is, the threshold corresponding to the detector when θ = θ l . According to the interpolation condition {γ(θ l ), use interpolation technology to establish an interpolation function The interpolation function can be obtained through offline calculation

[0009] 3) Use a second set of training data (with the same clutter statistical characteristics) independent of the main data to obtain a consistent estimate of the unknown parameter θ in the texture distribution, denoted as According to the detector proposed in 1)

[0010] and the interpolation function proposed in 2) Obtain a fully adaptive CFAR detector

[0011]

[0012] In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are as follows:

[0013] 1. The present invention designs a fully adaptive constant false alarm rate detection method and constructs a detector with the property of constant false alarm rate.

[0014] 2. The present invention can handle extended target detection.

[0015] 3. The present invention can handle the uncertainty problems of the spatial frequency and Doppler frequency of the target signal and shows high detection robustness.

[0016] 4. For a complex and changing clutter environment, the present invention can effectively estimate the unknown parameters of the clutter texture distribution to ensure a high detection probability.

[0017] 5. The present invention provides a two-dimensional interpolation technology, which adaptively adjusts the threshold of the detector according to the change of the clutter texture distribution, ensures the CFAR property, improves the reliability of the radar system in a complex clutter environment, and meets the real-time calculation requirements of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 FIG. is the overall technical framework diagram of a fully adaptive CFAR detection method provided by an embodiment of the present invention.

[0019] Figure 2 FIG. is the flowchart of an interpolation function for constructing a detection threshold provided by an embodiment of the present invention.

[0020] Figure 3It is a flowchart for estimating texture distribution parameters provided by an embodiment of the present invention. Detailed implementation manners

[0021] To more clearly illustrate the technical details of the embodiments of the present invention, a detailed description is now given in conjunction with the accompanying drawings. Obviously, the following description only covers some embodiments of the present invention. For those skilled in the art, other embodiments derived through these embodiments without departing from the basic idea of the present invention should be included within the protection scope of the present invention.

[0022] For the compound Gaussian distributed clutter of GIG texture, the present invention proposes a fully adaptive CFAR detector for extended targets. Referring to the Figure 1 flowchart, the specific implementation includes the following steps:

[0023] Step 1: For a radar system with N channels, let the main data matrix of multiple range cells to be detected be Consider the steering vector s of the target of interest in the l-th range cell to be detected l , which is located in the known signal subspace and satisfies s l = A l v l , l = 1,..., L, where represents the unknown position coordinates of the target in the signal subspace, the signal subspace A l has full column rank, r l represents the rank of A l (r1 < N), and L represents the number of range cells that the target to be detected may occupy. The auxiliary data matrix where K represents the sample size of the auxiliary data. For the convenience of subsequent narration, let the set Θ L = {1,..., L}, Θ K = {L + 1,..., L + K}.

[0024] The range extended target detection problem is modeled as the following binary hypothesis test

[0025]

[0026] where the clutter is the product of the texture component and the speckle component The speckle component u i follows a complex circular Gaussian distribution with zero mean and covariance matrix ∑, u i ∼ CN(0, ∑). The texture component τ i is modeled as a GIG distribution, and its probability density function is

[0027]

[0028] where Kλ (·) represents the third kind of modified Bessel function with exponent λ, where the value range of (λ, χ, ψ) is

[0029]

[0030] The GIG distribution is a class of generalized distribution families. When the parameters of the GIG distribution satisfy specific conditions, the GIG distribution can degenerate into the Gamma distribution (corresponding to K-distributed clutter), the inverse Gamma distribution (corresponding to t-distributed clutter), and the inverse Gaussian distribution. These three distributions are widely used in the modeling of texture components. Therefore, using the GIG distribution to model the texture components enables the designed detection method to have good generality and adaptability.

[0031] For the convenience of subsequent parameter estimation, the present invention only considers the (regular) GIG distribution, that is, ψ > 0, χ > 0. For the convenience of narration, define variables: ω > 0, η > 0.

[0032] For a non-Gaussian and non-uniform clutter environment, it is difficult to obtain a large number of independent and identically distributed auxiliary data from the surrounding of the unit to be detected. When the radar system adopts a linearly array with symmetric intervals and / or a pulse sequence with symmetric intervals, the scatter matrix ∑ will exhibit a wide symmetric structure:

[0033] ∑ = ∑ H and ∑ = J∑ * J,

[0034] where J is an N×N permutation matrix with elements on the anti-diagonal being 1 and the remaining elements being 0, (·) * and (·) H represent complex conjugate and complex conjugate transpose respectively. Utilizing the generalized symmetric structure, the radar system can achieve good detection performance with a relatively small training data sample size.

[0035] Step 2: Select the generalized likelihood ratio test (GLRT) criterion. According to the design strategy of the two steps, when the parameters (λ, χ, ψ) of the GIG texture distribution are known, a GIG-GLRT detector is designed:

[0036]

[0037] where X = [x1,..., x L+K , and the threshold γ(λ, ψχ) is defined according to Step 1 can be expressed as γ(λ, ω 2 ). Given the false alarm rate P fa , Since the test statistic satisfies Therefore, Holds. Under the null hypothesis, according to the above analysis, it can be known that the test statistic T (λ，x，ψ) (X)'s distribution function only depends on the parameters (λ, ω 2 ). Therefore, the threshold γ also only depends on the parameters (λ, ω 2 ).

[0038]

[0039] Among them, the estimate of the divergence matrix ∑

[0040]

[0041] is the convergence point of the fixed-point equation:

[0042]

[0043] Step 3: Refer to the process in Appendix Figure 2 , preset the false alarm probability P fa , use the Monte Carlo method to calculate the interpolation nodes of γ(λ, ω 2 ) offline, and then use the two-dimensional interpolation method to obtain the interpolation function of the texture distribution parameters (λ, ω 2 ) and the detection threshold γ. The specific process is as follows:

[0044] First, according to the environmental knowledge base, determine the value ranges of λ and ω 2 as λ ∈ [λ min , λ max , Select the interpolation nodes λ0 = λ min , and

[0045] Secondly, for each interpolation node conduct independent Monte Carlo experiments under the null hypothesis to generate MC composite Gaussian distribution data matrices X (1) ,..., X (MC) , Among them, the texture component follows the GIG distribution with parameters , and the speckle component follows the Gaussian distribution with zero mean and covariance matrix I N .

[0046] Then, for each X (i) calculate the statistic and obtain the empirical distribution By finding the upper P fa quantile of the empirical distribution, the threshold value of each interpolation point can be determined

[0047] Finally, using the parameter-threshold pair By means of two-dimensional piecewise linear interpolation (other two-dimensional interpolations such as spline interpolation can also be considered), calculate the interpolation function According to the convergence theorem of interpolation, when the maximum grid size of the interpolation is small enough, γ(λ, ω 2 ) satisfies certain smoothness conditions, and the number of Monte Carlo times MC is large enough, then the interpolation function can approximate to the true threshold γ(λ, ω 2 ) corresponding to any parameters λ, ω 2 ).

[0048] For any given (λ, ω 2 ), the interpolation function can be used to quickly and accurately estimate the threshold value of the test statistic T (λ，χ，ψ) (X). Although the computational amount of the interpolation function is large, it can be calculated and stored offline, so this process will not increase the online computational complexity of the detector.

[0049] Step 4: Considering the case where the parameters (λ, χ, ψ) are unknown, the above GIG-GLRT detector and the corresponding threshold γ(λ, ω 2 ) both depend on the unknown parameters (λ, χ, ψ). The present invention proposes a new CFAR technology to make the false alarm rate of the fully adaptive GIG-GLRT detector unaffected by the parameter changes of GIG. The specific steps are as follows:

[0050] First, in order to enable the radar system to sense the unknown parameters (λ, χ, ψ) of the (regular) GIG distribution, consider using a second set of training data with a sample size of K0 that is independently and identically distributed with the first set of training data [x L+1 ,..., x L+K . Let Then, construct a sample of the GIG distribution based on this set of training data According to the law of large numbers, when N is large enough, it can be considered that {y k} is an independent and identically distributed sample approximately obeying f GIG (τ; λ, χ, ψ). For the unknown ∑, use the consistent estimate of ∑ for substitution.

[0051] Note: In order to ensure that the subsequent fully adaptive GIG-GLRT detector satisfies the CFAR property, the requirement of mutual independence should be satisfied between {y k} and X = [x1,..., x L+K .

[0052] Secondly, the sample y k has a log-likelihood function of

[0053]

[0054] where

[0055]

[0056] On the premise that λ is fixed, the maximum likelihood estimation problem in the GIG texture distribution can be expressed as

[0057]

[0058] where

[0059]

[0060] Obviously, solving the univariate optimization problem significantly reduces the computational complexity and improves the computational efficiency.

[0061] Then, by means of a mature numerical calculation method, the optimal solution of this univariate optimization problem can be obtained and then the maximum likelihood estimation of the unknown parameters can be obtained or the corresponding

[0062] Finally, substituting the estimation of the unknown parameters into the GIG-GLRT detector to establish a fully adaptive GIG-GLRT detector:

[0063]

[0064] In the GIG compound Gaussian clutter, for the changes of the divergence matrix ∑ and (λ, χ, ψ) in the probability density function of the GIG texture component, this fully adaptive detector can guarantee the CFAR property.

Claims

1. A fully adaptive constant false alarm rate detection method for generalized clutter texture distribution, characterized in that It includes the following steps: Step 1: Construct a test statistic based on texture distribution knowledge, covariance matrix structure information, and signal subspace; Step 2: Use the Monte Carlo method to offline establish an interpolation function of the threshold, and estimate the corresponding threshold quickly and with high precision according to the parameters of the probability density function of the texture component; Step 3: In the process of radar target detection, use the second set of training data to estimate the unknown parameters in the texture distribution, combine the test statistic with the interpolation function of the threshold, construct a fully adaptive detector, and perform constant false alarm detection.

2. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 1, characterized in that The first step includes: selecting a detection criterion, using a two-step strategy, and establishing a detector where X is an observation matrix (including main data and a first set of training data), and θ is an unknown parameter in the probability density function of the texture component.

3. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 2, wherein When the parameters θ=(λ,χ,ψ) of the GIG texture distribution are known, construct a GIG-GLRT detector: Among them, X = [x1, …, x L+K , the threshold γ(λ, ψχ) can be expressed as γ(λ, ω 2 ), given the false alarm rate P fa . Since the test statistic satisfies Therefore,[[]] the distribution function of the test statistic T (λ,χ,ψ) (X) only depends on the parameters (λ, ω 2 ), and the threshold γ also only depends on the parameters (λ, ω 2 ).

4. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 1 or 2, characterized in that The second step includes: determining the value range of parameter θ according to the environmental knowledge base of the radar, and selecting an interpolation point set {θ l} within the value range. For each θ l , the empirical distribution of is obtained using the Monte Carlo method under the null hypothesis According to the preset false alarm probability P fa , the upper P fa quantile of the empirical distribution is obtained That is, the threshold corresponding to the detector when θ = θ l . According to the interpolation condition {γ(θ l )}, an interpolation function is established using interpolation techniques The interpolation function is obtained through offline calculation 5. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 4, characterized in that The specific content of the said Step 2 includes: S21: Determine the value ranges of parameters λ and ω according to the environmental knowledge base 2 as λ ∈ [λ min , λ max , select interpolation nodes in ascending order and S22: For each interpolation node perform independent Monte Carlo experiments under the null hypothesis to generate MC compound Gaussian distribution data matrices X( 1 ),..., X( MC ), where the texture component follows a GIG distribution with parameter and the speckle component follows a Gaussian distribution with zero mean and covariance matrix being the identity matrix I N ; S23: For each X (i) Calculate the statistic And obtain the empirical distribution By looking up the upper P fa quantile of the empirical distribution, determine the threshold value of each interpolation point ​ S24: Using the parameter-threshold pair Use the two-dimensional piecewise linear interpolation method to calculate the interpolation function 6. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 4, characterized in that Step 3 includes: using a second set of training data independent of the main data to obtain a consistent estimate of the unknown parameter θ in the texture distribution, denoted as According to the detector proposed in Step 1 and the interpolation function proposed in Step 2 to obtain a fully adaptive CFAR detector 7. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 6, wherein The second set of training data has the same clutter statistical characteristics as the main data and is independent of the first set of training data.

8. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 6, characterized in that The specific content of the said Step 3 includes: S31: Use the second set of training data with a sample size of K0 which is independently and identically distributed with the first set of training data [x L+1 ,..., x L+K , and let Construct samples of the GIG distribution based on the second set of training data According to the law of large numbers, when N is large enough, {y k} is considered to be an independent and identically distributed sample approximately following the probability density function f GIG (τ; λ, χ, ψ); for the unknown ∑, use the consistent estimate of ∑ for substitution.

9. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 8, characterized in that It also includes: S32: Sample y k The log-likelihood function of Wherein, On the premise that λ is fixed, the maximum likelihood estimation problem in the GIG texture distribution is expressed as Among them, S33: Solve the univariate optimization problem Obtain the optimal solution of the univariate optimization problem Furthermore, obtain the maximum likelihood estimate of the unknown parameter Or the corresponding 10. The fully adaptive constant false alarm rate detection method for generalized clutter texture distribution according to claim 9, characterized in that It also includes: S34: Substitute the maximum likelihood estimate of the unknown parameter into the GIG-GLRT detector to establish a fully adaptive GIG-GLRT detector:

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