Radar target detection constant false alarm rate control method and system based on sample quantile characteristics, terminal and storage medium

Abstract

The invention relates to the technical field of radar signal processing, and particularly provides a radar target detection constant false alarm rate control method and system based on sample quantile characteristics, a terminal and a storage medium, and the method comprises the steps: obtaining a radar echo signal of a to-be-detected unit; the method comprises the steps of grouping radar echo signals of a to-be-detected unit, constructing a sample set, and extracting quantile features from grouped samples according to a plurality of preset quantile levels to obtain quantile feature vectors; based on the quantile feature vector, calculating to obtain a statistic of the to-be-tested unit; comparing the statistical magnitude of the to-be-detected unit with a preset judgment threshold value, and if the statistical magnitude is greater than the judgment threshold value, judging that a target exists in the to-be-detected unit; and if the statistical magnitude is smaller than or equal to the judgment threshold value, judging that no target exists in the to-be-detected unit. According to the invention, the target detection sensitivity and the anti-clutter capability are significantly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to a constant false alarm rate control method, system, terminal and storage medium for radar target detection based on sample quantile features. Background Art

[0002] With the increasing frequency of maritime transportation, ocean monitoring and maritime missions, the detection of small targets at sea, as one of the important applications of radar detection technology, has received more and more attention. The radar system emits electromagnetic waves to the target area and receives the echo signal, and extracts target information from it, which is the key means to achieve all-weather and long-distance monitoring. However, in the actual marine environment, due to the large number of irregular fluctuations on the sea surface itself, the signal received by the radar is often mixed with a large amount of "sea clutter" signals formed by sea waves, spray, etc. Especially for small targets at sea with small volume and weak signal reflection intensity, such as buoys, small boats, rubber boats, etc., their echoes are extremely easy to be submerged in strong sea clutter, resulting in a significant reduction in the target signal-to-noise ratio (SNR), thereby affecting the accuracy and reliability of detection.

[0003] To solve this problem, the constant false alarm rate (CFAR) detection method has been widely applied to radar systems. The core idea of the CFAR method is: on the premise of ensuring a constant false alarm rate, that is, a constant false alarm probability, dynamically adjust the detection threshold to adapt to different background clutter conditions, so as to achieve stable and reliable target detection. With the development of radar technology, researchers have gradually realized that it is difficult to cope with complex environmental changes by relying solely on a single feature (such as echo amplitude) for detection, so the idea of multi-feature detection has been proposed, that is, extracting statistical features in multiple dimensions (such as frequency domain features, time-frequency features, Doppler features, etc.) from the radar echo signal to improve the discrimination ability between the target and the clutter.

[0004] Although current multi-feature detection methods have made certain progress in enhancing target recognition capabilities, they still face significant challenges in achieving constant false alarm rate (CFAR) control. First, traditional CFAR methods typically rely on the accurate modeling of feature distributions, that is, assuming that features follow a certain known probability distribution (such as Gaussian distribution, K distribution, log-normal distribution, etc.), and then deriving the mathematical relationship between the detection threshold and the false alarm rate based on this. However, in actual complex environments, the true distribution of features is often unknown and may exhibit highly non-Gaussian characteristics, such as heavy tails and skewness, resulting in difficulties for traditional modeling methods to accurately characterize the statistical differences between targets and backgrounds, thereby affecting detection performance. Second, there may be significant correlations or redundancies between multi-features, making it difficult to construct effective detection criteria in high-dimensional feature spaces. In addition, under multi-dimensional feature conditions, how to construct a unified statistic and accurately derive its distribution characteristics theoretically is the key to achieving CFAR control. However, most current multi-feature CFAR methods only set thresholds through simulation experience and are difficult to provide clear theoretical support. Summary of the Invention

[0005] In view of the problem in the prior art that traditional detection methods usually need to pre-assume the distribution type of radar feature data under background clutter, such as normal distribution or K distribution. However, in actual complex environments, the true distributions of these features are often unknown or vary unpredictably, and forced assumptions may lead to misjudgment problems. The present invention provides a method, system, terminal, and storage medium for constant false alarm rate control of radar target detection based on sample quantile features. Without making strong assumptions about feature distributions, multi-features with clear mathematical expressions and capable of precisely controlling the false alarm rate are constructed to solve the above technical problems.

[0006] In a first aspect, the present invention provides a method for constant false alarm rate control of radar target detection based on sample quantile features, including: Obtain the radar echo signal of the unit to be measured; Group the radar echo signal of the unit to be measured to construct a sample set, and extract quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector; Based on the quantile feature vector, calculate the statistic of the unit to be measured; Compare the statistic of the unit to be measured with a preset decision threshold. If the statistic is greater than the decision threshold, it is determined that there is a target in the unit to be measured; if the statistic is less than or equal to the decision threshold, it is determined that there is no target in the unit to be measured.

[0007] Further, the method for constructing the preset decision threshold includes: Obtain the radar echo signal in the reference unit and extract sea clutter sample data; Perform distribution fitting on the sea clutter samples to obtain the theoretical distribution model of the sea clutter; Calculate the theoretical quantile vector and the covariance matrix between each quantile under the theoretical distribution model according to a plurality of preset quantile levels; Obtain the decision threshold according to the theoretical quantile vector, the covariance matrix, the preset false alarm rate, and the pre-established statistical test model.

[0008] Further, performing distribution fitting on the sea clutter samples to obtain the theoretical distribution model of the sea clutter, including: Assume that the sea clutter amplitude x follows a K distribution, and the cumulative distribution function is :

[0009] The probability density function is :

[0010] Among them, is the scale parameter, is the shape parameter, is the modified Bessel function of the second kind, represents the gamma function; Denote the cumulative distribution function as and the probability density function as as the theoretical distribution model of the sea clutter.

[0011] Further, according to a plurality of preset quantile levels, calculate the theoretical quantile vector and the covariance matrix between each quantile under the theoretical distribution model, including: Set the sea clutter sample is a random sample obtained from As the number of samples , for any set quantile level The corresponding quantile estimate value will asymptotically converge to the theoretical quantile value , and asymptotically follow a normal distribution:

[0012] Among them, is an arbitrarily set quantile The theoretical quantile value under the theoretical distribution model satisfies:

[0013] And, ; Among them, represents The inverse function of; Based on the theoretical quantile values corresponding to multiple quantile levels , a theoretical quantile vector is formed ; Calculate the covariance matrix of the quantile estimates corresponding to multiple quantiles .

[0014] Furthermore, according to the theoretical quantile vector, the covariance matrix, a preset false alarm rate, and a pre-established statistical test model, a decision threshold is obtained, including: Based on the quantile estimates corresponding to multiple quantile levels , a quantile estimate vector is constructed, and the quantile estimate vector

[0015] asymptotically follows a normal distribution: where is the theoretical quantile vector, and is the covariance matrix of Based on the theoretical quantile vector and the covariance matrix , a statistic Q is constructed:

[0016] Then the statistic Q follows a chi-square distribution:

[0017] Based on the preset false alarm rate , the decision threshold is obtained: .

[0018] Furthermore, the radar echo signals of the unit under test are grouped to construct a sample set. From the grouped samples, quantile features are extracted according to multiple preset quantile levels to obtain a quantile feature vector, including: Samples are drawn from the unit under test and sorted in ascending order as ; Define the quantile estimate value at the quantile , and the value of the corresponding cumulative distribution function satisfies: , where , ; is an indicator function, which is 1 when and 0 otherwise; Calculate , a quantile feature vector is obtained, where represents rounding down.

[0019] Further, based on the quantile feature vector, a statistic of the unit to be measured is calculated, including: Based on the quantile feature vector of the unit to be measured and in combination with the theoretical quantile vector of the reference unit and the covariance matrix , the statistic of the unit to be measured is calculated: .

[0020] In a second aspect, the present invention provides a constant false alarm rate control system for radar target detection based on sample quantile features, including: A signal acquisition module for acquiring the radar echo signal of the unit to be measured; A feature vector calculation module for grouping the radar echo signal of the unit to be measured, constructing a sample set, and extracting quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector; A statistic calculation module for calculating a statistic of the unit to be measured based on the quantile feature vector; A target determination module for comparing the statistic of the unit to be measured with a preset determination threshold. If the statistic is greater than the determination threshold, it is determined that there is a target in the unit to be measured; if the statistic is less than or equal to the determination threshold, it is determined that there is no target in the unit to be measured.

[0021] In a third aspect, a terminal is provided, including: A processor and a memory, where the memory is used to store a computer program, the processor is used to call and run the computer program from the memory, so that the terminal executes the method of the above terminal.

[0022] In a fourth aspect, a computer storage medium is provided. Instructions are stored in the computer-readable storage medium. When it runs on a computer, the computer is made to execute the methods described in the above aspects.

[0023] The beneficial effects of the present invention are as follows. The constant false alarm rate (CFAR) control method, system, terminal, and storage medium for radar target detection based on sample quantile features provided by the present invention can construct a theoretically controllable CFAR detection criterion without relying on a specific noise distribution model, realizing a closed mathematical relationship between the detection threshold and the preset false alarm rate, thereby improving the reliability and engineering controllability of the detection process. By extracting sample quantile features at multiple quantiles, this method comprehensively characterizes the statistical characteristics of radar echoes in different amplitude regions, can effectively distinguish sea clutter from weak target signals, and significantly improves the target detection sensitivity and clutter rejection ability. Compared with traditional single-feature or fixed-threshold detection methods, the present invention uses non-parametric statistics to construct a detection vector, has good robustness, can adapt to complex background noise environments such as spikes and heavy tails, avoids the need for accurate modeling of the background clutter distribution, and improves the universality and deployment efficiency of the method. At the same time, the detection algorithm of the present invention has a simple structure and small computational complexity, only involving operations such as sample quantile extraction, mean and covariance calculation, and chi-square distribution look-up table, which is convenient for real-time implementation in embedded systems or edge computing devices, and is applicable to scenarios such as high-resolution radar systems, shipborne radars, and small target monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0025] Figure 1 is a schematic flowchart of the method according to an embodiment of the present invention.

[0026] Figure 2 is a schematic histogram for verifying the asymptotic normality of SQF using K-distributed simulated data according to an embodiment of the present invention.

[0027] Figure 3 is a schematic Q-Q plot for verifying the asymptotic normality of SQF using K-distributed simulated data according to an embodiment of the present invention.

[0028] Figure 4 is a schematic diagram comparing the amplitude, RAA feature, and 75% SQF according to an embodiment of the present invention.

[0029] Figure 5 is a schematic three-dimensional comparison diagram of the target and sea clutter SQF according to an embodiment of the present invention.

[0030] Figure 6It is a Q-Q plot schematic diagram for comparing the normality of amplitude characteristics and magnitude characteristics in an embodiment of the present invention.

[0031] Figure 7 It is a density distribution schematic diagram for comparing the normality of amplitude characteristics and magnitude characteristics in an embodiment of the present invention.

[0032] Figure 8 It is a schematic diagram of the FAR of bivariate SQF using simulated data in an embodiment of the present invention.

[0033] Figure 9 It is a schematic diagram of false alarm control in an embodiment of the present invention.

[0034] Figure 10 It is a schematic diagram of the detection result in an embodiment of the present invention.

[0035] Figure 11 It is an embodiment of the present invention Schematic diagram of sea clutter false alarm behavior.

[0036] Figure 12 It is an embodiment of the present invention Schematic diagram of sea clutter false alarm behavior.

[0037] Figure 13 It is an embodiment of the present invention Schematic diagram of sea clutter false alarm behavior.

[0038] Figure 14 It is an embodiment of the present invention Schematic diagram of the target detection result at

[0039] Figure 15 It is an embodiment of the present invention Schematic diagram of the target detection result at

[0040] Figure 16 It is an embodiment of the present invention Schematic diagram of the target detection result at

[0041] Figure 17 It is an embodiment of the present invention Schematic diagram for comparing the detection rates of different CFAR methods at

[0042] Figure 18 It is an embodiment of the present invention Schematic diagram for comparing the detection rates of different CFAR methods at

[0043] Figure 19 It is an embodiment of the present invention Schematic diagram for comparing the detection rates of different CFAR methods at

[0044] Figure 20 is a schematic block diagram of a system according to an embodiment of the present invention.

[0045] Figure 21 is a schematic structural diagram of a terminal provided by an embodiment of the present invention. Detailed implementation manners

[0046] In order to enable those skilled in the art of the present technology to better understand the technical solutions in the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0047] Unless otherwise defined, all technical and scientific terms used in this application have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the specification of the present invention in this application are only for the purpose of describing specific embodiments, and are not intended to limit the present invention.

[0048] The following explains the key terms that appear in the present invention.

[0049] CFAR: Constant False - Alarm Rate. In radar signal detection, when the intensity of external interference changes, the radar can automatically adjust its sensitivity so that the false - alarm probability of the radar remains unchanged. This characteristic is called the constant false - alarm rate characteristic.

[0050] The constant false - alarm rate control method for radar target detection based on sample quantile features provided by the embodiments of the present invention is executed by a computer device. Correspondingly, the constant false - alarm rate control system for radar target detection based on sample quantile features runs in the computer device.

[0051] Figure 1 is a schematic flowchart of a method according to an embodiment of the present invention. Among them, Figure 1 The execution subject can be a constant false - alarm rate control system for radar target detection based on sample quantile features. According to different requirements, the order of the steps in this flowchart can be changed, and some can be omitted.

[0052] For the convenience of understanding the present invention, the following further describes the constant false - alarm rate control method for radar target detection based on sample quantile features provided by the present invention with reference to the principle of the constant false - alarm rate control method for radar target detection based on sample quantile features of the present invention.

[0053] Specifically, asFigure 1 As shown, the constant false alarm rate control method for radar target detection based on sample quantile features includes: S1. Obtain the radar echo signal of the unit to be measured.

[0054] In this application, the determined target is designated as a light buoy, located approximately 2.97 nautical miles from the radar installation point, with an azimuth of 10.7°. The buoy is anchored and floating, with a red cylindrical structure. The buoy is made of steel, with a diameter of approximately 2.4 meters and a height above the water surface of approximately 4.1 meters.

[0055] This application uses two custom-designed X-band solid-state amplifier test radars. One of the radars uses HH polarization, and the other uses VV polarization. Both radars operate in a fixed-pointing mode and continuously point to the channel buoy throughout the experiment. During data acquisition, the radars transmit T1 signals (pulse width: 150 nanoseconds) and T2 linear frequency modulation signals (pulse width: 25 microseconds). The ranging resolution of the T1 waveform is 22.5 meters, while the ranging resolution of the T2 waveform with a bandwidth of 25 MHz is 6 meters.

[0056] In this application, the radar only transmits T1 and T2 signals during data acquisition.

[0057] The radar target detection problem can be formulated as a mathematical binary hypothesis testing problem. The received signal in each ranging unit is represented by ( ) If the ranging unit contains a target, including the target signal, sea clutter, and noise. Otherwise, only includes sea clutter and noise. Since the energy of the noise is significantly weaker than that of the sea clutter, the noise part can be ignored. Based on this assumption, target detection in sea clutter can be formulated as a binary hypothesis testing problem:

[0058] where and represent the signals of the cell under test (CUT) and the reference cell (RC), respectively. represents the target signal, and represent the sea clutter signals in the CUT and the reference cell, respectively. The parameter specifies the number of reference cells.

[0059] According to the hypothesis , the CUT does not contain a target, and the signal consists only of sea clutter, so it is a sea clutter cell (SCC). On the contrary, according to , the CUT contains the target signal and classifies it as the target cell (TC). Assume the RC signal contains only sea clutter, then it is modeled as . In addition, we also assume that the sea clutter in the reference cell is spatially uniform. This means that the statistical characteristics of the reference cell are the same as those of the CUT.

[0060] Assume a feature vector is extracted from the SCC , and its cumulative distribution function (CDF) is represented by . According to the feature vector , construct the detection statistic . By specifying the predefined FAR , determine the detection threshold to meet the following conditions:

[0061] The corresponding decision rule is defined as follows

[0062] S2. Group the radar echo signals of the cells to be measured, construct a sample set, and extract quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector.

[0063] Extract samples from the cells to be measured , sort the samples in ascending order as ; define the quantile estimate value At the quantile of , the value of the corresponding cumulative distribution function satisfies: , where , ; is the indicator function, which is 1 when and 0 otherwise; calculate to obtain the quantile feature vector, where represents rounding down.

[0064] S3. Based on the quantile feature vector, calculate the statistic of the cell to be measured.

[0065] Based on the quantile feature vector of the cell to be measured, combined with the theoretical quantile vector of the reference cell and the covariance matrix , calculate the statistic of the cell to be measured: .

[0066] S4. Compare the statistic of the unit under test with a preset determination threshold. If the statistic is greater than the determination threshold, it is determined that there is a target in the unit under test. If the statistic is less than or equal to the determination threshold, it is determined that there is no target in the unit under test.

[0067] In an implementable embodiment, it further includes: a method for constructing a preset determination threshold, including: Q1. Obtain the radar echo signal in the reference unit and extract the sea clutter sample data.

[0068] Q2. Perform distribution fitting on the sea clutter samples to obtain the theoretical distribution model of the sea clutter.

[0069] Assume that the sea clutter amplitude x follows a K distribution, and the cumulative distribution function is :

[0070] The probability density function is :

[0071] Wherein, is the scale parameter, is the shape parameter, is the modified Bessel function of the second kind, represents the gamma function; The cumulative distribution function is and the probability density function is are recorded as the theoretical distribution model of the sea clutter.

[0072] Q3. According to a preset plurality of quantile levels, calculate the theoretical quantile vector and the covariance matrix between each quantile under the theoretical distribution model.

[0073] Set the sea clutter sample is a random sample obtained from As the sample size , for any set quantile level The corresponding quantile estimate will asymptotically converge to the theoretical quantile value , and asymptotically follow a normal distribution:

[0074] Wherein, is an arbitrarily set quantile The theoretical quantile value under the theoretical distribution model satisfies:

[0075] And, ; wherein, denote the inverse function of; Based on the theoretical quantile values corresponding to multiple quantile levels , a theoretical quantile vector is formed ; Calculate the covariance matrix of the quantile estimates corresponding to multiple quantiles of .

[0076] Q4. According to the theoretical quantile vector, the covariance matrix, the preset false alarm rate, and the pre-established statistical test model, a decision threshold is obtained.

[0077] Based on the quantile estimates corresponding to multiple quantile levels , a quantile estimate vector is constructed , and the quantile estimate vector follows a normal distribution:

[0078] wherein, is the theoretical quantile vector, is the covariance matrix of; Based on the theoretical quantile vector and the covariance matrix , a statistic Q is constructed:

[0079] Then the statistic Q follows a chi-square distribution:

[0080] Based on the preset false alarm rate , a decision threshold is obtained: .

[0081] Specifically, the distribution of sea clutter characteristics is often difficult to determine. The present application proposes an extraction method based on SQF. As a non-parametric statistic, SQF can provide a robust statistical description without being affected by the sea clutter distribution.

[0082] Let represent the population of sea clutter amplitudes, represent the sample drawn from the population. Denote the order statistic of this sample as . The sample quantile is defined as the value corresponding to the CDF at the quantile level , satisfying:

[0083] Empirical CDF is given by the following formula:

[0084] where is the indicator function, which equals 1 if , and 0 otherwise.

[0085] In practice, the sample quantile at the level can be calculated using the actual data through formula (6):

[0086] where denotes the floor operation.

[0087] SQF effectively describes the sea clutter amplitude at a specific quantile level without considering the population distribution.

[0088] Theorem 1: Let be independent and identically distributed samples from the distribution , and assume that the inverse function of the quantile level is monotonically continuous , and the density function . Denote the sample quantile. Then, similar to , the asymptotic distribution of the sample quantile distribution is:

[0089] where is the inverse function, is the density function, denotes the normal distribution with mean 0 and variance , denotes the convergence of the distribution.

[0090] The K - distribution has been proven to effectively simulate the high - kurtosis and heavy - tail characteristics of sea clutter under various conditions

[27] . Without loss of generality, this study takes the K - distribution as an example for analysis and verification. When the sea clutter follows other distributions, similar methods can be used to obtain corresponding results.

[0091] Corollary 1: Assume that the sea clutter amplitude in a single ranging cell follows the K - distribution, its CDF is denoted by , and its probability density function (PDF) is denoted by , where is the scale parameter and is the shape parameter. For simplicity, and are simplified to and 。

[0092]

[0093]

[0094] is the modified Bessel function of the second kind, representing the gamma function.

[0095] Suppose is an independent and identically distributed random sample from . As the sample size , for a given quantization level , the sample quantization converges asymptotically to the true quantization , and asymptotically follows a normal distribution:

[0096] where the asymptotic expectation of is

[0097] where . Here, denotes the inverse function of

[0098] The formula for the asymptotic variance is

[0099] According to Corollary 1, the simulation procedure is described as follows: Step 1: Generate uniformly distributed random variables, .

[0100] Step 2: Use the inverse transformation, to generate random variables from the K - distribution.

[0101] Step 3: Given the sample size of , draw independent and identically distributed samples from the population. Repeat this process times, denoted as .

[0102] Step 4: Calculate for each sample.

[0103] Step 5: Conduct a normality test on .

[0104] Simulation: Set the shape parameter of the K - distribution and the scale parameter , with the overall scale being . Each sample consists of observations. Extract the SQF for verification. Figure 2 Shows the normal distribution fitting of the 75% SQF of the K - distribution samples, Figure 3 and shows the Q - Q plot. It can be seen that the SQF is very close to the normal distribution.

[0105] The effectiveness of the proposed SQF extraction method was verified using the dataset 20221115050306_stare_VV (the 508th cell was identified as TC). The comparison of the extracted 75% SQF, the original amplitude, and the common RAA feature is shown in Figure 4 .

[0106] As Figure 4 shown, the original amplitude cannot provide sufficient contrast between the target and the sea clutter, and there is color overlap between the sea clutter background and the target area. Compared with the original amplitude, the RAA improves the distinguishability between the target and the sea clutter. However, some clutter areas are still similar to the target area. The SQF significantly enhances the contrast, making the target more distinct from the sea clutter.

[0107] As Figure 5 shown, compared with the surrounding SCC, the SQF of the 508th range cell corresponding to the TC is significantly elevated.

[0108] Here, every 128 pulses within a single range cell are selected once to ensure the independence of the sampling process. Then the amplitude data is divided into 30 different groups. Calculate the 75% SQF for each group.

[0109] A normal comparison was made between the amplitude and the 75% SQF in the RC. As the QQ plot in Figure 6 shows, the amplitude deviates from the theoretical normal line, indicating a non - normal distribution. In contrast, the 75% SQF is closer to the normal line, indicating an approximate normal distribution. As Figure 7 shown, in terms of the density distribution, the amplitude distribution significantly deviates from the typical normal bell - shaped curve, while the distribution of the quantization feature is close to the normal distribution. This indicates that the result of the SQF feature extraction is an approximately normal - distributed feature. Given the complex statistical properties of the sea clutter signal (usually showing heavy - tailed behavior), the Anderson - Darling (AD) test is used to quantitatively evaluate the normality. This test is particularly sensitive to the deviation in the tails of the distribution and is therefore very suitable for evaluating the asymptotic normality of the SQF.

[0110] Using , representing the SQF extracted from the sea clutter signal, with the quantile level being . According to the sample data , the empirical CDF is calculated . Then construct the AD test statistic as follows:

[0112] In statistical hypothesis testing, the p-value plays a crucial role in determining the validity of the null hypothesis. If the p-value is lower than the predetermined significance level, the null hypothesis does not hold, indicating that the data deviates from the normal distribution. Conversely, the null hypothesis holds and the data is considered to be normally distributed. Additionally, the AD test p-value is 0.83, which further confirms the asymptotic normality of the quantile-level sample quantiles.

[0113] The SQF method can effectively capture the fluctuations of sea clutter at different quantile levels. Lower quantile levels reflect the changes in the lower tail of the distribution, while higher quantile levels are sensitive to the changes in the upper tail. By jointly analyzing the multivariate SQF, the characteristics of the upper and lower tails of sea clutter can be effectively captured.

[0114] Based on the multivariate normal distribution theory, the CFAR control theorem and detection boundary are derived and extended using the multivariate sample quantile characteristics.

[0115] Theorem 2: Assume that the multivariate sample quantiles approximately follow a d-dimensional normal distribution. For a given FAR , construct the test statistic:

[0116] where represents the mean vector, is the covariance, which is used to capture the dependencies between different quantile levels.

[0117] To achieve the predetermined FAR , the detection threshold must satisfy the following conditions:

[0118] This threshold can be expressed as

[0119] where represents at the significance level with The chi - square distribution of degrees of freedom.

[0120] Prove the hypothesis that the SQF vector approximately follows a multivariate normal distribution:

[0121] where is the mean vector, is the covariance matrix.

[0122] The test statistic is constructed as follows

[0123] The covariance matrix can be decomposed by the Cholesky decomposition method into where is a lower triangular matrix. Apply the linear transformation:

[0124] to obtain the standard multivariate normal random vector where is the identity matrix.

[0125] The components of

[0126] are independent standard normal random variables. Therefore, the test statistic

[0127] follows a chi - square distribution: For a given FAR the detection threshold satisfies . Therefore, the detection threshold

[0128] Use the sea clutter data of the reference cell to establish a statistical distribution model that best represents the data characteristics. Describe the distribution characteristics of SQF by calculating the mean vector and covariance matrix. Determine the detection threshold according to Theorem 2 for the specified FAR.

[0129] For the CUT (Cell Under Test), extract the sample quantile feature (SQF), calculate the test statistic Q, and compare it with the detection threshold T. If Q > T, it means that the current sample feature significantly deviates from the reference distribution, and the null hypothesis is not valid, indicating the presence of a target; otherwise, Q ≤ T, which means that the data fails to provide sufficient evidence to reject , and the null hypothesis is retained, considering that there is no target in this cell.

[0130] Based on Theorem 2, this detection method proposes a detection framework for multivariate SQF, assuming that the sea clutter amplitude follows K distribution. It is worth noting that this method is applicable to the case where sea clutter follows other distributions.

[0131] Step 1: Estimate the scale parameter of the K distribution using the maximum likelihood estimation (MLE) method and shape parameters According to the PDF of K distribution in formula (8), the clutter amplitude data The log-likelihood function of is expressed as:

[0132] and The parameter estimates of are obtained numerically through the partial derivatives of the log-likelihood function as follows:

[0133] Step 2: Determine the quantile level , representing different tails of the distribution to facilitate detailed analysis.

[0134] Step 3: Using K distribution , calculate the expected value of SQF ( ).

[0135] Step 4: According to the given , using rank square distribution to calculate the detection threshold :

[0136] Step 5: Assume that the reference unit is spatially homogeneous and use formula (6) to calculate the sample quantile value of CUT .

[0137] Step 6: Based on the calculated , calculate the test statistic, ,in and Each element Representative sample quantification and The covariance between is defined as follows:

[0138] in Is the sample quantification The variance of It is the overall quantitative and The correlation coefficient between

[0139] Step 7: Statistic is compared with the detection threshold . If , the null hypothesis holds. Otherwise, if , the null hypothesis does not hold.

[0140] Simulation and experimental verification of bivariate SQF detection: According to Theorem 2, for the bivariate SQF , the test statistic is defined as follows:

[0141] where is the mean vector, is the covariance matrix of the magnitudes, and its calculation formula is

[0142] where is and the correlation coefficient between , are respectively and the PDFs of.

[0143] For a given FAR , the detection threshold is expressed as

[0144] The bivariate SQF satisfies the elliptical boundary constraint defined by the detection threshold :

[0146] where the coefficient is defined as

[0147] Let , the calculation formula for the detection threshold is . The mean vector of the SQF is defined as , and the covariance matrix is given by .

[0148] A total of 1000 groups of two-dimensional sample quantile vectors are generated, and the quantitative levels are respectively and . Calculate the test statistic for each group , and compare it with the threshold . Figure 8 shows the results of the bivariate SQF simulation. The black ellipse boundary corresponds to the detection threshold . The blue dots represent SCC samples, and the red dots represent TC samples. The observed FAR is 0.001, confirming the effectiveness of the proposed detection method.

[0149] We further verified the proposed method using the dataset labeled 20221115050306_stare_VV. The sampling and grouping method is the same as above.

[0150] Using the MLE estimation method, the parameter estimates of the K - distribution are and . For the quantile levels and , the calculated quantile levels are and respectively. According to the K - distribution, the corresponding probability density values are determined to be and , and the correlation coefficient is .

[0151] When setting , the actual false - alarm rates are 0.1, 0.013, and 0.0008 respectively. For the target samples, the detection rate is 100%. The false - alarm rate control is as shown in Figure 9 , and the detection results are as shown in Figure 10 .

[0152] The false - alarm control results are as shown in Figure 11 , Figure 12 and Figure 13 . The red dots represent the false - alarm targets. The target detection results are as shown in Figure 14 , Figure 15 and Figure 16 . As decreases, the ellipse boundary gradually expands.

[0153] Currently, the target detection methods based on multivariate features face challenges in achieving CFAR and deriving a closed - form expression for the detection threshold. Therefore, this study compares the proposed method with several existing CFAR detection methods to evaluate.

[0154] To increase the sample size, we extracted the SQFs and compared them with the CFAR method under continuous sampling conditions. Specifically, for each group of 256 pulses, 25% and 75% of the SQFs were extracted, and the test statistic was calculated.

[0155] As shown in Figure 17, Figure 18 and Figure 19 As shown in , the is compared with CA - CFAR, GO - CFAR and OS - CFAR. The results show that at

[0156] In some embodiments, the radar target detection constant false alarm rate control system based on sample quantile features may include multiple functional modules composed of computer program segments. The computer programs of each program segment in the radar target detection constant false alarm rate control system based on feature sample quantiles can be stored in the memory of a computer device and executed by at least one processor to perform the functions of radar target detection constant false alarm rate control based on sample quantile features (see Figure 1 for description).

[0157] In this embodiment, the radar target detection constant false alarm rate control system based on sample quantile features can be divided into multiple functional modules according to the functions it performs, as shown in Figure 20 . The functional modules of system 200 may include: a signal acquisition module 210, a feature vector calculation module 220, a statistic calculation module 230, and a target determination module 240. The module referred to in the present invention means a series of computer program segments that can be executed by at least one processor and can complete fixed functions, and are stored in the memory. In this embodiment, the functions of each module will be described in detail in subsequent embodiments.

[0158] The signal acquisition module is used to acquire the radar echo signal of the unit to be measured; The feature vector calculation module is used to group the radar echo signals of the unit to be measured, construct a sample set, and extract quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector; The statistic calculation module is used to calculate the statistic of the unit to be measured based on the quantile feature vector; The target determination module is used to compare the statistic of the unit to be measured with a preset determination threshold. If the statistic is greater than the determination threshold, it is determined that there is a target in the unit to be measured; if the statistic is less than or equal to the determination threshold, it is determined that there is no target in the unit to be measured.

[0159] Figure 21 FIG.

[0160] Among them, the terminal 300 may include: a processor 310, a memory 320, and a communication unit 330. These components communicate via one or more buses. Those skilled in the art can understand that the structure of the server shown in the figure does not constitute a limitation on the present invention. It can be a bus structure, a star structure, and may also include more or fewer components than those shown, or combine certain components, or have different component arrangements.

[0161] Among them, the memory 320 can be used to store the execution instructions of the processor 310. The memory 320 can be implemented by any type of volatile or non-volatile storage terminal or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disc. When the execution instructions in the memory 320 are executed by the processor 310, the terminal 300 can execute some or all of the steps in the above method embodiments.

[0162] The processor 310 is the control center of the storage terminal, connecting various parts of the entire electronic terminal through various interfaces and lines. By running or executing the software programs and / or modules stored in the memory 320, and by calling the data stored in the memory, it executes various functions of the electronic terminal and / or processes data. The processor may be composed of an integrated circuit (IC), for example, it may be composed of a single packaged IC, or may be composed of multiple packaged ICs with the same or different functions connected together. For example, the processor 310 may only include a central processing unit (CPU). In the embodiment of the present invention, the CPU may be a single arithmetic core or may include multiple arithmetic cores.

[0163] The communication unit 330 is used to establish a communication channel, so that the storage terminal can communicate with other terminals. It receives user data sent by other terminals or sends user data to other terminals.

[0164] The present invention also provides a computer storage medium. Among them, the computer storage medium can store a program, and when the program is executed, it can include some or all of the steps in the various embodiments provided by the present invention. The storage medium can be a magnetic disk, an optical disc, a read-only memory (ROM), or a random access memory (RAM), etc.

[0165] Therefore, the present invention can construct a theoretically controllable constant false alarm rate (CFAR) detection criterion under the premise of any noise distribution model, realizing a closed mathematical relationship between the detection threshold and the preset false alarm rate, thereby improving the reliability and engineering controllability of the detection process. This method extracts the sample quantile features at multiple quantiles to comprehensively characterize the statistical characteristics of radar echoes in different amplitude regions, can effectively distinguish sea clutter from weak target signals, and significantly improves the target detection sensitivity and clutter rejection ability. Compared with traditional single-feature or fixed-threshold detection methods, the present invention uses non-parametric statistics to construct a detection vector, has good robustness, can adapt to complex background noise environments such as spikes and heavy tails, avoids the need for accurate modeling of the background clutter distribution, and improves the universality and deployment efficiency of the method. At the same time, the detection algorithm of the present invention has a simple structure and small computational complexity, only involves operations such as sample quantile extraction, mean and covariance calculation, and chi-square distribution look-up table, is easy to be implemented in real time in embedded systems or edge computing devices, and is applicable to scenarios such as high-resolution radar systems, shipborne radars, and small target monitoring. The technical effects that can be achieved in this embodiment can be referred to the description above, and will not be elaborated here.

[0166] Those skilled in the art can clearly understand that the technologies in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solutions in the embodiments of the present invention, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product is stored in a storage medium such as a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk, or an optical disc, etc., which can store program codes, and includes several instructions for causing a computer terminal (which can be a personal computer, a server, or a second terminal, a network terminal, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0167] For the same or similar parts among the various embodiments in this specification, reference can be made to each other. In particular, for the terminal embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the description in the method embodiments.

[0168] In several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For example, the division of the modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces. The indirect couplings or communication connections of the systems or modules can be in electrical, mechanical or other forms.

[0169] The modules described as separate components may or may not be physically separated. The components shown as modules may or may not be physical modules, that is, they can be located in one place or distributed to multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0170] In addition, in each embodiment of the present invention, the functional modules can be integrated in a processing module, or each module can exist physically alone, or two or more modules can be integrated in one module.

[0171] Although the present invention has been described in detail by referring to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, those of ordinary skill in the art can make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions should all be within the scope of the present invention. / Any person familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, and they should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A constant false alarm rate control method for radar target detection based on sample quantile characteristics, characterized in that: include: Obtaining the radar echo signal of the unit under test; The radar echo signals of the unit to be tested are grouped to construct a sample set, and quantile features are extracted from the grouped samples according to a plurality of preset quantile levels to obtain a quantile feature vector; Based on the quantile eigenvector, the statistics of the unit under test are calculated; Compare the statistic of the unit to be tested with a preset determination threshold, and if the statistic is greater than the determination threshold, it is determined that there is a target in the unit to be tested; If the statistic is less than or equal to the determination threshold, it is determined that there is no target in the unit to be tested.

2. The method according to claim 1, characterized in that Also includes: The method for constructing a preset determination threshold comprises: Acquire the radar echo signal in the reference unit and extract the sea clutter sample data; Perform distribution fitting on sea clutter samples to obtain the theoretical distribution model of sea clutter; According to the preset multiple quantile levels, the theoretical quantile vector and the covariance matrix between the quantiles under the theoretical distribution model are calculated; The determination threshold is obtained according to the theoretical quantile vector, the covariance matrix, the preset false alarm rate and the pre-established statistical test model.

3. The method according to claim 2, characterized in that The distribution of sea clutter samples is fitted to obtain the theoretical distribution model of sea clutter, including: Assuming that the sea clutter amplitude x follows K distribution, the cumulative distribution function is : The probability density function is : in, is the scale parameter, is the shape parameter, is a modified Bessel function of the second kind, represents the gamma function; The cumulative distribution function is And the probability density function is Denoted as the theoretical distribution model of sea clutter.

4. The method according to claim 3, characterized in that: According to the preset multiple quantile levels, the theoretical quantile vector and the covariance matrix between the quantiles under the theoretical distribution model are calculated, including: Setting up the sea clutter sample is from The random samples obtained from , for any set quantile level The corresponding quantile estimate will converge asymptotically to the theoretical quantile value , and asymptotically follows a normal distribution: in, For any set quantile The theoretical quantile value under the theoretical distribution model satisfies: and, ;in, express The inverse function of Theoretical quantile values ​​corresponding to multiple quantile levels , forming the theoretical quantile vector ; Calculate quantile estimates corresponding to multiple quantiles The covariance matrix of .

5. The method according to claim 4, characterized in that According to the theoretical quantile vector, covariance matrix, preset false alarm rate and pre-established statistical test model, the judgment threshold is obtained, including: Quantile estimates based on multiple quantile levels , construct the quantile estimation vector , and the quantile estimate vector Asymptotically normal distribution: in, is the theoretical quantile vector, for The covariance matrix of Based on the theoretical quantile vector and the covariance matrix , construct the statistic Q: Then the statistic Q follows the chi-square distribution: Based on preset false alarm rate , and get the decision threshold: 。 6. The method according to claim 1, characterized in that The radar echo signals of the unit to be tested are grouped to construct a sample set. From the grouped samples, quantile features are extracted according to multiple preset quantile levels to obtain a quantile feature vector, including: Extract samples from the unit under test , sort the samples in ascending order ; Defining quantile estimates In the quantile When , the corresponding cumulative distribution function The value of satisfies: ， in, , ； is the indicator function, when 1 when it is, otherwise 0; calculate ,get Horizontal lower quantile characteristics, where Indicates rounding down.

7. The method according to claim 5, characterized in that Based on the quantile eigenvector, the statistics of the unit under test are calculated, including: Based on the quantile eigenvector of the unit under test, combined with the theoretical quantile vector of the reference unit and the covariance matrix , calculate the statistics of the unit under test: 。 8. A constant false alarm rate control system for radar target detection based on sample quantile characteristics, characterized in that: include: A signal acquisition module, used to acquire the radar echo signal of the unit under test; The feature vector calculation module is used to group the radar echo signals of the unit to be tested, construct a sample set, extract quantile features from the grouped samples according to multiple preset feature quantile levels, and obtain a quantile feature vector; A statistics calculation module, used for calculating the statistics of the unit to be tested based on the quantile eigenvector; The target determination module is used to compare the statistic of the unit to be tested with a preset determination threshold value, and if the statistic is greater than the determination threshold value, it is determined that there is a target in the unit to be tested; If the statistic is less than or equal to the determination threshold, it is determined that there is no target in the unit to be tested.

9. A terminal, characterized in that: include: A memory, used for storing a constant false alarm rate control program for radar target detection based on sample quantile characteristics; A processor is used to implement the steps of the radar target detection constant false alarm rate control method based on sample quantile characteristics as described in any one of claims 1 to 7 when executing the radar target detection constant false alarm rate control program based on sample quantile characteristics.

10. A computer-readable storage medium storing a computer program, characterized in that: The readable storage medium stores a constant false alarm rate control program for radar target detection based on sample quantile characteristics. When the constant false alarm rate control program for radar target detection based on sample quantile characteristics is executed by a processor, the steps of the constant false alarm rate control method for radar target detection based on sample quantile characteristics as described in any one of claims 1 to 7 are implemented.

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