Constant false alarm rate control method, system, terminal and storage medium for radar target detection based on sample quantile characteristics

Abstract

The present invention relates to the field of radar signal processing technology, and specifically provides a constant false alarm rate control method, system, terminal, and storage medium for radar target detection based on sample quantile characteristics, comprising: obtaining a radar echo signal of a unit to be tested; grouping the radar echo signals of the unit to be tested to construct a sample set, extracting quantile characteristics from the grouped samples according to multiple preset quantile levels to obtain a quantile characteristic vector; calculating a statistic of the unit to be tested based on the quantile characteristic vector; comparing the statistic of the unit to be tested with a preset judgment threshold, and if the statistic is greater than the judgment threshold, determining that a target exists in the unit to be tested; and if the statistic is less than or equal to the judgment threshold, determining that no target exists in the unit to be tested. The present invention significantly improves target detection sensitivity and anti-clutter capability.

Description

Technical Field

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

[0002] With the increasing frequency of maritime transportation, ocean surveillance, and maritime missions, small target detection at sea, as a key application of radar detection technology, is gaining increasing attention. Radar systems transmit electromagnetic waves to a target area and receive echo signals to extract target information, making them a key means of achieving all-weather, long-range monitoring. However, in real-world marine environments, due to the numerous irregular fluctuations of the sea surface, the radar signals received are often contaminated by a significant amount of "sea clutter" generated by waves and spray. In particular, for small targets at sea with relatively small size and weak signal reflection, such as buoys, small boats, and rubber boats, their echoes are easily submerged in the intense sea clutter, significantly reducing the target signal-to-noise ratio (SNR), which in turn affects the accuracy and reliability of detection.

[0003] To address this issue, the Constant False Alarm Rate (CFAR) detection method is widely used in radar systems. The core concept of the CFAR method is to dynamically adjust the detection threshold to adapt to varying background clutter conditions while maintaining a constant false alarm rate, thereby achieving stable and reliable target detection. With the advancement of radar technology, researchers have gradually realized that relying solely on a single feature (such as echo amplitude) for detection is difficult to cope with complex environmental changes. Therefore, they have proposed the concept of multi-feature detection, which extracts statistical features from radar echo signals in multiple dimensions (such as frequency domain features, time-frequency features, and Doppler features) to improve the ability to distinguish between targets and clutter.

[0004] Although current multi-feature detection methods have made some progress in improving target recognition capabilities, achieving constant false alarm rate (CFAR) remains challenging. First, traditional CFAR methods typically rely on precise modeling of feature distributions. This assumes that features follow a known probability distribution (such as Gaussian, K, or lognormal), thereby deriving the mathematical relationship between detection thresholds and false alarm rates. However, in complex real-world environments, the true distribution of features is often unknown and may exhibit highly non-Gaussian characteristics, such as fat tails and skewness. This makes it difficult for traditional modeling methods to accurately characterize the statistical differences between the target and the background, thus affecting detection performance. Second, multiple features may exhibit significant correlation or redundancy, making it difficult to construct effective detection criteria in high-dimensional feature spaces. Furthermore, constructing a unified statistic and theoretically accurately deriving its distribution characteristics under multi-dimensional features is crucial for achieving CFAR control. However, most current multi-feature CFAR methods only set thresholds based on empirical simulations, lacking clear theoretical support. Summary of the Invention

[0005] Conventional detection methods in the prior art typically require a pre-assumption of the distribution type of radar feature data under background clutter, such as a normal distribution or a K distribution. However, in complex real-world environments, the true distribution of these features is often unknown or fluctuates, and forced assumptions can lead to misjudgments. The present invention provides a constant false alarm rate control method, system, terminal, and storage medium for radar target detection based on sample quantile features. Without making strong assumptions about feature distribution, this method constructs multiple features with clear mathematical expressions that can precisely control false alarm rates, thereby addressing the aforementioned technical issues.

[0006] In a first aspect, the present invention provides a constant false alarm rate control method for radar target detection based on sample quantile characteristics, comprising:

[0007] Obtaining the radar echo signal of the unit under test;

[0008] 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 multiple preset quantile levels to obtain a quantile feature vector;

[0009] Based on the quantile eigenvector, the statistics of the unit to be tested are calculated;

[0010] The statistic of the unit to be tested is compared with the preset judgment threshold. If the statistic is greater than the judgment threshold, it is determined that the target exists in the unit to be tested; if the statistic is less than or equal to the judgment threshold, it is determined that the target does not exist in the unit to be tested.

[0011] Furthermore, the method of constructing a preset determination threshold includes:

[0012] Acquire the radar echo signal in the reference unit and extract the sea clutter sample data;

[0013] Perform distribution fitting on sea clutter samples to obtain the theoretical distribution model of sea clutter;

[0014] 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;

[0015] The decision threshold is obtained according to the theoretical quantile vector, the covariance matrix, the preset false alarm rate and the pre-established statistical test model.

[0016] Furthermore, distribution fitting is performed on the sea clutter samples to obtain the theoretical distribution model of sea clutter, including:

[0017] Assuming that the sea clutter amplitude x follows K distribution, the cumulative distribution function is :

[0018]

[0019] The probability density function is :

[0020]

[0021] in, is the scale parameter, is the shape parameter, is a modified Bessel function of the second kind, represents the gamma function;

[0022] The cumulative distribution function is And the probability density function is Denoted as the theoretical distribution model of sea clutter.

[0023] Furthermore, according to the preset multiple quantile levels, the theoretical quantile vector under the theoretical distribution model and the covariance matrix between the quantiles are calculated, including:

[0024] Setting up sea clutter samples It 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 obeys the normal distribution:

[0025]

[0026] in, Any set quantile The theoretical quantile value under the theoretical distribution model satisfies:

[0027]

[0028] and, ;in, express The inverse function of

[0029] Theoretical quantile values ​​corresponding to multiple quantile levels , forming the theoretical quantile vector ;

[0030] Calculate quantile estimates corresponding to multiple quantiles The covariance matrix of .

[0031] Furthermore, based on the theoretical quantile vector, the covariance matrix, the preset false alarm rate and the pre-established statistical test model, a judgment threshold is obtained, including:

[0032] Quantile estimates based on multiple quantile levels , construct the quantile estimation vector , and the quantile estimate vector Asymptotically normally distributed:

[0033]

[0034] in, is the theoretical quantile vector, for The covariance matrix of

[0035] Based on the theoretical quantile vector and covariance matrix , construct the statistic Q:

[0036]

[0037] Then the statistic Q follows the chi-square distribution:

[0038]

[0039] Based on preset false alarm rate , and get the decision threshold:

[0040] .

[0041] 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:

[0042] Draw samples from the unit under test , sort the samples in ascending order ;

[0043] Defining quantile estimates At the quantile When , the corresponding cumulative distribution function The value of satisfies:

[0044] ,

[0045] in, , ; is the indicator function, when 1 when it is, otherwise 0;

[0046] calculate , we get the quantile eigenvector, where Indicates rounding down.

[0047] Furthermore, based on the quantile eigenvector, the statistics of the unit under test are calculated, including:

[0048] Based on the quantile eigenvector of the unit to be tested and combined with the theoretical quantile vector of the reference unit and covariance matrix , calculate the statistics of the unit under test:

[0049] .

[0050] In a second aspect, the present invention provides a radar target detection constant false alarm rate control system based on sample quantile characteristics, comprising:

[0051] A signal acquisition module is used to obtain the radar echo signal of the unit under test;

[0052] The feature vector calculation module is used to group the radar echo signals of the unit to be tested, construct a sample set, and extract quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector;

[0053] A statistics calculation module is used to calculate the statistics of the unit to be tested based on the quantile eigenvector;

[0054] The target determination module is used to compare the statistic of the unit to be tested with a preset determination threshold. If the statistic is greater than the determination threshold, it is determined that a target exists in the unit to be tested; if the statistic is less than or equal to the determination threshold, it is determined that no target exists in the unit to be tested.

[0055] According to a third aspect, a terminal is provided, including:

[0056] processor, memory, wherein

[0057] The memory is used to store computer programs,

[0058] The processor is used to call and run the computer program from the memory, so that the terminal executes the above-mentioned terminal method.

[0059] In a fourth aspect, a computer storage medium is provided, wherein the computer-readable storage medium stores instructions, which, when executed on a computer, enable the computer to execute the methods described in the above aspects.

[0060] The beneficial effects of the present invention lie in the fact that the provided constant false alarm rate control method, system, terminal, and storage medium for radar target detection based on sample quantile features can construct a theoretically controllable constant false alarm rate (CFAR) detection criterion without relying on a specific noise distribution model, achieving 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 quantile points, this method comprehensively characterizes the statistical characteristics of radar echoes in different amplitude regions, effectively distinguishing sea clutter from weak target signals, and significantly improving target detection sensitivity and anti-clutter capabilities. Compared to traditional single-feature or fixed-threshold detection methods, the present invention uses nonparametric statistics to construct detection vectors, exhibiting excellent robustness and adaptability to complex background noise environments such as spikes and heavy tails. This eliminates the need for precise modeling of background clutter distribution, thereby improving the method's universality and deployment efficiency. At the same time, the detection algorithm of the present invention has a simple structure and low computational complexity. It only involves operations such as sample quantile extraction, mean and covariance calculation, and chi-square distribution table lookup. It is easy to implement in real time in embedded systems or edge computing devices, and is suitable for scenarios such as high-resolution radar systems, shipborne radars, and small target monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0062] Figure 1is a schematic flow chart of a method according to an embodiment of the present invention.

[0063] Figure 2 FIG. 4 is a histogram diagram illustrating verification of the asymptotic normality of SQF using K-distribution simulated data according to an embodiment of the present invention.

[0064] Figure 3 FIG. 1 is a schematic diagram of a QQ plot for verifying the asymptotic normality of SQF using K distribution simulated data according to an embodiment of the present invention.

[0065] Figure 4 1 is a schematic diagram showing a comparison of the amplitude, RAA characteristics, and 75% SQF of an embodiment of the present invention.

[0066] Figure 5 FIG. 3 is a schematic diagram of a three-dimensional comparison diagram of a target and sea surface clutter SQF according to an embodiment of the present invention.

[0067] Figure 6 1 is a schematic diagram of a QQ plot comparing the normality of amplitude features and magnitude features according to an embodiment of the present invention.

[0068] Figure 7 4 is a density distribution diagram showing a comparison of the normality of amplitude features and magnitude features according to an embodiment of the present invention.

[0069] Figure 8 FIG. 4 is a graph illustrating the FAR of a bivariate SQF using simulated data according to an embodiment of the present invention.

[0070] Figure 9 Schematic diagram of false alarm control according to an embodiment of the present invention.

[0071] Figure 10 Schematic diagram of the detection results of one embodiment of the present invention.

[0072] Figure 11 An embodiment of the present invention Schematic diagram of sea clutter false alarm behavior.

[0073] Figure 12 An embodiment of the present invention Schematic diagram of sea clutter false alarm behavior.

[0074] Figure 13 An embodiment of the present invention Schematic diagram of sea clutter false alarm behavior.

[0075] Figure 14 An embodiment of the present invention Schematic diagram of target detection results when .

[0076] Figure 15 An embodiment of the present invention Schematic diagram of target detection results when .

[0077] Figure 16 An embodiment of the present invention Schematic diagram of target detection results when .

[0078] Figure 17 An embodiment of the present invention Schematic diagram comparing the detection rates of different CFAR methods.

[0079] Figure 18 An embodiment of the present invention Schematic diagram comparing the detection rates of different CFAR methods.

[0080] Figure 19 An embodiment of the present invention Schematic diagram comparing the detection rates of different CFAR methods.

[0081] Figure 20 FIG. 4 is a schematic block diagram of a system according to an embodiment of the present invention.

[0082] Figure 21 A schematic diagram of the structure of a terminal provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0083] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0084] Unless otherwise defined, all technical and scientific terms used in this application have the same meaning as those commonly understood by those skilled in the art to which the present invention pertains. The terms used in this application and in the specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention.

[0085] The key terms appearing in the present invention are explained below.

[0086] CFAR stands for Constant False-Alarm Rate. In radar signal detection, when the intensity of external interference changes, the radar can automatically adjust its sensitivity to keep the false alarm probability of the radar unchanged. This characteristic is called the constant false alarm rate characteristic.

[0087] The constant false alarm rate control method for radar target detection based on sample quantile characteristics provided by the embodiment of the present invention is executed by a computer device. Accordingly, the constant false alarm rate control system for radar target detection based on sample quantile characteristics runs in the computer device.

[0088] Figure 1 is a schematic flow chart of a method according to an embodiment of the present invention. Figure 1 The execution subject may be a constant false alarm rate control system for radar target detection based on sample quantile characteristics. According to different requirements, the order of the steps in the flowchart can be changed, and some steps can be omitted.

[0089] To facilitate understanding of the present invention, the following further describes the constant false alarm rate control method for radar target detection based on sample quantile characteristics provided by the present invention based on the principle of the constant false alarm rate control method for radar target detection based on sample quantile characteristics.

[0090] Specifically, such as Figure 1 As shown, the constant false alarm rate control method for radar target detection based on sample quantile characteristics includes:

[0091] S1. Obtain the radar echo signal of the unit to be tested.

[0092] In this application, the identified target is designated as a lightweight buoy located approximately 2.97 nautical miles from the radar installation, at a bearing of 10.7°. The buoy is an anchored, floating, red cylindrical structure. Made of steel, it has a diameter of approximately 2.4 meters and stands approximately 4.1 meters above the water.

[0093] This application employed two custom-designed X-band solid-state amplifier test radars. One radar employed HH polarization, and the other employed VV polarization. Both radars operated in a fixed pointing mode and remained pointed toward the channel buoy throughout the experiment. During data acquisition, the radars transmitted a T1 signal (pulse width: 150 nanoseconds) and a T2 linear frequency modulated signal (pulse width: 25 microseconds). The T1 waveform provided a ranging resolution of 22.5 meters, while the T2 waveform, with a bandwidth of 25 MHz, provided a ranging resolution of 6 meters.

[0094] In this application, the radar only transmits T1 and T2 signals during data acquisition.

[0095] The radar target detection problem can be expressed as a mathematical binary hypothesis testing problem. The received signal in each ranging unit is expressed as ( ) indicates that if the ranging unit contains a target, Including target signal, sea clutter and noise. Otherwise, Only sea clutter and noise are included. Since the energy of noise is significantly weaker than that of 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:

[0096]

[0097] in and Represent the signals of the cell under test (CUT) and the reference cell (RC), respectively. Indicates the target signal, and Represent the sea clutter signals in the CUT and reference cells respectively. Specifies the number of reference cells.

[0098] According to the assumption , the CUT does not contain the target, and the signal consists only of sea clutter, so it is a surface clutter cell (SCC). , CUT contains the target signal, which is classified as the target cell (TC). Assuming that the RC signal Containing only sea clutter, 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.

[0099] Assume that a feature vector is extracted from SCC , whose cumulative distribution function (CDF) is According to the eigenvector , construct the test statistic By specifying a predefined FAR , determine the detection threshold , which satisfies the following conditions:

[0100]

[0101] The corresponding decision rule is defined as follows

[0102]

[0103] S2. Grouping the radar echo signals of the units to be tested to construct a sample set, extracting quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector.

[0104] Draw samples from the unit under test , sort the samples in ascending order ; Define quantile estimates At the quantile When , the corresponding cumulative distribution function The value of satisfies: ,in, , ; is the indicator function, when 1 when , otherwise 0; , we get the quantile eigenvector, where Indicates rounding down.

[0105] S3. Based on the quantile eigenvector, the statistics of the unit to be tested are calculated.

[0106] Based on the quantile eigenvector of the unit to be tested and combined with the theoretical quantile vector of the reference unit and covariance matrix , calculate the statistics of the unit under test:

[0107] .

[0108] 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 the target exists in the unit under test. If the statistic is less than or equal to the determination threshold, it is determined that the target does not exist in the unit under test.

[0109] In one embodiment, the method further includes: constructing a preset determination threshold, including:

[0110] Q1. Obtain the radar echo signal in the reference unit and extract the sea clutter sample data.

[0111] Q2. Perform distribution fitting on sea clutter samples to obtain the theoretical distribution model of sea clutter.

[0112] Assuming that the sea clutter amplitude x follows K distribution, the cumulative distribution function is :

[0113]

[0114] The probability density function is :

[0115]

[0116] in, is the scale parameter, is the shape parameter, is a modified Bessel function of the second kind, represents the gamma function;

[0117] The cumulative distribution function is And the probability density function is Denoted as the theoretical distribution model of sea clutter.

[0118] Q3. Based on the preset multiple quantile levels, calculate the theoretical quantile vector and the covariance matrix between each quantile under the theoretical distribution model.

[0119] Setting up sea clutter samples It 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 obeys the normal distribution:

[0120]

[0121] in, Any set quantile The theoretical quantile value under the theoretical distribution model satisfies:

[0122]

[0123] and, ;in, express The inverse function of

[0124] Theoretical quantile values ​​corresponding to multiple quantile levels , forming the theoretical quantile vector ;

[0125] Calculate quantile estimates corresponding to multiple quantiles The covariance matrix of .

[0126] Q4. Obtain the judgment threshold based on the theoretical quantile vector, covariance matrix, preset false alarm rate and pre-established statistical test model.

[0127] Quantile estimates based on multiple quantile levels , construct the quantile estimation vector , and the quantile estimate vector Normal distribution:

[0128]

[0129] in, is the theoretical quantile vector, for The covariance matrix of

[0130] Based on the theoretical quantile vector and covariance matrix , construct the statistic Q:

[0131]

[0132] Then the statistic Q follows the chi-square distribution:

[0133]

[0134] Based on preset false alarm rate , and get the decision threshold:

[0135] .

[0136] Specifically, the distribution of sea clutter characteristics is often difficult to determine. This application proposes an extraction method based on SQF. As a non-parametric statistic, SQF can provide a robust statistical description that is not affected by the distribution of sea clutter.

[0137] let represents the total sea clutter amplitude, represents a sample drawn from the population. The order statistics of this sample are recorded as . Sample quantification It is defined as the difference between the CDF and Corresponding value ,satisfy:

[0138]

[0139] Empirical CDF It is given by the following formula:

[0140]

[0141] in is an indicator function, if , then the function is equal to 1, otherwise it is equal to 0.

[0142] In actual operation, the actual data can be used to calculate the formula (6) The sample quantile of the level :

[0143]

[0144] in Indicates a floor operation.

[0145] The SQF effectively describes the sea clutter amplitude at a specific quantile level without considering the population distribution.

[0146] Theorem 1: Assume Is from the distribution independent and identically distributed samples, and assuming The inverse function of the quantile level is monotonically continuous , density function . represents the sample quantile. Then, Similarly, the asymptotic distribution of the sample quantitative distribution is:

[0147]

[0148] in, is the inverse function, yes The density function of The mean is 0 and the variance is The normal distribution of Indicates that the distribution converges.

[0149] The K distribution has been shown to be effective in simulating the high kurtosis and heavy-tail characteristics of sea clutter under various conditions

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

[0150] Corollary 1: Assuming that the sea clutter amplitude in a single ranging unit follows a K distribution, its CDF is expressed as Its probability density function (PDF) is represented by Indicates that is the scale parameter, is the shape parameter. For simplicity, and Simplified to and .

[0151]

[0152]

[0153] is a modified Bessel function of the second kind, Represents the gamma function.

[0154] Assumptions Is from Independent and identically distributed random samples of . As the sample size , for a given quantization level , sample quantization Asymptotically converges to true quantization , and asymptotically obeys the normal distribution:

[0155]

[0156] in The asymptotic expectation of ,satisfy

[0157]

[0158] in .here, express The inverse function of .

[0159] The formula for calculating the asymptotic variance is

[0160]

[0161] According to Corollary 1, the simulation procedure is detailed as follows:

[0162] Step 1: Generate uniformly distributed random variables, .

[0163] Step 2: Using the inverse transform, Generated from K distribution random variable.

[0164] Step 3: Given The sample size is to draw independent and identically distributed samples from the population Repeat this process times, recorded as .

[0165] Step 4: Calculate the .

[0166] Step 5: Perform a normality test.

[0167] Simulation: Setting the shape parameters of the K distribution and scale parameters , the overall scale is Each sample includes Observations. Extract SQF to verify. Figure 2 Shows the normal distribution fit of the K-distributed sample 75% SQF, Figure 3 The QQ plot is shown. As can be seen, the SQF is very close to a normal distribution.

[0168] The effectiveness of the proposed SQF extraction method was verified using the dataset 20221115050306_stare_VV (the 508th unit was identified as TC). The comparison of the extracted 75% SQF, original amplitude and commonly used RAA features is shown in Figure 4 .

[0169] like Figure 4 As shown in the image above, the original amplitude does not provide sufficient contrast between the target and sea clutter, resulting in overlapping colors between the sea clutter background and the target area. Compared to the original amplitude, RAA improves the distinction between the target and sea clutter. However, some clutter areas still resemble the target. SQF significantly enhances the contrast, making the target more distinct from the sea clutter.

[0170] like Figure 5 As shown, the SQF of the 508th ranging unit corresponding to the TC is significantly higher compared with the surrounding SCC.

[0171] Here, every 128 pulses within a single range cell are sampled to ensure independence of the sampling process. The amplitude data is then divided into 30 different groups. The 75% SQF is calculated for each group.

[0172] A normal comparison was performed on the amplitude and 75% SQF in RC, as shown in Figure 6 The QQ plot shows that 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 approximately normal distribution. Figure 7 As shown in the figure, the amplitude distribution deviates significantly from the typical normal bell curve in terms of density distribution, while the distribution of quantitative features is close to normal. This indicates that the results of SQF feature extraction are approximately normally distributed. Given the complex statistical characteristics of sea clutter signals (often exhibiting heavy-tailed behavior), the Anderson-Darling (AD) test is used to quantitatively assess normality. This test is particularly sensitive to deviations in the tails of the distribution and is therefore well suited for evaluating the asymptotic normality of SQF.

[0173] use , represents the SQF extracted from the sea clutter signal, and the quantile level is According to the sample data , calculate the empirical CDF . Then construct the AD test statistic as follows:

[0174]

[0175]

[0176] In statistical hypothesis testing, -value plays a vital role in determining the validity of the null hypothesis. If the - value is lower than the predetermined significance level, the null hypothesis is not established, indicating that the data deviates from the normal distribution. Otherwise, the null hypothesis is established and the data is considered to be normally distributed. -The value is 0.83, which further confirms the asymptotic normality of the sample quantiles at the quantile level.

[0177] The SQF method effectively captures sea clutter fluctuations at different quantile levels. Lower quantile levels reflect changes in the lower tail of the distribution, while higher quantile levels are sensitive to changes in the upper tail. By jointly analyzing the multivariate SQF, the characteristics of both the upper and lower tails of sea clutter can be effectively captured.

[0178] Based on the multivariate normal distribution theory, the CFAR control theorem and detection boundary are derived and extended using the multivariate sample size characteristics.

[0179] Theorem 2: Assuming the multivariate sample size is Approximate obedience -dimensional normal distribution. For a given FAR , construct the test statistic:

[0180]

[0181] in, represents the mean vector, yes Covariance, used to capture the dependencies between different quantile levels.

[0182] To achieve the predetermined FAR , detection threshold The following conditions must be met:

[0183]

[0184] This threshold can be expressed as

[0185]

[0186] in Indicates that at the significance level The following has Chi-square distribution with 1 degree of freedom.

[0187] Proof Assumption SQF Vector Approximately follows a multivariate normal distribution:

[0188]

[0189] in is the mean vector, yes Covariance matrix.

[0190] The test statistic is constructed as follows

[0191]

[0192] Covariance matrix It can be decomposed into ,in is a lower triangular matrix. Applying linear transformations:

[0193]

[0194] Get the standard multivariate normal random vector ,in is the identity matrix.

[0195] The components of are independent standard normal random variables. Therefore, the test statistic

[0196]

[0197] Follows a chi-square distribution:

[0198]

[0199] For a given FAR , detection threshold satisfy Therefore, the detection threshold .

[0200] Using sea clutter data from a reference cell, a statistical distribution model that best represents the data is established. The mean vector and covariance matrix are calculated to describe the SQF distribution. Based on the specified FAR, the detection threshold is determined according to Theorem 2.

[0201] For CUT (unit to be tested), 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 deviates significantly from the reference distribution, and the null hypothesis can be determined. If it does not hold, it indicates that the target exists; otherwise, Q≤T, which means that the data does not provide enough evidence to deny , retain the null hypothesis , it is considered that there is no target for this unit.

[0202] Based on Theorem 2, this detection method proposes a multivariate SQF detection framework, assuming that the sea clutter amplitude follows a K distribution. It is worth noting that this method is applicable to the case where the sea clutter follows other distributions.

[0203] 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:

[0204]

[0205] and The parameter estimates of are obtained numerically through the partial derivatives of the log-likelihood function, as follows:

[0206]

[0207] Step 2: Determine the quantile level , representing different tails of the distribution to facilitate detailed analysis.

[0208] Step 3: Using K distribution , calculate the expected value of SQF ( ).

[0209] Step 4: According to the given , using rank square distribution to calculate the detection threshold :

[0210]

[0211] Step 5: Assume that the reference unit is spatially homogeneous and use formula (6) to calculate the sample quantile value of CUT .

[0212] 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:

[0213]

[0214] in Is sample quantification The variance of is the overall quantitative and The correlation coefficient between .

[0215] Step 7: Statistics and detection threshold Compare. If , then the null hypothesis Established, otherwise, if , the null hypothesis Not true.

[0216] Simulation and experimental validation of bivariate SQF detection:

[0217] According to Theorem 2, for the binary SQF , the test statistic is defined as follows:

[0218]

[0219] in, is the mean vector, is the covariance matrix of the magnitude, which is calculated as

[0220]

[0221] in yes and The correlation coefficient between , They are and PDF.

[0222] For a given FAR , detection threshold Expressed as

[0223]

[0224] Bivariate SQF Meet the detection threshold Define the ellipse boundary constraints:

[0225]

[0226]

[0227] Among them, the coefficient The definition of

[0228] set up , the calculation formula of the detection threshold is The mean vector of SQF is defined as , the covariance matrix is ​​given by given.

[0229] Generate a total of 1000 sets of two-dimensional sample quantile vectors , the quantitative levels are and . Calculate the test statistic for each group and with the threshold Make a comparison. Figure 8 The results of the bivariate SQF simulation are shown. The black ellipse boundary corresponds to the detection threshold , the blue points represent SCC samples, and the red points represent TC samples. The observed FAR is 0.001, which confirms the effectiveness of the proposed detection method.

[0230] We further validated the proposed method using the dataset labeled 20221115050306_stare_VV. The sampling and grouping method is the same as above.

[0231] Using the MLE estimation method, the parameter estimate of the K distribution is and For the quantile level and The calculated quantile levels are and According to the K distribution, the corresponding probability density value is determined to be and , the correlation coefficient is .

[0232] When setting When , the actual false alarm rates are 0.1, 0.013 and 0.0008 respectively. For the target sample, the detection rate is 100%. The false alarm rate control is as follows Figure 9 As shown, the test results are Figure 10 shown.

[0233] False alarm control results such as Figure 11 、 Figure 12 and Figure 13 As shown in , the red points represent false positive targets. The target detection results are as follows Figure 14 、 Figure 15 and Figure 16 As shown, with As decreases, the boundary of the ellipse gradually expands.

[0234] Current object detection methods based on multivariate features face challenges in achieving a closed-form expression for CFAR and deriving detection thresholds. Therefore, this study compares the proposed method with several existing CFAR detection methods to evaluate the proposed method.

[0235] To increase the sample size, we extracted SQFs and compared them with the CFAR method under continuous sampling conditions. Specifically, for each group of 256 pulses, the 25% and 75% SQFs were extracted and the test statistic was calculated. .

[0236] like Figure 17 、 Figure 18 and Figure 19 As shown, The results show that CA-CFAR, GO-CFAR and OS-CFAR are compared. ,The detection rates of the proposed method are 0.98633, 0.98242, and 0.97656, respectively, which are the highest detection rates among ,different false alarm rate settings.

[0237] In some embodiments, the radar target detection constant false alarm rate control system based on sample quantile features may include a plurality of functional modules composed of computer program segments. The computer program of each program segment in the radar target detection constant false alarm rate control system based on feature sample quantile features may be stored in a memory of a computer device and executed by at least one processor to perform (see Figure 1 Description) Function for constant false alarm rate control of radar target detection based on sample quantile characteristics.

[0238] In this embodiment, the radar target detection constant false alarm rate control system based on sample quantile characteristics can be divided into multiple functional modules according to the functions it performs, such as Figure 20 As shown. The functional modules of system 200 may include: a signal acquisition module 210, a feature vector calculation module 220, a statistics calculation module 230, and a target determination module 240. A module as referred to in the present invention refers to a series of computer program segments that can be executed by at least one processor and can perform fixed functions, and is stored in a memory. In this embodiment, the functions of each module will be described in detail in subsequent embodiments.

[0239] A signal acquisition module is used to obtain the radar echo signal of the unit under test;

[0240] The feature vector calculation module is used to group the radar echo signals of the unit to be tested, construct a sample set, and extract quantile features from the grouped samples according to multiple preset quantile levels to obtain a quantile feature vector;

[0241] A statistics calculation module is used to calculate the statistics of the unit to be tested based on the quantile eigenvector;

[0242] The target determination module is used to compare the statistic of the unit to be tested with a preset determination threshold. If the statistic is greater than the determination threshold, it is determined that a target exists in the unit to be tested; if the statistic is less than or equal to the determination threshold, it is determined that no target exists in the unit to be tested.

[0243] Figure 21This is a structural diagram of a terminal 300 provided in an embodiment of the present invention. The terminal 300 can be used to execute the constant false alarm rate control method for radar target detection based on sample quantile characteristics provided in an embodiment of the present invention.

[0244] 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 will appreciate that the server structure shown in the figure does not limit the present invention. The server structure may be a bus structure or a star structure, and may include more or fewer components than shown, or may combine certain components or arrange the components differently.

[0245] Memory 320 can be used to store execution instructions of processor 310. Memory 320 can be implemented by any type of volatile or non-volatile storage device, 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, magnetic disk, or optical disk. When the execution instructions in memory 320 are executed by processor 310, terminal 300 can perform some or all of the steps in the above-described method embodiments.

[0246] The processor 310 is the control center of the storage terminal. It uses various interfaces and lines to connect various parts of the entire electronic terminal. It executes various functions of the electronic terminal and / or processes data by running or executing software programs and / or modules stored in the memory 320, and calling data stored in the memory. The processor can be composed of an integrated circuit (IC), for example, it can be composed of a single packaged IC, or it can be composed of multiple packaged ICs with the same or different functions. For example, the processor 310 can only include a central processing unit (CPU). In the embodiment of the present invention, the CPU can be a single computing core or multiple computing cores.

[0247] The communication unit 330 is configured to establish a communication channel so that the storage terminal can communicate with other terminals, receive user data sent by other terminals, or send user data to other terminals.

[0248] The present invention also provides a computer storage medium, wherein the computer storage medium may store a program that, when executed, may include some or all of the steps of each embodiment provided herein. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0249] Therefore, the present invention can construct a theoretically controllable constant false alarm rate (CFAR) detection criterion under the premise of an arbitrary noise distribution model, achieving 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, effectively distinguishing sea clutter from weak target signals, and significantly improving target detection sensitivity and anti-clutter capabilities. Compared with traditional single-feature or fixed-threshold detection methods, the present invention uses non-parametric statistics to construct detection vectors, which have good robustness and can adapt to complex background noise environments such as spikes and heavy tails. It avoids the need for precise modeling of 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. It only involves operations such as sample quantile extraction, mean and covariance calculation, and chi-square distribution table lookup. It is easy to implement in real time in embedded systems or edge computing devices, and is suitable for scenarios such as high-resolution radar systems, shipborne radars, and small target monitoring. The technical effects that can be achieved by this embodiment can be found in the description above and will not be repeated here.

[0250] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software plus a necessary general-purpose hardware platform. Based on this understanding, the technical solutions in the embodiments of the present invention, or the portion 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 drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, among other media capable of storing program code, and includes 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 various embodiments of the present invention.

[0251] In this specification, the same or similar parts between the various embodiments can be referred to each other. In particular, for the terminal embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the description in the method embodiment.

[0252] In the 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 merely a logical function division. In actual implementation, there may be other division methods, such as multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of systems or modules, and can be electrical, mechanical or other forms.

[0253] The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules may be selected to achieve the purpose of the present embodiment according to actual needs.

[0254] In addition, each functional module in each embodiment of the present invention may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0255] Although the present invention has been described in detail with reference to the accompanying drawings and in combination with preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, a person of ordinary skill in the art may make various equivalent modifications or substitutions to the embodiments of the present invention, and such modifications or substitutions shall be within the scope of the present invention. Any person skilled in the art who is familiar with the present invention may easily conceive of changes or substitutions within the technical scope disclosed in the present invention, and such changes or substitutions shall be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection 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 multiple preset quantile levels to obtain a quantile feature vector; Based on the quantile eigenvector, the statistics of the unit to be tested are calculated; Compare the statistic of the unit to be tested with a preset judgment threshold. If the statistic is greater than the judgment threshold, it is determined that a target exists in the unit to be tested. If the statistic is less than or equal to the judgment threshold, it is determined that there is no target in the unit to be tested; Also included is a method for constructing a preset determination threshold, comprising: 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 decision threshold is obtained according to the theoretical quantile vector, the covariance matrix, the preset false alarm rate and the pre-established statistical test model.

2. The method according to claim 1, characterized in that Distribution fitting is performed on sea clutter samples 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.

3. The method according to claim 2, 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 It 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 obeys the normal distribution: in, 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 .

4. The method according to claim 3, 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 normally distributed: in, is the theoretical quantile vector, for The covariance matrix of Based on the theoretical quantile vector and 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: 。 5. The method according to claim 1, wherein 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 quantile feature vectors, including: Draw samples from the unit under test , sort the samples in ascending order ; Defining quantile estimates At 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 quantile characteristics, where Indicates rounding down.

6. The method according to claim 4, 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 to be tested, combined with the theoretical quantile vector of the reference unit and covariance matrix , calculate the statistics of the unit under test: 。 7. A constant false alarm rate control system for radar target detection based on sample quantile characteristics, characterized in that: include: A signal acquisition module is used to obtain 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, and extract quantile features from the grouped samples according to multiple preset feature quantile levels to obtain a quantile feature vector; A statistics calculation module is used to calculate 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. If the statistic is greater than the determination threshold, it is determined that a target exists in the unit to be tested; If the statistic is less than or equal to the judgment threshold, it is determined that there is no target in the unit to be tested; Also included is a method for constructing a preset determination threshold, comprising: 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 decision threshold is obtained according to the theoretical quantile vector, the covariance matrix, the preset false alarm rate and the pre-established statistical test model.

8. 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; The processor is configured to implement the steps of the constant false alarm rate control method for radar target detection based on sample quantile features as described in any one of claims 1 to 6 when executing the constant false alarm rate control program for radar target detection based on sample quantile features.

9. 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 features. When the constant false alarm rate control program for radar target detection based on sample quantile features is executed by a processor, the steps of the constant false alarm rate control method for radar target detection based on sample quantile features according to any one of claims 1 to 6 are implemented.

Images