A false alarm rate controllable sea surface small target anomaly detection general threshold calibration method

Abstract

The application discloses a general threshold calibration method for sea surface small target anomaly detection with controllable false alarm rate, which aims at the problem that existing anomaly detection thresholds mainly rely on empirical quantiles, Monte Carlo or geometric boundaries, and it is difficult to provide stable constraints on the real false alarm rate. The method first extracts multi-domain features from sea surface echoes and trains an anomaly detector to obtain an anomaly score, then uses an independent sea clutter calibration set to count the number of samples exceeding the threshold, combines the Clopper-Pearson one-sided confidence upper bound to calculate the maximum allowed false alarm point number that meets the target false alarm rate and confidence level constraints, and determines the detection threshold in the anomaly score sorting sequence accordingly. The method does not depend on target samples or simulated targets, is suitable for various anomaly detectors such as one-class support vector machine, isolation forest, autoencoder, variational autoencoder and deep support vector data description, and has the advantages of strong universality, simple calibration and high reliability of low false alarm rate control.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a universal threshold calibration method for detecting small surface anomalies with controllable false alarm rate. Background Technology

[0002] Detection of small targets on the sea surface has always been a challenge in radar signal processing. The main reasons include: weak target echoes, strong sea clutter energy with non-Gaussian, non-stationary, and nonlinear characteristics, and significant background non-uniformity in complex scenarios such as near-shore, near-island, and near large targets. Under these conditions, traditional detection methods relying on statistical distribution modeling of sea clutter are prone to problems such as model mismatch, unstable parameter estimation, and insufficient engineering adaptability.

[0003] Existing feature-based detection methods typically extract multidimensional information from the time, frequency, time-frequency, or phase domains, and then combine this information with anomaly detection or binary classification models to achieve target discrimination. While these methods improve the separability of targets from sea clutter to some extent, their false alarm rate control relies heavily on empirical quantiles, Monte Carlo thresholds, geometric decision boundaries, or simulated targets for training. This makes it difficult to provide stable and verifiable confidence constraints on the true false alarm rate under limited sample conditions. Furthermore, some methods use simulated target echoes for training or threshold design. Due to the complex and varied types, attitudes, motion states, and scattering characteristics of small targets on the real sea surface, simulated targets often fail to cover all situations in practical applications, thus affecting the detector's generalization ability in unknown scenarios.

[0004] For example, Nanjing University of Information Science and Technology disclosed a method for detecting small targets on the sea surface based on multi-domain multi-dimensional feature fusion in its patent application "A method for detecting small targets on the sea surface based on multi-domain multi-dimensional feature fusion" (application number: CN202010596437.1, publication number: CN111580064A). This method jointly processes echo data under four polarizations (HH, HV, VH, and VV) to extract multi-dimensional feature information in the time domain, frequency domain, time-frequency domain, and polarization domain. Through linear fusion of the polarization domain and the feature domain, the multi-dimensional features are compressed into a 3D feature space, ensuring high-dimensional information while reducing computational cost. In the 3D feature space, a fast convex hull algorithm is used to obtain a decision region with controllable false alarms, thereby achieving target detection. This method uses the fast convex hull algorithm to adjust the false alarm rate by deleting boundary samples, but its essence is still based on empirical control of the sample ratio, which makes it difficult to provide stable and verifiable confidence constraints on the true false alarm rate under limited sample conditions. At the same time, this method relies on the construction of geometric boundaries in the three-dimensional feature space, which limits its applicability to scenarios with high-dimensional features or where the anomaly detector outputs a one-dimensional anomaly score.

[0005] For example, the patent document "A method for detecting small targets on the sea surface based on random forest" (application number: CN202010915183.5, publication number: CN112147601A) discloses a method for detecting small targets on the sea surface based on random forest, including the following steps: obtaining the echo vector of the distance cell to be detected and the echo vector of the surrounding reference distance cells; extracting multi-dimensional features in the time domain, frequency domain, and time-frequency domain; constructing high-dimensional feature vectors; normalizing the feature vectors; extracting normalized feature vectors based on simulated target echo data and sea clutter data, and constructing two types of balanced training samples; using the two types of training samples as input to the random forest, establishing a mathematical function expression between the splitting factor and the false alarm rate, and obtaining a random forest binary classifier with controllable false alarms; substituting the normalized feature vectors into the random forest binary classifier to obtain the output classification label, and determining whether the echo vector contains a target. This method constructs balanced training samples by introducing simulated target echo data and sea clutter data, and establishes a mapping relationship between the splitting factor and the false alarm rate during the training of the random forest classifier, thereby achieving a certain degree of false alarm rate control. However, its false alarm rate constraint is strongly coupled with the structure of the random forest classifier and the construction method of the training samples, and relies on the approximation of the scattering characteristics of the simulated target echo to the real target, making it difficult to cover the complex diversity of small targets on the sea surface under changes in attitude, scale, motion state and sea state. At the same time, this method belongs to a binary classification training framework, and its applicable objects are mainly limited to the random forest model, making it difficult to reuse as a general threshold calibration module for different anomaly detectors. Summary of the Invention

[0006] To address the aforementioned problems, this invention aims to provide a general threshold calibration method for detecting anomalies of small targets on the sea surface. This method enables the anomaly detector to select a threshold based on an independent sea clutter calibration set after outputting anomaly scores, and to impose a statistically meaningful constraint on the true false alarm rate under given target false alarm rate and confidence level.

[0007] The technical solution adopted by this invention to solve its technical problem is as follows:

[0008] Step 1: Acquire the radar echo signal over the sea surface;

[0009] Step 2: Extract features from the sea surface radar echo signal to obtain sample feature vectors;

[0010] Step 3: Divide the samples into a training set and a calibration set;

[0011] Step 4: Train the anomaly detector using the training set to obtain an anomaly detector that can output anomaly scores;

[0012] Step 5: Input the calibration set into the anomaly detector to obtain the calibration anomaly score, and determine the detection threshold using the Clopper-Pearson one-sided confidence upper bound based on the target false alarm rate and confidence level.

[0013] Step 6: After processing the sample to be detected according to the feature extraction method in Step 2, input it into the anomaly detector to obtain the anomaly score to be detected, and compare the anomaly score to be detected with the detection threshold. If the anomaly score to be detected is greater than the detection threshold, it is determined to be a target; otherwise, it is determined to be sea clutter.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] First, this invention does not rely on a specific anomaly detector structure, but instead performs a unified threshold calibration on the anomaly scores output by the anomaly detector. Therefore, it can be connected to various models such as single-class support vector machines, isolated forests, autoencoders, variational autoencoders, and deep support vector data descriptions, making it more versatile.

[0016] Second, this invention does not use simple empirical quantiles or Monte Carlo thresholds, but instead uses the Clopper-Pearson one-sided confidence upper bound to conservatively estimate the true false alarm rate, which can improve the reliability of the low false alarm rate threshold under limited clutter calibration samples.

[0017] Third, this invention does not require the construction of simulated target echoes for training, but mainly relies on sea clutter samples to complete the training and calibration, thus avoiding the generalization problem caused by the difficulty of simulated targets in covering the scattering differences of real targets.

[0018] Fourth, under the premise of satisfying the false alarm rate confidence constraint, the present invention selects the minimum threshold that satisfies the condition, thereby maintaining the detection probability as much as possible and taking into account both false alarm rate control and target detection capability. Attached Figure Description

[0019] Figure 1 This is an overall flowchart of an embodiment of the present invention;

[0020] Figure 2 shows the detection comparison results of using a single-class support vector machine as a detector in the embodiment of the present invention. Figure 2(a) is a comparison of detection probabilities, and Figure 2(b) is a comparison of actual false alarm rates. Both Figure 2(a) and Figure 2(b) show the results under four polarization channels: HH, HV, VH, and VV, respectively.

[0021] Figure 3 shows the detection comparison results of using isolated forest as detector in the embodiment of the present invention. Figure 3(a) is a comparison of detection probabilities, and Figure 3(b) is a comparison of actual false alarm rates. Figures 3(a) and 3(b) respectively show the results under four polarization channels: HH, HV, VH and VV.

[0022] Figure 4 shows the detection comparison results of using an autoencoder as a detector in the embodiment of the present invention. Figure 4(a) is a comparison diagram of detection probability, and Figure 4(b) is a comparison diagram of actual false alarm rate. Figures 4(a) and 4(b) respectively show the results under four polarization channels: HH, HV, VH and VV.

[0023] Figure 5 shows the detection comparison results of the variational autoencoder as the detector in the embodiment of the present invention. Figure 5(a) is a comparison of detection probabilities, and Figure 5(b) is a comparison of actual false alarm rates. Both Figure 5(a) and Figure 5(b) show the results under the four polarization channels HH, HV, VH and VV, respectively.

[0024] Figure 6 shows the detection comparison results of the detector using deep support vector data description in the embodiment of the present invention. Figure 6(a) is a comparison of detection probabilities, and Figure 6(b) is a comparison of actual false alarm rates. Both Figure 6(a) and Figure 6(b) show the results under four polarization channels: HH, HV, VH, and VV, respectively.

[0025] Figure 7 This is a comparison chart of the overall performance of the embodiments of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0027] Reference Figure 1 The implementation steps of the embodiments of the present invention will be further described below.

[0028] Step 1: Acquire the radar echo signal over the sea surface;

[0029] This invention uses the IPIX (Intelligent Pixel Processing X-band) dataset as the experimental data. This data consists of a large amount of high-resolution sea clutter data collected by a team led by Professor Haykin at McMaster University in Canada in 1993 and 1998 using IPIX radar. IPIX radar can emit horizontally and vertically polarized electromagnetic waves and can complete horizontal and vertical reception using two linear receivers. Therefore, when the radar collects data, it can usually obtain radar echo data with four polarizations: HH, VV, HV, and VH.

[0030] The dataset of this invention mainly includes: 10 sets of data selected from the 1993 IPIX dataset, and another 10 sets of data selected from the 1998 IPIX dataset, for a total of 20 sets of data containing 4 polarizations, or 80 sets of data. Each set of data contains multiple range cells, where the main range cell is the target and influences multiple nearby range cells, while the other range cells provide pure sea clutter data.

[0031] The IPIX radar pulse repetition frequency is 1000Hz. In this embodiment, samples are constructed using a sliding window method along the slow time direction. The window length is 0.512s, corresponding to 512 pulses, and the sliding window step size is set to 64 pulses.

[0032] Step 2: Extract features from the sea surface radar echo signal to obtain sample feature vectors;

[0033] This embodiment uses a 10-dimensional multi-domain feature vector, which includes: normalized Hurst exponent, relative Doppler peak height, relative vector entropy, relative Doppler coefficient of variation, ridge integral, number of connected regions, maximum size of connected regions, number of phase zero crossings, maximum value of phase difference probability density function, and phase difference decorrelation time.

[0034] Step 2-1: Normalized Hurst Exponent (NHE).

[0035] The amplitude sequence is modeled as a random walk process, and the structure function is calculated. :

[0036]

[0037] Where m is the time scale, in this scheme m is taken as 2. 5 Up to half the current echo length. Then according to The Hurst exponent is obtained by fitting the slope using a log-log method. Using the mean of the Hurst exponent of the reference unit. and standard deviation Hurst exponent for CUT Standardize:

[0038]

[0039] Step 2-2: Relative Doppler Peak Height (RDPH);

[0040] This feature takes advantage of the fact that the target echo has more concentrated energy in the Doppler domain and is normalized to eliminate the influence of clutter fluctuations.

[0041] First, for vectors Perform Discrete Fourier Transform (DFT) to calculate the Doppler amplitude spectrum. :

[0042]

[0043] in, It is the pulse repetition period. It is the Doppler frequency.

[0044] Next, find the maximum value (peak value) of the amplitude spectrum and its corresponding frequency position:

[0045]

[0046]

[0047] Then, define the reference Doppler interval. In this invention, the following are selected: Used to calculate the ratio of the peak value to the average amplitude within the reference interval surrounding the peak value:

[0048]

[0049] The denominator represents the average spectral amplitude near the peak frequency (excluding the narrow band where the peak itself is located).

[0050] Finally, the RPH value of the CUT is divided by the mean RPH value of the reference cell to obtain the final feature RDPH:

[0051]

[0052] Steps 2-3: Relative Vector Entropy (RVE);

[0053] This feature leverages the characteristic that target echoes are more concentrated (lower entropy) in the Doppler domain, while sea clutter is more dispersed (higher entropy). First, the Doppler amplitude spectrum... Normalized to probability mass function :

[0054]

[0055] Next, calculate the Shannon entropy of the CUT vector Doppler spectrum:

[0056]

[0057] Finally, the vector entropy of the CUT is divided by the mean of the vector entropy of the reference cell to obtain the final feature RVE:

[0058]

[0059] Steps 2-4: Relative Doppler Coefficient of Variation (RCV);

[0060] First, calculate the ratio of the standard deviation to the mean of the Doppler amplitude spectrum to obtain the coefficient of variation (CV):

[0061]

[0062] Finally, the relative ratio is calculated to obtain the RCV:

[0063]

[0064] Steps 2-5: Ridge Integration (RI), Number of Connected Regions (NR), and Maximum Size of Connected Regions (MS)

[0065] The calculation of these three features is based on the normalized smoothed pseudo-Wigner-Ville distribution (Normalized SPWVD). The detailed calculation steps are as follows:

[0066] First, the time series of the test unit and surroundings Time series of reference units Calculate SPWVD separately:

[0067]

[0068] in, and These are time-smoothing windows and frequency-smoothing windows, respectively. In this embodiment, Kaiser windows with lengths of 31 and 63 are used. It is a time index. It is a frequency index.

[0069] Next, the SPWVD of the reference cell is used to estimate the mean function of sea clutter in the time-frequency plane. Sum of standard deviation function :

[0070]

[0071]

[0072] Then, the SPWVD of the test unit (CUT) is normalized to obtain the normalized SPWVD, which is represented as follows: :

[0073]

[0074] Finally, based on this, three time-frequency features were extracted:

[0075] Time-frequency characteristic 1: RI

[0076] This feature reflects the degree of concentration of target energy along the instantaneous frequency curve. In each time slice of the normalized SPWVD... Find the frequency point with the highest energy and extract the time-frequency ridge (TF Ridge):

[0077]

[0078] Add up the normalized energy values ​​at the ridge lines of all time slices and calculate the integral value:

[0079]

[0080] Time-frequency characteristic 2: NR

[0081] In each row of the normalized SPWVD (each time slice) In the first part, select the one with the largest value. One point is set to 1; in this embodiment, L=50. The remaining points are set to 0 to generate a binary image. :

[0082]

[0083] This step aims to remove background noise, retaining only the most significant energy points. In the generated binary image, connected regions are searched according to the 8-neighborhood rule. Assume the set of found connected regions is... Then NR is the total number of connected components. ,Right now

[0084]

[0085] Time-frequency characteristic 3: MS

[0086] MS is the maximum number of pixels contained in all connected regions, which can be expressed as:

[0087]

[0088] Steps 2-6: Number of Phase Crossing Zero Points (NCZP);

[0089] NCZP characterizes the rate of phase change over time. Target echoes exhibit slower phase changes (fewer zero-crossings), while sea clutter shows faster phase changes (more zero-crossings). Firstly, for radar echo segments... ,in, The length of each segment and the phase of each sampling point are calculated using the following formula:

[0090]

[0091] in, This indicates taking the argument (phase) of a complex variable, with an output range of... or equivalent to .

[0092] Then, in the phase sequence In the process, we find all points where adjacent points have opposite phase signs, i.e., points where the phase transitions from positive to negative or vice versa. The set of these zero-crossing points is:

[0093]

[0094] in, Indicates the first The sampling point index position of each phase zero-crossing point. When the phase product of two adjacent points is less than zero, it indicates that the signs are opposite, that is, there is a zero-crossing.

[0095] Finally, the fragment Total number of phase zero crossings Defined as the first phase feature NCZP:

[0096]

[0097] Steps 2-7: Maximum Value of the PhaseDifference PDF (MPDF);

[0098] MPDF characterizes the concentration of the phase difference distribution. The phase difference PDF of the target echo is mainly concentrated in... Nearby (high peak), while the phase difference PDF distribution of sea clutter is more dispersed (lower peak and deviates from the target area). ).

[0099] First, regarding radar echo segments Given time interval In this embodiment of the invention, for the IPIX radar, the pulse repetition frequency is 1000Hz. Take 0.002s, which is the time interval between two adjacent pulses, the first... The phase difference of each sampling point is calculated using the following formula:

[0100]

[0101] The superscript * indicates complex conjugation. yes The complex conjugate of . This formula actually calculates the interval. The phase difference between the two sampling points, the result range is: .

[0102] Then, based on the phase difference sequence The probability density function of the phase difference is estimated using the kernel density estimation method. This PDF reflects the phase difference at... or Distribution within the range.

[0103] Finally, the estimated probability density function Above, the maximum value of the PDF at all phase difference points is defined as the second phase feature MPDF:

[0104]

[0105] Steps 2-8: Decorrelation Time of the Phase Difference (DT);

[0106] Phase difference decorrelation time (DT) characterizes how quickly the phase difference decorrelates over time. Target echoes, due to the presence of stable scatterers, maintain phase difference correlation for a longer time (larger DT value), while sea clutter phase differences decorrelate rapidly (smaller DT value).

[0107] First, regarding radar echo segments Take a series of increasing time intervals For each time interval Repeat the first two steps in the feature MPDF above to obtain each The corresponding phase difference probability density function Thus, each The corresponding MPDF value:

[0108]

[0109] A fixed PDF threshold is set; in this embodiment, it is set to 0.004. This threshold corresponds to the peak level of the phase difference PDF when the echo field is decorrelated to a certain extent. Finally, along the increasing time interval... Direction, find the MPDF value The time interval corresponding to the first time it is less than or equal to the threshold of 0.004 ,Right now:

[0110]

[0111] Should This refers to the decorrelation time, defined as the third phase feature DT:

[0112] Steps 2-9: Combine the above 10 features to obtain the sample feature vector.

[0113] Step 3: Divide the samples into a training set and a calibration set;

[0114] Step 3-1: Split the dataset;

[0115] Preferably, 80% of the pure sea clutter feature samples are first selected as training and calibration samples, while the remaining pure sea clutter samples and all target samples are used only for testing and evaluation. Subsequently, the training and calibration samples are further divided into an anomaly detector training set and a false alarm rate calibration set. The anomaly detector training set is used to learn the sea clutter background distribution, while the false alarm rate calibration set does not participate in model parameter training and is only used for subsequent threshold calibration.

[0116] Regarding parameter selection, the false alarm rate calibration set ratio can be between 0.25 and 0.5; in this embodiment of the invention, 0.5 is selected. (The last sentence appears to be incomplete and possibly refers to a different topic: "Target false alarm rate...") Confidence level In the embodiments, the number of valid samples in the calibration set is preferably not less than 6905; if the calibration samples are insufficient, the confidence level can be appropriately reduced, the target false alarm rate requirement can be increased, or a more conservative threshold selection strategy can be adopted.

[0117] Step 3-2: Data preprocessing;

[0118] The mean and standard deviation of each feature dimension are calculated using the training set, and these mean and standard deviation are then used to standardize the calibration set and subsequent test samples. The standardization parameters are calculated only from the training set to avoid information leakage from the calibration set or subsequent test set.

[0119]

[0120] in, and Training set The mean and standard deviation of each dimension of the feature.

[0121] Step 4: Train the anomaly detector using the training set to obtain an anomaly detector that can output anomaly scores;

[0122] The anomaly detector in this invention is used to map the radar multi-domain feature vectors standardized in step 3 into one-dimensional anomaly scores. The specific type of anomaly detector is not limited, as long as it can learn the normal background distribution based on sea clutter samples and output anomaly scores representing the degree of sample deviation, it can be connected to the subsequent Clopper-Pearson threshold calibration module. To verify the universality of the threshold calibration method of this invention, in the embodiments of this invention, single-class support vector machines, isolated forests, autoencoders, variational autoencoders, and deep support vector data descriptions are selected as anomaly detectors. The construction methods and parameters of the anomaly scores for each detector are as follows.

[0123] For single-class support vector machines, only pure clutter samples are used to learn the normal sample distribution boundary. Features are standardized to zero mean and unit variance before training. During detection, the deviation of a sample from the single-class decision boundary is calculated; the further the deviation from the normal region, the higher the degree of anomaly. The kernel function is the radial basis function; the outlier proportion control parameter is 0.05; and the kernel width parameter uses adaptive scaling estimation.

[0124] For isolated forests, the detector consists of multiple randomly isolated trees. Each tree is constructed by randomly selecting a feature dimension and generating a segmentation threshold within that dimension's range, recursively partitioning the sample space. The easier a sample is to isolate, the shorter its path length, and the higher its anomaly level. The current default anomaly score is the inverse of the average path length; a higher score indicates a greater anomaly. The number of randomly isolated trees is 100; the maximum number of samples per tree is 256; and the maximum tree depth is 8 by default.

[0125] For the autoencoder, a symmetric fully connected encoder-decoder structure is adopted. The encoder structure is "input feature dimension, 32, 16, 6", and the decoder structure is "6, 16, 32, input feature dimension". The hidden layer uses the hyperbolic tangent activation function. The model learns the normal data manifold by reconstructing pure clutter samples, and the average reconstruction error per sample is used as the outlier score during detection. The training epochs are 40; the batch size is 128; the learning rate is 0.005; the optimization method is adaptive moment estimation; the loss function is mean squared error; zero-mean, unit variance standardization is performed before training.

[0126] For the variational autoencoder, the encoder structure is "input feature dimension, 32, 16", followed by the output latent variable mean and log-variance, respectively; the latent variable dimension is 6. Latent variable samples are obtained through reparameterization during training, and the latent variable mean is used during testing. The decoder structure is "6, 16, 32, input feature dimension". The outlier score is a weighted sum of the reconstruction error and the latent variable distribution constraint term. The training epochs are 40; the batch size is 128; the learning rate is 0.005; the latent variable dimension is 6; the distribution constraint weight is 0.005; the optimization method is adaptive moment estimation; zero-mean, unit-variance standardization is performed before training.

[0127] For deep support vector data description, an autoencoder is first pre-trained during training. The pre-trained encoder and decoder structures are consistent with the autoencoder in this invention example. The pre-trained encoder is then retained, and the hypersphere center is initialized based on the average representation of pure clutter samples in the latent space. In the second stage, the squared distance from the latent representation of a sample to the hypersphere center is minimized to ensure a compact distribution of pure clutter samples within the latent space. During detection, the squared distance from the latent representation of the test sample to the hypersphere center is used as the anomaly score. The autoencoder pre-training rounds are 40; the deep support vector data description optimization rounds are 15; the batch size is 128; the pre-training learning rate is 0.005; the second-stage learning rate is 0.0005; the latent space dimension is 6; the optimization method is adaptive moment estimation; and the second-stage weight decay coefficient is 10. -6 Zero-mean, unit-variance standardization was performed before training.

[0128] It should be noted that the above-described anomaly detectors and parameter settings are merely specific embodiments of the present invention and do not constitute a limitation on the scope of protection of the present invention. In practical applications, the type and parameters of the anomaly detectors can be adjusted according to the radar system, feature dimensions, clutter sample size, and computing resources. For the raw scores output by different detectors, the present invention uniformly converts them into anomaly score forms where "the larger the score, the more abnormal it is"; if the original output of the detector is a normality score, the anomaly score can be obtained by taking the opposite number, the reciprocal, or other monotonic transformations. The subsequent false alarm rate control method only relies on the anomaly scores of the calibration set and the number of samples exceeding the threshold, therefore it can be connected to different anomaly detectors as an independent threshold calibration module.

[0129] Step 5: Input the calibration set into the anomaly detector to obtain the calibration anomaly score, and determine the detection threshold using the Clopper-Pearson one-sided confidence upper bound based on the target false alarm rate and confidence level.

[0130] Step 5-1: Set the target false alarm rate;

[0131] Set the target false alarm rate This indicates that the probability of a pure sea clutter sample being misidentified as a target or an anomaly sample should not exceed this value. In one embodiment of the present invention, the false alarm rate is set to 0.001, meaning that the probability of a normal sea clutter sample being misidentified as a target should not exceed one in a thousand.

[0132] For any anomaly detector, let it be that it is effective for samples The output anomaly score is The higher the anomaly score, the greater the deviation of the sample from the sea clutter background distribution. For candidate thresholds... The true false alarm rate can be expressed as:

[0133]

[0134] in, Indicating the clutter hypothesis, This indicates that clutter samples were misidentified as targets or anomalous samples.

[0135] Step 5-2: Count the number of samples that exceed the threshold;

[0136] Suppose that A calibration set is composed of pure sea clutter samples. Each calibration sample is processed by an anomaly detector to obtain an anomaly score. ,in Indicates the first Anomaly scores for each calibrated clutter sample. Given a candidate threshold. Afterwards, if If this happens, the clutter sample will be mistakenly identified as an anomalous sample, resulting in a false alarm. For candidate thresholds... The number of samples exceeding the threshold is defined as:

[0137]

[0138] in, For indicator functions. When hour, ;when hour, .therefore, express In a pure sea clutter calibration sample, the outlier score exceeded the candidate threshold. The number of samples.

[0139] In practice, the impact of sample correlation on the upper bound of the false alarm rate confidence level can be reduced by increasing the sliding window step size, sampling across distance units, sampling across time segments, or making a conservative estimate based on the number of effective samples.

[0140] Step 5-3: Calculate the upper bound of the Clopper-Pearson one-sided confidence level;

[0141] For a given candidate threshold This can be used to determine if the "clutter sample anomaly score exceeds a threshold". "Consider it a Bernoulli event," The sample size is The true false alarm rate The binomial distribution. This invention uses the Clopper-Pearson one-sided confidence upper bound to estimate the true false alarm rate. The conservative upper bound. Let the one-sided confidence level be... In one embodiment of the present invention, the value is taken as 0.999. At that time, the Clopper-Pearson one-sided confidence upper bound for the true false alarm rate is:

[0142]

[0143] in, The quantile function representing the beta distribution. Indicates the confidence level. This indicates that the candidate threshold has been exceeded in the calibration set. The number of samples, Indicates the total number of calibration samples. This represents the true false alarm rate when the number of calibrated samples is n and the number of samples exceeding the threshold is k(T). The upper confidence bound of the Clopper-Pearson one-sided confidence level at confidence level γ. When this occurs, it indicates that all calibrated samples exceed the candidate threshold, which is significantly too low, resulting in a high risk of false alarms. Therefore, in this case, we set... .

[0144] It should be noted that this invention does not require the empirical false alarm rate to meet a certain standard. Instead, it requires that the Clopper-Pearson one-sided confidence upper bound be satisfied:

[0145]

[0146] In other words, a candidate threshold is considered only when the upper confidence bound of the true false alarm rate does not exceed the target false alarm rate. It meets the requirements for false alarm rate control. This method is more stringent than directly using empirical false alarm rates and is more suitable for radar detection scenarios of small targets on the sea surface with high requirements for low false alarm rates.

[0147] Step 5-4: Determine the final detection threshold;

[0148] In the candidate threshold set, the present invention selects the threshold that satisfies... The minimum threshold is used as the final detection threshold. :

[0149]

[0150] The reason for choosing the minimum acceptable threshold is that, under the premise of satisfying the false alarm rate confidence constraint, a lower threshold is more conducive to improving the detection probability of weak targets. Therefore, this threshold selection method can maintain detection capability as much as possible while controlling the false alarm rate.

[0151] Determine the final detection threshold Then, for new samples to be tested First, calculate its abnormal score. .like If so, it is determined to be a target sample or an abnormal sample; if If it is, then it is determined to be a clutter sample.

[0152] Note: Requirements for the number of calibration samples

[0153] Under conditions of low false alarm rate and high confidence level, the number of calibration samples has a significant impact on the reliability of threshold calibration. Even if no samples in the calibration set exceed the candidate threshold, i.e. The Clopper-Pearson one-sided confidence upper bound is still not zero, but rather:

[0154]

[0155] To demonstrate the true false alarm rate at the confidence level The false alarm rate should not exceed the target. It needs to meet the following requirements:

[0156]

[0157] Equivalently, the number of calibration samples should satisfy:

[0158]

[0159] For example, when and At that time, the calculation yielded At least 6905. This means that even if no samples exceeding the threshold are observed in the calibration set, at least approximately 6905 independent pure sea clutter calibration samples are needed to demonstrate that the true false alarm rate is below 0.001 at a 0.999 confidence level. If the number of calibration samples is insufficient, even if the empirical false alarm rate is zero, it cannot reliably demonstrate that the true false alarm rate meets the target false alarm rate requirement. Therefore, when using the method of this invention, the size of the clutter calibration set needs to be reasonably set according to the target false alarm rate and confidence level.

[0160] In addition, when there is a correlation between the calibrated samples, the number of valid samples should be calculated based on the degree of correlation, or a more conservative confidence level and threshold selection strategy should be adopted.

[0161] To facilitate practical use, a method for quickly calculating the threshold is presented here.

[0162] After training the anomaly detector, the calibration set samples are input into the detector to obtain the calibration set of anomaly scores. ,in To determine the number of samples in the calibration set, a higher anomaly score indicates that the sample deviates more from the sea clutter background distribution. To avoid repeatedly searching for each consecutive threshold, this invention transforms the threshold search problem into a problem of selecting the anomaly score ranking position. The specific steps are as follows:

[0163] Step 5-1: Sort the outlier scores in the calibration set in ascending order to obtain an ordered outlier score sequence. ;

[0164] Step 5-2: Delete duplicate outlier scores from the sorted sequence, retaining only unique values ​​to obtain a candidate outlier score sequence. To cover all possible decision cases, add two boundary candidate points at the beginning and end of this sequence: one value less than the minimum outlier score and one value greater than the maximum outlier score. The difference between these two numbers and the minimum and maximum outlier scores is the minimum precision floating-point number. The former corresponds to all calibrated samples being judged as outliers, and the latter corresponds to all calibrated samples not being judged as outliers.

[0165] Step 5-3: Based on the number of samples in the calibration set Target false alarm rate and confidence level Calculate the maximum number of false alarms allowed under the Clopper-Pearson one-sided confidence upper bound constraint. .in, satisfy:

[0166]

[0167] And for any ,have:

[0168]

[0169] Step 5-4: Based on the allowed number of false alarms Determine the detection threshold. Since higher anomaly scores correlate with a stronger likelihood of targeting, the maximum number of anomalies allowed in the calibration set should be limited. If any sample exceeds the threshold, the threshold should be selected as the last one in the sorted sequence. The abnormal score is near the threshold. In practice, the corresponding candidate point can be directly selected as the detection threshold, so that the number of samples in the calibration set exceeding the threshold does not exceed the threshold. .

[0170] This method does not require repeatedly searching for the threshold within a continuous range of real numbers; instead, it selects from only a finite number of sorted anomaly score positions. Since the Clopper-Pearson constraint is actually only related to the number of calibration samples exceeding the threshold, and not directly dependent on the continuous values ​​of the threshold, the detection threshold satisfying the false alarm rate confidence constraint can be quickly determined by the sorting position. For the same calibration set size, target false alarm rate, and confidence level, the allowed number of false alarm points is fixed; however, the specific anomaly scores corresponding to different calibration sets are different, so the final threshold value will still vary with the calibration data.

[0171] Step 6: After processing the sample to be detected according to the feature extraction method in Step 2, input it into the anomaly detector to obtain the anomaly score to be detected, and compare the anomaly score to be detected with the detection threshold. If the anomaly score to be detected is greater than the detection threshold, it is determined to be a target; otherwise, it is determined to be sea clutter.

[0172] The technical effects of the present invention will be further described below in conjunction with experimental results.

[0173] Figure 2 shows the results of the single-class support vector machine detector. As can be seen from Figures 2(a) and 2(b), after introducing the threshold calibration method of the present invention, the detection probability remains stable overall, while the actual false alarm rate converges significantly, indicating that the method can effectively control the false alarm rate of the anomaly score output by the single-class support vector machine.

[0174] Figure 3 shows the results of the isolated forest detector. As can be seen from Figures 3(a) and 3(b), after adopting the method of the present invention, the actual false alarm rate is reduced in all datasets and polarization channels. Although the detection probability is somewhat conservative, it still remains at an usable level overall.

[0175] Figure 4 shows the results of the autoencoder detector. As can be seen from Figures 4(a) and 4(b), the method of the present invention can significantly reduce the actual false alarm rate while maintaining a high detection probability, indicating that the threshold calibration method is also effective for reconstruction error anomaly detectors.

[0176] Figure 5 shows the results of the variational autoencoder detector. As can be seen from Figures 5(a) and 5(b), the method of the present invention controls the actual false alarm rate to near or below the target value on most datasets, while maintaining a good detection probability.

[0177] Figure 6 shows the results of the deep support vector data description detector. As can be seen from Figures 6(a) and 6(b), the method of the present invention can further improve the threshold stability of this type of detector in low false alarm rate scenarios.

[0178] Figure 7 The overall comparison results of five types of anomaly detectors before and after adopting the threshold calibration method of this invention are presented. Overall, this invention can be used as a general threshold calibration module to connect to different anomaly detectors and achieve more stable false alarm rate control under finite clutter calibration sample conditions.

[0179] From the perspective of average detection probabilities, the detection probabilities of all detectors decreased to some extent after adopting the threshold calibration method of this invention, which is due to the more conservative thresholds. Specifically, the probability decreased from 0.9143 to 0.8871 for single-class support vector machine, from 0.9252 to 0.8886 for autoencoder, from 0.9324 to 0.8976 for variational autoencoder, from 0.8856 to 0.8342 for deep support vector data description, and from 0.7247 to 0.6016 for isolated forest. This result indicates that while this invention reduces the false alarm rate, it incurs a certain cost in detection probability, but most detectors still maintain a high detection level.

[0180] From the perspective of average actual false alarm rate, without the threshold calibration method of this invention, the average actual false alarm rate of all five types of detectors is higher than the target false alarm rate. After adopting the method of this invention, the average actual false alarm rate of all five types of detectors is reduced to below the target false alarm rate, with the average actual false alarm rate of single-class support vector machine, isolated forest, and variational autoencoder being approximately 0.0006, autoencoder approximately 0.0007, and deep support vector data description approximately 0.0004. This result shows that this invention can effectively suppress the problem of excessive actual false alarm rate of different anomaly detectors.

[0181] From the perspective of the standard deviation of the actual false alarm rate, the fluctuation of the false alarm rate of each detector is significantly reduced after adopting the method of this invention. The standard deviation of the single-class support vector machine and the isolated forest both decreased from about 0.0018 to 0.0008, the autoencoder and variational autoencoder decreased from about 0.0031 and 0.0030 to about 0.0010, respectively, and the deep support vector data description decreased from 0.0014 to 0.0007. These results indicate that this invention can not only reduce the average actual false alarm rate, but also improve the consistency and stability of false alarm rate control under different datasets and different polarization channels.

[0182] From the perspective of the number of data points falling within the target false alarm rate tolerance range, the number of data points falling within the target false alarm rate tolerance range for all five types of detectors significantly increased after adopting the method of this invention. Specifically, the number of single-class support vector machines increased from 44 to 75, isolated forests from 57 to 74, autoencoders from 40 to 71, variational autoencoders from 31 to 74, and deep support vector data descriptions from 56 to 77. This result further illustrates that the threshold calibration method of this invention can make the actual false alarm rate more concentrated near the target false alarm rate, reducing the situation of excessively high and fluctuating false alarm rates.

Claims

1. A general threshold calibration method for detecting small surface anomalies with controllable false alarm rate, characterized in that, The one-dimensional anomaly score output by the anomaly detector is used as a unified threshold calibration object. A calibration set containing only sea clutter samples is used, and the detection threshold is determined by conservatively constraining the true false alarm rate based on the Clopper-Pearson one-sided confidence upper bound. The steps include: Step 1: Acquire the radar echo signal over the sea surface; Step 2: Extract features from the sea surface radar echo signal to obtain sample feature vectors; Step 3: Divide the samples into a training set and a calibration set; Step 4: Train the anomaly detector using the training set to obtain an anomaly detector that can output anomaly scores; Step 5: Input the calibration set into the anomaly detector to obtain the calibration anomaly score, and determine the detection threshold using the Clopper-Pearson one-sided confidence upper bound based on the target false alarm rate and confidence level. Step 6: After processing the sample to be detected according to the feature extraction method in Step 2, input it into the anomaly detector to obtain the anomaly score to be detected, and compare the anomaly score to be detected with the detection threshold. If the anomaly score to be detected is greater than the detection threshold, it is determined to be a target; otherwise, it is determined to be sea clutter.

2. The general threshold calibration method for detecting small sea surface anomalies with controllable false alarm rate as described in claim 1, characterized in that, The features extracted in step 2 include the normalized Hurst exponent, relative Doppler peak height, relative vector entropy, relative Doppler coefficient of variation, ridge integral, number of connected regions, maximum size of connected regions, number of phase zero crossings, maximum value of phase difference probability density function, and phase difference decorrelation time, which constitute a 10-dimensional feature vector.

3. The general threshold calibration method for detecting small surface anomalies with controllable false alarm rate according to claim 1, characterized in that, The training set and calibration set in step 3 consist only of sea clutter samples, and the calibration set does not participate in the parameter training of the anomaly detector.

4. The general threshold calibration method for detecting small sea surface anomalies with controllable false alarm rate as described in claim 1, characterized in that, The anomaly detector in step 4 is any one of a single-class support vector machine, an isolated forest, an autoencoder, a variational autoencoder, or a deep support vector data description; the original output of the anomaly detector is uniformly converted into anomaly scores after monotonic transformation, and the larger the anomaly score, the more abnormal the sample.

5. The general threshold calibration method for detecting small sea surface anomalies with controllable false alarm rate according to claim 1, characterized in that, Step 5 includes: setting the target false alarm rate. With a confidence level of γ, the calibration set is input into the anomaly detector to obtain a set of calibrated anomaly scores. Where n is the number of samples in the calibration set; for a candidate detection threshold T, count the number of samples k(T) whose calibration anomaly scores exceed the candidate detection threshold T: in, For indicator functions; when hour, ;when hour, .

6. The general threshold calibration method for detecting small sea surface anomalies with controllable false alarm rate according to claim 5, characterized in that, The event "the anomaly score of the sea clutter sample exceeds the candidate detection threshold T" is considered a Bernoulli event, and the Clopper-Pearson one-sided confidence upper bound is used. The true false alarm rate corresponding to the candidate detection threshold T Make a conservative estimate; when At that time, the Clopper-Pearson one-sided confidence upper bound is: in, Represents the quantile function of the beta distribution, when hour, .

7. A general threshold calibration method for detecting small sea surface anomalies with controllable false alarm rate, as described in claim 6, is characterized in that... In step 5, the qualification condition for the candidate detection threshold T is that the Clopper-Pearson one-sided confidence upper bound is satisfied as follows: As a qualification condition for the candidate detection threshold T, the smallest candidate detection threshold among those that meet this condition is selected as the final detection threshold: in, This is the final detection threshold.

8. A general threshold calibration method for detecting small sea surface anomalies with controllable false alarm rate, as described in claim 7, is characterized in that... Step 5 also includes a threshold determination method based on sorting: based on the number of samples in the calibration set n and the target false alarm rate. Given a confidence level γ, determine the maximum allowable number of samples exceeding the threshold, k. max , where k max To meet The largest non-negative integer; sort the calibrated outlier scores in ascending order to obtain The final detection threshold is determined based on the sorted anomaly scores. This causes the calibration set to exceed the final detection threshold. The number of samples is no greater than k max .

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