Radar detection performance calibration method and system based on gradient sensitivity matrix

Abstract

This application discloses a radar detection performance calibration method and system based on a gradient sensitivity matrix, involving radar performance analysis and calibration techniques. The offline stage involves using Sobol global sensitivity analysis to screen dominant parameters such as signal-to-noise ratio (SNR) and clutter ratio (CNR), constructing a detection probability response surface model, and calculating the gradient sensitivity matrix at a reference point. In the online stage, real-time incremental prediction of the detection probability is achieved based on the gradient matrix; a blind-zone-free observation detection probability is obtained by injecting a digital baseband signal or using a built-in calibration signal from an orthogonal protection unit; and the gradient matrix is ​​dynamically updated based on the prediction error using a recursive least squares (RLS) algorithm with a sleep mechanism. This application significantly reduces the online computational load, can adapt to environmental changes and system aging, and improves the radar's perception reliability and intelligent resource scheduling level in complex electromagnetic environments.

Description

Technical Field

[0001] This application relates to the fields of radar performance analysis and calibration technology, and in particular to a radar detection performance calibration method and system based on gradient sensitivity matrix. Background Technology

[0002] Radar detection probability (Pd) is a key indicator of radar detection capability. Real-time knowledge of the current Pd is crucial for adaptive threshold setting, waveform selection, power allocation, and anti-jamming decisions. However, accurate calculation of Pd typically requires complex numerical integration (such as the detection probability formula for Swerling undulating targets) or Monte Carlo simulations, resulting in high computational costs that cannot be completed within millisecond-level pulse repetition periods. Current engineering practices often employ fixed thresholds or offline table lookups, which are ill-suited to rapidly changing environments.

[0003] Existing improvement methods include: Analytical approximation formulas (such as the Albersheim formula and the Shhnidman formula) are faster to calculate, but they are only applicable to ideal Gaussian noise environments and have large deviations from actual conditions such as clutter and interference.

[0004] Neural network proxy models: can be trained offline and make predictions quickly, but lack interpretability and are difficult to update adaptively online (requiring retraining).

[0005] Kalman filter tracking SNR: It only tracks the signal-to-noise ratio, does not directly output Pd, and does not utilize gradient information.

[0006] Therefore, a real-time Pd prediction method with low computational cost, clear physical meaning, and online adaptive calibration is needed. Summary of the Invention

[0007] This application provides a radar detection performance calibration method and system based on a gradient sensitivity matrix, which provides a lightweight, online adaptive method for real-time prediction and calibration of radar detection probability.

[0008] This application provides a radar detection performance calibration method based on a gradient sensitivity matrix, including: Identify the dominant parameters that affect the radar detection probability, construct a response surface model with the dominant parameters as input and the detection probability as output, and calculate the gradient sensitivity matrix of the response surface model at a preset reference point; Obtain the real-time values ​​of the dominant parameters within the current coherent processing interval, and use the gradient sensitivity matrix and the preset benchmark point to predict the detection probability. The observed detection probability is obtained by means of the built-in calibration signal. The observed detection probability is compared with the predicted detection probability. When the prediction error meets the preset calibration conditions, the gradient sensitivity matrix is ​​updated based on the recursive least squares algorithm. The state vector of the recursive least squares algorithm consists of the incremental value of the dominant parameter and the bias term. The incremental value of the dominant parameter is the difference between the current real-time value of the dominant parameter and the preset reference point.

[0009] This application provides a radar detection performance calibration system based on a gradient sensitivity matrix, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the radar detection performance calibration method based on a gradient sensitivity matrix as described above.

[0010] This application provides a lightweight, online adaptive method for real-time prediction and calibration of radar detection probability. It utilizes an offline-constructed gradient sensitivity matrix combined with an online first-order Taylor expansion to achieve real-time prediction of radar detection probability, and calibrates the gradient matrix online using observations obtained through a built-in calibration signal.

[0011] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0012] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a schematic diagram illustrating the overall process of the offline and online stages of the method in the embodiments of this application; Figure 2 This is a visual bar chart illustrating the gradient sensitivity matrix of the method in the embodiments of this application; Figure 3 This is a timing diagram illustrating the online prediction and calibration method of the embodiments of this application; Figure 4 This is a schematic diagram of the data flow for online gradient matrix updating using RLS in the embodiments of this application; Figure 5 This is a comparison curve of the prediction error before and after calibration for the method in the embodiments of this application; Figure 6 This is a schematic diagram of adaptive threshold adjustment based on predicted detection probability in the method of this application embodiment. Detailed Implementation

[0013] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0014] This application provides a radar detection performance calibration method based on a gradient sensitivity matrix, such as... Figure 1 As shown, the steps include the following stages: Offline modeling stage S1: Identify the dominant parameters affecting radar detection probability, construct a response surface model with the dominant parameters as input and the detection probability as output, and calculate the gradient sensitivity matrix of the response surface model at a preset reference point. In a specific example, the main parameters affecting detection probability are determined, including signal-to-noise ratio (SNR), clutter-to-noise ratio (CNR), interference-to-noise ratio (JNR), accumulated pulse number (N), and target fluctuation type.

[0015] In some embodiments, identifying the dominant parameters affecting the radar detection probability includes: The Sobol global sensitivity analysis method was used to calculate the contribution of signal-to-noise ratio, clutter-to-noise ratio, interference-to-noise ratio, accumulated pulse number, and target fluctuation type to the detection probability.

[0016] Parameters with contributions greater than a preset threshold are selected as dominant parameters. A dimensionality reduction mapping matrix is ​​constructed to map the high-dimensional parameter space to a low-dimensional space composed of the dominant parameters. The gradient sensitivity matrix and the state vector are both located in the low-dimensional space. For example, SNR and CNR contribute the most. Latin hypercube sampling is performed in the dominant dimension space. The corresponding Pd values ​​are obtained through high-fidelity radar performance simulation or actual measurement. The response surface is fitted by using a polynomial chaotic expansion PCE or radial basis function network to establish Pd = f An approximate model of (SNR,CNR,JNR,…), also known as a response surface model.

[0017] Calculating the gradient sensitivity matrix of the response surface model at a preset reference point includes: selecting a typical operating point x0, such as... Figure 2 As shown, for example, x0 includes SNR0, CNR0, ... as benchmarks under the nominal environment. The typical range of variation and marginal contribution of the dominant parameters are shown in Table 1: Table 1 Calculate the partial derivative of the response surface at that point to obtain the gradient matrix G = [∂Pd / ∂SNR, ∂Pd / ∂CNR, ∂Pd / ∂JNR, ...]. If the response surface is in polynomial form, it can be analytically differentiated; otherwise, the finite difference method is used.

[0018] Online prediction phase S2: Obtain the real-time values ​​of the dominant parameters within the current coherent processing interval. Based on the first-order Taylor expansion, predict the detection probability using the gradient sensitivity matrix and the preset benchmark point. For example, at each coherent processing interval CPI, measure or estimate the value of the current dominant dimension. SNR can be estimated by the output power of the matched filter, CNR by the noise floor in the targetless region, and JNR by the interference detection algorithm.

[0019] In some embodiments, the detection probability is predicted using the gradient sensitivity matrix and the preset reference point as follows: in, Let be the predicted detection probability at time t. Preset reference point The detection probability at point G is the gradient sensitivity matrix. The value of the dominant parameter at time t is the real-time value.

[0020] Online calibration phase S3: The observed detection probability is obtained through the built-in calibration signal. The observed detection probability is compared with the predicted detection probability. When the prediction error meets the preset calibration conditions, the gradient sensitivity matrix is ​​updated based on the recursive least squares algorithm. The state vector of the recursive least squares algorithm consists of the incremental value of the dominant parameter and the bias term. The incremental value of the dominant parameter is the difference between the current real-time value of the dominant parameter and the preset reference point.

[0021] In a specific example, the prediction error e is calculated as follows: - , This represents the probability of observation and detection.

[0022] Set error threshold For example, 0.05. If |e| continuously exceeds the threshold... Upon reaching K iterations, calibration is triggered, activating the RLS calibration module. After activation, subsequent observation data are input into the RLS algorithm for real-time recursive updates. For example... Figure 3 As shown, at CPI=25, the continuous observation error exceeds the threshold, triggering RLS calibration based on the incremental model. After calibration, the predicted value quickly tracks the true value, and the deviation is significantly reduced.

[0023] In some embodiments, obtaining the observation detection probability through a built-in calibration signal includes: A calibration coherent processing interval (CPI) is inserted every Ncal interval of regular coherent processing.

[0024] Within the calibration coherent processing interval CPI, a built-in calibration signal orthogonal to the current radar operating waveform is generated; The built-in calibration signal is directly injected into the receiving link in the digital baseband, or the built-in calibration signal is placed in a target-free protected range cell in the range dimension for transmission and reception. The observation detection probability is obtained by statistically analyzing the ratio of the number of successful detections of the built-in calibration signal to the total number of transmissions within the sliding window. .

[0025] The method of this application does not depend on external targets, can work in any environment, and the sampling period can be set by the user, for example, calibrating once every 10 CPIs, with a time of about 0.2 seconds, which meets the real-time requirements.

[0026] In some embodiments, a hibernation control step is also included: When the absolute value of the prediction error is less than the error threshold for M consecutive prediction periods, the update process of the recursive least squares algorithm is suspended, and the current gradient sensitivity matrix remains unchanged. Based on the above example, when the error for M consecutive prediction periods falls back to within the safety threshold, the RLS calibration module is put into sleep mode, keeping the current gradient matrix unchanged to save computational resources.

[0027] If the absolute value of the prediction error exceeds the error threshold K times consecutively, the update process of the recursive least squares algorithm is reactivated.

[0028] The online gradient matrix update process of this application includes: The gradient matrix G is updated using the Recursive Least Squares (RLS) algorithm. The observation model is established in the incremental space to maintain consistency with the prediction model. In some embodiments, a state vector is defined. = ,in = - The observation model of the recursive least squares algorithm is expressed as follows: = ⋅Δ , where Δ = b is the bias term. To observe noise.

[0029] The parameter vector to be estimated is θ=[G,b], which has m+1 dimensions, where m is the number of dominant parameters.

[0030] RLS update formula: = • / (λ+ • • ) = + •( - • ) =(I- • )• / λ in = λ is the forgetting factor (typically 0.95~0.99), and θ is the parameter vector to be estimated [G,b]. For example... Figure 4 As shown, the input increment vector = - That is, the difference between the current conditions and the benchmark, and the probability of observation and detection. Parameters from the previous time step and covariance The error calculation, gain calculation, parameter update and covariance update are performed sequentially, and finally the updated gradient matrix G and bias b are output.

[0031] Figure 5 The comparison curves of prediction errors before and after calibration are shown. Before calibration, the prediction errors were more dispersed and had a larger standard deviation; after calibration, the prediction errors were concentrated near zero and the distribution was sharper. A normal distribution curve is superimposed for easier comparison.

[0032] In some embodiments, an adaptive control step is also included: The absolute value of each element in the updated gradient sensitivity matrix is ​​used as the environmental sensitivity index. If the absolute value of the gradient corresponding to the interference-to-noise ratio exceeds the preset alarm limit, an anti-interference trigger command is generated to control the radar system to switch the anti-interference waveform or start airspace filtering. If the predicted detection probability is determined to be lower than the preset performance index, the false alarm threshold of the radar system will be adjusted or the number of accumulated pulses will be increased.

[0033] For example, in some examples, the predicted Output to the detection threshold calculation module. If If the value is lower than expected, the false alarm threshold can be automatically lowered (to improve sensitivity) or the number of accumulated pulses can be increased. The absolute value of each element in the gradient matrix is ​​used as an indicator of parameter importance: if ∂ A large / ∂JNR indicates that the radar is sensitive to interference, and anti-interference measures should be initiated, such as waveform switching and spatial filtering.

[0034] Figure 6 A schematic diagram of adaptive threshold adjustment based on predicted detection probability is shown. When When the threshold is below the expected threshold of 0.8 (e.g., CPI = 15~30), the system automatically lowers the threshold factor to increase the detection probability, at the cost of a slight increase in the false alarm rate; when After recovery, the threshold factor also increases. This adaptive mechanism achieves a dynamic balance between detection performance and false alarm rate.

[0035] The method in this application employs online RLS updates, and the choice of the forgetting factor λ determines the algorithm's tracking capability. RLS tracks slowly changing data using the forgetting factor λ; if a sudden change in the environment occurs and the prediction error is detected to be continuously increasing, RLS is reset, and learning begins again. Resetting RLS restores the initial values ​​of the covariance matrix, and the parameters revert to their offline values.

[0036] In some embodiments, the recursive least squares algorithm employs an adaptive forgetting factor, which is dynamically adjusted based on the magnitude of the prediction error. When the absolute value of the prediction error shows an increasing trend over multiple consecutive periods, the forgetting factor is reduced to accelerate the tracking speed. When the absolute value of the prediction error for multiple consecutive periods converges within a safety threshold, the forgetting factor is increased.

[0037] In some embodiments, a mutation reset step is also included: If a sudden change in the radar operating environment is detected, causing the prediction error to diverge, the covariance matrix in the recursive least squares algorithm is reset to its initial value, the gradient sensitivity matrix is ​​rolled back to its initial value in the offline modeling stage, and the online learning process is restarted.

[0038] This application also proposes an example of real-time prediction and calibration of the detection probability of a certain X-band pulse Doppler radar based on the radar detection performance calibration method of this application. In this example: The radar operates in air search mode, targeting a drone (small RCS, fluctuating Swerling I). The detection probability Pd is required to be no less than 0.8 (false alarm rate). =1e-5). Each radar phased processing interval (CPI) is 20ms and contains 16 pulses. Real-time prediction of the current Pd is required to determine whether to increase the dwell time or adjust the threshold.

[0039] Offline modeling stage: Dominant Dimension Identification: Influenced by Sobol sensitivity analysis. The main parameters are: signal-to-noise ratio (SNR) (contributing 65%), clutter-to-noise ratio (CNR) (contributing 20%), interference-to-noise ratio (JNR) (contributing 10%), and accumulated pulse number N (contributing 5%). SNR and CNR are selected as the dominant dimensions (for simplification), while JNR and N are treated as correction terms or constants during the online phase.

[0040] Experimental Design: Latin hypercube sampling was performed within the SNR range of -5 to 20 dB and the CNR range of -5 to 15 dB, for a total of 100 points. A radar performance simulation model was used to calculate the values ​​for each point. .

[0041] Response surface fitting: Second-order polynomial fitting was used. = + ·SNR+ ·CNR + ·SNR 2 + ·CNR 2 + ·SNR·CNR Gradient calculation: Calculate the gradient at the operating point SNR0=10dB, CNR0=5dB: ∂ / ∂SNR=0.04,∂ / ∂CNR=-0.035 The gradient matrix G = [0.04, -0.035] is the reference point. f ( =0.85.

[0042] During the online forecasting phase, each CPI undergoes the following steps: Parameter estimation: The matched filter output is estimated to have SNRt=9dB and CNRt=6dB.

[0043] First-order prediction: =0.85+0.04×(9-10)+(-0.035)×(6-5)=0.85-0.04-0.035=0.775.

[0044] Output and Decision: The predicted value is 0.8 lower than the expected value. The system decides to increase the accumulated pulse count to 24 and re-predict. Increased to 0.83, accepted.

[0045] Observation acquisition and calibration, calibration signal injection: A calibration CPI is inserted every 10 CPIs of radar, transmitting a calibration pulse with known power and range. After matched filtering at the receiver, a successful detection is directly determined. The sliding window length M = 20 calibration events (approximately 4 seconds). The number of successful detections is counted, and the observation value is calculated. .

[0046] Example of normal environment: 18 out of 20 calibration tests were successful. =0.90. Predicted value =0.89, error e=0.01, no calibration triggered.

[0047] Example of triggering calibration: Assuming a sudden increase in interference, in reality... It dropped to 0.70. Calibration statistics show... =0.68, while the prediction is still 0.78, e=-0.10, exceeding the threshold of 0.05 for 3 consecutive times, triggering RLS calibration.

[0048] Set the increment vector Δ =[SNRt-SNR0,CNRt-CNR0]=[9-10,6-5]=[-1, 1].

[0049] State vector = = .

[0050] initial parameters =[0.04, -0.035, 0.85] (the last digit is the bias b).

[0051] Forgetting factor λ = 0.98, initial covariance =0.1•I.

[0052] Using the most recent 10 calibration data (each data contains) and ), and perform RLS updates sequentially.

[0053] After the update, we get θ̂=[0.038,-0.042,0.83]. The new gradient G=[0.038,-0.042].

[0054] Validation: Predict using the new gradient: =0.83 + 0.038 × (-1) + (-0.042) × 1 = 0.83 - 0.038 - 0.042 = 0.75 Closer to reality =0.68, and further calibration will converge.

[0055] Using prediction Automatically adjust the CFAR detection threshold coefficient. When If the threshold is too low, the threshold factor is reduced (increasing the risk of false alarms in exchange for a higher detection probability). The system sets a maximum safe false alarm rate of 1e-4, and adjusts it dynamically within this range.

[0056] This application also proposes a radar detection performance calibration system based on a gradient sensitivity matrix, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the radar detection performance calibration method based on the gradient sensitivity matrix as described above.

[0057] It should be noted that, in the embodiments of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0058] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0059] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0060] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A radar detection performance calibration method based on gradient sensitivity matrix, characterized in that, include: Identify the dominant parameters that affect the radar detection probability, construct a response surface model with the dominant parameters as input and the detection probability as output, and calculate the gradient sensitivity matrix of the response surface model at a preset reference point; Obtain the real-time values ​​of the dominant parameters within the current coherent processing interval, and use the gradient sensitivity matrix and the preset benchmark point to predict the detection probability. The observed detection probability is obtained by means of the built-in calibration signal. The observed detection probability is compared with the predicted detection probability. When the prediction error meets the preset calibration conditions, the gradient sensitivity matrix is ​​updated based on the recursive least squares algorithm. The state vector of the recursive least squares algorithm consists of the incremental value of the dominant parameter and the bias term. The incremental value of the dominant parameter is the difference between the current real-time value of the dominant parameter and the preset reference point.

2. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 1, characterized in that, The dominant parameters affecting radar detection probability include: The Sobol global sensitivity analysis method was used to calculate the contribution of signal-to-noise ratio, clutter-to-noise ratio, interference-to-noise ratio, accumulated pulse number, and target fluctuation type to the detection probability. Parameters with a contribution greater than a preset threshold are selected as the dominant parameters; A dimensionality reduction mapping matrix is ​​constructed to map the high-dimensional parameter space to a low-dimensional space composed of the dominant parameters. The gradient sensitivity matrix and the state vector are both located in the low-dimensional space.

3. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 1, characterized in that, The probability of observation and detection is obtained through the built-in calibration signal, including: A calibration coherent processing interval is inserted every Ncal of regular coherent processing intervals; Within the calibration coherent processing interval, a built-in calibration signal orthogonal to the current radar operating waveform is generated; The built-in calibration signal is directly injected into the receiving link in the digital baseband, or the built-in calibration signal is placed in a target-free protected range cell in the range dimension for transmission and reception. The observation detection probability is obtained by statistically analyzing the ratio of the number of successful detections of the built-in calibration signal to the total number of transmissions within the sliding window.

4. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 1, characterized in that, The recursive least squares algorithm employs an adaptive forgetting factor, which is dynamically adjusted based on the magnitude of the prediction error. When the absolute value of the prediction error shows an increasing trend over multiple consecutive periods, the forgetting factor is reduced to accelerate the tracking speed. When the absolute value of the prediction error for multiple consecutive periods converges within a safety threshold, the forgetting factor is increased.

5. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 1, characterized in that, It also includes hibernation control steps: When the absolute value of the prediction error is less than the error threshold for M consecutive prediction periods, the update process of the recursive least squares algorithm is suspended, and the current gradient sensitivity matrix remains unchanged. If the absolute value of the prediction error exceeds the error threshold K times consecutively, the update process of the recursive least squares algorithm is reactivated.

6. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 5, characterized in that, The detection probability is predicted using the gradient sensitivity matrix and the preset reference point: in, Let be the predicted detection probability at time t. Preset reference point The detection probability at point G is the gradient sensitivity matrix. The real-time value of the dominant parameter at time t; The observation model of the recursive least squares algorithm is expressed as follows: = ⋅Δ , where Δ = b is the bias term. To observe noise.

7. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 6, characterized in that, It also includes adaptive control steps: The absolute value of each element in the updated gradient sensitivity matrix is ​​used as the environmental sensitivity index. If the absolute value of the gradient corresponding to the interference-to-noise ratio exceeds the preset alarm limit, an anti-interference trigger command is generated to control the radar system to switch the anti-interference waveform or start airspace filtering. If the predicted detection probability is determined to be lower than the preset performance index, the false alarm threshold of the radar system will be adjusted or the number of accumulated pulses will be increased.

8. The radar detection performance calibration method based on gradient sensitivity matrix as described in claim 6, characterized in that, It also includes a mutation reset step: If a sudden change in the radar operating environment is detected, causing the prediction error to diverge, the covariance matrix in the recursive least squares algorithm is reset to its initial value, the gradient sensitivity matrix is ​​rolled back to its initial value in the offline modeling stage, and the online learning process is restarted.

9. A radar detection performance calibration system based on a gradient sensitivity matrix, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, which, when executed by the processor, implements the steps of the radar detection performance calibration method based on the gradient sensitivity matrix as described in any one of claims 1 to 8.

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