A target detection method based on square root detection and CA-CFAR

Abstract

The application relates to a target detection method based on square root detection and CA-CFAR, which comprises the following steps: step 1, after a baseband signal containing a complex field of a real part and an imaginary part is acquired, the baseband signal is filtered through a matched filter to obtain an output signal of the matched filter which is also a complex number; step 2, the output signal of the matched filter is transformed according to a square root detection law; and step 3, the signal transformed according to the square root detection law is detected through a cell average constant false alarm rate detector, if the signal is greater than a threshold value on a certain detection cell, it is judged that a target exists on the detection cell, otherwise, it is judged that no target exists on the detection cell. The application can obviously improve the suppression capacity of a shielding effect caused by an interference target without bringing additional detection loss, the calculation amount is small, and the application is convenient for engineering implementation, therefore, the application has important theoretical innovation significance and engineering popularization value.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a target detection method based on square root detection and CA-CFAR. Background Technology

[0002] The main function of a radar receiver is to transform the information-carrying portion of the received signal into a baseband signal. We are interested in the case where the baseband signal contains both real and imaginary parts. Assuming that the real and imaginary parts of the background signal or noise are both zero-mean Gaussian random processes, the magnitude of the noise signal follows a Rayleigh distribution, the square of the magnitude follows an exponential distribution, and the phase angle is uniformly distributed within (0, 2π]. The echo signal caused by the target is a deterministic signal containing multiple unknown parameters, such as the initial phase of the echo signal. This is because the initial phase of the echo signal is closely related to the distance between the target and the radar. For example, when the change in distance is equal to one-quarter of the wavelength, the change in the initial phase of the echo is equal to π. However, the distance between the target and the radar cannot be precisely known; therefore, the initial phase is often treated as a random quantity uniformly distributed within (0, 2π). Reference [Mark...] [A. Richards, Radar Signal Processing Fundamentals (2nd Edition), pp. 245-246, Electronic Industry Press, August 2018] The optimal detection process for echo signals containing unknown phases is derived. Specifically, the modulus of the matched filter output signal is calculated, and then compared with a threshold after passing it through the memoryless nonlinear operator log[I(x)]. If the modulus is greater than the threshold, a target is determined to exist; otherwise, no target is determined to exist. Here, I(·) represents the Bessel function, and log(·) represents the logarithmic function. Because the nonlinear operator log[I(x)] involves a huge amount of computation, we are very concerned about whether log[I(x)] can be removed.

[0003] In the literature [Mark A. Richards, translated by Xing Mengdao et al., Radar Signal Processing Fundamentals (Second Edition), pp. 249-250, Electronic Industry Press, August 2018], the output of log[I(x)] is approximated by the modulus or the square of the modulus of the matched filter output signal through approximation processing. This eliminates the need to calculate the Bessel function and the natural logarithm, and has been widely used in engineering. The method using the modulus is called the linear detection law, and the method using the square of the modulus is called the square detection law. The literature [RS Raghavan, Analysis of CA-CFAR Processors for Linear-Law Detection, IEEE Transactions on Aerospace and Electronic Systems, pp. 661-665, vol. 28, No. 3, July 1992.] shows that the linear law and the square law have comparable performance.

[0004] Setting the detection threshold mentioned above requires knowledge of the noise power. However, in practical applications, the noise power is constantly changing due to factors such as the temperature of electronic devices, amplifier gain, and external interference signals. The most widely used detection strategy in the radar field is Constant False Alarm Rate (CFAR) detection, which requires the false alarm rate to remain constant. Therefore, when the noise power changes, the detection threshold must be automatically adjusted. Let's first assume the following two preconditions:

[0005] (1) The noise statistics on the unit under test are the same as those on the neighboring units;

[0006] (2) The neighboring unit does not contain the target signal.

[0007] When the above two preconditions are met, data is extracted from the neighboring cells of the cell to be detected as samples to estimate the noise power on the cell to be detected (or data is extracted from cells on both sides of the cell to be detected to estimate the noise power on the cell to be detected). The result of the maximum likelihood estimation is the average of the samples. This method is called the cell average (CA) method. After estimating the noise power using the cell average method, the noise power estimate is multiplied by a threshold coefficient to obtain the detection threshold. Thus, constant false alarm rate detection can be achieved [Mark A. Richards, Radar Signal Processing Fundamentals (Second Edition), pp. 268-269, Electronic Industry Press, August 2018].

[0008] Although CA-CFAR (Cell Average Constant False Alarm Rate) detection has been widely used, it has significant drawbacks. For example, the thresholds on both sides of a target are too high. If two targets are close to each other, at least the second of the two assumptions mentioned above will not be met, and the target signal will be included in the sample data. The estimated noise power will be significantly higher than the true noise power, thus raising the detection threshold and causing a decrease in detection performance. This is known as the masking effect [Mark A. Richards, Radar Signal Processing Fundamentals (Second Edition), p. 274, Electronic Industry Press, August 2018]. When one target is used as a sample of another target, it is called an interfering target. To address the masking effect caused by interfering targets, numerous improved CFAR techniques have emerged, such as the constant false alarm rate (CFAR) method with the smaller average cell selection: This method first estimates the noise power on both sides of the cell to be detected, then selects the smaller value as the final noise power estimate [Mark A. Richards, Radar Signal Processing Fundamentals (2nd Edition), p. 278, Electronic Industry Press, August 2018]. The drawback of this method is that it introduces significant detection loss, and when interfering targets are present on both sides, a severe masking effect is unavoidable. Furthermore, the audit CFAR [Mark A. Richards, Radar Signal Processing Fundamentals (2nd Edition), p. 280, Electronic Industry Press, August 2018] removes the larger values ​​from the sample cells. It has two main drawbacks: firstly, the computational cost of searching for peak values ​​is high; secondly, it is effective for one interfering target but becomes ineffective for two or more interfering targets.

[0009] In addition, OS-CFAR (Ordered Statistical Constant False Alarm Rate) detection and logarithmic detection methods can effectively address the masking effect. OS-CFAR sorts the samples and then selects an element (or the average of multiple elements) from a fixed position in the queue as the noise power estimate. OS-CFAR has two main drawbacks: First, it introduces additional detection loss. The literature [Hermann Rohling, Radar CFAR Thresholding in Clutter and Multiple Target Situations, IEEE Transactions on Aerospace and Electronic Systems, vol. 19, no. 4, pp. 608-620, July 1983.] analyzes that when the number of samples is 16, 24, and 32, the additional detection loss is 0.93 dB, 0.63 dB, and 0.48 dB, respectively. The literature [Stephen Blake, OS-CFAR Theory for Multiple Targets and Nonuniform Clutter, IEEE Transactions on Aerospace and Electronic Systems, vol. 24, no. 6, pp. 785-790, November 1988.] analyzes that when the number of samples is 64, the detection loss for adjacent edges is 0.23 dB. The literature [Mordechai Shor, Nadav Levanon, Performances of Order Statistics]... [CFAR, IEEE Transactions of Aerospace and Electronic Systems, vol. 27, no. 2, pp. 214-224, March 1991.] This paper analyzes the gain of noncoherent accumulation of multiple pulses. Taking 10 pulses as an example, OS-CFAR has an additional loss of 0.2 to 0.35 dB compared to CA-CFAR. Secondly, OS-CFAR requires sorting, which involves a very large amount of computation, and this is the main difficulty in engineering.

[0010] Converting the input signal into a logarithmic form before passing it through a CA-CFAR detector can also reduce the losses caused by interfering targets to the radar system. We can call this transformation method the logarithmic detection law. The logarithmic detection law has two disadvantages: first, it is computationally complex, as the logarithm of the value on each detection unit must be calculated; second, it has a large detection loss. In the literature [V. Gregers Hansen, Harold R. Ward, Detection Performance of the Cell Averaging LOG / CFAR Receiver, IEEE Transactions on Aerospace and Electronic Systems, vol. AES-8, No. 5, pp. 648-652, September 1972.], it is argued that if the number of samples is the same, the loss caused by the logarithmic detection law is 65% greater than that of the linear detection law. To illustrate with specific numerical values, when the sample size is 64 and the false alarm rate is 1e-6, a signal-to-noise ratio (SNR) of 12.4 dB is required to achieve a 50% detection probability. However, according to this research, under the same conditions and requirements, linear detection requires an SNR of 11.6 dB. When the false alarm rate is 1e-4, logarithmic detection requires an SNR of 10 dB, while this research shows that linear detection requires an SNR of 9.5 dB. Therefore, under conventional requirements, the additional detection loss introduced by logarithmic detection is within 0.5–1.0 dB. Thus, a detection method that does not introduce additional losses and has high engineering efficiency needs to be designed. Summary of the Invention

[0011] To address the existing technical problems, this invention provides a target detection method based on square root detection and CA-CFAR, which does not introduce additional losses, has high engineering implementation efficiency, and has significant promotional value.

[0012] The specific content of this invention is as follows: A target detection method based on square root detection and CA-CFAR, comprising the following steps:

[0013] Step 1: After obtaining the baseband signal in the complex domain containing the real and imaginary parts, filter it through a matched filter to obtain the output signal of the matched filter, which is also a complex number.

[0014] Step 2: Transform the output signal of the matched filter according to the square root detection law;

[0015] Step 3: The signal after transformation by the square root detection law is passed through the unit average constant false alarm rate detector. If the signal is greater than the threshold in a certain detection unit, it is determined that there is a target in that detection unit; otherwise, it is determined that there is no target in that detection unit.

[0016] Furthermore, in step 1, the unit response of the matched filter is matched to the waveform of the input signal;

[0017] Let the radar signal waveform be s[0], s[1], ..., s[N-1]. The unit response of the matched filter can be obtained by folding this signal along the time axis and taking its conjugate value, as shown in the following formula:

[0018] h[n] = s*[N-1-n].

[0019] Furthermore, step 2 includes:

[0020] Step 2.1: Calculate the power of the output signal of the matched filter;

[0021] Step 2.2: If there are two or more pulses for noncoherent accumulation, then after obtaining the power of each pulse in Step 2.1, add up the power of all pulses; if there is only one pulse, this step is omitted.

[0022] Step 2.3: If there are two or more pulses performing non-coherent accumulation, calculate the fourth root of the sum of the power of all pulses; if there is only one pulse, calculate the fourth root of the power of this single pulse.

[0023] After step 2.3, the signal transformed by the square root detection law is equal to the square root of the voltage in terms of dimensions.

[0024] Furthermore, step 3 involves transforming the signal according to the square root detection law and then performing unit average constant false alarm rate detection, including:

[0025] Step 3.1: Calculate the sum of M elements, such as x[n-(M-1)], x[n-(M-1)+1], ..., x[n], which equals y[n], expressed by the following formula:

[0026] y[n]=x[n]+x[n-1]+…+x[n-(M-1)]

[0027] Step 3.2: The next summation equals the previous summation plus one element and then subtracting one element:

[0028] y[n+1] = y[n] + x[n+1] - x[n-M+1]

[0029] Step 3.3: Repeat step 3.2 until the summation results for all the units to be detected are obtained;

[0030] Step 3.4: Divide the summation result of each step 3.1 to 3.3 by the number of samples M to obtain the estimated value of the background noise, and then multiply it by the threshold coefficient to obtain the threshold. If the value on the detection unit is greater than the threshold, it is determined that a target exists; otherwise, it is determined that no target exists.

[0031] Furthermore, the threshold coefficient is used to adjust the false alarm rate: increasing the threshold coefficient lowers the false alarm rate; decreasing the threshold coefficient increases the false alarm rate.

[0032] The target detection method based on square root detection and CA-CFAR of the present invention: by introducing the square root detection law and inheriting the CA-CFAR algorithm, it can significantly improve the ability to suppress the masking effect caused by interfering targets without introducing additional detection loss. Moreover, the computational load is small and it is easy to implement in engineering. Therefore, the results of the present invention have significant theoretical innovation significance and engineering promotion value. Attached Figure Description

[0033] The specific embodiments of the present invention will be further explained below with reference to the accompanying drawings.

[0034] Figure 1 This is a flowchart of a classic object detection process;

[0035] Figure 2 This is a flowchart of the processing based on square root detection law and CA-CFAR of the present invention.

[0036] Figure 3 The graph shows the input-output relationship between three signal transformation methods.

[0037] Figure 4 The graph shows the relationship between the false alarm rate and the threshold coefficient (with one pulse).

[0038] Figure 5 A graph showing the relationship between the probability of detecting non-fluctuating targets and the signal-to-noise ratio.

[0039] Figure 6 A graph showing the relationship between the target detection probability and the signal-to-noise ratio, where the echo power fluctuates according to the chi2 law and the pulses are perfectly correlated.

[0040] Figure 7 The graph shows the relationship between the target detection probability and the signal-to-noise ratio, where the echo power fluctuates according to the chi2 law and the pulses are completely uncorrelated.

[0041] Figure 8 Example image of measured data containing isolated point targets. Detailed Implementation

[0042] To better understand the above-mentioned objects, features and advantages of the present invention, a detailed description is provided below in conjunction with the accompanying drawings.

[0043] After the radar receiver converts the received signal to baseband, it needs to determine whether a target exists based on the baseband signal. When using a constant false alarm rate (CFAR) strategy for target detection, if a target signal appears in the sample used to estimate noise power, the estimated noise power will be greater than the true value, leading to a decrease in radar detection performance, a phenomenon known as the masking effect. This invention provides a target detection method that can suppress the masking effect of interfering targets. The method includes:

[0044] Step 1: Filter the baseband signal in the complex domain using a matched filter.

[0045] Radar detection performance improves with increasing signal-to-noise ratio (SNR). Filtering the signal through a matched filter maximizes the SNR. The unit response of the matched filter is matched to the waveform of the input signal; in this case, the matched filter is designed with the radar signal waveform to be processed as the reference signal.

[0046] Let the radar signal waveform be s[0], s[1], ..., s[N-1]. The unit response of the matched filter can be obtained by folding this signal along the time axis and taking its conjugate value, which can be expressed mathematically as:

[0047] h[n] = s*[N-1-n]

[0048] The output signal of the matched filter can be obtained by calculating the convolution sum of the baseband signal obtained by the radar receiver mentioned above and the unit impulse response.

[0049] Step 2: Transform the output signal of the matched filter according to the square root detection law (the transformed signal is equal to the square root of the voltage in terms of dimension).

[0050] The transformation of a signal according to predefined rules constitutes the content of a detection law. For example, the classic linear detection law transforms a complex number into a voltage signal, while the square detection law transforms a complex number into a power signal. For ease of comparison and analysis, Figure 1 The classic processing flow based on linear detection law / square detection law and CA-CFAR is given: If using linear detection law, after matched filtering, the magnitude of each pulse is first calculated, then accumulated (accumulation equals addition, the same below), and finally processed by CA-CFAR. If using square detection law, then... Figure 1 The calculation of the modulus was changed to the calculation of the power and then the results were added together.

[0051] In the technical solution disclosed in this application, the detection law includes a two-stage signal transformation and pulse accumulation process, such as... Figure 2 As shown:

[0052] Square root detection specifically includes the following sub-steps:

[0053] Step 2.1: Perform the first-stage transformation, i.e., calculate the power of the output signal of the matched filter;

[0054] In step 1, the received signal in the complex domain is filtered by a matched filter, and the output signal of the matched filter is still a complex signal. When the input data is complex, it is more convenient to calculate the power than to calculate the modulus: first calculate the squares of the real and imaginary parts, and then add them together to get the power; only by taking the square root of the power can the modulus be obtained.

[0055] Step 2.2: If there are two or more pulses for non-coherent accumulation, calculate the power of all pulses according to Step 2.1 and add the power of all pulses together; if there is only one pulse, this step is omitted.

[0056] Step 2.3: Perform the second-level transformation. Specifically, if there are two or more pulses for non-coherent accumulation, calculate the fourth root of the sum of the power values ​​after summing the power of all pulses; if there is only one pulse, calculate the fourth root of the power of the single pulse.

[0057] The technology disclosed in this application aims to solve the masking effect caused by interfering targets. The desired effect is that when interfering targets are used as samples in CA-CFAR to estimate background noise power, radar detection performance is not severely affected. Specifically, we hope that the technical solution disclosed in this application can suppress the impact of target signals on the estimation of background noise power using the cell averaging method. To qualitatively analyze the suppression capability of different detection laws for interfering targets, Figure 3 Three signal transformation methods are presented, from top to bottom: squaring (corresponding to square detection law), modulus (corresponding to linear detection law), and square root of modulus (corresponding to the square root detection law disclosed in this application). As can be seen from the figure, compared with the classical linear detection law and square detection law, the square root detection law has a more concentrated output signal distribution and a smaller dynamic range. When interference target signals are mixed into the sample, the degree to which the interference target signals deviate from the average value of the background noise is significantly reduced. Therefore, the influence of the interference target signals on the sample mean is weakened, and the sample mean is closer to the true value of the noise power.

[0058] Steps 2.1 to 2.3 above are referred to as the square root detection law. From a computational perspective, square root detection is even more advantageous than classical linear detection. For example, when the number of noncoherent accumulation pulses is equal to 2, the computational cost of square root detection is the same as that of classical linear detection. When the number of pulses is greater than 2, square root detection is more computationally efficient than classical linear detection because it only requires calculating the square root twice, while linear detection requires calculating the square root for each pulse. Therefore, the square root detection law has very high implementation efficiency.

[0059] Step 3: Use the unit averaging method to perform constant false alarm rate detection on the results of Step 2.

[0060] The key to the unit averaging method is to calculate the cumulative sum of M samples. This application adopts a recursive method to achieve the cumulative sum of multiple consecutive samples.

[0061] For example, the sum of x[n-(M-1)], x[n-(M-1)+1], ..., x[n] is represented as y[n], and y[n-1] and y[n+1] are obtained in a similar way, as shown by the following formula:

[0062] y[n-1]=x[n-1]+x[n-2]+…+x[nM]

[0063] y[n]=x[n]+x[n-1]+…+x[n-(M-1)]

[0064] y[n+1]=x[n+1]+x[n]+…+x[n-M+2]

[0065] Subtracting the first row from the second row, and making appropriate transformations, yields the following relationship:

[0066] y[n] = y[n-1] + x[n] - x[nM]

[0067] Similarly, subtracting the first row from the third row and performing an adaptive transformation, we can obtain the following relationship:

[0068] y[n+1] = y[n] + x[n+1] - x[n-M+1]

[0069] Therefore, given the previous summation calculation, subsequent summation calculations become very simple. Specifically, it includes the following sub-steps:

[0070] Step 3.1: Calculate the sum of the first M elements, expressed by the following formula:

[0071] y[M-1] = x[0] + x[1] + ... + x[M-1]

[0072] Step 3.2: The next summation is based on the previous summation, adding one element and subtracting one element:

[0073] y[M]=y[M-1]+x[M]-x[0]

[0074] Step 3.3: Repeat step 3.2 until the summation results of samples on all units to be detected are obtained, as shown below:

[0075] y[M+1]=y[M+1]+x[M+1]-x[1]

[0076] y[M+2]=y[M+2]+x[M+2]-x[2]

[0077] …=…

[0078] Therefore, given the first accumulated sum y[M-1], calculating the second accumulated sum y[M] only requires one addition and one subtraction, independent of the number of samples M. The same applies to the third accumulated sum y[M+1], the fourth accumulated sum y[M+2], and so on. Thus, the unit averaging method is highly efficient. In the above proof, y[n] was originally a finite impulse response (FIR) filter for the sequence x[n]. However, this application uses a recursive algorithm commonly used in infinite impulse response (IIR) filters to implement the FIR filter, effectively saving computational resources.

[0079] Step 3.4: Calculate the detection threshold and perform constant false alarm rate detection.

[0080] Dividing the summation result of the samples in steps 3.1 to 3.3 by the number of samples M yields the estimated background noise. After obtaining the noise power estimate, multiplying it by a constant coefficient gives the threshold (this constant coefficient is called the threshold coefficient). This allows for constant false alarm rate (CFRR) detection: if the signal at a detection unit exceeds the estimated threshold, it is determined that a target exists at that detection unit; otherwise, it is determined that no target exists at that detection unit. In this case, the CFRR remains constant; the constant coefficient is used to adjust the CFRR: increasing the coefficient lowers the CFRR; decreasing the coefficient increases the CFRR.

[0081] The square root detection law mentioned above does not cause additional detection loss when used with a CA-CFAR detector. Next, we will use Monte Carlo experiments to study the detection performance of the square root detection law under the premise of satisfying the two assumptions of CA-CFAR.

[0082] The three methods are compared and analyzed here, as shown in Table 1: Method 1 is the classic method based on linear detection law, Method 2 is the classic method based on square detection law, and Method 3 is a new method introduced here for discussion. When the number of pulses is equal to 1, the accumulation process in the table no longer exists.

[0083] Table 1. Comparison of the three methods

[0084]

[0085] Basic setup for Monte Carlo simulation experiments:

[0086] 1. The background noise is white Gaussian noise (complex), generated using the wgn function built into Matlab 2014a. The power of the simulated target is known, and the phase is a random variable with a uniform value distribution between 0 and 2π, implemented using the rand function built into Matlab 2014a. The simulated echo data is obtained by adding the signal and noise.

[0087] 2. CA-CFAR parameters: Take 32 samples from each side of the detection unit and calculate the average to estimate the background noise.

[0088] 3. Each frame contains 10,000 distance gates, and there are a total of 100,000 frames of data. The total number of detection units is 1e9.

[0089] Regarding the relationship between false alarm rate and threshold coefficient: Taking one pulse as an example, the relationship between false alarm rate and threshold coefficient is as follows: Figure 4 As shown, the relationship between the false alarm rate and the threshold coefficient is not the same under different detection laws. The threshold coefficient needs to be adjusted according to the detection method used and the desired false alarm rate.

[0090] Tables 2, 3, and 4 below show the threshold coefficients when the false alarm rate is 1e-4, 1e-5, and 1e-6, respectively. The values ​​in the first column of each table are equal to... Figure 4 The corresponding result in the middle:

[0091] Table 2. Threshold coefficients (unit: dB) corresponding to a false alarm rate Pfa equal to 1e-4

[0092] 1 pulse 2 pulses 3 pulses 4 pulses 5 pulses Method 1 10.98 8.61 7.38 6.62 6.05 Method 2 09.92 7.85 6.78 6.08 5.58 Method 3 11.68 8.71 7.35 6.50 5.92

[0093] Table 3. Threshold coefficients corresponding to a false alarm rate Pfa equal to 1e-5 (Pfa = 1e-5, unit: dB)

[0094]

[0095]

[0096] Table 4. Threshold coefficients corresponding to a false alarm rate Pfa equal to 1e-6 (Pfa = 1e-6, unit: dB)

[0097] 1 pulse 2 pulses 3 pulses 4 pulses 5 pulses Method 1 12.93 10.27 8.90 8.01 7.37 Method 2 11.87 9.46 8.22 7.42 6.83 Method 3 13.65 10.33 8.79 7.83 7.16

[0098] The detection rate is a function of the false alarm rate and the signal-to-noise ratio (SNR). The following analysis examines the variation of the detection rate with the input SNR in three different scenarios:

[0099] (1) Non-fluctuating target;

[0100] (2) The target fluctuates and the echo power satisfies the chi2 distribution with 4 degrees of freedom. When the number of pulses is greater than 1, the pulses are completely correlated (Swiss-3 model).

[0101] (3) The target fluctuates and the echo signal power satisfies the chi2 distribution with 4 degrees of freedom. When the number of pulses is greater than 1, the pulses are completely different (Swiss-4 model).

[0102] The research results for the above three scenarios are summarized as follows: Figure 5 , Figure 6 , Figure 7 As shown: There are 5 sets of curves, corresponding to pulse numbers 1 to 5. Each set of curves contains 3 curves, corresponding to methods 1 to 3. The following conclusions can be drawn from the graph:

[0103] (1) Taking a detection rate of 0.5 as an example, the difference between the three methods is within 0.1 dB. Therefore, using the square root detection law does not introduce additional detection loss.

[0104] (2) with Figure 5 Taking method 3 as an example, to achieve a detection rate of 0.5, the required signal-to-noise ratio (SNR) for a single pulse is: 11dB, 8.28dB, 6.88dB, 5.94dB, and 5.20dB. Therefore, the cumulative gain for 2 to 5 pulses is: 2.72dB, 4.12dB, 5.06dB, and 5.80dB, respectively. Thus, the cumulative gain of the square root detection law is approximately equal to the number of accumulated pulses raised to the power of 0.85.

[0105] After using the method based on square root detection law and CA-CFAR detector disclosed in this application, the radar's ability to suppress interfering targets is significantly improved. The following uses experimental data to verify the suppression capability of the square root detection law against interfering targets. The experimental data, after being processed by methods 1, 2, and 3 as described above, is shown in the example below. Figure 8 After using the square-root detection law, the noise estimate near the target increased significantly, followed by linear detection, while the change in noise estimate was minimal when using the square-root detection law. Figure 8 In this study, six protection units were set on each side of the detection unit, and 32 samples were taken from the outside of each protection unit to estimate the background noise. The target signal-to-noise ratio was about 40dB. After using square detection, linear detection, and square root detection, the estimated background noise was improved by 27.2, 16.8, and 8.8dB, respectively. Therefore, square root detection improved by 8dB compared to linear detection and by 18.4dB compared to square root detection.

[0106] In summary, the performance of the square root detection law proposed in this application was studied through Monte Carlo experiments. It can be seen that the square root detection law does not cause additional detection loss compared with the linear detection law and the square detection law, under the premise of satisfying the two assumptions of CA-CFAR. Furthermore, after verification with measured radar echo data, it can be seen that the square root detection law has significant improvements over the linear detection law and the square detection law in suppressing the shielding effect of interfering targets.

[0107] It is evident that by introducing a new detection method and inheriting the classic CA-CFAR algorithm, this application can significantly improve the ability to suppress the masking effect of interfering targets without introducing additional detection loss, and the implementation efficiency is relatively high. Therefore, the technical solution disclosed in this application has significant theoretical innovation significance and great engineering promotion value.

[0108] Compared with existing technologies, this technology differs in the following ways: (1) Before CA-CFAR detection, after transformation by the square root detection law, the dimension of the signal is equal to the square root of the voltage, while the dimension of the classical linear detection law is equal to the voltage, and the dimension of the square detection law is equal to the square of the voltage; (2) The traditional accumulation method is to apply the detection law to transform the signal for each pulse and then add the transformation results of all pulses. The method proposed here first adds the power and then transforms the power to the square root of the voltage. Therefore, the detection law here combines pulse accumulation with signal transformation; (3) Considering the huge computational load of OS-CFAR, the square root detection law proposed here is used in conjunction with the CA-CFAR algorithm and can effectively suppress the masking effect of the interfering target.

[0109] Many specific details have been set forth in the foregoing description to provide a thorough understanding of the present invention. However, the above description is merely a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed above. Furthermore, any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, using the methods and techniques disclosed above, without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A target detection method based on square root detection and CA-CFAR, characterized in that: Includes the following steps: Step 1: After obtaining the baseband signal in the complex domain containing the real and imaginary parts, filter it through a matched filter to obtain the output signal of the matched filter, which is also a complex number. Step 2: Transform the output signal of the matched filter according to the square root detection law; Step 3: The signal after transformation by the square root detection law is passed through the unit average constant false alarm rate detector. If the signal is greater than the threshold in a certain detection unit, it is determined that there is a target in that detection unit; otherwise, it is determined that there is no target in that detection unit. Step 2 includes: Step 2.1: Calculate the power of the output signal of the matched filter; Step 2.2: If there are two or more pulses for noncoherent accumulation, then after obtaining the power of each pulse in Step 2.1, add up the power of all pulses; if there is only one pulse, this step is omitted. Step 2.3: If there are two or more pulses performing non-coherent accumulation, calculate the fourth root of the sum of the power of all pulses; if there is only one pulse, calculate the fourth root of the power of this single pulse. After step 2.3, the signal transformed by the square root detection law is equal to the square root of the voltage in terms of dimension. Step 3 involves transforming the signal according to the square root detection law and then performing a unit average constant false alarm rate (CFAR) test, including: Step 3.1: Calculation The sum of elements, such as Adding equals The formula is as follows: ， Step 3.2: The next summation equals the previous summation plus one element and then subtracting one element: ， Step 3.3: Repeat step 3.2 until the summation results for all the units to be detected are obtained; Step 3.4: Divide the summation result from steps 3.1 to 3.3 by the number of samples. The estimated value of the background noise is obtained, and then multiplied by the threshold coefficient to obtain the threshold. If the value on the detection unit is greater than the threshold, it is determined that a target exists; otherwise, it is determined that no target exists.

2. The target detection method based on square root detection and CA-CFAR according to claim 1, characterized in that: In step 1, the unit response of the matched filter matches the waveform of the input signal; Let the radar signal waveform be The unit response of a matched filter can be obtained by convoluting this signal along the time axis and taking its conjugate, as shown in the following formula: 。 3. The target detection method based on square root detection and CA-CFAR according to claim 1, characterized in that: The threshold coefficient is used to adjust the false alarm rate: increasing the threshold coefficient lowers the false alarm rate. Decreasing the threshold coefficient increases the false alarm rate.

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