Weak signal detection method based on improved double-coupling system and cross-section variance method

Abstract

The application discloses a weak signal detection method based on an improved double coupling system and a cross-section variance method, changes a coupling mode of a Duffing oscillator and a Van Der Pol-Duffing oscillator, so that higher initial sensitivity and better detection performance are obtained. In addition, the application also proposes a state discrimination method for judging the state of the system through the cross-section variance. The dispersion of each point on the phase diagram cross-section of the system is taken as an index for measuring the chaotic degree of the system, and state discrimination is performed. The cross-section variance method is simple to operate, can quickly and accurately distinguish the state of the system, and has better detection performance under a low SNR condition compared with traditional Duffing and double coupling Duffing detection methods.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and more specifically, to a weak signal detection method based on an improved dual-coupling system and cross-sectional variance method. Background Technology

[0002] Classical weak signal detection methods, such as correlation detection, higher-order statistical methods, adaptive filtering, and wavelet transform, all improve the signal-to-noise ratio by suppressing noise. However, while suppressing noise, they also weaken the useful weak signal, thus limiting their performance in weak signal detection. The emergence of nonlinear detection methods based on chaos theory offers a new approach to weak signal detection. Chaotic systems are sensitive to initial conditions but insensitive to noise, allowing them to effectively identify weak signals submerged in strong noise and convert them into system state outputs. A commonly used chaotic system is the Duffing system. Duffing systems exhibit a critical state during the transition from a chaotic to a periodic state because their initial condition sensitivity is insufficient, resulting in slow convergence from the chaotic to the periodic state. This leads to errors in system state judgment and reduces the accuracy of weak signal detection. Researchers have proposed coupling the Duffing oscillator with a Van Der Pol-Duffing oscillator to improve the system's initial condition sensitivity. However, even with dual coupling, a significant critical state still exists during state transitions, and the initial condition sensitivity can be further improved. In addition, traditional state determination methods based on Lyapunov exponents are not suitable for real-time decision-making because they require phase space reconstruction of the data, have high computational complexity, and take a long time to make decisions.

[0003] Existing technology discloses a weak signal detection method based on a weak signal detection device using a Duffing chaotic system, belonging to the field of weak signal detection. The specific process of this method is as follows: a signal generator generates a weak signal and sends it to an ADC; the ADC samples the signal and sends the data to an FPGA; the FPGA uses the received data as input to the Duffing equation and calculates the numerical solution of the Duffing equation using a peak difference detection algorithm; the FPGA determines the current state based on the numerical solution and then obtains the frequency of the input signal; the FPGA sends the detection result to a host computer via a USB chip. This method, using a Duffing system, also suffers from insufficient initial value sensitivity and slow convergence speed from a chaotic state to a periodic state, which can lead to errors in system state judgment and reduce the accuracy of weak signal detection. Summary of the Invention

[0004] This invention provides an improved weak signal detection method using a dual-coupling system and the cross-sectional variance method, which changes the coupling mode of the Duffing oscillator and the Van Der Pol-Duffing oscillator to obtain higher initial sensitivity and better detection performance.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0006] A weak signal detection method based on an improved dual-coupling system and cross-sectional variance method includes the following steps:

[0007] S1: Input a noisy, weak signal;

[0008] S2: Initialize the signal frequency search range;

[0009] S3: Set the built-in driving force frequency of the improved dual-coupled system as the lower bound of the signal frequency search range, wherein the improved dual-coupled system is the coupling between the Duffing oscillator system and the Van Der Pol-Duffing equation;

[0010] S4: Input the signal into the improved dual-coupled system and use the fourth-order Runge-Kutta method to solve for the system output;

[0011] S5: Divide the system output into segments and use the cross-sectional variance method to detect whether there is a periodic waveform in each segment of the system output. If there is, it indicates that a signal has been detected. If there is no periodic waveform, increase the built-in driving force frequency of the improved dual-coupled system and return to step S4 until the built-in driving force frequency of the improved dual-coupled system is greater than the upper limit of the signal frequency search range. Then there is no signal in the signal frequency search range.

[0012] Preferably, in step S1, the noisy weak signal is a noisy weak chirp signal s(t), specifically:

[0013]

[0014] In the formula, A is the signal amplitude, f0 is the signal frequency, k0 is the chirp signal frequency modulation slope, and t is time.

[0015] Preferably, in step S2, the signal frequency search range [f] is initialized. L f H ], where f L f is the lower bound of the signal frequency search range. H This is the upper bound of the signal frequency search range.

[0016] Preferably, the improvement of the dual-coupled system in step S3 is specifically as follows:

[0017]

[0018] In the formula, x and y are variables that change with time t. Let x be the first and second derivatives, respectively. y represents the first and second derivatives, respectively; d is the coupling coefficient; μ is the damping coefficient; and F and ω are the amplitude and angular frequency of the built-in driving force, respectively.

[0019] Preferably, in step S4, the signal is input into the improved dual-coupled system, specifically as follows:

[0020]

[0021] In the formula, t = ωτ, x τ y τ A variable that changes in accordance with the change of variable τ. x τ The first and second derivatives, y τ The first and second derivatives.

[0022] Preferably, in step S4, the system output is obtained by solving the fourth-order Runge-Kutta method, specifically as follows:

[0023] The equations for the improved dual-coupled system inputting the signal are rewritten as follows:

[0024]

[0025] Will and Let g be a function of x1, x2, and t, and then written in vector form:

[0026]

[0027] In the formula, X0 is the initial value, and X = [x1 x2] T Let h be the vector to be solved, and let the iteration step size be h. Applying the fourth-order Runge-Kutta algorithm, we can obtain the recurrence equation:

[0028]

[0029] This allows us to obtain the numerical solution output by the system.

[0030] Preferably, the cross-sectional variance method described in step S5 is specifically as follows:

[0031] Based on the numerical solution output by the system, the phase diagram and time-domain diagram of the improved dual-coupled system are obtained;

[0032] The point passing through the section x2 = 0 in the phase diagram is recorded. The dispersion of the point on the section reflects the degree of chaos of the improved dual-coupled system. The variance of the cut-off point is used as a measure of the degree of chaos of the improved dual-coupled system, and the state of the improved dual-coupled system is judged accordingly. The driving force of the improved dual-coupled system is changed to obtain the variance under different driving force amplitudes.

[0033] The critical threshold F at which the improved dual-coupled system transitions from a chaotic state to a large-scale periodic state is denoted as F. d The decision threshold ∈ is given. When the variance of the cutoff point is less than ∈, the decision is a periodic state, and a signal exists. When the variance is greater than ∈, the decision is a chaotic state, and a signal does not exist.

[0034] Preferably, increasing the built-in driving force frequency of the improved dual-coupling system in step S5 specifically involves:

[0035] The built-in drive frequency has been updated to 1.174 times the original.

[0036] Preferably, when there is a frequency difference between the input signal frequency and the system's built-in driving force frequency, the frequency difference detection method is as follows:

[0037] For an improved dual-coupled system with an input frequency difference of Δω:

[0038]

[0039] The driving force in the above formula is equivalent to:

[0040] F cos(ωt)+λcos((ω+Δω)t+φ)

[0041] =F cos(ωt)+λ(cos(ωt)cos(Δω+φ)-sin(ωt)sin(Δω+φ))

[0042] =(F+λcos(Δω+φ))cos(ωt)-λsin(Δω+φ)sin(ωt)

[0043] =F′cos(ωt+θ(t))

[0044] in:

[0045]

[0046]

[0047] Equivalent periodic force amplitude F′ The period of the output changes continuously from F-λ to F+λ, causing the system output to change back and forth between a periodic state and a chaotic state. The period of this change is also T. The frequency difference Δω can be obtained by measuring the period T of the intermittent chaos of the output.

[0048] Preferably, the step S5 is followed by the following step:

[0049] S6: Let the frequency at which the signal is detected be f, and set up one of the improved dual-coupling systems at intervals of 0.08f to form a detection array;

[0050] S7: Input the signal into each of the improved dual-coupled systems in the detection array for detection;

[0051] S8: Segment the output of each improved dual-coupled system and use the cross-sectional variance method to detect it. At this time, the improved dual-coupled systems of different frequencies have periodic waveforms in different time periods. The time t′ of the periodic waveform and the corresponding system frequency f′ are obtained, and a series of points (t′, f′) are obtained.

[0052] S9: Perform linear fitting on the series of points (t′, f′) to obtain the slope. This is the estimate of the chirp signal frequency modulation slope k0.

[0053] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0054] This invention is based on an improved dual-coupling and cross-sectional variance method for weak signal detection. Compared with traditional detection methods based on Duffing systems and conventional dual-coupling systems, it has higher detection performance and faster detection speed. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the method flow provided in Example 1.

[0056] Figure 2 This is a schematic diagram of the method flow provided in Example 3.

[0057] Figure 3 The improved phase diagram and time-domain diagram of the dual-coupled system are provided for the embodiments.

[0058] Figure 4 The Duffing system phase diagram and time-domain diagram provided for the embodiment.

[0059] Figure 5 A schematic diagram of the cross-sectional variance method provided for an embodiment.

[0060] Figure 6 The example provides a schematic diagram showing how the intercept variance changes with the amplitude of the system driving force.

[0061] Figure 7 A schematic diagram of intermittent chaotic state provided for an embodiment.

[0062] Figure 8This is a schematic diagram of the frequency modulation slope of the chirp signal provided in the embodiment.

[0063] Figure 9 The curve showing the relationship between the detection rate and SNR of the sinusoidal signal provided in the example is shown.

[0064] Figure 10 The chirp signal detection output result diagram provided in the embodiment.

[0065] Figure 11 The curve showing the relationship between the accuracy of frequency modulation slope k0 estimation and SNR provided in the example. Detailed Implementation

[0066] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0067] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions;

[0068] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0069] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0070] Example 1

[0071] This embodiment provides a weak signal detection method based on an improved dual-coupling system and the cross-sectional variance method, such as... Figure 1 As shown, it includes the following steps:

[0072] S1: Input a noisy, weak signal;

[0073] S2: Initialize the signal frequency search range;

[0074] S3: Set the built-in driving force frequency of the improved dual-coupled system as the lower bound of the signal frequency search range, wherein the improved dual-coupled system is the coupling between the Duffing oscillator system and the Van Der Pol-Duffing equation;

[0075] S4: Input the signal into the improved dual-coupled system and use the fourth-order Runge-Kutta method to solve for the system output;

[0076] S5: Divide the system output into segments and use the cross-sectional variance method to detect whether there is a periodic waveform in each segment of the system output. If there is, it indicates that a signal has been detected. If there is no periodic waveform, increase the built-in driving force frequency of the improved dual-coupled system and return to step S4 until the built-in driving force frequency of the improved dual-coupled system is greater than the upper limit of the signal frequency search range. Then there is no signal in the signal frequency search range.

[0077] Example 2

[0078] This embodiment, based on Embodiment 1, continues to disclose the following content:

[0079] In step S1, the noisy weak signal is a noisy weak chirp signal s(t), specifically:

[0080]

[0081] In the formula, A is the signal amplitude, f0 is the signal frequency, k0 is the chirp signal frequency modulation slope, and t is time.

[0082] In step S2, the signal frequency search range [f] is initialized. L f H ], where f L f is the lower bound of the signal frequency search range. H This is the upper bound of the signal frequency search range.

[0083] The improvement of the dual-coupled system in step S3 is as follows:

[0084]

[0085] In the formula, x and y are variables that change with time t. Let x be the first and second derivatives, respectively. y represents the first and second derivatives, respectively; d is the coupling coefficient; k and μ are the damping coefficients; and F and ω are the amplitude and angular frequency of the built-in driving force, respectively.

[0086] This embodiment improves the dual-coupling system. For a Duffing oscillator system, with a fixed damping coefficient k, as the damping factor F increases, the system output will successively exhibit different states: attractor, homoclinic orbit, period-doubling bifurcation, chaos, and large-scale periodicity. Adjusting F to the critical point where the chaotic state transitions to the large-scale periodic state, if a weak signal of the same frequency is input to the system at this point, the system will transition from the chaotic state to the large-scale periodic state; otherwise, the system will remain in the chaotic state. The presence of a signal can be determined by judging the system state. The Van Der Pol-Duffing equation is as follows: The Van Der Pol-Duffing property is similar to the Duffing property. Coupling the two can improve the sensitivity of the system and enhance detection performance. A common coupling method is to directly connect the first and last terms and add the coupling terms directly, as shown in the equation below:

[0087]

[0088] In the case of weak coupling, the coupling method of this embodiment can further improve the system sensitivity. Under the same weak signal input, the system can reach the large-scale periodic state more quickly, thereby reducing the probability of state misjudgment and improving detection performance.

[0089] In step S4, the signal is input into the improved dual-coupled system, specifically: to detect arbitrary frequencies, a scaling transformation needs to be performed on formula (1) first, letting t = ωτ, then The original expression can be written as:

[0090]

[0091] x τ y τ A variable that changes in accordance with the change of variable τ. x τ The first and second derivatives, y τ The first and second derivatives.

[0092] In step S4, the system output is obtained by using the fourth-order Runge-Kutta method, specifically as follows:

[0093] The equations for the improved dual-coupled system inputting the signal are rewritten as follows:

[0094]

[0095] Will and Let g be a function of x1, x2, and t, and then written in vector form:

[0096]

[0097] In the formula, X0 is the initial value, and X = [x1 x2] T Let h be the vector to be solved, and let the iteration step size be h. Applying the fourth-order Runge-Kutta algorithm, we can obtain the recurrence equation:

[0098]

[0099] This allows us to obtain the numerical solution output by the system.

[0100] The cross-sectional variance method described in step S5 is specifically as follows:

[0101] Based on the numerical solution output by the system, the phase diagram and time-domain diagram of the improved dual-coupled system are obtained, such as... Figure 3 As shown, Figure 3 (a) and Figure 3 (b) is F = 0.746, a chaotic state. Figure 3 (c) and Figure 3(d) is F = 0.747, a large-scale periodic state.

[0102] like Figure 5 As shown, the points passing through the cross section x2 = 0 in the phase diagram are recorded. The dispersion of the points on the cross section reflects the degree of chaos in the improved dual-coupled system. The variance of the cut-off point is used as a measure of the degree of chaos in the improved dual-coupled system, and this is used to determine the state of the improved dual-coupled system. By changing the driving force of the improved dual-coupled system, the variance under different driving force amplitudes is obtained, as shown below. Figure 6 As shown in the figure; the magnitude of the variance reflects the degree of chaos in the system. Around F = 0.75, the variance magnitude decreases rapidly, indicating that the system transitions from a chaotic state to a large-scale periodic state. The F at this transition point is denoted as the critical threshold F. d .exist Figure 6 A decision threshold is defined: when the variance is less than ∈, the state is considered periodic; when the variance is greater than ∈, the state is considered chaotic.

[0103] The phase diagram and time-domain diagram of the Duffing system can be obtained using the same method, such as Figure 4 As shown, Figure 4 (a) and Figure 4 (b) is F = 0.825, a chaotic state. Figure 4 (c) and Figure 4 (d) represents F = 0.826, the critical state. Figure 4 (e) and Figure 4 (f) is F = 0.827, a large-scale periodic state. From Figure 3 and Figure 4 As can be seen, both systems increase their driving force amplitude by the same amount. The improved dual-coupled system can directly transition from a chaotic state to a large-scale periodic state, while the Duffing system requires passing through a critical state between the chaotic and large-scale periodic states. This indicates that the Duffing system is less sensitive than the improved dual-coupled system, requiring a higher signal amplitude to cause a change in the system state when detecting weak signals.

[0104] In step S5, the built-in driving force frequency of the improved dual-coupling system is increased, specifically as follows:

[0105] The built-in drive frequency has been updated to 1.174 times the original.

[0106] When there is a frequency difference between the input signal frequency and the system's built-in driving force frequency, the system will exhibit an intermittent chaotic state. This intermittent chaotic state can be used to detect weak signals of unknown frequencies. The principle is as follows:

[0107] For an input frequency difference of Δω in the improved dual-coupled system, equation (1) becomes:

[0108]

[0109] The driving force in the above formula is equivalent to:

[0110] F cos(ωt)+λcos((ω+Δω)t+φ)

[0111] =F cos(ωt)+λ(cos(ωt)cos(Δω+φ)-sin(ωt)sin(Δω+φ))

[0112] =(F+λcos(Δω+φ))cos(ωt)-λsin(Δω+φ)sin(ωt)

[0113] =F′cos(ωt+θ(t))

[0114] in:

[0115]

[0116]

[0117] Equivalent periodic force amplitude F′ The period of the output continuously varies from F-λ to F+λ, causing the system output to fluctuate between periodic and chaotic states, with a period of T. The frequency difference Δω can be obtained by measuring the period T of the intermittent chaotic output. A schematic diagram of the intermittent chaotic state of the system is shown below. Figure 7 As shown. Let the driving force frequency of the system be ω, then the input signal frequency that can cause intermittent chaotic state is 0.92ω~1.08ω. Compared with the input signal frequency range of 0.97ω~1.03ω of the Duffing system, the improved dual-coupled system has a larger search range and stronger detection capability for unknown frequency signals.

[0118] Example 3

[0119] This embodiment is based on Embodiments 1 and 2, such as Figure 2 As shown, the following content will continue to be disclosed:

[0120] Step S5 is followed by the following steps:

[0121] S6: Let the frequency at which the signal is detected be f, and set up one of the improved dual-coupling systems at intervals of 0.08f to form a detection array;

[0122] S7: Input the signal into each of the improved dual-coupled systems in the detection array for detection;

[0123] S8: Segment the output of each improved dual-coupled system and use the cross-sectional variance method to detect it. At this time, the improved dual-coupled systems of different frequencies have periodic waveforms in different time periods. The time t′ of the periodic waveform and the corresponding system frequency f′ are obtained, and a series of points (t′, f′) are obtained.

[0124] S9: Perform linear fitting on the series of points (t′, f′) to obtain the slope. This is the estimate of the chirp signal frequency modulation slope k0.

[0125] Steps S6-S9 are the parameter estimation process for the chirp signal. The chirp signal expression is as follows: Because the real part is often taken in practical applications, the real part is omitted here. The detection was performed, and the frequency modulation slope k0, an important parameter, was estimated. A schematic diagram of the frequency modulation slope of the chirp signal is shown below. Figure 8 As shown.

[0126] An improved dual-coupled system with different driving force frequencies is configured to form a chirp signal detection array. The chirp signal is input into the detection array. Because the chirp signal frequency varies with time, the system at different frequencies exhibits intermittent chaotic states (appearing as a periodic waveform) at different time points. Therefore, by detecting each system segment, the time of occurrence of the periodic waveform at different frequencies can be obtained and recorded as a series of points (t′, f′). Linear fitting of these points yields an estimate of the frequency modulation slope k0.

[0127] In the specific implementation process, a weak sinusoidal signal was input into the Duffing system, the dual-coupled system, and the improved dual-coupled system, respectively. The detection rate of the signal was determined based on the system output, and the detection rates of the three systems for weak sinusoidal signals were compared to demonstrate the superiority of the improved dual-coupled system. The signal frequency was set to 20kHz, and the amplitude to 0.01. The sampling rate was set to 5MHz, and the sampling process lasted for 0.01s. The detection rates of the three systems changed as the signal-to-noise ratio decreased from -35dB to -5dB, as shown below. Figure 9 As shown in the diagram. In this simulation, all sampling points were retained for state determination, which better reflects the system's sensitivity to initial values. From... Figure 9 It can be seen that the improved dual-coupled system has a significantly better detection rate than other systems at low signal-to-noise ratios, indicating that the improved dual-coupled system has higher sensitivity and better performance for weak signals.

[0128] Chirp signals were detected. The target's weak chirp signal had a frequency range of 20kHz to 30kHz, an amplitude of 0.1, and a duration of 0.01s. The frequency modulation slope was found to be k0 = 10. 6The frequency scan range is set to 10kHz to 50kHz. Since the frequency range of intermittent chaos in the improved dual-coupled system is 0.92ω to 1.08ω, the frequency update parameter during the frequency scan is... Figure 10 The output results of a partial scan of a 0dB chirp signal are shown, revealing that the improved dual-coupled system responds to signals within the 20kHz–30kHz frequency range. At the system frequency f = 22301.8292Hz, the system output exhibits a continuous chaotic waveform from 0.002s to 0.003s. This is because the initial state of the system when entering the intermittent chaotic state is chaotic, in which case no signal can be detected. At the system frequency f = 26182.347Hz, the system output exhibits a continuous periodic waveform from 0.006s to 0.007s. This is because the initial state of the system when entering the intermittent chaotic state is periodic, indicating that a signal has been detected. Weak signals at frequencies near the system's built-in frequency can induce the system into an intermittent chaotic state; the initial state of the system entering intermittent chaos is related to the signal phase.

[0129] Frequency scanning determined that the chirp signal frequency was around 26 kHz, so a detection array was set up around 26 kHz to estimate the parameters of the chirp signal. An improved dual-coupling system was set up at intervals of approximately 0.08f to form a detection array. The detection results of the detection array for the chirp signal are as follows: Figure 10 As shown in the figure, the output of each system in the detection array is segmented, and the state is determined using the cross-sectional variance method. The time intervals of periodic waveforms appearing in the output of systems at different frequencies are obtained. These time intervals correspond to frequencies, forming a series of points (t′, f′). Linear fitting of these points yields an estimate of the frequency modulation slope k0. The accuracy of the frequency modulation slope k0 estimation as a function of SNR is shown in the figure. Figure 11 As shown, the proposed detection method exhibits better detection performance than other methods under low signal-to-noise ratio (SNR) conditions. Below -12 dB, the detection method based on the dual-coupled system demonstrates similar performance, while the Duffing detection method struggles to achieve an accuracy of 1. Simulation results demonstrate that the detection method based on the improved dual-coupled system and cross-sectional variance method achieves high detection accuracy under low SNR conditions.

[0130] The same or similar labels correspond to the same or similar parts;

[0131] The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0132] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A weak signal detection method based on an improved dual-coupling system and the cross-sectional variance method, characterized in that, Includes the following steps: S1: Input a noisy, weak signal; S2: Initialize the signal frequency search range; S3: Set the built-in driving force frequency of the improved dual-coupled system as the lower bound of the signal frequency search range, wherein the improved dual-coupled system is the coupling between the Duffing oscillator system and the Van Der Pol-Duffing equation; S4: Input the signal into the improved dual-coupled system and use the fourth-order Runge-Kutta method to solve for the system output; S5: Divide the system output into segments and use the cross-sectional variance method to detect whether there is a periodic waveform in each segment of the system output. If there is, it indicates that a signal has been detected. If there is no periodic waveform, increase the built-in driving force frequency of the improved dual coupling system and return to step S4 until the built-in driving force frequency of the improved dual coupling system is greater than the upper limit of the signal frequency search range. Then there is no signal in the signal frequency search range. The improvement of the dual-coupled system in step S3 is as follows: In the formula, , To follow time Variables that change with change , They are respectively The first and second derivatives, , They are respectively The first and second derivatives, The coupling coefficient is... The damping coefficient is... and These are the amplitude and angular frequency of the built-in driving force, respectively. The cross-sectional variance method described in step S5 is specifically as follows: Based on the numerical solution output by the system, the phase diagram and time-domain diagram of the improved dual-coupled system are obtained; Recording phase diagrams through cross sections The degree of dispersion of points on the cross section reflects the degree of chaos of the improved dual-coupled system. The variance of the cut-off point is used as a measure of the degree of chaos of the improved dual-coupled system, and the state of the improved dual-coupled system is judged accordingly. The driving force of the improved dual-coupled system is changed to obtain the variance under different driving force amplitudes. This improves the transition point of a dual-coupled system from a chaotic state to a large-scale periodic state. This is denoted as the critical threshold. And give the judgment threshold. When the variance at the cutoff point is less than If the decision is periodic, then a signal exists, and the variance is greater than 1. If the judgment is in a chaotic state, then there is no signal.

2. The weak signal detection method based on the improved dual-coupling system and cross-sectional variance method according to claim 1, characterized in that, In step S1, the noisy weak signal is a noisy weak chirp signal. Specifically: In the formula, The signal amplitude, For signal frequency, The chirp signal frequency modulation slope, For time.

3. The weak signal detection method based on the improved dual-coupling system and cross-sectional variance method according to claim 2, characterized in that, In step S2, the signal frequency search range is initialized. ,in, This is the lower bound of the signal frequency search range. This is the upper bound of the signal frequency search range.

4. The weak signal detection method based on the improved dual-coupling system and cross-sectional variance method according to claim 1, characterized in that, In step S4, the signal is input into the improved dual-coupled system, specifically as follows: In the formula, , , , , For following variables Variables that change with change , They are respectively The first and second derivatives, , They are respectively The first and second derivatives.

5. The weak signal detection method based on the improved dual-coupling system and cross-sectional variance method according to claim 4, characterized in that, In step S4, the system output is obtained by using the fourth-order Runge-Kutta method, specifically as follows: The equations for the improved dual-coupled system inputting the signal are rewritten as follows: Will and Indicated as about , and function Then write it in vector form: In the formula, It is the initial value. Let the vector to be solved be , and let the iteration step size be . The recursive equation can be obtained by applying the fourth-order Runge-Kutta algorithm: This allows us to obtain the numerical solution output by the system.

6. The weak signal detection method based on the improved dual-coupling system and cross-sectional variance method according to claim 1, characterized in that, In step S5, the built-in driving force frequency of the improved dual-coupling system is increased, specifically as follows: The built-in drive frequency has been updated to 1.174 times the original.

7. The weak signal detection method based on the improved dual-coupling system and cross-sectional variance method according to claim 6, characterized in that, When there is a frequency difference between the input signal frequency and the system's built-in driving force frequency, the frequency difference detection method is as follows: The input frequency difference of the improved dual-coupled system is Signal: The driving force in the above formula is equivalent to: in: Equivalent periodic force amplitude by The cycle is in The constant changes cause the system output to fluctuate between periodic and chaotic states, with a period of variation of [missing information]. By measuring the period of the intermittent chaos in the output The frequency difference can then be calculated.

8. The weak signal detection method based on an improved dual-coupling system and cross-sectional variance method according to any one of claims 1 to 7, characterized in that, Step S5 is followed by the following steps: S6: Let the frequency at which the signal is detected be... Each interval Set up the improved dual-coupling system to form a detection array; S7: Input the signal into each of the improved dual-coupled systems in the detection array for detection; S8: Segment the output of each improved dual-coupled system and use the cross-sectional variance method for detection. At this time, the improved dual-coupled systems of different frequencies have periodic waveforms in different time periods, and the occurrence time of the periodic waveforms is obtained. and the corresponding system frequency A series of points were obtained. ; S9: For series points Perform linear fitting to obtain the slope That is, the frequency modulation slope of the chirp signal. The estimate.

Images