A method and system for detecting aero-magnetic anomalies based on stochastic resonance systems

Abstract

This invention discloses an airborne magnetic anomaly detection method based on a stochastic resonance system, comprising the following steps: S1: Acquiring geomagnetic field data. The data is processed using airborne magnetic compensation technology. S2: Establishing a stochastic resonance detection system and calculating a binary hypothesis detection statistic. The binary hypothesis detection statistic is the standard deviation of the output of the stochastic resonance system. S3: Calculating a threshold and detecting the target. The threshold is calculated using the unit averaging method. The presence of a target is determined by comparing the binary hypothesis detection statistic with the threshold. A target is considered to exist when the binary hypothesis detection statistic of any subsystem in the stochastic resonance system is greater than the corresponding threshold; the measurement is considered pure noise only when both subsystem statistics are less than the threshold. This method addresses the problems of low signal-to-noise ratio and the severe influence of noise type on correlation matching detection methods during magnetic anomaly detection in complex environments.

Description

Technical Field

[0001] This invention relates to the field of magnetic anomaly detection technology, specifically to an airborne magnetic anomaly detection method and system based on a stochastic resonance system. Background Technology

[0002] Airborne magnetic anomaly detection technology involves installing high-sensitivity magnetometers on aircraft to detect and identify underwater targets by measuring local magnetic anomalies caused by the distortion of the geomagnetic field resulting from magnetic objects (submarines, shipwrecks, mines, etc.) in the ocean. During airborne magnetic anomaly detection, due to the long detection distance and the extremely complex geomagnetic field and external magnetic noise interference, the magnetic anomaly signal of the target is extremely weak. This weak signal is easily masked by complex geomagnetic environmental noise, significantly affecting detection performance. Airborne magnetic anomaly detection algorithms mainly focus on studying the characteristics of the target signal and the noise characteristics, such as standard orthogonal basis function decomposition algorithms, wavelet decomposition and reconstruction algorithms, principal component analysis algorithms, higher-order zero-crossing algorithms, and intelligent algorithms based on neural network models. However, these algorithms have certain technical barriers: 1) the detection performance is not ideal under low signal-to-noise ratio conditions; 2) matched filtering algorithms are heavily dependent on the target signal waveform and have certain limitations; 3) intelligent algorithms rely heavily on a large amount of training data. Summary of the Invention

[0003] To address the problems of low signal-to-noise ratio and severe influence of noise type on correlation matching detection methods during magnetic anomaly detection in complex environments, this invention proposes an airborne magnetic anomaly detection method based on a stochastic resonance system.

[0004] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0005] A method for detecting aero-magnetic anomalies based on stochastic resonance systems includes the following steps:

[0006] S1: Collect geomagnetic field data. The data mentioned above is processed using aeromagnetic compensation technology.

[0007] S2: Establish a stochastic resonance detection system and calculate the binary hypothesis detection statistic. The stochastic resonance system involves a parallel bistable stochastic resonance system with different initial states, and the system parameters can be adaptively selected. The binary hypothesis detection statistic is the standard deviation of the output of the stochastic resonance system.

[0008] S3: Calculate the threshold and detect the target. The threshold is calculated using the unit averaging method. The presence of a target is determined by comparing the binary hypothesis detection statistic with the threshold. A target is considered to exist when the binary hypothesis detection statistic of any subsystem in the stochastic resonance system is greater than the corresponding threshold; the measurement is considered pure noise if and only if the statistics of both subsystems are less than the threshold.

[0009] As a preferred approach, magnetic anomaly detection technology is divided into aeromagnetic compensation technology and magnetic anomaly signal detection technology. Aeromagnetic compensation technology compensates for platform magnetic and geomagnetic interference in real time, suppressing interference and noise to a level sufficient for effective detection of magnetic anomaly signals, thus providing accurate target magnetic field data for magnetic anomaly detection. This technology effectively reduces the impact of platform noise on the magnetic detector. Essentially, it calculates and compensates for the deterministic and modelable components of the total magnetic field data detected by the magnetic detector. This invention primarily studies magnetic anomaly signal detection technology, assuming that all data used has undergone compensation techniques to eliminate platform noise, containing only uncompensated geomagnetic noise, other noise, and the target signal. Since the target signal itself is very weak, the signal-to-noise ratio of the signal obtained after aeromagnetic compensation is generally less than 1.

[0010] As a preferred option, step S2 specifically involves: Stochastic resonance was first proposed in 1981 by Benzi et al. in Italy, during their research on paleoclimate and glaciation, to explain the periodic alternation of glacial and warm climate periods in paleometeorology. Applying the principle of stochastic resonance for weak signal enhancement and detection is a new technology with practical application value. The core of the stochastic resonance signal detection method is to use noise to enhance the signal, improve the signal-to-noise ratio, and is not limited by the precise shape of the target signal. However, in applications such as airborne magnetic exploration, stochastic resonance still faces challenges such as difficulty in selecting system parameters, complex environmental noise, and extremely low signal-to-noise ratio.

[0011] As a preferred method, the following approach is used to establish a bistable stochastic resonance system:

[0012] Langevin's equation was proposed during the study of Brownian motion of particles, and stochastic resonance is built upon it. When an oscillator of mass m moves at velocity v in a fluid, inevitable collisions occur between the particle and fluid molecules, manifesting as viscosity at the macroscopic level. These collisions are random, and at the microscopic level, Brownian motion exhibits significant randomness in both direction and velocity. To further analyze particle motion, Langevin's equation was proposed. That is:

[0013]

[0014] Where F(t) is the net external force acting on the particle during its Brownian motion after the damping effect is removed, γ = a / m, η(t) = F(t) / m.

[0015] In the study of the impact of noise on nonlinear systems, bistable systems are the most frequently studied class of nonlinear systems. They are typically represented by a symmetric bistable state function U(x):

[0016]

[0017] Where x represents the displacement of the Brownian particle, and a and b are real coefficients greater than zero, called system parameters. When the external driving force is 0, the steady-state equation dx / dt = 0 indicates that the system has three equilibrium points, including two stable equilibrium points. and an unstable equilibrium point (x) max =0). There exists a potential function with a height of ΔU = a in the middle. 2 The potential barrier of / 4b is divided into two potential wells.

[0018] When the system is driven by both signal and noise, the system's dynamic equations are described by the nonlinear Langevin equations as follows:

[0019]

[0020] Where s(t) is the signal, n(t) is the random noise, and x is the output of the stochastic resonance system. At this time, the system output x can be understood as the horizontal position of the oscillator in the potential well, and the system input corresponds to the random collision in Brownian motion.

[0021] According to the bistable potential function, the system output will either jump over the potential barrier and switch back and forth between two steady states (between potential wells) or remain in one steady state. Stochastic resonance systems have three typical output modes: When the system input signal is a sufficiently strong periodic signal, and the signal, noise, and system achieve a certain synergistic effect, the signal will periodically adjust the system's output state, i.e., stochastic resonance occurs; when the system input noise is too strong, the output will be dominated by noise, resulting in between-potential-well transitions; however, when both the signal and noise energy are weak, the system can only remain in a certain potential well, oscillating back and forth around a stable point. In this case, which of the two potential wells the particle is located in depends on the initial state of the system.

[0022] In target detection using a stochastic resonance system, the signal, noise, and system need to reach a certain cooperative state; that is, the signal and noise cannot drive the system to transition independently, but they will occur when they act together. Stochastic resonance can not only detect signals but also significantly amplify them. Essentially, it expands the amplitude of the signal to a larger range through the stochastic resonance system. This range is positively correlated with the distance between the positive and negative equilibrium points of the potential well.

[0023] As a preferred method, the adaptive system parameter selection method is as follows:

[0024] Stochastic resonance is a synergistic effect among signal, noise, and nonlinear systems. There are two main approaches to achieving stochastic resonance: one is to introduce an external signal to adjust the potential barrier height, thus generating the stochastic resonance phenomenon; the other is to adjust system parameters to improve the matching relationship between the signal, noise, and nonlinear system, thereby leading to stochastic resonance. The method based on external signal adjustment is the classic approach to achieving stochastic resonance. However, adjusting noise is not easy in practical signal processing, and noise adjustment is unidirectional; it can only add noise, not reduce it. Especially when the system's input signal already contains strong noise, the intensity of which may exceed the system's allowable range, making further noise addition meaningless. In airborne magnetic exploration, target signals are often hidden in complex background noise, resulting in generally low signal-to-noise ratios. In such cases, the stochastic resonance method based on external signals or noise is ineffective. However, if appropriate system parameters are selected, it is still possible to achieve a certain matching relationship between the system, signal, and noise to realize stochastic resonance. The parameter adjustment method then demonstrates superior flexibility and operability. Based on this, this invention proposes a stochastic resonance method based on adaptive parameter adjustment, which is more suitable for weak signal detection.

[0025] In practical applications of stochastic resonance, the selection of system structural parameters is mostly based on experience, choosing a relatively "suitable" value, or selecting commonly used values ​​(such as a=1, b=1), or using search algorithms to perform extensive calculations and iterations across the entire value space of a and b to find the optimal value. All these methods use the same set of fixed parameters to handle various inputs, which not only limits the applicability of the stochastic resonance system and makes it unable to cope with environments with large noise variations, but also increases the system's load. Using a bistable stochastic resonance system for target detection requires the following conditions to be met: the signal or noise itself is insufficient to drive the system to overcome the potential barrier and enter another state; the mixture of signal and noise may drive the system to enter another state. To overcome this potential barrier, the system input (signal and noise) must be greater than a threshold A. c Assuming the system input is a constant A, the system potential function is:

[0026]

[0027] When the poles and inflection points coincide, we have:

[0028]

[0029] Solving the above system of equations, we obtain the system input threshold as:

[0030]

[0031] When A<A cAt this time, the oscillator cannot overcome the potential barrier to achieve a transition between potential wells, and stochastic resonance cannot occur. Literature research indicates that the convergence condition for numerical simulation of bistable stochastic resonance systems is:

[0032]

[0033] In this invention, the optimal value of τ is 1 / 5. To improve convergence efficiency, we compress parameters a and b to the following range:

[0034]

[0035] In the research content of this invention, the system parameters need to ensure that the system can undergo random resonance while maximizing the standard deviation of the system output. Equation (6) is transformed as follows:

[0036]

[0037] Where A c It can be calculated based on the environmental noise collected by the magnetic detector. To prevent the system from being overly sensitive to noise, A c The average absolute value of the acquired signal amplitude is selected, and this value is dynamically updated as the environment changes to achieve adaptive parameter adjustment. When a transition occurs in the system output, its standard deviation will change abruptly, and the range of this change depends on the equilibrium point of the two potential wells (±x). min The distance between them. Therefore, we obtain the following relationship:

[0038]

[0039] As shown above, the binary hypothesis test statistic reaches its maximum value when a = 1. The adaptive parameter selection criteria adopted by the system are as follows:

[0040]

[0041] Where u represents the input of the stochastic resonance system, i.e. the magnetic anomaly signal contaminated by noise, and n is the number of sampling points.

[0042] As a preferred option, the impact of different initial states on the system:

[0043] Initial research on stochastic resonance was limited to cases where the input was a periodic signal. The transformation from a periodic signal to a signal of arbitrary shape is not easily understood intuitively. Magnetic anomaly signals are typical aperiodic wide-pulse signals, including positive signals, negative signals, and composite signals combining both. Unlike the multiple transitions observed in periodic signals, only a single potential well transition occurs when processing aperiodic signals. The positive signal drives the system from -x... min Equilibrium state towards +x minEquilibrium transitions occur in equilibrium states, while negative signals follow the opposite pattern. For composite signals, which are essentially asymmetrical signals biased towards either positive or negative, the same conditions apply. Therefore, to successfully detect different waveform signals, the stochastic resonance detection algorithm employs a parallel structure with different initial states. Due to the influence of the initial system value, during continuous detection, the system needs to restore its initial state after each target detection or after a prolonged period without a target detection to continue detecting the next target.

[0044] As a preferred method, numerical calculation methods for stochastic resonance systems

[0045] The fourth-order Runge-Kutta method is primarily used in computer simulations when the derivatives and initial values ​​of the equations are known, thus eliminating the complex process of solving differential equations. The numerical model of a stochastic resonance system can be calculated using the fourth-order Runge-Kutta method, as specifically stated in the following equation:

[0046]

[0047] Where x represents the system output, u represents the input of the stochastic resonance system, i.e. the magnetic anomaly signal contaminated by noise, τ represents the system iteration step size, and a and b are the stochastic resonance system parameters.

[0048] In the formulation of the Runge-Kutta method for stochastic resonance numerical computation, the core idea is to represent the integral of the differential equation using area. The area within a single step size is determined by the product of the step size τ and an estimated slope k, which is a weighted average of a series of intermediate slopes. For ease of understanding, we rewrite equation (12) as follows:

[0049]

[0050] Where k1 is the slope at the beginning of the time interval; k2 is the slope in the middle of the time interval, calculated using the Euler method with slope k1; k3 is also the slope at the midpoint of the time interval, calculated using the Euler method with slope k2; and k4 is the slope at the end of the time interval, calculated from k3. When averaging the four slopes, the slope at the midpoint has a greater weight.

[0051] In the numerical calculation of differential equations, choosing an appropriate step size is crucial. From the perspective of each step alone, a smaller step size results in a smaller truncation error; however, as the step size decreases, the number of steps required within a given solution interval increases. This leads to an increase in computational load and a significant accumulation and propagation of rounding errors. In the numerical calculation of stochastic resonance systems, the input is known and discrete. The Runge-Kutta method performs single-step calculations between two input points. A suitable step size determines whether stochastic resonance can occur and directly affects the final detection result of the system. From equations (12) and (13), it can be seen that the variation amplitude of the system output is determined by τk. Here, k is the value based on the input u and the current integral x. n x is calculated based on system parameters a and b. According to the system output pattern, x... n This can be viewed as the equilibrium point of the potential well where the current output is located. Therefore, for identical systems with the same input, the value of k is the same. Thus, the step size τ directly determines the intensity of the output change in the stochastic resonance system. Here, we introduce the sampling frequency fs of the Runge-Kutta method, making the step size τ = 1 / fs. The sampling frequency fs in the numerical calculation affects the amplitude of the system output change, thereby determining whether the stochastic resonance phenomenon occurs.

[0052] We conducted multiple simulations at different sampling frequencies to find a suitable value for fs. A typical magnetic anomaly signal was superimposed with Gaussian noise to simulate a noisy signal with a signal-to-noise ratio (SNR) of -20 to 0 dB. At the same sampling frequency and SNR, the detection probability was obtained through 1000 repeated simulations. The results show that when fs = 5, the system not only maintains a high detection probability but also meets the false alarm rate requirements. Therefore, in this invention, fs = 5 was selected as the sampling frequency for the Runge-Kutta method, with a step size τ = 1 / 5.

[0053] As a preferred method, calculate the binary hypothesis test statistic.

[0054] When the target signal is present, the output state of the stochastic resonance system will switch, and the standard deviation of this part will increase significantly. This invention uses the standard deviation of the output x of the stochastic resonance system as the binary hypothesis test statistic. This standard deviation is calculated by the moving window according to equation (14), and the length of the window is set to 73 according to the length of the magnetic anomaly signal.

[0055] STD(n)=std(x(n-36:n+36))(14)

[0056] As a preferred option, step S3 specifically involves:

[0057] Constant false alarm rate (CFAR) detection technology for signals has wide applications in airborne magnetic exploration. In airborne magnetic exploration systems, one of the following two assumptions must hold true during the detection process:

[0058] (1) H0: The measured value is only interference;

[0059] (2)H1: The measured value is the superposition of the interference and target signals.

[0060] If H0 is true, it means there is no target at the distance, angle, or position coordinates corresponding to the measured value. If H1 is true, it means the target exists. Typically, the two hypotheses are modeled using probability density functions to determine which hypothesis is true, defining the following two probabilities:

[0061] (1) Detection probability P D The probability of a target being detected if it actually exists.

[0062] (2) False alarm probability P FA The probability of a target being detected when the target does not exist.

[0063] To select the optimal hypothesis from the two hypotheses, a suitable criterion must be determined. One of the most commonly used criterions is the Neyman-Pearson criterion, which calculates the false alarm probability P... FA The constraint is within a certain constant range, so that the detection probability P D To reach the maximum. The primary consideration is the system's tolerance for false alarms, followed by how to improve the detection probability.

[0064] Accurately known noise power is a prerequisite for setting a fixed threshold. However, in airborne magnetic detection, it is unknown and variable. If a fixed threshold is still used in this situation, the false alarm probability will vary over a large scale when the noise power changes, thus affecting the system's stability. Therefore, this invention uses a cell averaging detection algorithm to calculate the detection threshold. By estimating the interference noise power in real time from the measured data, the system adaptively selects the threshold and ensures that the system has a constant false alarm probability P. FA The adaptive threshold is calculated by Th = α·z, where α is the product factor and z is the noise power.

[0065] Because the random resonance process lasts for a certain period, the standard deviation of the system output is a relatively wide bell-shaped signal. At this time, traditional threshold detection will continuously detect the presence of a target within cells immediately adjacent to the target location, leading to a large number of false alarms. To solve this problem, it is now stipulated that a target is considered to exist only when the detection statistic is greater than the adaptive threshold for a consecutive number of points. For parallel systems, the detection criterion is that a target is considered to exist if the detection statistic of any subsystem is greater than the corresponding threshold; noise is considered to exist only if and only if the detection statistics of two subsystems are both less than the threshold. The cell averaging detection algorithm can achieve real-time adaptive threshold selection, enabling the system to better cope with interference from complex environmental noise.

[0066] This invention also discloses an airborne magnetic anomaly detection system based on a stochastic resonance system, comprising:

[0067] The data acquisition module is used to acquire the magnetic field data, and the data needs to be processed by aeromagnetic compensation technology.

[0068] The data processing module uses a stochastic resonance system to process the magnetic field data, and treats the standard deviation of the system output as a binary hypothesis detection statistic.

[0069] The magnetic anomaly signal detection module is used to compare the binary hypothesis detection statistic with a threshold to determine whether a target signal exists during detection.

[0070] This invention has the following characteristics and beneficial effects:

[0071] 1. This invention effectively overcomes strong background noise, successfully detects targets from low signal-to-noise ratio signals, and has detection capabilities over a wider range of signal-to-noise ratios.

[0072] 2. This invention is based on a stochastic resonance system, which requires less prior information about the target signal and is not limited by the waveform of the target signal.

[0073] 3. This invention solves the problem of adaptive parameter selection for stochastic resonance systems, enabling it to adapt to detection tasks under various complex environments.

[0074] 4. This invention is easy to implement and has a high detection rate. Attached Figure Description

[0075] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a structural diagram of an airborne magnetic anomaly detection method based on a stochastic resonance system;

[0077] Figure 2 Schematic diagram of the output of a stochastic resonance system under different input intensities;

[0078] Figure 3 This is a schematic diagram of a typical magnetic anomaly signal in simulation.

[0079] Figure 4 This is a spatial distribution map of the magnetic anomaly signal;

[0080] Figure 5The detection probability diagram of the stochastic resonance method at different sampling frequencies;

[0081] Figure 6 This is a schematic diagram of the output and standard deviation of the output of a random resonant subsystem (positive signal).

[0082] Figure 7 This is a schematic diagram of the output and standard deviation of the output of a random resonant subsystem (negative signal).

[0083] Figure 8 A schematic diagram of the output and standard deviation of the output of a random resonant subsystem (composite signal);

[0084] Figure 9 The graph shows the detection performance of the stochastic resonance method and the standard orthogonal basis function decomposition algorithm. Detailed Implementation

[0085] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0086] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0087] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0088] This invention provides an embodiment of an airborne magnetic anomaly target detection method based on a stochastic resonance system, such as... Figure 1As shown, the method for detecting aerospace magnetic anomalies based on a stochastic resonance system includes:

[0089] S1: Collect geomagnetic field data. The data used in this invention is processed using aeromagnetic compensation technology.

[0090] It should be noted that aeromagnetic compensation technology and magnetic anomaly detection technology are parallel technologies, with aeromagnetic compensation being a pre-processing technology for magnetic anomaly detection. It can be directly integrated into signal acquisition equipment. Aeromagnetic compensation technology possesses a complete technical system, including numerous data processing methods, and can be considered a preprocessing method for magnetic anomaly data. This invention primarily studies magnetic anomaly detection technology, processing pre-processed data. Therefore, aeromagnetic compensation technology is not discussed in detail.

[0091] Specifically, in the detection of airborne magnetic anomalies, the target can be regarded as a single magnetic dipole, which generates a magnetic field B. s This can be described by the following magnetic dipole model:

[0092]

[0093] Where m(m x ,m y ,m z )=(m il cos 2 α+m it sin 2 α,m il cosαsinα-m it cosαsinα,-m iv ) is the target magnetic moment and is determined by the induced magnetic moment m i (m il ,m it ,m iv In this expression, α is the target heading, r(x,y,z) is the displacement vector between the target and the detector, and μ0 = 4π × 10⁻⁶. 7 H / m (henry / meter) is the permeability of free space. The permeability of seawater is approximately equal to that of free space.

[0094] Scalar magnetic anomaly signal B a It can be achieved through target signal B s In the geomagnetic field B e Approximated by projection in the direction:

[0095]

[0096] Simulation conditions, including target and platform parameters, were set. A magnetic dipole model was used to simulate magnetic anomaly signals, while Gaussian noise with different signal-to-noise ratios was superimposed to generate noisy signals under complex environments. The simulation data was assumed to have been processed using aeromagnetic compensation technology and contained only the target magnetic anomaly signal and the uncompensated noise signal. Simulation conditions are shown in Table 1.

[0097] Table 1 Simulation conditions

[0098]

[0099]

[0100] Typical magnetic anomaly signals include Figure 3 As shown, the spatial distribution surface of the simulated magnetic anomaly signal is as follows: Figure 4 As shown.

[0101] S2: Establish a stochastic resonance detection system and calculate the binary hypothesis detection statistic. Figure 2 These are three typical output modes of a random resonant system. We take a typical sinusoidal signal superimposed with Gaussian noise as an example (see...). Figure 2 (a) When the signal, noise, and system are well-matched, i.e., when the SR phenomenon occurs, the signal will periodically modulate the system state (see Figure 2 (b) When the input noise is too strong, the output mainly transitions between the two potential wells due to the noise (see...). Figure 2 (c)). However, when the signal and noise are weak, neither can dominate the output, and the oscillator can only remain in a potential well and oscillate near the steady point (see [link]). Figure 2 (d) The potential well in which the oscillator will remain depends on the initial state of the system.

[0102] To detect different signals, the SR detection method employs a parallel structure and uses left and right balance points ±x. min As the initial state, the parameters of the stochastic resonance system are selected according to the following criteria:

[0103]

[0104] Where u represents the input of the stochastic resonance system, i.e. the magnetic anomaly signal contaminated by noise, and n is the number of sampling points.

[0105] The numerical model of a stochastic resonance system can be calculated using the fourth-order Runge-Kutta method, as expressed in the following equation:

[0106]

[0107] Where x represents the system output, u represents the system input, fs represents the sampling frequency, τ = 1 / fs represents the system step size, and a and b are the parameters of the stochastic resonance system.

[0108] This invention uses the standard deviation of the output x of the stochastic resonance system as the binary hypothesis test statistic. This standard deviation is calculated by a moving window according to STD = std(x(n-36:n+36)), and the length of the window is set to 73 based on the length of the magnetic anomaly signal.

[0109] Specifically, the stochastic resonance system adopts a parallel structure and uses left and right equilibrium points ±x min As the initial state. System parameters are: Where A c Select the average of the absolute values ​​of the acquired signal amplitudes, i.e.

[0110] A suitable fs value was found by performing multiple simulations at different sampling frequencies. The detection probability of a typical magnetic anomaly signal at different sampling frequencies and signal-to-noise ratios is as follows: Figure 5 As shown in the figure, sampling frequencies were 3, 4, 5, 6, 8, and 20. The dashed lines in the figure represent the false alarm rates for the corresponding sampling frequencies. The signal-to-noise ratio (SNR) range was set to -20 to 0 dB. The detection probability was statistically calculated through 1000 repeated simulations at the same sampling frequency and SNR. Figure 5 As can be seen, the target detection probability increases as the sampling frequency fs decreases (and increases as the step size increases). However, when fs = 4, the false alarm rate exceeds the acceptable value on the battlefield. When fs = 3, the detection probability is significantly low, and the false alarm rate far exceeds the acceptable range (P). f The probability of false alarms (fs) is ≤1.5%, which is insufficient for target detection. When fs = 5, the system can not only maintain a high detection probability but also meet the requirements for false alarm rate. Therefore, fs = 5 is selected as the sampling frequency of the Runge-Kutta method in this invention. The output of the stochastic resonance system is calculated according to the fourth-order Runge-Kutta method shown in equation (14).

[0111] To facilitate understanding the detection process of stochastic resonance systems, Figure 6 , 7 Figures 8 and 9 respectively show the output and standard deviation of the parallel subsystem for three typical signals: positive signal, negative signal, and composite signal, at a signal-to-noise ratio of -15dB. In each figure, (a) represents the typical target signal; (b) represents the noisy signal containing the target signal; and (c) represents the initial state x0 = x min The output of the subsystem; (d) represents the initial state x0 = -x min The output of the subsystem; (e) shows the initial state x0 = x min The standard deviation of the subsystem's output; (f) is the initial state x0 = -x min The standard deviation of the output of the subsystem is given by the dashed line, where the threshold is the threshold value.

[0112] This invention uses a moving window to calculate the standard deviation of the system output based on STD = std(x(n-36:n+36)) and uses it as the binary hypothesis detection statistic. The moving window length is set to 73.

[0113] S3: Calculate the threshold and detect the target. This invention uses a unit average detection algorithm to select a suitable threshold. The threshold Th is calculated by Th = α·z, where α is the product factor and z is the noise power. A target is considered to exist only when the detection statistic is greater than the adaptive threshold for a certain number of consecutive points. For parallel systems, the detection criteria are: H1 is true if the result of any subsystem is greater than the corresponding threshold; H0 is true if and only if the outputs of both subsystems are less than the threshold.

[0114] Specifically, to verify the effectiveness of this invention in detecting weak magnetic anomaly signals, a simulation experiment was designed and compared with the standard orthogonal basis function decomposition algorithm. The Monte Carlo method was used to perform 1000 repeated simulations to calculate the detection probability at the same signal-to-noise ratio.

[0115] This invention employs a unit average detection algorithm to calculate a threshold and compares it with the binary hypothesis detection statistic. A target is considered to exist only when the detection statistic is greater than the adaptive threshold for 50 consecutive points. For parallel systems, the detection criterion is that a target is considered to exist if the detection statistic of any subsystem is greater than the corresponding threshold; noise is considered to exist only if and only if the detection statistics of both subsystems are less than the threshold.

[0116] Figure 9 This paper demonstrates the detection probabilities of a magnetic anomaly detection method based on stochastic resonance and the standard orthogonal basis function decomposition (SOD) method under different signal-to-noise ratios (SNRs). Both algorithms achieve a false alarm rate that meets battlefield requirements within their effective detection range. Compared to the traditional SOD method, the stochastic resonance-based detection method exhibits a higher detection probability and a wider detection range. When the input SNR is -17 dB, the SOD method maintains a 62% detection rate, while the stochastic resonance-based magnetic anomaly detection method achieves a detection probability as high as 99%. However, when the input SNR is -20 dB, the SOD method is no longer able to detect the presence of underwater targets, while the stochastic resonance-based magnetic anomaly detection method still maintains a detection probability of over 60%, fully demonstrating the excellent detection performance of this adaptive algorithm under extremely low SNR conditions.

[0117] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments, including components, without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. An airborne magnetic anomaly detection method based on a stochastic resonance system, characterized in that, Includes the following steps: S1. Collect geomagnetic field data and perform aeromagnetic compensation processing on the geomagnetic field data; S2. Establish a stochastic resonance detection system and calculate the binary hypothesis detection statistic, where the binary hypothesis detection statistic is the standard deviation of the output of the stochastic resonance system; the stochastic resonance detection system is a parallel bistable stochastic resonance system with different initial states, and the system parameters of the stochastic resonance detection system are adaptively selected; The adaptive selection method for system parameters is as follows: After the signal and noise are mixed, the input signal and noise of the stochastic resonance system must be greater than a certain threshold. Assume the system input is a constant. The potential function of the stochastic resonance system is: in, , For parameters of the stochastic resonance system, This represents the displacement of the Brownian particle; When the poles and inflection points coincide, we have: Solving the above system of equations, we obtain the input threshold for the stochastic resonance system as: when When the oscillator cannot overcome the potential barrier to achieve a transition between potential wells, random resonance cannot occur. The convergence condition for the numerical simulation of the bistable random resonance system is: in, This represents the system iteration step size, and the optimal value is... To improve convergence efficiency, the parameters are... and Compress to the following range: The system parameters need to ensure that the stochastic resonance system can exhibit stochastic resonance while simultaneously maximizing the standard deviation of the system's output. The system input threshold is modified as follows: in Based on the environmental noise collected by the magnetic detector, the standard deviation of the system output will change abruptly when a transition occurs. The range of this change depends on the equilibrium point of the two potential wells. The distance between them gives us the following relationship: ； when When the binary hypothesis detection statistic is at its maximum value, the adaptive parameter selection criteria adopted by the system are as follows: in This represents the input to the stochastic resonance system, specifically the magnetic anomaly signal contaminated with noise. This represents the number of sampling points; S3. Calculate the threshold and detect the target. The threshold calculation method is the unit average method. The detection statistic of the binary hypothesis is compared with the threshold to confirm whether the target exists.

2. The method for detecting aero-magnetic anomalies based on a stochastic resonance system according to claim 1, characterized in that, The method for establishing the bistable stochastic resonance system is as follows: Based on Langevin's equation, the Langevin equation is proposed, namely: in, For quality, For speed, It is the net external force acting on the particle during its Brownian motion after the damping effect is removed. , , Symmetric bistable state function express: in and These are real coefficients greater than zero, representing parameters of the stochastic resonance system. When the external driving force is 0, they are determined by the stationary state equation. It can be seen that the system has three equilibrium points, including two stable equilibrium points. and an unstable equilibrium point The potential function has a height of [value missing]. The potential barrier is divided into two potential wells; When the system is driven by both signal and noise, the dynamic equations of the stochastic resonant system are described by the nonlinear Langevin equations as follows: in For signal, The system output is random noise. This can be understood as the horizontal position of the oscillator in the potential well, with the system input corresponding to random collisions in Brownian motion.

3. The method for detecting aero-magnetic anomalies based on a stochastic resonance system according to claim 2, characterized in that, The numerical calculation of the bistable stochastic resonance system is as follows: Using the fourth-order Runge-Kutta calculation method, the specific expression is as follows: in, This represents the input to the stochastic resonance system, specifically the magnetic anomaly signal contaminated with noise. Represents the system iteration step size. , For parameters of the stochastic resonance system, The area within a single step size is determined by the step size. and an estimated slope Determined by the product of , the slope is a weighted average of a series of intermediate slopes, which can be rewritten as the fourth-order Runge-Kutta expression: in It is the slope at the start of the time period; It is the slope in the middle of the time period, which is used by Euler's method to utilize the slope. Calculated; It is also the slope in the middle of the time period, which can be used by Euler's method to utilize the slope. Calculated; It is the slope at the end of the time period, from Calculations show that when the average of the four slopes is taken, the slope at the midpoint has a greater weight. The variation range of the system output is from Decision, among which It is based on the input Current points and system parameters , Calculated based on the system output pattern, This represents the equilibrium point position of the potential well where the current output is located. The values ​​are the same, therefore, the step size This directly determines the intensity of the output change in the stochastic resonance system; therefore, the sampling frequency of the Runge-Kutta method is introduced here. , make step size Sampling frequency in numerical calculation By influencing the magnitude of changes in the system output, the occurrence of stochastic resonance can be determined. Multiple simulations were performed at different sampling frequencies to find a suitable one. The magnetic anomaly signal was superimposed with Gaussian noise to simulate a noisy signal with a signal-to-noise ratio of -20 to 0 dB. The detection probability was obtained through 1000 repeated simulations at the same sampling frequency and the same signal-to-noise ratio.

4. The method for detecting aero-magnetic anomalies based on a stochastic resonance system according to claim 3, characterized in that, In step S2, select As the sampling frequency of the Runge-Kutta method, the step size .

5. The method for detecting aero-magnetic anomalies based on a stochastic resonance system according to claim 4, characterized in that, In step S2, the method for calculating the binary hypothesis detection statistic is as follows: When the target signal is present, the output state of the bistable stochastic resonance system will switch, and the standard deviation of this part will increase significantly. The standard deviation of is used as the binary hypothesis testing statistic. This standard deviation is calculated using a moving window, and the expression is as follows: The calculated window length is set to 73 based on the length of the magnetic anomaly signal.

6. The method for detecting aero-magnetic anomalies based on a stochastic resonance system according to claim 5, characterized in that, The specific steps of step S3 are as follows: S3-1. In a bistable stochastic resonance system, given two assumptions, which must hold during the detection process: (1) The measured values ​​are only interference; (2) The measured value is the superposition of the interference and target signals; if If true, it means that there is no target at the distance, angle, or position coordinates corresponding to the measured value; if If it is true, it means that the target exists; S3-2. Typically, the probability density function is used to model two hypotheses to determine which hypothesis is true. The following two probabilities are defined: (1) Detection probability The probability of a target being detected if it actually exists. (2) False alarm probability The probability of a target being detected when the target does not exist; S3-3, Using the Neyman-Pearson criterion to reduce spurious probabilities Constrained within a certain constant range, the detection probability is made Reaching the maximum; S3-4. The detection threshold is calculated using a unit averaging detection algorithm. By estimating the interference noise power in real time from the measured data, the system adaptively selects the threshold. The adaptive threshold is determined by... Calculate, where It is a product factor. Noise power; S3-5 stipulates that a target is considered to exist only when the detection statistic is greater than the adaptive threshold for a certain number of consecutive points. For parallel systems, the detection criterion is that if the detection statistic of any subsystem is greater than the corresponding threshold, a target is considered to exist; if and only if the detection statistics of two subsystems are less than the threshold, noise is considered to exist.

7. A magnetic anomaly signal detection system applying the airborne magnetic anomaly detection method based on a stochastic resonance system as described in any one of claims 1-6, characterized in that, include: The data acquisition module is used to acquire the magnetic field data, and the data needs to be processed by aeromagnetic compensation technology; The data processing module applies a stochastic resonance system to process the magnetic field data, and treats the standard deviation of the system output as a binary hypothesis detection statistic. The magnetic anomaly signal detection module is used to compare the binary hypothesis detection statistic with a threshold to determine whether a target signal exists during detection.

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