A physical embedded bidirectional nonlinear feedback network and a weak target detection method

Abstract

The application discloses a kind of physical embedding bidirectional nonlinear feedback network and weak target detection method, it is related to radar signal processing technical field, the application adopts unbalanced statistical physics stochastic resonance mechanism to construct limited nonlinear dynamics model, combines fourth order Runge-Kutta discretization and infinite norm constraint to guarantee numerical calculation stability;Introduce Jacobian orthogonal decoupling mechanism, completely isolate high-level semantic classification gradient to bottom layer radar physical energy dimension interference;Design frequency domain subspace energy aggregation sparse detection loss function, eliminate gradient attenuation problem under low signal-to-noise ratio, and through error feedback bifurcation control mechanism drives physical system adaptive state transition, realizes the nonlinear conversion and gain compensation of noise energy to weak target signal energy, finally realizes accurate detection to weak target under low signal-to-noise ratio.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, specifically to a physically embedded bidirectional nonlinear feedback network and a weak target detection method. Background Technology

[0002] With the rapid development of autonomous driving and Advanced Driver-Assistance Systems (ADAS) towards Level 4 / 5, vehicle-mounted FMCW radar has become an indispensable core sensor in intelligent transportation multimodal perception systems due to its all-weather operation and high-precision range-Doppler joint estimation capabilities. However, in complex urban road environments, pedestrians with low radar cross-sections (RCS), distant stationary obstacles, or severely obscured targets constitute significant blind spots in environmental perception. The microwave echo energy reflected by these weak targets is limited and is often completely submerged in strong background clutter and inherent system thermal noise. Under these low signal-to-noise ratio (SNR) observation conditions, achieving high-fidelity perception and extraction of weak multi-target targets remains a major challenge limiting the performance of vehicle-mounted radar.

[0003] Existing vehicle-mounted radar signal processing architectures primarily rely on linear orthogonal transforms. Whether it's the classic detection architecture based on two-dimensional Fast Fourier Transform (FFT) combined with Constant False Alarm Rate (CFAR), or high-resolution spectral estimation algorithms such as Multi-Signal Classification (MUSIC), the effectiveness of their feature extraction operators is strictly limited by the system's signal-to-noise ratio (SNR) threshold. In the asymptotically high SNR region, the variance of the linear estimator can approach the Cramér-Rao Lower Bound (CRLB); however, when the environmental SNR falls below the critical threshold, the projection difference of weak target features onto the orthogonal basis decays sharply. Signal feature values ​​in subspace methods sink into background noise, leading to subspace aliasing, and the CFAR architecture exhibits a significant threshold collapse effect. At this point, the estimation error no longer manifests as local fluctuations around the true frequency point, but evolves into a random discrete distribution covering the entire prior frequency range, causing the characteristic spectral lines of weak targets to be completely masked by clutter and noise. Because real-time response in autonomous driving has strict time truncation requirements for the Coherent Processing Interval (CPI), any attempt to extract weak targets by extending the coherent processing interval within a linear framework loses its engineering applicability.

[0004] To address the challenge of weak target extraction under low signal-to-noise ratio (SNR) conditions, numerous researchers have introduced deep learning techniques to the forefront of radar sensing in recent years. By constructing one-dimensional convolutional neural networks (1D-CNNs) or attention networks to directly process time-series radar beat signals or range-Doppler (RD) topology maps, purely data-driven models demonstrate superior generalization feature extraction capabilities compared to classical algorithms in conventional scenarios. However, when the observed target features are significantly weak, these models reveal an inherent problem of lacking physical constraints. Due to the lack of underlying microscopic physical evolution logic, neural networks are often dominated by macroscopic functionals such as global mean squared error (MSE) or cross-entropy during backpropagation. This black-box mechanism, which relies solely on fitting high-dimensional data spaces, is highly susceptible to falling into the trap of "oversmoothing" local minima under low SNR conditions. In order to minimize global loss, the network tends to adopt a more conservative smoothing strategy, which directly destroys the inherent physical amplitude of the radar signal. This results in the indiscriminate suppression of weak peaks in multi-target scenarios, leading to a significant increase in the false negative rate in complex high-order scenarios.

[0005] In summary, current radar weak target detection technologies suffer from multiple defects, including linear algorithms being limited by the signal-to-noise ratio threshold, deep learning models being overly smooth and causing missed detections, physical embedding models being numerically unstable, and physical features being distorted. There is an urgent need for a novel network architecture that integrates physical mechanisms and deep learning and has bidirectional nonlinear feedback capabilities to achieve high-precision and high-fidelity detection of radar weak targets under low signal-to-noise ratio conditions. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, this invention provides a physically embedded bidirectional nonlinear feedback network and a weak target detection method, which solves the problem that current radar weak target detection technologies struggle to accurately detect weak targets at low signal-to-noise ratios.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: A physically embedded bidirectional nonlinear feedback network is provided, comprising: The physical parameter spatial inference subnetwork is used to infer the control parameters of the micro-physical evolution layer from the intermediate frequency signal sequence of the radar, including potential field parameters and energy scale variables. The micro-physical evolution layer is used to convert the disordered energy of noise in the radar's intermediate frequency signal sequence into effective gain of weak target signals based on potential field parameters and a constrained nonlinear dynamics model, thereby outputting a time-domain enhancement sequence. The frequency domain transformation and decoupling module is used to convert the time-domain enhancement sequence into an enhancement amplitude spectrum and generate a normalized enhancement amplitude spectrum based on the energy scale variable through the Jacobian orthogonal decoupling mechanism. The macroscopic semantic feature recognition layer is used to classify targets based on the normalized enhancement amplitude spectrum, output the number of targets, and complete the detection of weak targets.

[0008] Furthermore, the physical parameter space inference subnetwork is constructed based on the information bottleneck principle, comprising sequentially connected one-dimensional convolutional layers, batch normalization layers, activation layers, and fully connected projection layers. The optimization objective of the physical parameter space inference subnetwork is to minimize the Lagrange functional, whose expression is: in Indicates mutual information, For radar intermediate frequency signal sequence observation tensor; Observation tensor for radar intermediate frequency signal sequence The latent variable compressed feature representation obtained after layer-by-layer feature compression of the physical parameter space inference subnetwork; For target labels; This represents the information bottleneck weighting coefficient. The Lagrange loss function is the information bottleneck loss function for the physical parameter space inference subnetwork constructed based on the information bottleneck principle.

[0009] Furthermore, the constrained nonlinear dynamics model adopts the nonequilibrium statistical physics stochastic resonance mechanism, the expression of which is: in For state variables, that is, a single value in a time-domain augmented sequence; For state variables The gradient operator is used to solve for the spatial rate of change of the potential energy function; This is a fourth-order bistable potential energy function, used to construct the nonlinear potential field topology; Indicates time; These are the potential field parameters; The radar is input with a periodic drive signal for weak targets, which is the radar's intermediate frequency signal; It is the thermodynamic wave intensity coefficient; It is a standard Wiener process that characterizes the thermal noise of the radar system and satisfies the zero-mean Gaussian random distribution characteristics.

[0010] Furthermore, the expression for the fourth-order bistable potential energy function is: ; To form a symmetrical topological structure with a single barrier and two potential wells, where the peak position of the barrier is... Stable position of potential well The barrier height is This enables the conversion of noise energy into a transpotential well for weak target signals.

[0011] Furthermore, the microscopic physical evolution layer employs the fourth-order Runge-Kutta method to discretize the constrained nonlinear dynamics model, and introduces a constrained projection operator. Apply Norm constraints, their discretization evolution formula is: in For the fourth-order Runge-Kutta method on state variables After discretization, at the 1st The state variables at each time step; For the fourth-order Runge-Kutta method on state variables After discretization, at the 1st The state variables at each time step; This is the integration step size; , , and These are the four slope estimates for the fourth-order Runge-Kutta method; Indicates constraints; This is the upper limit of the state magnitude, used to constrain the upper bound of the gradient norm and avoid gradient explosion and numerical divergence. express Norm.

[0012] Furthermore, the Jacobi orthogonal decoupling mechanism introduces a gradient blocking operator. The expression for generating the normalized enhanced amplitude spectrum is as follows: in To normalize the enhanced amplitude spectrum; To enhance the amplitude spectrum; For energy scale variables; To prevent division by zero of extremely small constants; For frequency domain coordinate variables.

[0013] Furthermore, it also includes: The joint functional constraint module is used to calculate the frequency domain subspace energy aggregation sparse detection loss and the target number classification cross-entropy loss of the physically embedded bidirectional nonlinear feedback network, and then obtain the total loss. The error feedback and bifurcation control module is used to backpropagate the gradient generated by the total loss to the physical parameter space inference subnetwork. By perturbing the maximum Lyapunov exponent of the microphysical evolution layer, it triggers local bifurcation, breaks the local non-physical steady state, and thus realizes the update of the bidirectional nonlinear feedback network.

[0014] Furthermore, the expression for the frequency domain subspace energy-gathering sparse detection loss of the physically embedded bidirectional nonlinear feedback network is as follows: in This represents the frequency domain subspace energy-intensive sparse detection loss of a physically embedded bidirectional nonlinear feedback network. , and These are all hyperparameters, used to adjust the weights of target fidelity, background sparsity, and contrast constraint, respectively; For frequency domain coordinate variables; For the target frequency set; This represents the amplitude spectrum of a real radar. The enhanced amplitude spectrum predicted by the frequency domain transformation and decoupling module; This is the set of background noise frequency points; This is the L2 norm operator, used for target region fidelity constraints; This is a norm operator used for sparse noise reduction in the background region; This is a frequency domain contrast loss used to amplify the energy difference between the target and the background.

[0015] Furthermore, the expression for the maximum Lyapunov exponent of the microscopic physical evolution layer is: in For the maximum Lyapunov exponent of the microscopic physical evolution layer, when When the value changes abruptly from negative to positive, it indicates that the microscopic physical evolution layer has undergone a transcritical or folding bifurcation, and has changed from a steady-state absorption state to a cross-well evolution state. The updated potential field parameters make the Kramers escape rate of the physically embedded bidirectional nonlinear feedback network match the characteristic period of the weak target signal, thereby continuously converting the disordered broadband energy of background noise and clutter into pump energy that drives the periodic transition of the weak target signal across the potential well, and thus realizing the nonlinear amplification of the weak target signal. It is the natural logarithm; This is the limit operator; Iteration time; For the first Step state variable Jacobian matrix; This is the cumulative multiplication operator.

[0016] A weak target detection method based on a physically embedded bidirectional nonlinear feedback network is provided, which includes the following steps: The intermediate frequency (IF) signal sequence of the radar is collected, and the control parameters of the microscopic physical evolution layer, including potential field parameters and energy scale variables, are inferred from the IF signal sequence of the radar. Based on the potential field parameters, the disordered energy of noise in the radar's intermediate frequency signal sequence is converted into the effective gain of the weak target signal through a restricted nonlinear dynamic model, thereby outputting a time-domain enhancement sequence. The time-domain enhancement sequence is converted into an enhancement amplitude spectrum, and a normalized enhancement amplitude spectrum is generated based on the energy scale variable through the Jacobi orthogonal decoupling mechanism. The normalized enhancement amplitude spectrum is used to classify targets, output the number of targets, and complete the weak target detection.

[0017] The beneficial effects of this invention are as follows: 1. This invention breaks through the signal-to-noise ratio threshold limitation of traditional linear detectors, improves detection sensitivity by 2~3dB in low signal-to-noise ratio environments, and achieves 100% detection probability at a signal-to-noise ratio of -12dB, significantly reducing the false negative rate in complex multi-target scenarios. It is suitable for weak target detection tasks of vehicle-mounted frequency modulated continuous wave (FMCW) radar.

[0018] 2. This invention, based on the nonequilibrium statistical physics stochastic resonance mechanism, constructs a bidirectional nonlinear feedback topology that integrates a microscopic physical evolution system and a macroscopic semantic network, building a blind stochastic resonance frequency network. This invention employs the nonequilibrium statistical physics stochastic resonance mechanism to construct a constrained nonlinear dynamic model, combining fourth-order Runge-Kutta discretization and infinite norm constraints to ensure numerical computation stability; it introduces a Jacobi orthogonal decoupling mechanism to completely isolate the interference of high-level semantic classification gradients on the underlying radar physical energy dimension; it designs a frequency domain subspace energy aggregation sparse detection loss function to eliminate gradient attenuation problems under low signal-to-noise ratios, and drives the physical system's adaptive state transitions through an error feedback bifurcation control mechanism, realizing the nonlinear conversion and gain compensation of noise energy to weak target signal energy, ultimately achieving accurate detection of weak targets under low signal-to-noise ratios. Attached Figure Description

[0019] Figure 1 The overall architecture diagram of the physically embedded bidirectional nonlinear feedback network; Figure 2 This is a comparison chart of the detection probability curves of various detectors under different signal-to-noise ratios in Example 3; Figure 3 This is a comparison chart of classification accuracy curves under different signal-to-noise ratios in Example 3. Detailed Implementation

[0020] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0021] Example 1: like Figure 1 As shown, the physically embedded bidirectional nonlinear feedback network includes: The input layer is used to receive the discrete intermediate frequency (IF) signal sequence from the vehicle-mounted FMCW radar after chirping and low-pass filtering. The physical parameter spatial inference subnetwork is used to infer the control parameters of the micro-physical evolution layer from the intermediate frequency signal sequence of the radar, including potential field parameters and energy scale variables. The micro-physical evolution layer is used to convert the disordered energy of noise in the radar's intermediate frequency signal sequence into effective gain of weak target signals based on potential field parameters and a constrained nonlinear dynamics model, thereby outputting a time-domain enhancement sequence. The frequency domain transformation and decoupling module is used to convert the time-domain enhancement sequence into an enhancement amplitude spectrum and generate a normalized enhancement amplitude spectrum based on the energy scale variable through the Jacobian orthogonal decoupling mechanism. The macroscopic semantic feature recognition layer is used to classify targets based on the normalized enhancement amplitude spectrum, output the number of targets, and complete the detection of weak targets.

[0022] In practical implementation, under the FMCW mechanism, when electromagnetic waves propagate in a complex urban environment and are... When an anisotropic scatterer is intercepted, the intermediate frequency sequence of the echo at the receiving antenna port can be modeled as a multidimensional complex random process: in This is the intermediate frequency signal sequence for radar; For the first The amplitude term of each target, reflecting its radar cross section and characterizing its fluctuation characteristics in the microwave band, is modeled in this invention as a random process following a Swerling I / II distribution. For natural index; The imaginary unit; is the discrete sampling sequence number; K is the number of target scatterers, taking a positive integer value from 1 to 4, corresponding to multi-target detection scenarios; For the first The characteristic beat frequency of each target mapping, within an extremely short observation window The inner can be approximated as a constant by a first-order Taylor expansion. ,in For the chirping rate, At the speed of light, The distance to the k-th target. For radar carrier frequency, The radial velocity of the k-th target; The initial phase of the k-th target follows a uniform distribution. ; Environmental clutter is modeled as non-Gaussian correlated clutter that follows a K-distribution; The thermodynamic fluctuations caused by the random thermal motion of electrons in the receiver's low-noise amplifier follow a complex zero-mean Gaussian distribution. ; For fast sampling intervals, For fast sampling rate; For integration time; This represents the noise variance.

[0023] The enhancement effect of the stochastic resonance dynamics equations is highly dependent on the precise matching of the system potential parameters (a, b) with the characteristic time scales of the input signal. Given the objective condition of unknown target state in radar detection applications, this embodiment constructs a physical parameter space inference subnetwork. By performing real-time variational inference in the observation space, it seeks the optimal control parameters for the nonlinear dynamics.

[0024] Specifically, the physical parameter space inference subnetwork is constructed based on the information bottleneck principle, including sequentially connected one-dimensional convolutional layers, batch normalization (BN) layers, activation layers, and fully connected projection layers; the radar observation matrix (the radar's intermediate frequency signal sequence) is first reconstructed into a complex isomorphic tensor. Cascaded one-dimensional convolutional kernels form continuously differentiable mapping operators in the feature space. Based on the information bottleneck principle in information theory, the layer-by-layer processing of deep networks aims to find latent variables. The optimal compressed representation of this is equivalent to solving the extremum problem of the Lagrange functional: in Indicates mutual information, For radar intermediate frequency signal sequence observation tensor; Observation tensor for radar intermediate frequency signal sequence The latent variable compressed feature representation obtained after layer-by-layer feature compression of the physical parameter space inference subnetwork; For target labels; This represents the information bottleneck weighting coefficient. The Lagrange loss function is the information bottleneck loss function for the physical parameter space inference subnetwork constructed based on the information bottleneck principle.

[0025] By integrating the cross-correlation within the local receptive field, the convolution operator progressively filters out redundant entropy strongly correlated with Gaussian white noise (minimizing...). Simultaneously extracting local micro-oscillation features in the frequency domain (maximizing) Subsequently, the feature tensor undergoes batch normalization to eliminate internal covariate bias: in, The input features for the batch normalization layer; This is the batch average. This represents the batch variance. and These are learnable scaling and offset parameters; To prevent division by zero of extremely small constants.

[0026] Geometrically, this operation is equivalent to translating the high-dimensional feature space to the origin and performing isotropic scaling, which prepares the space for subsequent parallel projection onto the physical control parameter domain. and energy scale variables It provides a well-defined metric space. The fully connected projection layer simultaneously outputs physical quantities: potential field parameters. and energy scale variables .

[0027] In some embodiments, the microphysical evolution layer employs a constrained stochastic dynamics enhancement mechanism. Based on the bistable stochastic resonance principle driven by Itō's stochastic differential equations, it transforms the broadband energy fluctuations of background noise and clutter into a pump source that drives weak periodic signals to achieve cross-well transitions, thereby achieving nonlinear enhancement of weak target signals at the physical level. Specifically, the system's microstate variables... The continuous-time evolution is described by an overdamped Langevin stochastic differential equation, which, within the framework of Itō calculus, has the following differential form: in For state variables The gradient operator is used to solve for the spatial rate of change of the potential energy function; It is a fourth-order bistable potential energy function used to construct nonlinear potential field topology (bistable manifold with topological asymmetry). Indicates time; These are the potential field parameters; The radar is input with a periodic drive signal for weak targets, which is the radar's intermediate frequency signal; It is the thermodynamic wave intensity coefficient; For the standard Wiener process, satisfying , It is a Dirac delta function, characterizing the thermal noise of the radar system, and satisfies the zero-mean Gaussian random distribution characteristics.

[0028] It should be noted that state variables The time-domain enhanced sequence of the final output of the microphysical evolution layer has a direct one-to-one correspondence with the "continuous-time dynamic solution" and the "discretized stable output". First, It is a continuous-time solution to a constrained nonlinear dynamic model (overdamped Langevin stochastic differential equation), describing a fourth-order bistable system under a periodic drive signal from a weak target input to the radar. and system thermal noise The instantaneous evolution state under the combined effect. This evolution process itself is a physical process of nonlinear conversion of noise energy into weak target signal energy: when the potential field parameters When matching the characteristic time scale of the input signal, It will periodically jump between the two potential wells at the frequency of the target signal, realizing the random resonant amplification of the weak signal.

[0029] The expression for the fourth-order bistable potential energy function is: ; To form a symmetrical topological structure with a single barrier and two potential wells, where the peak position of the barrier is... Stable position of potential well The barrier height is This enables the conversion of noise energy into a transpotential well for weak target signals.

[0030] To embed continuous-time stochastic differential equations into the forward computation tensor of deep learning, this embodiment employs a fourth-order Runge-Kutta (RK4) method with backward difference compensation for high-precision discretization to minimize local truncation error. ,in This is the integration step size. However, when the RK4 evolution matrix undergoes time-domain recursive evolution, the spectral radius of its Jacobian matrix under strong clutter perturbation... It is easy to exceed the unit circle, leading to numerical nonlinear divergence or gradient explosion. To restore the stability of the discrete-time state space, this embodiment introduces a boundary-constrained projection operator. Explicit application Norm constraints: in For the fourth-order Runge-Kutta method on state variables After discretization, at the 1st The state variables at each time step; For the fourth-order Runge-Kutta method on state variables After discretization, at the 1st The state variables at each time step; This is the integration step size; , , and These are the four slope estimates for the fourth-order Runge-Kutta method; Indicates constraints; This is the upper limit of the state magnitude, used to constrain the upper bound of the gradient norm and avoid gradient explosion and numerical divergence. express Norm.

[0031] This operator fundamentally alters the topological space properties of the system, forcibly restricting the upper bound of the global gradient norm of the nonlinear vector field to a certain value. According to the discrete-time Lyapunov exponent theory, as long as the integration step size satisfies the RK4 real-axis stability boundary, the spectral norm of state transitions in the infinite time domain will be firmly locked within the bounded space. This fundamentally alleviates the risk of gradient explosion during time backpropagation, ensuring that the macroscopic evolution of stochastic dynamics always focuses on the dual-state trap region and maintains the physical topology required for resonance.

[0032] It should be noted that the above operations are to embed continuous-time physical dynamics into the discrete tensor computation framework of deep learning, using the fourth-order Runge-Kutta (RK4) method. High-precision discretization is performed to obtain the discrete time step. Corresponding state variables To address the numerical divergence and gradient explosion problems under strong clutter perturbations, a boundary-constrained projection operator is introduced. right Apply Norm constraints strictly limit the state amplitude to a certain value. Within this range, the numerical stability of the dynamic evolution is guaranteed. The discrete state sequence after processing with the boundary-constrained projection operator is... It is the time-domain enhanced sequence that is ultimately output by the microphysical evolution layer. The discrete sampling number of the radar signal Discrete time steps of the dynamic system There is a perfect one-to-one correspondence. In other words, the time-domain enhancement sequence is essentially the stable discrete state evolution trajectory of a stochastic resonant dynamic system driven by a radar intermediate frequency signal.

[0033] In some embodiments, the system barrier crossing rate is calculated based on Kramers escape rate theory. Adaptive adjustment via network The parameters enable the system evolution timescale to match the period of the weak target signal, thereby achieving efficient conversion of noise energy into the weak target signal.

[0034] In this embodiment, the frequency domain conversion and decoupling module first processes the time-domain enhancement sequence output by the microphysical evolution layer. Perform Fast Fourier Transform (FFT) and amplitude extraction to obtain the enhanced amplitude spectrum. .

[0035] In the joint optimization architecture, there is a potential coupling risk that the backpropagation gradient of the high-level semantic classification error may interfere with the parameter dimensions of the underlying physical system. To ensure that the underlying dynamic evolution only enhances the signal saliency without destroying the inherent amplitude physical magnitude of the radar echo, this embodiment constructs a scale-invariant quotient space projection operator. This refers to the Jacobi orthogonal decoupling mechanism.

[0036] Specifically, the Jacobi orthogonal decoupling mechanism introduces a gradient blocking operator. (Stopping gradient: forward computation preserves, backpropagation blocks), which will enhance the amplitude spectrum. Mapped to by Norm-normalized quotient space: in To normalize the enhanced amplitude spectrum; To enhance the amplitude spectrum; This is the energy scale variable, i.e., the maximum value of the enhanced amplitude spectrum; To prevent division by zero of extremely small constants; For frequency domain coordinate variables.

[0037] When introduced After constraints, partial derivatives Found. At this point, the output... Relative to the original variable The Jacobian matrix strictly degenerates into a purely diagonal scaling matrix: in, The identity matrix is ​​used to force the classification error gradient to be projected onto the null space, which is strictly orthogonal to the energy scale space, thus ensuring that the physical energy scale of the radar signal is not disturbed by the high-level semantic classification gradient.

[0038] In the field of functional analysis, this constraint mechanism is equivalent to forcing the gradient update vector field to be projected onto a null space that is strictly orthogonal to the energy scale space. Therefore, the classification error gradient can only propagate backward along the topological path that alters the relative shape of the signal, and is mathematically restricted from interfering with the dimensional basis of the global physical energy across space. This Jacobi orthogonal decoupling theorem mathematically establishes the independence and synergy between low-level physical enhancement and high-level semantic recognition.

[0039] In some embodiments, the macroscopic semantic feature recognition layer receives the normalized enhanced amplitude spectrum output by the Jacobi orthogonal decoupling module. The system classifies targets using a fully connected layer and a Softmax classifier, and outputs the number of targets. probability distribution: in, and These are the weights and bias parameters for the fully connected layer. The final target number of... Choose the category with the highest probability.

[0040] In some embodiments, the physically embedded bidirectional nonlinear feedback network further includes a joint functional constraint module and an error feedback and bifurcation control module.

[0041] The joint functional constraint module is used to compute the frequency domain subspace energy-gathering sparse detection loss of physically embedded bidirectional nonlinear feedback networks. Cross-entropy loss for target quantity classification Thus, the total loss is obtained. ,in The weighting coefficients for the cross-entropy loss of the target number of categories.

[0042] Traditional mean squared error (MSE) loss suffers from severe gradient vanishing problems at high-resolution spectra. When performing high-resolution FFT (i.e., ... The number of target frequency points When the backpropagation gradient expectation of the weak target region remains unchanged, it will strictly converge to 0 (with the remainder of 0). (rate decay). This means that the detection error of weak targets is smoothed out by the massive number of samples in irrelevant frequency bands during backpropagation, causing the network to get stuck in a local minimum and degenerate into a trivial all-zero output solution. In order to eliminate this gradient decay phenomenon, the expression for the frequency domain subspace energy clustering sparse detection loss proposed in this invention is as follows: in This represents the frequency domain subspace energy-intensive sparse detection loss of a physically embedded bidirectional nonlinear feedback network. , and These are all hyperparameters, used to adjust the weights of target fidelity, background sparsity, and contrast constraint, respectively; For frequency domain coordinate variables; For the target frequency set; This represents the amplitude spectrum of a real radar. The enhanced amplitude spectrum predicted by the frequency domain transformation and decoupling module; This is the set of background noise frequency points; This is the L2 norm operator, used for target region fidelity constraints; This is a norm operator used for sparse noise reduction in the background region; This is a frequency domain contrast loss used to amplify the energy difference between the target and the background.

[0043] The functional removes the sequence length from the denominator. This makes the weak peak value Backpropagation gradient magnitude Dimensionality invariance was achieved. Simultaneously, induced higher-order sparsity was introduced into non-target regions. Norm. This spatially heterogeneous regularization design ensures that the gradient backpropagation intensity in weak target regions is not suppressed by the increase in observation sequence length, providing a clear optimization guide for the underlying dynamical system. Furthermore, The first term in the expression is the L2 norm constraint of the target subspace, which ensures the accuracy of the amplitude of weak target frequency points and eliminates the gradient decay caused by the sequence length; the second term is the L1 norm sparsity constraint of the background subspace, which suppresses the global clutter noise floor; the third term is the contrast loss, which amplifies the relative energy difference between the target and the background and avoids weak target suppression caused by global smoothing.

[0044] Target Quantity Classification Cross Entropy Loss The expression is: in, The maximum target quantity; One-hot encoding of the actual label; The first output of the network Class probability.

[0045] The error feedback and bifurcation control module is used to backpropagate the gradient generated by the total loss to the physical parameter space inference subnetwork. By perturbing the maximum Lyapunov exponent of the microphysical evolution layer, it triggers local bifurcation, breaks the local non-physical steady state, and thus realizes the update of the bidirectional nonlinear feedback network.

[0046] Specifically, the core of this physical embedding bidirectional nonlinear feedback network's evolution lies in using high-level semantic feedback errors to guide state transitions in the underlying physical system. At extremely low signal-to-noise ratio boundaries, the underlying fidelity functional... In the early stages of iteration, noise may dominate, suppressing the signal and causing the system to converge to an undesirable local steady state. At this point, the top-level semantic recognition layer fails to extract effective target features, and its cross-entropy functional... This will produce a significant classification error gradient.

[0047] The potential field parameters a and b of the microphysical evolution layer are directly perturbed by the backpropagation of the total loss gradient. The error feedback and bifurcation control module will jointly handle the functional total loss. The resulting gradient is backpropagated unbiased to the physical parameter space inference subnetwork, directly updating the Langevin equation control coefficients output by that subnetwork. The coordinates in the parameter phase space are the only direct disturbance object in the entire bifurcation control mechanism; the potential field parameters are... The displacement will affect the following core physical quantities in sequence through a chain reaction: 1. Fourth-order bistable potential energy function topology: changing the stable position of the potential well and barrier height Reshaping the energy landscape of nonlinear systems; 2. The state Jacobian matrix at each step The core element of the Jacobian matrix is Its spectral characteristics are entirely determined by the potential field parameters. and instantaneous state Decide; 3. Maximum Lyapunov index Changes in potential field parameters a and b will lead to changes in the spectral norm of the cumulative product of the Jacobian matrices, which in turn directly result in... A sudden change occurs; this is the core criterion for system state transitions. When... When the value abruptly changes from negative to positive, the system undergoes a transcritical or folding bifurcation, transitioning from a steady-state absorption state to a cross-well evolution state. At this point, by adaptively adjusting the potential field parameters a and b, the Kramers escape rate of the system can be controlled. By precisely matching the characteristic period of the weak target signal, the disordered broadband energy of background noise and clutter is continuously converted into pump energy that drives the periodic transition of the weak target signal across the potential well, ultimately achieving physical-level nonlinear resonant amplification of the weak signal.

[0048] The largest Lyapunov exponent (MLE) is among them. The expression is: in, It is the natural logarithm; This is the limit operator; Iteration time; For the first Step state variable Jacobian matrix; This is the cumulative multiplication operator.

[0049] When parameter When the system is pushed out of its original attraction basin by a higher-order gradient, the Jacobian spectral characteristics at the target frequency point undergo a sudden change. During the transient process, the system abruptly changes from negative to positive values ​​(negative values ​​represent steady-state absorption and feature suppression, while positive values ​​represent cross-well evolution and feature amplification). This disrupts the local steady state, triggering nonlinear evolution across potential wells, continuously converting noise energy into weak target signal gain, and achieving adaptive awakening of submerged weak targets. This process triggers strict local bifurcation, such as transcritical bifurcation or folding bifurcation. This bifurcation control mechanism based on error feedback destabilizes the local nonphysical steady state dominated by strong clutter, transitioning the system to a new state space capable of coherent resonance with weak beat signals. Ultimately, the target features deeply embedded in the broadband noise substrate obtain physical-level gain compensation through nonlinear resonance effects, establishing the core mathematical and physical foundation for this physical embedding of a bidirectional nonlinear feedback network to transcend the linear detection limit.

[0050] In some embodiments, the training process of this physically embedded bidirectional nonlinear feedback network includes the following steps: A1. Construct a synthetic multi-target radar dataset containing radar intermediate frequency signal sequences with different signal-to-noise ratios (-25dB to 0dB), different numbers of targets (1 to 4), and different target spacings; A2. Initialize network parameters, including the initial potential field parameters of the micro-physical evolution layer, the convolution kernels and fully connected layer weights of the physical parameter space inference sub-network, and the classifier weights of the macro-semantic recognition layer; A3. Input the training samples into the network and perform forward propagation to obtain the temporal enhancement sequence, enhancement amplitude spectrum, normalized enhancement amplitude spectrum, and target quantity prediction. A4. Calculate the total loss ; A5. The gradient generated by the total loss is backpropagated through the error feedback and bifurcation control module to update the network parameters; A6. Repeat steps A3-A5 until the network converges.

[0051] Example 2: This embodiment is a further extension based on Embodiment 1. This embodiment discloses a weak target detection method, which includes the following steps: B1. Collect the intermediate frequency signal sequence of the radar and infer the control parameters of the microscopic physical evolution layer from the intermediate frequency signal sequence of the radar, including potential field parameters and energy scale variables. B2 converts disordered energy into an effective gain for weak target signals, thereby outputting a time-domain enhanced sequence. B3. Convert the time-domain enhancement sequence into an enhancement amplitude spectrum, and generate a normalized enhancement amplitude spectrum based on the energy scale variable through the Jacobi orthogonal decoupling mechanism; B4. Classify the normalized enhancement amplitude spectrum into targets, output the number of targets, and complete the weak target detection.

[0052] Example 3: This embodiment is a further extension based on Embodiment 1. This embodiment was verified using a low signal-to-noise ratio (SNR) simulated radar dataset ranging from -25dB to 0dB. Figure 2 and Figure 3 As shown, compared with traditional FFT peak detectors, PSO-TSR detectors, and pure data-driven one-dimensional convolutional neural networks (Pure-FreqNet), this physically embedded bidirectional nonlinear feedback network improves detection sensitivity by 2-3dB, achieves 100% detection probability for multiple targets under a signal-to-noise ratio of -12dB, and improves target classification accuracy by more than 12% compared with pure data-driven models under a signal-to-noise ratio of -15dB. It effectively solves the technical problems of weak target omission, physical feature distortion, and background clutter residue under low signal-to-noise ratio, and can meet the real-time high-precision perception requirements of autonomous driving radar.

Claims

1. A weak target detection method based on a physically embedded bidirectional nonlinear feedback network, characterized in that, Includes the following steps: The intermediate frequency (IF) signal sequence of the radar is collected, and the control parameters of the microscopic physical evolution layer, including potential field parameters and energy scale variables, are inferred from the IF signal sequence of the radar. Based on the potential field parameters, the disordered energy of noise in the radar's intermediate frequency signal sequence is converted into the effective gain of the weak target signal through a restricted nonlinear dynamic model, thereby outputting a time-domain enhancement sequence. The time-domain enhancement sequence is converted into an enhancement amplitude spectrum, and a normalized enhancement amplitude spectrum is generated based on the energy scale variable through the Jacobi orthogonal decoupling mechanism. The normalized enhancement amplitude spectrum is used to classify targets, output the number of targets, and complete the weak target detection. The physically embedded bidirectional nonlinear feedback network includes: The physical parameter spatial inference subnetwork is used to infer the control parameters of the micro-physical evolution layer from the intermediate frequency signal sequence of the radar, including potential field parameters and energy scale variables. The micro-physical evolution layer is used to convert the disordered energy of noise in the radar's intermediate frequency signal sequence into effective gain of weak target signals based on potential field parameters and a constrained nonlinear dynamics model, thereby outputting a time-domain enhancement sequence. The frequency domain transformation and decoupling module is used to convert the time-domain enhancement sequence into an enhancement amplitude spectrum and generate a normalized enhancement amplitude spectrum based on the energy scale variable through the Jacobian orthogonal decoupling mechanism. The macroscopic semantic feature recognition layer is used to classify targets based on the normalized enhancement amplitude spectrum, output the number of targets, and complete the detection of weak targets.

2. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 1, characterized in that, The physical parameter space inference subnetwork is constructed based on the information bottleneck principle, consisting of sequentially connected one-dimensional convolutional layers, batch normalization layers, activation layers, and fully connected projection layers. The optimization objective of the physical parameter space inference subnetwork is to minimize the Lagrange functional, whose expression is: in Indicates mutual information, For radar intermediate frequency signal sequence observation tensor; Observation tensor for radar intermediate frequency signal sequence The latent variable compressed feature representation obtained after layer-by-layer feature compression of the physical parameter space inference subnetwork; For target labels; This represents the information bottleneck weighting coefficient. The Lagrange loss function is the information bottleneck loss function for the physical parameter space inference subnetwork constructed based on the information bottleneck principle.

3. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 1, characterized in that, The constrained nonlinear dynamics model employs the nonequilibrium statistical physics stochastic resonance mechanism, and its expression is as follows: in For state variables, that is, a single value in a time-domain augmented sequence; For state variables The gradient operator is used to solve for the spatial rate of change of the potential energy function; This is a fourth-order bistable potential energy function, used to construct the nonlinear potential field topology; Indicates time; These are the potential field parameters; The radar is input with a periodic drive signal for weak targets, which is the radar's intermediate frequency signal; It is the thermodynamic wave intensity coefficient; It is a standard Wiener process that characterizes the thermal noise of the radar system and satisfies the zero-mean Gaussian random distribution characteristics.

4. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 3, characterized in that, The expression for the fourth-order bistable potential energy function is: ； To form a symmetrical topological structure with a single barrier and two potential wells, where the peak position of the barrier is... Stable position of potential well The barrier height is This enables the conversion of noise energy into a transpotential well for weak target signals.

5. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 3, characterized in that, The microscopic physical evolution layer uses the fourth-order Runge-Kutta method to discretize the constrained nonlinear dynamics model and introduces a constrained projection operator. Apply Norm constraints, their discretization evolution formula is: in For the fourth-order Runge-Kutta method on state variables After discretization, at the 1st The state variables at each time step; For the fourth-order Runge-Kutta method on state variables After discretization, at the 1st The state variables at each time step; This is the integration step size; , , and These are the four slope estimates for the fourth-order Runge-Kutta method; Indicates constraints; This is the upper limit of the state magnitude, used to constrain the upper bound of the gradient norm and avoid gradient explosion and numerical divergence. express Norm.

6. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 1, characterized in that, Jacobi orthogonal decoupling mechanism introduces gradient blocking operator The expression for generating the normalized enhanced amplitude spectrum is as follows: in To normalize the enhanced amplitude spectrum; To enhance the amplitude spectrum; For energy scale variables; To prevent division by zero of extremely small constants; For frequency domain coordinate variables.

7. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 1, characterized in that, Also includes: The joint functional constraint module is used to calculate the frequency domain subspace energy aggregation sparse detection loss and the target number classification cross-entropy loss of the physically embedded bidirectional nonlinear feedback network, and then obtain the total loss. The error feedback and bifurcation control module is used to backpropagate the gradient generated by the total loss to the physical parameter space inference subnetwork. By perturbing the maximum Lyapunov exponent of the microphysical evolution layer, it triggers local bifurcation, breaks the local non-physical steady state, and thus realizes the update of the bidirectional nonlinear feedback network.

8. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 7, characterized in that, The expression for the frequency domain subspace energy-gathering sparse detection loss of a physically embedded bidirectional nonlinear feedback network is as follows: in This represents the frequency domain subspace energy-intensive sparse detection loss of a physically embedded bidirectional nonlinear feedback network. , and These are all hyperparameters, used to adjust the weights of target fidelity, background sparsity, and contrast constraint, respectively; For frequency domain coordinate variables; For the target frequency set; This represents the amplitude spectrum of a real radar. The enhanced amplitude spectrum predicted by the frequency domain transformation and decoupling module; This is the set of background noise frequency points; This is the L2 norm operator, used for target region fidelity constraints; This is a norm operator used for sparse noise reduction in the background region; This is a frequency domain contrast loss used to amplify the energy difference between the target and the background.

9. The weak target detection method based on a physically embedded bidirectional nonlinear feedback network according to claim 7, characterized in that, The expression for the maximum Lyapunov exponent of the microscopic physical evolution layer is: in For the maximum Lyapunov exponent of the microscopic physical evolution layer, when When the value changes abruptly from negative to positive, it indicates that the microscopic physical evolution layer has undergone a transcritical or folding bifurcation, and has changed from a steady-state absorption state to a cross-well evolution state. The updated potential field parameters make the Kramers escape rate of the physically embedded bidirectional nonlinear feedback network match the characteristic period of the weak target signal, thereby continuously converting the disordered broadband energy of background noise and clutter into pump energy that drives the periodic transition of the weak target signal across the potential well, and thus realizing the nonlinear amplification of the weak target signal. It is the natural logarithm; This is the limit operator; Iteration time; For the first Step state variable Jacobian matrix; This is the cumulative multiplication operator.

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