A quantum navigation counter-defense and data purification method and system based on inverse diffusion of stochastic differential equation

Abstract

This invention discloses a quantum navigation adversarial defense and data cleansing method and system based on backward diffusion of stochastic differential equations, relating to the fields of high-confidence navigation and adversarial machine learning security technology. It includes: constructing a multidimensional state observation tensor; using forward stochastic differential equations for continuous-time modeling to simulate the diffusion distribution characteristics of noise and adversarial perturbations; constructing a scoring function network with physical energy constraints and performing physical consistency regularization training on the scoring network; using a backward-time SDE solver to perform backward sampling and cleansing of real-time observation data; calculating the reconstruction variance and physical residual during the backward diffusion process; when both are below a preset security threshold, outputting cleaned magnetic field data for navigation calculation; otherwise, triggering a defense circuit breaker mechanism. This invention achieves "zero-sample" defense against unknown attack modes.

Description

Technical Field

[0001] This invention relates to the field of high-confidence navigation and adversarial machine learning security technology, and more specifically to a quantum navigation adversarial defense and data cleansing method and system based on stochastic differential equation reverse diffusion. Background Technology

[0002] With breakthroughs in quantum sensing technology, quantum magnetic navigation systems based on cold atom interferometry or diamond NV centers have become a key technology to replace satellite navigation (GNSS) due to their advantages such as being passive, autonomous, and having high anti-interference potential. However, in the increasingly complex electromagnetic warfare (EW) environment, quantum sensors face a severe threat of "smart deception".

[0003] Traditional defense methods, such as Kalman filtering (KF) or particle filtering (PF), typically assume that noise follows a Gaussian distribution and cannot distinguish between natural noise and carefully designed "adversarial examples." Attackers can induce navigation systems to drift slowly by emitting statistically consistent but physically spurious magnetic field signals. This "boiling frog" deception attack is highly penetrable by existing filters.

[0004] In recent years, Generative Adversarial Networks (GANs) have been used for data augmentation and denoising. However, GANs have inherent defects such as training instability and mode collapse. Furthermore, it is difficult to embed the complex Maxwell's Equations as hard constraints into the generation process, which often results in reconstructed data that, although "looks real," is physically illegal and cannot meet the stringent requirements of high-precision navigation.

[0005] Therefore, this paper proposes a quantum navigation adversarial defense and data cleansing method and system based on the reverse diffusion of stochastic differential equations to address the problem of how to provide a new technological paradigm that can provide "zero-shot" defense against unknown and complex adversarial attacks while ensuring that the reconstructed data strictly conforms to the laws of physics and achieves a high level of intrinsic security. This is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, this invention provides a quantum navigation adversarial defense and data cleansing method and system based on stochastic differential equation reverse diffusion. This invention aims to overcome the dual challenges of "difficulty in identifying adversarial examples" and "difficulty in integrating physical constraints" faced by existing navigation defense technologies, and creatively proposes a novel technical paradigm of "Physics-Guided Reverse Diffusion." Through a paradigm shift at the stochastic differential equation modeling level, the adversarial defense process is transformed into a mathematical "reverse-time data cleansing process," thereby constructing an active defense system that combines mathematical completeness and physical interpretability.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A quantum navigation adversarial defense and data sanitization method based on stochastic differential equation reverse diffusion includes the following steps: S1. Collect the magnetic field observation sequence of the quantum magnetometer and the motion state sequence of the inertial measurement unit, and construct a multidimensional state observation tensor; S2. Treat the multidimensional state observation tensor as the initial state of a contaminated stochastic process, and use forward stochastic differential equations for continuous-time modeling to simulate the diffusion distribution characteristics of noise and adversarial disturbances. S3. Construct a scoring function network with physical energy constraints, and use the electromagnetic field divergence and curl characteristics of Maxwell's equations to construct a physical gradient field, and perform physical consistency regularization training on the scoring network. S4. Using the inverse-time SDE solver, the output of the scoring function network is used as the guiding gradient of the drift term to perform inverse sampling and purification of the real-time observation data, and the disturbed observation trajectory is restored to the geomagnetic manifold space that conforms to the physical laws. S5. Calculate the reconstruction variance and physical residual during the reverse diffusion process. When both are below the preset safety threshold, output the purified magnetic field data for navigation calculation; otherwise, trigger the defense circuit breaker mechanism.

[0008] Optionally, the forward stochastic differential equation in S2 is modeled using an Ornstein-Uhlenbeck process, with the mathematical expression as follows:

[0009] in, For navigation observation state vector, The drift coefficient is used to describe the natural evolution of the signal; is the diffusion coefficient, used to describe the injection intensity to counteract noise; This is standard Brownian motion.

[0010] Optionally, the scoring function network for physical energy constraints in S3 is based on learning the logarithmic gradient of the data distribution. loss function Includes physical priors:

[0011] in, For the output of the scoring network, This is a physical penalty term based on Maxwell's equations. For physical constraint weights, As expected, For noisy samples, To gradient operator, Let log be the probability density function. This is the original data.

[0012] Optional, physical penalty item Specifically defined as:

[0013] in, To reconstruct the magnetic field, For Hamiltonian operators, To reconstruct the electric field, magnetic field The partial derivatives, For time The partial differential components.

[0014] Optionally, the reverse-time SDE solver in S4 adopts the Euler-Maruyama discretization method, and the iterative formula is as follows:

[0015] in, The noise is standard Gaussian noise. Adversarial perturbation components in the observed data are removed iteratively. This is the state after iteration. This is the current state. The drift coefficient, The square of the diffusion coefficient, For score function estimation, For time step, Where is the diffusion coefficient. It is standard Gaussian noise.

[0016] Optionally, the specific details of the circuit breaker defense mechanism in S5 are as follows: Perform multiple parallel inverse SDE samplings on the same observation and calculate the variance between the different sampling results. ; like If the system determines that there is a high-level deception attack in the current environment that is beyond the understanding of the physical model, it will automatically cut off the magnetic assist, switch to pure inertial navigation mode and issue an alarm.

[0017] A quantum navigation adversarial defense and data cleansing system based on stochastic differential equation reverse diffusion, executing any of the aforementioned quantum navigation adversarial defense and data cleansing methods based on stochastic differential equation reverse diffusion, includes a heterogeneous sensing module, an SDE diffusion modeling module, a physics scoring calculation module, a reverse cleansing engine module, and a defense decision module connected in sequence; wherein, Heterogeneous sensing module: used to simultaneously acquire raw data from the quantum magnetometer and inertial navigation components; SDE diffusion modeling module: used to build a forward diffusion model that describes the distribution of adversarial attacks and environmental noise; Physics score calculation module: Embedded Maxwell's equation operator, used to calculate the physical gradient of data in manifold space and output guided score; Reverse Cleanup Engine Module: Used to perform reverse SDE solving, enabling proactive stripping of adversarial examples and data reconstruction; Defense Decision Module: Used to determine whether a high-level deception attack exists based on the uncertainty indicators of the purification process, and to control the switching of navigation modes.

[0018] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a quantum navigation countermeasure defense and data cleansing method and system based on the reverse diffusion of stochastic differential equations, the beneficial effects of which are: (1) Achieved "zero-sample" defense against unknown attack patterns (general robustness): Unlike GANs, which require a large number of attack samples for adversarial training, this invention is based on the diffusion mechanism of SDE, which only needs to learn the distribution of normal physical fields; any adversarial perturbation that deviates from the physical manifold, no matter how covert its pattern, will be regarded as "noise" in a high-energy state and automatically stripped away through the reverse SDE process, which makes the system naturally immune to unknown future attacks. (2) A physical-level data consistency barrier (physical security) has been constructed: This invention transforms Maxwell's equations into a guided gradient of a scoring function. During the data cleansing process, physical laws are no longer post-hoc verification indicators, but rather the driving force for data generation. This ensures that the output magnetic field data strictly satisfies electromagnetic field theory in terms of divergence and curl, fundamentally eliminating false signals that violate physical rules. (3) Provides quantifiable defense confidence (system reliability): The backward sampling process of the diffusion model has inherent probabilistic properties. By calculating the variance (uncertainty) of multiple samplings, the system can assess the "unreliability" of the current environment in real time. When encountering a super-strong saturation attack, the system can automatically circuit break and switch to pure inertial mode based on mathematical indicators, avoiding the catastrophic consequences caused by the "blind confidence" of traditional algorithms. Attached Figure Description

[0019] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 The flowchart of the Stochastic Differential Equation (SDE) adversarial defense architecture provided by this invention; Figure 2 This is a schematic diagram of the reverse diffusion trajectory guided by the physical gradient field in this invention; Figure 3 This is a block diagram of the SDE purification and navigation fusion system module provided by the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See Figure 1 As shown, this invention discloses a quantum navigation adversarial defense and data sanitization method based on stochastic differential equation reverse diffusion, comprising the following steps: S1. Collect the magnetic field observation sequence of the quantum magnetometer and the motion state sequence of the inertial measurement unit, and construct a multidimensional state observation tensor; S2. Treat the multidimensional state observation tensor as the initial state of a contaminated stochastic process, and use forward stochastic differential equations for continuous-time modeling to simulate the diffusion distribution characteristics of noise and adversarial disturbances. S3. Construct a scoring function network with physical energy constraints, and use the electromagnetic field divergence and curl characteristics of Maxwell's equations to construct a physical gradient field, and perform physical consistency regularization training on the scoring network. S4. Using the inverse-time SDE solver, the output of the scoring function network is used as the guiding gradient of the drift term to perform inverse sampling and purification of the real-time observation data, and the disturbed observation trajectory is restored to the geomagnetic manifold space that conforms to the physical laws. S5. Calculate the reconstruction variance and physical residual during the reverse diffusion process. When both are below the preset safety threshold, output the purified magnetic field data for navigation calculation; otherwise, trigger the defense circuit breaker mechanism.

[0023] Furthermore, the forward stochastic differential equation in S2 is modeled using an Ornstein-Uhlenbeck process, and its mathematical expression is:

[0024] in, For navigation observation state vector, The drift coefficient is used to describe the natural evolution of the signal; is the diffusion coefficient, used to describe the injection intensity to counteract noise; This is standard Brownian motion.

[0025] Specifically, the forward stochastic differential equation is modeled using the Ornstein-Uhlenbeck (OU) process, which gradually smooths the distribution of arbitrarily complex adversarial perturbations into a standard Gaussian distribution, thereby mathematically erasing the attack characteristics.

[0026] Furthermore, the core of the scoring function network for physical energy constraints in S3 lies in learning the logarithmic gradient of the data distribution. loss function Includes physical priors:

[0027] in, For the output of the scoring network, This is a physical penalty term based on Maxwell's equations. For physical constraint weights, As expected, For noisy samples, To The gradient operator; For time step The log probability density function of the time data distribution; This is the original data.

[0028] Specifically, the Score Network in S3 does not directly generate data, but instead learns the logarithmic gradient of the data distribution, i.e., the "score". This gradient indicates the steepest descent direction from the "noise / interference domain" back to the "real physical manifold".

[0029] Furthermore, physical penalty items Specifically defined as:

[0030] in, To reconstruct the magnetic field, For Hamiltonian operators, To reconstruct the electric field, magnetic field The partial derivatives, For time The partial differential components.

[0031] Furthermore, the reverse-time SDE solver in S4 employs the Euler-Maruyama discretization method, with the following iterative formula:

[0032] in, The noise is standard Gaussian noise. Adversarial perturbation components in the observed data are removed iteratively. This is the state after iteration. This is the current state. The drift coefficient, The square of the diffusion coefficient, For score function estimation, For time step, Where is the diffusion coefficient. It is standard Gaussian noise.

[0033] Furthermore, the specific details of the circuit breaker defense mechanism in S5 are as follows: Perform multiple parallel inverse SDE samplings on the same observation and calculate the variance between the different sampling results. ; like If the system determines that there is a high-level deception attack in the current environment that is beyond the understanding of the physical model, it will automatically cut off the magnetic assist, switch to pure inertial navigation mode and issue an alarm.

[0034] See Figure 2 The diagram shown illustrates the reverse diffusion trajectory guided by the physical gradient field in this invention. (See also...) Figure 3 The diagram shown is a block diagram of the SDE purification and navigation fusion system provided by the present invention.

[0035] This invention also discloses a quantum navigation adversarial defense and data cleansing system based on stochastic differential equation reverse diffusion, used for the specific implementation of the method, including a heterogeneous sensing module, an SDE diffusion modeling module, a physics scoring calculation module, a reverse cleansing engine module, and a defense decision module connected in sequence; wherein, Heterogeneous sensing module: used to simultaneously acquire raw data from the quantum magnetometer and inertial navigation components; SDE diffusion modeling module: used to build a forward diffusion model that describes the distribution of adversarial attacks and environmental noise; Physics score calculation module: Embedded Maxwell's equation operator, used to calculate the physical gradient of data in manifold space and output guided score; Reverse Cleanup Engine Module: Used to perform reverse SDE solving, enabling proactive stripping of adversarial examples and data reconstruction; Defense Decision Module: Used to determine whether a high-level deception attack exists based on the uncertainty indicators of the purification process, and to control the switching of navigation modes.

[0036] Embodiment 1 of this invention discloses a quantum navigation adversarial defense and data sanitization method based on the reverse diffusion of stochastic differential equations, such as... Figure 1 As shown, the core idea is to use the theory of continuous-time stochastic processes to combat malicious attacks in discrete time.

[0037] S1: Construction of the Multidimensional State Observation Tensor

[0038] The system first acquires scalar / vector magnetic field data using a quantum magnetometer in an atomic gas cell. Angular velocity is obtained through a MEMS inertial measurement unit. And comparison Align these heterogeneous data along the time dimension to construct the observation tensor. At this time It may include environmental noise. Deceptive signals injected by the enemy ,Right now .

[0039] S2: Forward SDE diffusion modeling (noising process)

[0040] Unlike traditional noise reduction methods that attempt to directly remove noise, this invention takes the opposite approach. Utilizing forward SDE, in continuous time... Gaussian noise is gradually injected into the observed data until the data becomes a completely disordered distribution of Gaussian white noise.

[0041] The mathematical expression is:

[0042] The physical significance of this step lies in: regardless of the original attack signal No matter how sophisticated the structure is (e.g., a decoy waveform for a specific filter), its structural features will be "dissolved" in Brownian motion over time, eventually losing their aggressiveness.

[0043] S3: Construction of the Physics-Oriented Scoring Function (Core Steps)

[0044] In order to "reverse" the extraction of the true physical signal from Gaussian white noise, a scoring network needs to be trained. .

[0045] The innovation of this invention lies in the introduction of explicit physical energy constraints during network training. The physical loss function is defined as follows:

[0046] The first term constrains the magnetic field to be non-dispersion, and the second term constrains the magnetic induction equation.

[0047] The final scoring function not only learns the statistical distribution of the geomagnetic map, but also "memorizes" the shape of Maxwell's equations. It acts like a "gravitational wave" of a physical field, pushing all points that violate the laws of physics towards the conforming manifold surface in the state space.

[0048] S4: Reverse SDE purification solution (defense and reconstruction)

[0049] This is the practical phase of counter-defense. The system from Starting at time (pure noise state), using inverse SDE to... Evolution in time:

[0050] in, It is the direct gradient guiding term of the physical energy function. These are guiding weights used to control the strength of the influence of the physical energy function gradient on the generation process. This refers to the Standard Wiener Process or Brownian Motion.

[0051] In this process, the initial observation data In practice, this is injected as conditional information. The inverse solver continuously asks the scoring network: "Does this data resemble a real magnetic field? Does it conform to Maxwell's equations?" If it does not, the drift term will forcibly correct the trajectory.

[0052] go through Step-by-step iteration (e.g., using Euler-Maruyama numerical integration), the final output is It is "purified data" that has been removed to counteract disturbances and strictly satisfy the laws of physics.

[0053] S5: Circuit Breaker Mechanism

[0054] Since the diffusion model is randomly generated, it can be used for the same observation. Secondary parallel inverse sampling. Calculation The variance of the results .

[0055] like This indicates that the model's recovery of the data is extremely uncertain, and it is highly likely that it has encountered a strong adversarial attack beyond the scope of the physical model's understanding. At this point, the system immediately triggers a circuit breaker, isolating the quantum sensor input and maintaining short-term accuracy solely through pure inertial navigation, while also issuing an alarm.

[0056] Example 2: This embodiment discloses a system architecture for implementing the above method.

[0057] The SDE diffusion modeling module runs on high-performance FPGA or GPU edge computing units and uses a pipelined design to accelerate the numerical integration of stochastic differential equations.

[0058] The physics scoring calculation module uses a lightweight neural network (such as the U-Net architecture) and fixes Maxwell operators (divergence operator, curl operator) as non-trainable fixed layers to ensure the hard execution of physical constraints.

[0059] The defense decision module is integrated into the navigation computer and monitors the residuals of the reverse process in real time, acting as the system's "security watchdog".

[0060] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0061] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A quantum navigation adversarial defense and data sanitization method based on stochastic differential equation reverse diffusion, characterized in that, Includes the following steps: S1. Collect the magnetic field observation sequence of the quantum magnetometer and the motion state sequence of the inertial measurement unit, and construct a multidimensional state observation tensor; S2. Treat the multidimensional state observation tensor as the initial state of a contaminated stochastic process, and use forward stochastic differential equations for continuous-time modeling to simulate the diffusion distribution characteristics of noise and adversarial disturbances. S3. Construct a scoring function network with physical energy constraints, and use the electromagnetic field divergence and curl characteristics of Maxwell's equations to construct a physical gradient field, and perform physical consistency regularization training on the scoring network. S4. Using the inverse-time SDE solver, the output of the scoring function network is used as the guiding gradient of the drift term to perform inverse sampling and purification of the real-time observation data, and the disturbed observation trajectory is restored to the geomagnetic manifold space that conforms to the physical laws. S5. Calculate the reconstruction variance and physical residual during the reverse diffusion process. When both are below the preset safety threshold, output the purified magnetic field data for navigation calculation; otherwise, trigger the defense circuit breaker mechanism.

2. The quantum navigation countermeasures and data cleansing method based on stochastic differential equation reverse diffusion according to claim 1, characterized in that, The forward stochastic differential equation in S2 is modeled using the Ornstein-Uhlenbeck process, and its mathematical expression is: in, For navigation observation state vector, The drift coefficient is used to describe the natural evolution of the signal; is the diffusion coefficient, used to describe the injection intensity to counteract noise; This is standard Brownian motion.

3. The quantum navigation countermeasures and data cleansing method based on stochastic differential equation reverse diffusion according to claim 1, characterized in that, The core of the scoring function network for physical energy constraints in S3 lies in learning the logarithmic gradient of the data distribution. loss function Includes physical priors: in, For the output of the scoring network, This is a physical penalty term based on Maxwell's equations. For physical constraint weights, As expected, For noisy samples, To The gradient operator; For time step The log probability density function of the time data distribution; This is the original data.

4. The quantum navigation countermeasures and data cleansing method based on stochastic differential equation reverse diffusion according to claim 3, characterized in that, Physical penalty items Specifically defined as: in, To reconstruct the magnetic field, For Hamiltonian operators, To reconstruct the electric field, magnetic field The partial derivatives, For time The partial differential components.

5. A quantum navigation countermeasure and data sanitization method based on stochastic differential equation reverse diffusion according to claim 1, characterized in that, The reverse-time SDE solver in S4 uses the Euler-Maruyama discretization method, and the iterative formula is as follows: in, The noise is standard Gaussian noise. Adversarial perturbation components in the observed data are removed iteratively. This is the state after iteration. This is the current state. The drift coefficient, The square of the diffusion coefficient, For the score function estimation, For time step, The diffusion coefficient is... It is standard Gaussian noise.

6. The quantum navigation countermeasures and data cleansing method based on stochastic differential equation reverse diffusion according to claim 1, characterized in that, The specific details of the circuit breaker defense mechanism in S5 are as follows: Perform multiple parallel inverse SDE samplings on the same observation and calculate the variance between the different sampling results. ; like If the system determines that there is a high-level deception attack in the current environment that is beyond the understanding of the physical model, it will automatically cut off the magnetic assist, switch to pure inertial navigation mode and issue an alarm.

7. A quantum navigation countermeasure defense and data sanitization system based on stochastic differential equation reverse diffusion, characterized in that... A quantum navigation adversarial defense and data cleansing method based on stochastic differential equation reverse diffusion, as described in any one of claims 1-6, comprises a heterogeneous sensing module, an SDE diffusion modeling module, a physical scoring calculation module, a reverse cleansing engine module, and a defense decision module connected in sequence; wherein, Heterogeneous sensing module: used to simultaneously acquire raw data from the quantum magnetometer and inertial navigation components; SDE diffusion modeling module: used to build a forward diffusion model that describes the distribution of adversarial attacks and environmental noise; Physics score calculation module: Embedded Maxwell's equation operator, used to calculate the physical gradient of data in manifold space and output guided score; Reverse Cleanup Engine Module: Used to perform reverse SDE solving, enabling proactive stripping of adversarial examples and data reconstruction; Defense Decision Module: Used to determine whether a high-level deception attack exists based on the uncertainty indicators of the purification process, and to control the switching of navigation modes.

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