A GNSS / INS tightly coupled adaptive anti-spoofing method based on generalized likelihood ratio and sequential decision

Abstract

This invention belongs to the field of anti-spoofing and interference technology for satellite navigation and inertial navigation integrated systems. It provides a GNSS / INS tightly coupled adaptive anti-spoofing method based on generalized likelihood ratio and sequential decision-making, applicable to multi-satellite spoofing interference and micro-ramp spoofing scenarios in autonomous driving. The method includes: first, constructing a GNSS / INS tightly coupled model; second, constructing a GNSS spoofing and interference model; third, constructing a generalized likelihood ratio statistic and designing an iterative isolation strategy, improving detection accuracy through sequential hypothesis testing; and fourth, embedding the detection results into a filter and constructing an adaptive factor to achieve anomaly weighting and prediction adjustment. This method integrates spoofing detection and spoofing suppression, significantly improving the anti-spoofing capability of the navigation system.

Description

Technical Field

[0001] This invention belongs to the field of anti-spoofing and interference technology for satellite navigation and inertial navigation combined systems, and specifically relates to a tightly coupled adaptive anti-spoofing method for GNSS / INS based on generalized likelihood ratio and sequential decision-making. Background Technology

[0002] Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) have been widely used in both civilian and military fields. A combined GNSS / INS navigation system can provide users with all-weather, continuous, real-time, high-precision position, velocity, and attitude information. While GNSS has brought convenient and accurate positioning information to fields such as intelligent transportation and autonomous driving, its security issues are becoming increasingly prominent. Because navigation satellites are approximately 20,000 to 36,000 km above the Earth, satellite signals are extremely weak during propagation, making GNSS terminals vulnerable to malicious spoofing and interference.

[0003] Spoofing jamming technology refers to a deception source broadcasting false satellite signals to a target receiver, intruding into the receiver's baseband signal processing module, and then guiding the target to an incorrect location. Existing research generally categorizes spoofing jamming methods into repeater-based spoofing jamming and generator-based spoofing jamming. Repeater-based spoofing jamming adds a time delay to the real satellite signal and sends it to the target receiver by adjusting the power. Generator-based spoofing jamming uses a signal simulation source to generate a false GNSS signal based on a deceptive location, and sends the deceptive signal to the target receiver by adjusting the power, causing the target to receive incorrect navigation and positioning information.

[0004] Currently, domestic and international research on GNSS / INS anti-spoofing mainly focuses on two aspects: GNSS spoofing interference detection technology and GNSS spoofing suppression technology. GNSS spoofing detection methods are mainly divided into three categories: The first category is GNSS signal encryption processing technology. This method improves the system's anti-interference and security by modifying the GNSS signal structure, but it increases system costs and affects system performance and response speed during encryption and decryption. The second category is based on detecting signal characteristics, including carrier-to-noise ratio, signal power, direction of arrival, and Doppler effect carrier frequency shift. In recent years, machine learning, as an intelligent algorithm, has been widely used in the field of fault detection. By analyzing the signal characteristics of GNSS when subjected to spoofing interference, and using signal strength, time deviation, and frequency as input features to train a machine learning model, it can effectively identify forged signals, thereby improving the navigation system's anti-attack capability. Although machine learning methods can accurately identify GNSS spoofing signals, they come at the cost of time and data costs. Considering the complexity and diversity of spoofing signals, the training cost may be greatly increased, making it difficult to meet the needs of real-time spoofing detection. Besides machine learning methods, spoofing detection methods based on Time of Arrival (ToA) and Direction of Arrival (DoA) show promise in spoofing detection. These methods require precise time synchronization and multiple receivers, but still face many limitations in practical applications, especially with low-cost equipment and in complex environments. These methods do not rely on auxiliary information, but rather on analyzing and identifying the differences between normal and malicious GNSS signals. The third category is multimodal sensor technology. This system achieves spoofing detection by comprehensively analyzing information from different modalities, exhibiting stronger robustness compared to other technologies. Inertial Measurement Unit (IMU)-assisted identification is currently the mainstream solution in the field of GNSS spoofing detection using multimodal sensor technology.For slowly varying deception detection, Wu and Zhang constructed robust deception detection methods based on combined epoch innovation and innovation rate robust estimation, respectively. Although these methods can identify slowly varying deception interference by setting a false alarm rate, the static mapping relationship between the false alarm rate and the detection threshold cannot adaptively match the dynamic changes in deception intensity, increasing the risk of missed detections and false detections. To address the insufficient adaptability of the static threshold, Zhou et al. proposed a GNSS deception detection method based on velocity consistency verification, directly calculating the user velocity from the original Doppler measurements. This forms a dual-path independent velocity estimation with the traditional indirect velocity determination method based on pseudorange positioning. This method outperforms traditional receiver autonomous integrity monitoring and Doppler frequency difference methods, but the velocity consistency verification may fail because all pseudorange and Doppler observations are synchronously induced. Jin proposed a slowly varying deception detection method for tightly coupled GNSS / INS systems based on weighted Kalman gain. This method uses weighted Kalman gain to enhance the sensitivity of the extended Kalman filter (EKF) to slowly varying deception, targeting a deception rate of 0.1. The detection probability of extremely low drift spoofing (m / s) is 81.8%. To improve the spoofing detection rate, Song et al. proposed an INS-assisted GNSS spoofing detection method based on hybrid optimization. This method combines a particle swarm optimization temporal convolutional network with an interactive multi-model adaptive Kalman filter. It uses the INS output to establish a mapping relationship with GNSS measurements, generating a virtual GNSS trajectory. However, the hybrid model has high requirements for data volume and computational complexity, and the spoofing signal is complex and variable, posing a challenge to real-time performance. Therefore, while existing spoofing detection methods have their advantages in specific scenarios, they still lack robustness against complex spoofing interference environments with multi-satellite pseudoranges and pseudorange rates. In GNSS spoofing suppression, many research teams have used Adaptive Robust Kalman Filters (ARKFs) to resist GNSS spoofing. Yang proposed adaptive robust Kalman filters (ARKFs) based on two-factor equivalent weights, which have been widely used in the GNSS / INS combination field. Although ARKF can suppress deception interference in the combined system, ARKF's robustness factor design relies on a pre-set false alarm probability threshold. When the deception signal gradually interferes with the system with small deviations, the system cannot reduce the weight in time, resulting in the target being slowly deceived.

[0005] To address the aforementioned problems, this invention proposes a tightly coupled adaptive anti-spoofing method for GNSS / INS that integrates generalized likelihood ratio (GLR) and sequential decision-making. This method first quantifies and identifies single-satellite spoofing interference by constructing a GLR statistic. Based on this, a sequential decision-making mechanism is introduced, iteratively isolating multi-satellite observation information to continuously track and isolate spoofing observation updates, effectively avoiding false detections and missed detections caused by traditional single threshold methods. Then, the detection results are embedded into a filtering system, constructing local equivalent weighting factors and global adaptive factors based on the GLR statistic to dynamically adjust the system's observation noise matrix and covariance matrix. This ensures rapid response to spoofing interference while maintaining the system's high-precision navigation capability. Summary of the Invention

[0006] To address the performance degradation of traditional detection methods and the difficulty in identifying subtle ramp-type spoofing in autonomous driving systems caused by multi-satellite spoofing interference, this invention proposes a tightly coupled adaptive anti-spoofing method for GNSS / INS based on generalized likelihood ratio and sequential decision-making. This method theoretically achieves a deep integration of spoofing detection and suppression, providing a guarantee for the safety of autonomous driving in complex electromagnetic environments.

[0007] A tightly coupled adaptive anti-spoofing method for GNSS / INS based on generalized likelihood ratio and sequential decision-making includes the following steps:

[0008] Step 1: Construct a tightly coupled GNSS / INS model. Combine the INS error state equation with the GNSS error state equation to construct a tightly coupled system state equation. Take the pseudorange and pseudorange rate difference between GNSS and INS as the system measurement values ​​and construct the system measurement equation.

[0009] Step 2: Construct a GNSS deception jamming model. Generative deception jamming autonomously generates deception signals and applies a controllable offset to their code phase. It artificially constructs pseudorange and pseudorange rate deviations. Based on the deviation change characteristics, it can be divided into step-type and ramp-type deception, thereby inducing the target receiver to smoothly deviate from the real navigation trajectory.

[0010] Step 3: Propose a multi-satellite deception sequential decision-making method based on generalized likelihood ratio. Quickly eliminate the non-deception case through global chi-square test. For the deception case, calculate the conditional anomaly statistics one by one based on the current set of remaining satellites. Use Cholesky decomposition to ensure numerical stability and remove the most suspicious satellite corresponding to the maximum statistic until all remaining satellites pass the consistency test, so as to achieve accurate isolation between deception signal and normal signal.

[0011] Step 4: An adaptive filtering method based on generalized likelihood ratio statistics is proposed. By constructing equivalent weighting factors to dynamically adjust the observation noise covariance, and combining it with global adaptive factors to correct the state covariance update, the standard Kalman filter is maintained under normal conditions, and the observation correction is reduced or cut off under abnormal conditions, thus forming a closed-loop mechanism that integrates detection and suppression, taking into account both anti-spoofing robustness and anti-spoofing filtering accuracy.

[0012] Step 1 describes the construction of a tightly coupled GNSS / INS model, which involves constructing a tightly coupled system state equation by combining the INS error state equation with the GNSS error state equation. The pseudorange and pseudorange rate difference between GNSS and INS are taken as system measurement values, and the system measurement equation is constructed.

[0013] The specific steps are as follows:

[0014] Step 1-1: In a tightly coupled GNSS / INS navigation system, construct the tightly coupled system state equations from the INS error state equations and the GNSS error state equations:

[0015] (1)

[0016] Right now:

[0017] (2)

[0018] In the formula, the system state vector is:

[0019] (3)

[0020] In the formula, For attitude error, For speed error, For position error, For zero bias of the gyroscope, For accelerometer zero bias, For receiver clock bias, For the deviations between each satellite system relative to the GPS system, For receiver clock drift, , , , and These represent the inter-system biases of GLONASS, Galileo, BDS, and QZSS relative to GPS, respectively.

[0021] Steps 1-2: In a tightly coupled GNSS / INS navigation system, the pseudorange and pseudorange rate difference between GNSS and INS are taken as system measurement values, and the system measurement equations are constructed as follows:

[0022] (4)

[0023] In the formula, Represents the observation matrix; The measurement noise vector is represented by the following formula: ;

[0024] Observation vector It can be represented as:

[0025] (5)

[0026] (6)

[0027] In the formula, and These refer to the original pseudorange and Doppler observations, respectively, indicated by the superscript. Indicates frequency, This refers to satellite systems, including GPS, GLONASS, GALILEO, BDS, and QZSS; and These represent the distance from the receiver to the satellite predicted by INS and the rate of change of that distance, respectively. and These are the sum of error corrections related to the receiver clock for pseudorange and Doppler, respectively; and The observation matrix in the measurement equation is represented as follows: (The original text contains several grammatical errors and inconsistencies, which have been omitted from the translation.)

[0028] (7)

[0029] In the formula, This represents the line-of-sight vector from the receiver to the satellite; It is the transformation matrix that converts position disturbance errors from the navigation coordinate system to the Earth coordinate system; It is the transformation matrix that converts the velocity error from the navigation coordinate system to the Earth coordinate system.

[0030] Step 2 describes the construction of a GNSS deception jamming model, which autonomously generates deception signals through generative deception jamming, applies a controllable offset to its code phase, and artificially constructs pseudorange and pseudorange rate deviations. Based on the deviation change characteristics, it can be divided into step-type and ramp-type deception, thereby inducing the target receiver to smoothly deviate from the real navigation trajectory.

[0031] The specific steps are as follows:

[0032] Step 2-1: The GNSS receiver provides the real satellite signal; the detection module provides the target's position and velocity in real time; the deception generation module generates a corresponding deception signal according to the deception strategy, and the transmission power is adjusted to the target antenna by the deception signal transmission module; at the RF front end of the GNSS receiver, the received signal contains the real signal, the deception signal, and noise, and its expression is as follows:

[0033] (8)

[0034] In the formula, the subscript and These respectively represent identifiers for real satellite signals and deceptive satellite signals; and These represent the sets of real satellite signals and spoofed satellite signals, respectively. , , , , These represent the power, navigation message, code delay, carrier phase, and Doppler frequency of the actual satellite signal, respectively. , , , , These represent the power of the deception satellite signal, the navigation message, the code delay, the carrier phase, and the Doppler frequency, respectively. It has a mean of zero and a variance of 0, with a variance of 0. Gaussian white noise.

[0035] Step 2-2: The actual signal received by the target receiver is :

[0036] (9)

[0037] In the formula, This is the nominal carrier frequency of the GNSS signal.

[0038] Ignoring the internal frequency conversion error of the deception device, the frequency of the deception signal received by the target is: :

[0039] (10)

[0040] In the formula, For the interference source relative to the satellite Doppler shift.

[0041] The offset of the deceptive signal frequency relative to the real signal frequency is:

[0042] (11)

[0043] Multiplying both sides of the above equation by the carrier wavelength and rearranging the terms, we obtain the speed deception mathematical model:

[0044] (12)

[0045] In the formula, For the deception of the first The pseudorange rate of a single satellite; The pseudorange rate is the actual measurement rate of the satellite signal. To achieve speed deception against the first The carrier frequency offset applied by the satellite signal; based on the characteristics of step spoofing and ramp spoofing, the model is established as follows:

[0046] (13)

[0047] In the formula, To deceive and interfere with the slope; The deviation between the true pseudorange rate and the deceptive pseudorange rate; when At that time, it represents a ramp-type pseudo-range rate deception; At this time, it represents a step-like pseudo-range rate deception;

[0048] Steps 2-3: The receiver measures the pseudorange of multiple satellites. Solve its own position and clock difference Its expression is:

[0049] (14)

[0050] When the target receives a GNSS spoofing signal, the spoofing signal guides the target to follow a spoofed navigation trajectory by modifying pseudorange observation information; assuming Deception at all times causes the first pseudorange of a satellite There is a deviation Then the first The pseudorange of the satellite after being deceived is:

[0051] (15)

[0052] make , The code phase delay of the deception signal is calculated based on the characteristics of step deception and ramp deception, and the model is established as follows:

[0053] (16)

[0054] In the formula, To deceive and interfere with the slope; This represents the deviation between the true pseudorange and the deceptive pseudorange. When At that time, it represents a ramp-type pseudo-distance deception; At this time, it represents a step-like pseudo-distance deception.

[0055] Step 3 proposes a multi-satellite deception sequential decision-making method based on generalized likelihood ratio. It quickly eliminates the non-deception case through global chi-square test. For the deception case, it calculates the conditional anomaly statistics based on the current set of remaining satellites one by one, uses Cholesky decomposition to ensure numerical stability, and removes the most suspicious satellite corresponding to the maximum statistic until all remaining satellites pass the consistency test, thus achieving accurate isolation between deception signals and normal signals.

[0056] The specific steps are as follows:

[0057] Step 3-1: The tightly coupled GNSS / INS system fuses the original satellite measurements with the predicted values ​​based on INS solutions, improving the accuracy of the navigation system. The discrete-time dynamic model can be written in the following form:

[0058] (17)

[0059] Considering tightly coupled GNSS / INS systems The Kalman filter update at time step 1 makes This is the pseudorange observation vector; The observation matrix; Predict the state in one step; To predict state covariance; To observe the noise covariance matrix.

[0060] Define the innovation vector as:

[0061] (18)

[0062] In the absence of deception, the innovation follows a zero-mean Gaussian distribution:

[0063] (19)

[0064] In the formula, The new information covariance matrix represents the uncertainty between prediction and observation.

[0065] When the When a satellite is subjected to deception interference, its pseudorange observations and pseudorange rate observations contain an unknown bias. This causes the new information to shift on that component; at this point, the new information can be expressed as:

[0066] (20)

[0067] In the formula, To avoid deceiving the new information, For the first One standard basis vector; if multiple satellites are deceived and interfered with, then , For the set of deception.

[0068] Step 3-2: When a single satellite is subjected to deception interference, assume that the first... The satellite has a deviation. All other observation satellites are functioning normally; therefore, the null and alternative hypotheses are:

[0069] (twenty one)

[0070] In the formula, To provide an interference-free environment; To avoid disturbing the environment; Below, the innovation vector follows a Gaussian distribution. To detect this bias, a generalized likelihood ratio statistic is constructed:

[0071] (twenty two)

[0072] According to the probability density function of the multivariate Gaussian distribution:

[0073] (twenty three)

[0074] After taking the logarithm, the bias caused by deception To maximize; let ,have to:

[0075] (twenty four)

[0076] Substituting the likelihood ratio and simplifying, we obtain the test statistic:

[0077] (25)

[0078] exist Down, ,therefore This refers to a chi-square distribution with 1 degree of freedom; this distribution characteristic originates from the classic conclusion of Gaussian quadratic forms, for... ,have ;and Consider the quadratic form in a given direction The degrees of freedom of the chi-square distribution of the projection on the surface are determined by the constraint dimension;

[0079] To further reveal the physical meaning of this statistic, Divide into blocks, let

[0080] (26)

[0081] In the formula, Indicates the first The variance of the information of each observation; Indicates the first The covariance of one observation with the rest of the observations; This means removing the first... After one observation, the covariance submatrix among the remaining observations;

[0082] Then, according to the formula for finding the inverse of a block matrix, we can obtain:

[0083] (27)

[0084] therefore,

[0085] (28)

[0086] Given other observations, The conditional distribution is ,therefore It is the first The square of the conditionally standardized residual of the nth observation represents the... This statistic measures the degree of deviation between an observation and a predicted value based on other observations, while fully preserving the correlation information between observations; this statistic is obtained through conditional mean. The influence of other observations was eliminated, thus achieving optimal detection performance in the single-fault scenario; a significance level was set. Calculate the upper quantile of the chi-square distribution. ;like If so, then refuse. Determine the first The satellite is subject to deception and interference;

[0087] Step 3-3: When multiple satellites are involved in deception, directly applying the generalized likelihood ratio test for single-satellite deception to each pseudorange channel independently will lead to misjudgment, because the deception interference will pass through the information covariance matrix. The off-diagonal elements affect the conditional mean of other pseudorange channels, causing normal satellites to... It also becomes larger; therefore, the multi-fault identification problem is transformed into a series of sequential hypothesis tests, in which the most likely spoofing satellites are identified and separated based on the current remaining set at each step, until the statistics of the remaining satellites all pass the consistency test.

[0088] First, calculate the global chi-square statistic:

[0089] (29)

[0090] In a deception-free environment ;like If there is no fault at the current moment and all satellites are fault-free, then filtering and calculation can be performed directly; this global check can quickly eliminate fault-free cases and reduce computational complexity.

[0091] If the global check fails, it indicates that at least one source of deception exists in the current observation set, and the sequential decision-making process begins; let the current set of remaining satellite indexes be denoted as . ,initial Deceiving the collection ; in the Step, based on the observed subvectors of the current remaining set Covariance Submatrix For each Calculate the statistic:

[0092] (30)

[0093] In the formula, yes China's corresponding satellite Standard basis vectors; It measures the degree of conditional anomaly of each satellite relative to the other remaining satellites in the current remaining set;

[0094] To further ensure numerical stability, Cholesky decomposition is adopted; let... ,but:

[0095] (31)

[0096] Expanding it, we get:

[0097] (32)

[0098] In the formula, The statistic can be written as:

[0099] (33)

[0100] According to sequential decision theory, at each step, the satellite with the greatest impact on the current global anomaly should be removed; this decision is achieved by the following maximization criterion:

[0101] (34)

[0102] From the perspective of likelihood ratio, The corresponding observed value causes the generalized likelihood function to reach its maximum value among the candidate hypotheses, thus making it statistically the most likely source of the fault. Therefore, it is considered the most likely source to deceive the satellite and is added to the deception set. And remove from the remaining set: ;

[0103] The updated residual set should be used to recalculate the statistics, but to simplify the calculation, the following identity can be used to avoid recalculating the inverse:

[0104] (35)

[0105] In the formula, Is it removal? The remaining set before; when the remaining set All satellites in China If the remaining satellites are deemed to be functioning normally, the iteration stops. In the sequential decision-making process, each iteration iterates through the set of remaining satellites. All satellites are examined simultaneously, and the observations of the deceitful satellites are isolated from those of the normal satellites. A locally optimal choice is made, ultimately achieving accurate identification of multi-satellite deception.

[0106] Step 4 proposes an adaptive filtering method based on generalized likelihood ratio statistics. This method constructs equivalent weighting factors to dynamically adjust the observation noise covariance and combines it with global adaptive factors to correct the state covariance update. Under normal conditions, it maintains the standard Kalman filter and reduces the weighting or cuts off the observation correction under abnormal conditions, thus forming a closed-loop mechanism that integrates detection and suppression, taking into account both anti-spoofing robustness and anti-spoofing filtering accuracy.

[0107] The specific steps are as follows:

[0108] Step 4-1: Based on the generalized likelihood ratio statistic, construct the first... Equivalent weighting factors for each observation:

[0109] (36)

[0110] It can be seen from equation (36) that The larger the value, the more significant the deviation between observations and model predictions; while IMUs possess short-term high-precision characteristics, GNSS observation noise is significant; when hour, Normal observation weights remain unchanged; when hour, And follow Increase the monotonically decreasing weight to reduce the weight of abnormal observations;

[0111] Construct the equivalent observation noise covariance matrix using equivalent weight factors:

[0112] (37)

[0113] In the formula, This is equivalent to reducing the variance of the original observation noise. In the Kalman filter framework, the observation noise covariance is inversely proportional to the gain matrix, therefore... The smaller the value, the lower the weight of the corresponding observation in the state update; when When the value approaches 0, the corresponding observation can be considered to have been completely eliminated;

[0114] Step 4-2: To address the overall change in deception intensity, a global adaptive factor is introduced. Dynamically adjust the prediction covariance matrix:

[0115] (38)

[0116] In the formula, This is the global chi-square statistic; This is a preset lower threshold value; For degrees of freedom The upper quantile of the chi-square distribution, For another significance level; when At that time, the formula is reduced to the covariance update of the standard Kalman filter. GNSS observations showed no abnormalities, and the filter was functioning normally; when When the correction of covariance by the observations is partially weakened, the filter's confidence in the current observations decreases, but it still retains a certain correction capability, balancing anti-spoofing and convergence speed under normal observation conditions; when At this point, the overall information significantly exceeds the chi-square threshold, indicating strong deception, and the covariance update formula degenerates into... At this point, the filter updates its state solely through time propagation, effectively preventing the covariance from being pulled toward an incorrect value by deceiving the observations and preventing the filter from exhibiting "false convergence".

[0117] global adaptive factor Substituting into the covariance update formula, we get:

[0118] (39)

[0119] The equivalent weighting factors and global adaptive metric constructed through equations (36)-(39) essentially dynamically adjust the observation noise matrix and the state covariance matrix by deceiving the detection statistic. When the system is normal, the filter performs a standard Kalman filter update to maintain optimal estimation performance. When there are weak anomalies, the observation values ​​affect the observation noise matrix. and covariance matrix Dynamic adjustments are made to avoid over-response of the filter due to slight disturbances; when strong spoofing is detected, the observations are completely cut off from the covariance. The correction retains only time propagation, while also incorporating the observation noise matrix. The adjustment allows the filter to maintain its state through inertial recursion, thereby isolating the influence of deception interference on the state uncertainty and effectively balancing the robustness against deception with the filtering accuracy under deception-free conditions.

[0120] Beneficial effects of this invention:

[0121] 1. To reduce redundant computational overhead in a deception-free environment, this invention proposes a global chi-square test for rapid screening. Before updating the integrated navigation filter, the overall observation consistency is pre-judged. When the statistic does not exceed the threshold, the standard filter solution is directly executed, effectively avoiding the real-time loss caused by complex anomaly detection throughout the entire time period.

[0122] 2. To address the misjudgment problem caused by the coupling of information covariance under multi-satellite deception interference, this invention proposes a sequential decision isolation method based on generalized likelihood ratio. It utilizes Cholesky decomposition to ensure numerical stability, calculates the conditional anomaly statistics of the remaining satellite set one by one, and removes the most suspicious satellites until all pass the consistency test, effectively achieving accurate separation of deception signals from normal observations.

[0123] 3. In order to retain the ability to utilize effective observation information while suppressing deception interference, this invention proposes a dynamic adjustment method for observation noise covariance based on equivalent weight factors. Based on the generalized likelihood ratio statistic, a monotonically decreasing weight function is constructed to smoothly reduce the weight of abnormal observations while maintaining the standard gain of normal observations, effectively balancing anti-deception robustness and filtering accuracy under normal operating conditions.

[0124] 4. To avoid false convergence of the filter due to strong deception interference, this invention proposes a closed-loop mechanism for global adaptive factor correction of state covariance update. When the overall innovation is severely abnormal, the observation correction is automatically cut off and the state estimation is maintained by inertial recursion alone. This effectively constructs an adaptive filtering framework that integrates detection and suppression, taking into account both system stability and estimation accuracy under different deception intensities. Attached Figure Description

[0125] Figure 1 is a flowchart of a tightly coupled adaptive anti-spoofing method for GNSS / INS based on generalized likelihood ratio and sequential decision-making according to the present invention.

[0126] Figure 2 is a detailed flowchart of step 1 of one embodiment of the present invention;

[0127] Figure 3 is a detailed flowchart of step 2 of one embodiment of the present invention;

[0128] Figure 4 is a detailed flowchart of step 3 of one embodiment of the present invention;

[0129] Figure 5 is a detailed flowchart of step 4 of one embodiment of the present invention;

[0130] Figure 6 is a summary flowchart of one embodiment of the present invention;

[0131] Figure 7 shows the vehicle motion trajectory in the experimental scenario of this invention;

[0132] Figure 8 shows the satellite observation situation under the experimental scenario of this invention;

[0133] Figure 9 is a residual diagram of pseudorange rate after deception interference according to the present invention;

[0134] Figure 10 is a pseudorange residual diagram after the deception interference of the present invention;

[0135] Figure 11 shows the deception detection results of the present invention;

[0136] Figure 12 is a comparison chart of the trajectories of different algorithms of the present invention;

[0137] Figure 13 is a comparison chart of navigation errors of different algorithms of the present invention. Detailed Implementation

[0138] An embodiment of the present invention will be further described below with reference to the accompanying drawings.

[0139] In this embodiment of the invention, a tightly coupled adaptive anti-spoofing method for GNSS / INS based on generalized likelihood ratio and sequential decision-making is provided, such as... Figure 1 As shown, it includes the following steps:

[0140] Step 1: Construct a tightly coupled GNSS / INS model. Combine the INS error state equation with the GNSS error state equation to construct a tightly coupled system state equation. Take the pseudorange and pseudorange rate difference between GNSS and INS as the system measurement values ​​and construct the system measurement equation.

[0141] Step 1-1: In a tightly coupled GNSS / INS navigation system, construct the tightly coupled system state equations from the INS error state equations and the GNSS error state equations:

[0142] (1)

[0143] Right now:

[0144] (2)

[0145] In the formula, the system state vector is:

[0146] (3)

[0147] In the formula, For attitude error, For speed error, For position error, For zero bias of the gyroscope, For accelerometer zero bias, For receiver clock bias, For the deviations between each satellite system relative to the GPS system, This is due to receiver clock drift. , , , and These represent the inter-system biases of GLONASS, Galileo, BDS, and QZSS relative to GPS, respectively.

[0148] Steps 1-2: In a tightly coupled GNSS / INS navigation system, the pseudorange and pseudorange rate difference between GNSS and INS are taken as system measurement values, and the system measurement equations are constructed as follows:

[0149] (4)

[0150] In the formula, Represents the observation matrix; The measurement noise vector is represented by the following formula: ;

[0151] Observation vector It can be represented as:

[0152] (5)

[0153] (6)

[0154] In the formula, and These refer to the original pseudorange and Doppler observations, respectively, indicated by the superscript. Indicates frequency, This refers to satellite systems, including GPS, GLONASS, GALILEO, BDS, and QZSS; and These represent the distance from the receiver to the satellite predicted by INS and the rate of change of that distance, respectively. and These are the sum of error corrections related to the receiver clock for pseudorange and Doppler, respectively; and These represent the sum of other error corrections for pseudorange and Doppler, respectively. The observation matrix in the measurement equation is expressed as:

[0155] (7)

[0156] In the formula, This represents the line-of-sight vector from the receiver to the satellite; It is the transformation matrix that converts position disturbance errors from the navigation coordinate system to the Earth coordinate system; It is the transformation matrix that converts the velocity error from the navigation coordinate system to the Earth coordinate system.

[0157] Step 2: Construct a GNSS deception jamming model. Generative deception jamming autonomously generates deception signals and applies a controllable offset to their code phase. It artificially constructs pseudorange and pseudorange rate deviations. Based on the deviation change characteristics, it can be divided into step-type and ramp-type deception, thereby inducing the target receiver to smoothly deviate from the real navigation trajectory.

[0158] Step 2-1: The GNSS receiver provides the real satellite signal; the detection module provides the target's position and velocity in real time; the deception generation module generates a corresponding deception signal according to the deception strategy, and the transmission power is adjusted to the target antenna by the deception signal transmission module. At the GNSS receiver's RF front-end, the received signal contains the real signal, the deception signal, and noise, expressed as follows:

[0159] (8)

[0160] In the formula, the subscript and These respectively represent identifiers for real satellite signals and deceptive satellite signals; and These represent the sets of real satellite signals and spoofed satellite signals, respectively. , , , , These represent the power, navigation message, code delay, carrier phase, and Doppler frequency of the actual satellite signal, respectively. , , , , These represent the power of the deception satellite signal, the navigation message, the code delay, the carrier phase, and the Doppler frequency, respectively. It has a mean of zero and a variance of 0, with a variance of 0. Gaussian white noise.

[0161] Step 2-2: The actual signal received by the target receiver is :

[0162] (9)

[0163] In the formula, This is the nominal carrier frequency of the GNSS signal.

[0164] Ignoring the internal frequency conversion error of the deception device, the frequency of the deception signal received by the target is: :

[0165] (10)

[0166] In the formula, For the interference source relative to the satellite Doppler shift.

[0167] The offset of the deceptive signal frequency relative to the real signal frequency is:

[0168] (11)

[0169] Multiplying both sides of the above equation by the carrier wavelength and rearranging the terms, we obtain the speed deception mathematical model:

[0170] (12)

[0171] In the formula, For the deception of the first The pseudorange rate of a single satellite; The pseudorange rate is the actual measurement rate of the satellite signal. To achieve speed deception against the first The carrier frequency offset applied by the satellite signal. Based on the characteristics of step spoofing and ramp spoofing, the model is established as follows:

[0172] (13)

[0173] In the formula, To deceive and interfere with the slope; This represents the deviation between the true pseudorange rate and the deceptive pseudorange rate. When At that time, it represents a ramp-type pseudo-range rate deception; At this time, it represents a step-like pseudo-range rate deception.

[0174] Steps 2-3: The receiver measures the pseudorange of multiple satellites. Solve its own position and clock difference Its expression is:

[0175] (14)

[0176] When the target receives a GNSS spoofing signal, the spoofing signal guides the target to follow a spoofed navigation trajectory by modifying pseudorange observation information. Assume... Deception at all times causes the first pseudorange of a satellite There is a deviation Then the first The pseudorange of the satellite after being deceived is:

[0177] (15)

[0178] make , The code phase delay of the deception signal is calculated based on the characteristics of step deception and ramp deception, and the model is established as follows:

[0179] (16)

[0180] In the formula, To deceive and interfere with the slope; This represents the deviation between the true pseudorange and the deceptive pseudorange. When At that time, it represents a ramp-type pseudo-distance deception; At this time, it represents a step-like pseudo-distance deception.

[0181] Step 3: Propose a multi-satellite deception sequential decision-making method based on generalized likelihood ratio. Quickly eliminate the non-deception case through global chi-square test. For the deception case, calculate the conditional anomaly statistics one by one based on the current set of remaining satellites. Use Cholesky decomposition to ensure numerical stability and remove the most suspicious satellite corresponding to the maximum statistic until all remaining satellites pass the consistency test, so as to achieve accurate isolation between deception signal and normal signal.

[0182] Step 3-1: The tightly coupled GNSS / INS system fuses the original satellite measurements with the predicted values ​​based on INS solutions, improving the accuracy of the navigation system. The discrete-time dynamic model can be written in the following form:

[0183] (17)

[0184] Considering tightly coupled GNSS / INS systems The Kalman filter update at time step 1 makes This is the pseudorange observation vector; The observation matrix; Predict the state in one step; To predict state covariance; To observe the noise covariance matrix.

[0185] Define the innovation vector as:

[0186] (18)

[0187] In the absence of deception, the innovation follows a zero-mean Gaussian distribution:

[0188] (19)

[0189] In the formula, The new information covariance matrix represents the uncertainty between prediction and observation.

[0190] When the When a satellite is subjected to deception interference, its pseudorange observations and pseudorange rate observations contain an unknown bias. This causes the information to shift on that component. The information can then be expressed as:

[0191] (20)

[0192] In the formula, To avoid deceiving the new information, For the first A standard basis vector. If multiple satellites are subjected to deception interference, then... , For the set of deception.

[0193] Step 3-2: When a single satellite is subjected to deception interference, assume that the first... The satellite has a deviation. All other observation satellites are functioning normally; therefore, the null and alternative hypotheses are:

[0194] (twenty one)

[0195] In the formula, To provide an interference-free environment; To disrupt the environment. Below, the innovation vector follows a Gaussian distribution. To detect this bias, a generalized likelihood ratio statistic is constructed:

[0196] (twenty two)

[0197] According to the probability density function of the multivariate Gaussian distribution:

[0198] (twenty three)

[0199] After taking the logarithm, the bias caused by deception Find the maximum value. Let ,have to:

[0200] (twenty four)

[0201] Substituting the likelihood ratio and simplifying, we obtain the test statistic:

[0202] (25)

[0203] exist Down, ,therefore This is a chi-square distribution with 1 degree of freedom. This distribution characteristic originates from the classic conclusion of the Gaussian quadratic form. ,have ;and Consider the quadratic form in a given direction The degrees of freedom of the chi-square distribution of the projection on the surface are determined by the constraint dimension.

[0204] To further reveal the physical meaning of this statistic, Divide into blocks, let

[0205] (26)

[0206] In the formula, Indicates the first The variance of the information of each observation; Indicates the first The covariance of one observation with the rest of the observations; This means removing the first... The covariance submatrix among the remaining observations after one observation.

[0207] Then, according to the formula for finding the inverse of a block matrix, we can obtain:

[0208] (27)

[0209] therefore,

[0210] (28)

[0211] Given other observations, The conditional distribution is ,therefore It is the first The square of the conditionally standardized residual of the nth observation represents the... This statistic measures the deviation between an observation and a predicted value based on other observations, while fully preserving the correlation information between observations. It is calculated using the conditional mean. The influence of other observations is eliminated, thus achieving optimal detection performance in the single-fault scenario. A significance level is set. Calculate the upper quantile of the chi-square distribution. .like If so, then refuse. Determine the first The satellite is subject to deception and interference.

[0212] Step 3-3: When multiple satellites are involved in deception, directly applying the generalized likelihood ratio test for single-satellite deception to each pseudorange channel independently will lead to misjudgment, because the deception interference will pass through the information covariance matrix. The off-diagonal elements affect the conditional mean of other pseudorange channels, causing normal satellites to... It also becomes larger. Therefore, the multi-fault identification problem is transformed into a series of sequential hypothesis tests, in which the most likely spoofing satellites are identified and separated based on the current remaining set at each step, until the statistics of the remaining satellites all pass the consistency test;

[0213] First, calculate the global chi-square statistic:

[0214] (29)

[0215] In a deception-free environment .like If no fault is found at the current moment, and all satellites are fault-free, filtering and calculation can be performed directly. This global check can quickly eliminate fault-free cases and reduce computational complexity.

[0216] If the global check fails, it indicates that at least one source of deception exists in the current observation set, and the sequential decision-making process begins. Let the current set of remaining satellite indexes be denoted as . ,initial Deceiving the collection In the first Step, based on the observed subvectors of the current remaining set Covariance Submatrix For each Calculate the statistic:

[0217] (30)

[0218] In the formula, yes China's corresponding satellite The standard basis vectors. It measures the degree of conditional anomaly of each satellite relative to the other remaining satellites in the current remaining set.

[0219] To further ensure numerical stability, Cholesky decomposition is employed. Let... ,but:

[0220] (31)

[0221] Expanding it, we get:

[0222] (32)

[0223] In the formula, The statistic can be written as:

[0224] (33)

[0225] According to sequential decision theory, at each step, the satellite with the greatest impact on the current global anomaly should be removed. This decision is achieved by the following maximization criterion:

[0226] (34)

[0227] From the perspective of likelihood ratio, The corresponding observed value causes the generalized likelihood function to reach its maximum value among the candidate hypotheses, thus making it statistically the most likely source of the fault. Therefore, it is considered the most likely source to deceive the satellite and is added to the deception set. And remove from the remaining set: ;

[0228] The updated residual set should be used to recalculate the statistics, but to simplify the calculation, the following identity can be used to avoid recalculating the inverse:

[0229] (35)

[0230] In the formula, Is it removal? The previous remaining set. When the remaining set... All satellites in China If all remaining satellites are deemed normal, the iteration stops. In the sequential decision-making process, each iteration involves analyzing the set of remaining satellites. All satellites are examined simultaneously, and the observations of the deceitful satellites are isolated from those of the normal satellites. A locally optimal choice is made, ultimately achieving accurate identification of multi-satellite deception.

[0231] Step 4: Propose an adaptive filtering method based on generalized likelihood ratio statistics. By constructing equivalent weight factors to dynamically adjust the observation noise covariance, and combining it with global adaptive factors to correct the state covariance update, the standard Kalman filter is maintained under normal conditions, and the observation correction is reduced or cut off under abnormal conditions, thus forming a closed-loop mechanism that integrates detection and suppression, taking into account both anti-spoofing robustness and anti-spoofing filtering accuracy.

[0232] Step 4-1: Based on the generalized likelihood ratio statistic, construct the first... Equivalent weighting factors for each observation:

[0233] (36)

[0234] It can be seen from equation (36) that The larger the value, the more significant the deviation between observations and model predictions. IMUs, with their short-term high accuracy, exhibit significant GNSS observation noise. When... hour, Normal observation weights remain unchanged; when hour, And follow Increase the monotonically decreasing weight to reduce the weight of anomaly observations.

[0235] Construct the equivalent observation noise covariance matrix using equivalent weight factors:

[0236] (37)

[0237] In the formula, This is equivalent to reducing the variance of the original observation noise. The observation noise covariance is inversely proportional to the gain matrix within the Kalman filtering framework. Therefore, The smaller the value, the lower the weight of the corresponding observation in the state update. When the value approaches 0, the corresponding observation can be considered to have been completely eliminated;

[0238] Step 4-2: To address the overall change in deception intensity, a global adaptive factor is introduced. Dynamically adjust the prediction covariance matrix:

[0239] (38)

[0240] In the formula, This is the global chi-square statistic; This is a preset lower threshold value; For degrees of freedom The upper quantile of the chi-square distribution, For another level of significance. When At that time, the formula is reduced to the covariance update of the standard Kalman filter. GNSS observations showed no abnormalities, and the filter was functioning normally; when When the correction of covariance by the observations is partially weakened, the filter's confidence in the current observations decreases, but it still retains a certain correction capability, balancing anti-spoofing and convergence speed under normal observation conditions; when At this point, the overall information significantly exceeds the chi-square threshold, indicating strong deception, and the covariance update formula degenerates into... At this point, the filter updates its state solely through time propagation, effectively preventing deceptive observations from pulling the covariance to incorrect values ​​and preventing the filter from exhibiting "false convergence".

[0241] global adaptive factor Substituting into the covariance update formula, we get:

[0242] (39)

[0243] The equivalent weighting factors and global adaptive metric constructed through equations (36)-(39) essentially dynamically adjust the observation noise matrix and the state covariance matrix by deceiving the detection statistic. When the system is normal, the filter performs a standard Kalman filter update to maintain optimal estimation performance; when there are weak anomalies, the observation values ​​adjust the observation noise matrix. and covariance matrix Dynamic adjustments are made to avoid over-response of the filter due to slight disturbances; when strong spoofing is detected, the observations are completely cut off from the covariance. The correction retains only time propagation, while also incorporating the observation noise matrix. The adjustment allows the filter to maintain its state through inertial recursion, thereby isolating the influence of deception interference on the state uncertainty and effectively balancing the robustness against deception with the filtering accuracy under deception-free conditions.

[0244] like Figure 7 As shown, to verify the practical performance of the GNSS / INS tightly coupled adaptive anti-spoofing method based on generalized likelihood ratio and sequential decision-making of this invention, a vehicle trajectory map for a sports car experiment was designed. The data acquisition platform was equipped with a Trimble R10 receiver with a frequency of 1Hz and a tactical-level IMU with a frequency of 200Hz, as well as an accurate reference solution from the NovAtel-SPAN-CPT system. The experiment lasted for 28 minutes, and the satellite observations are as follows. Figure 8 As shown, signals were received from 14 different satellites, namely SV 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 111, 118, 119, and 120.

[0245] The effectiveness of the deception interference method was verified by artificially applying different deception interference methods to the raw GNSS data. The deception interference situations are shown in Table 1. During the movement of the sports car, four different modes of deception interference were applied. In scenarios 1 and 2, step-type deception interference with deception deviations of 500 m and 50 m / s was applied to the pseudorange and pseudorange rate of SV 96, 97, and 98, respectively, for a duration of 699 s. In scenarios 3 and 4, ramp-type deception interference with deception rates of 1 m / s and 0.2 m / s² was applied to the pseudorange and pseudorange rate of SV 96, 97, and 98, respectively, for a duration of 518 s.

[0246] EKF consists of two loops: a state filtering loop and a gain calculation loop. When the GNSS is subjected to deception interference, gross errors will be generated through the observation vector. Introduced into the filter loop, affecting the system state vector Due to the observation noise matrix of EKF Since the weights remain unchanged, the system cannot adjust the weights between GNSS and IMU, leading to malfunction in the filtering system. To analyze the impact of deception interference on the EKF-based tightly coupled GNSS / INS system, based on the experimental conditions described above, EKF was used to fuse GNSS and INS. Deception interference in the system's pseudorange and pseudorange rate for the four scenarios was investigated, and the pseudorange rate residual and pseudorange residual of the filtering system were plotted as follows: Figure 9 , 10 As shown.

[0247] from Figure 9 , 10 It can be seen that during the time period of 358301 s-358999 s, the deception interference only caused a step shift in range and velocity for PRN 96, 97, and 98. However, all pseudorange and pseudorange rate residuals of the system contained gross errors. This is because when the GNSS began to be attacked by deception, the pseudorange and pseudorange rate of PRN 96, 97, and 98 were shifted, and at this time the observation noise matrix... The measurement noise in the system is constant, causing the system to assign excessive weights to erroneous observations, ultimately leading to a significant deviation in the system's navigation information. Furthermore, when GNSS and INS are fused in the next epoch, the distorted navigation and positioning information will cause the INS to predict the distances from the receiver to all satellites. and distance change rate The presence of step-like gross errors will ultimately cause all pseudoranges and pseudorange rate residuals to contain gross errors during spoofing attacks. Once the spoofing interference ends, the system will adjust the noise matrix based on the observation noise matrix. The invariant characteristics gradually converge. During the period from 359301s to 359817s, the deception interference gradually skewed the distance and velocity of PRNs 96, 97, and 98. The residuals in the system were gradually skewed to varying degrees according to the characteristics of the ramp-like deception, ultimately achieving the deception objective. Therefore, if the gross errors caused by the deception are not effectively suppressed when deception interference occurs, all observation residuals in the filtering system will contain gross errors to varying degrees, leading to false positives in deception detection and affecting the system's security.

[0248] To verify the effectiveness of the GNSS / INS tightly coupled adaptive anti-spoofing method integrating generalized likelihood ratio and sequential decision-making in deception detection and prevention, based on the experimental conditions described above, the deception interference detection rate and navigation accuracy of the tightly coupled system were compared among three different methods. Method 1 is a least-squares residual test algorithm based on extended Kalman filtering, denoted as EKF+LSRT; Method 2 is a residual test algorithm based on adaptive robust Kalman filtering, denoted as ARKF+RT; Method 3 is an adaptive anti-spoofing method integrating generalized likelihood ratio and sequential decision-making, denoted as DCRF+GLRT. The detection results are shown below. Figure 11 As shown, from Figure 11 It is known that due to the EKF algorithm fusion used in the tightly coupled GNSS / INS system, after the pseudorange and pseudorange rate of PRN 96, 97, and 98 were deceived, other observation channels were affected to varying degrees, resulting in a large number of false alarms in the LSRT method. Its pseudorange and pseudorange rate detection rates were 99.64% and 99.82%, respectively, and its false alarm rates were 80.54% and 70.26%, respectively. After adaptive robustness, the RT method achieved pseudorange and pseudorange rate detection rates of 95.29% and 95.80%, respectively, and false alarm rates of 1.17% and 0.23%, respectively. Compared to the LSRT method, the false alarm rate was significantly reduced, but the detection rate was still lower, especially when ramp-type deception interference occurred, as this method failed to accurately identify the small deviations generated at the beginning of ramp-type deception interference. Compared to the LSRT method, the GLRT method reduced the false alarm rates of pseudorange and pseudorange rate by 80.32%. The pseudorange and pseudorange rate detection rates were improved by 4.59% and 4.14% respectively compared to the RT method, preventing deceptive interference from affecting other observation channels through the residual vector. In particular, the method showed stable detection performance for the small deviations caused by ramp-type deceptive interference.

[0249] Based on spoofing detection, the anti-spoofing performance of EKF+LSRT, ARKF+RT, and DCRF+GLRT methods is compared, and their positioning trajectories are as follows: Figure 12 As shown, deception interference causes the EKF+LSRT calculated trajectory to deviate significantly from the reference trajectory, due to the observation noise matrix in the EKF algorithm. The values ​​are fixed, making it impossible to adjust the weights between GNSS pseudorange and pseudorange rate and INS estimated pseudorange and pseudorange rate based on current observations. The combined system over-relies on GNSS observations, leading to EKF system malfunction. While the ARKF+RT calculated trajectory is generally consistent with the reference trajectory, when the tightly coupled GNSS / INS system suffers from minor ramp-type deception interference, the RT method cannot identify small gross errors in the pseudorange and pseudorange rate at the start of the ramp-type deception. This prevents the ARKF system from adjusting the observation noise matrix during this stage. This leads to the phenomenon that tightly coupled GNSS / INS systems are deceived when they cannot detect subtle ramp-type deception interference; the DCRF+GLRT method dynamically adjusts the equivalent weight factor based on the GLRT detection results. and global adaptive factor Its trajectory coincides with the reference trajectory, demonstrating stronger robustness compared to the EKF+LSRT and ARKF+RT methods.

[0250] To better compare the navigation accuracy of EKF+LSRT, ARKF+RT, and DCRF+GLRT methods in terms of anti-spoofing, the navigation errors of the three methods were statistically analyzed, such as... Figure 13 As shown, when deception interference occurs, the position, velocity, and attitude information of the EKF+LSRT method diverges rapidly, the filtering system becomes disordered, and navigation information becomes unusable; however, after the deception interference ends, its position and velocity information gradually recovers and converges. In contrast, the ARKF+RT method exhibits more stable position, velocity, and attitude information and higher navigation accuracy during deception interference than the EKF+LSRT method. However, when dealing with small slope-type deception interference, the small deviations generated in the initial stage of deception are not identified in time, causing the navigation information during this period to still be affected by deception. The DCRF+GLRT method shows higher stability and robustness compared to the former two.

[0251] In terms of accuracy, the DCRF+GLRT method achieved position RMS of 0.90 m, 1.03 m, and 2.35 m in the east, north, and altitude directions, respectively; velocity RMS of 0.02 m / s, 0.03 m / s, and 0.04 m / s; and pitch, roll, and heading RMS of 0.05°, 0.07°, and 0.37°, respectively. Compared to the ARKF+RT method, the DCRF+GLRT method improved position RMS by 90.1%, 94.1%, and 87.0% in the north, east, and altitude directions, respectively; velocity RMS by 92.1%, 94.7%, and 91.7%; and pitch, roll, and heading RMS by 64.7%, 54.2%, and 88.5%, respectively, significantly enhancing navigation accuracy.

[0252] The above description is merely the most basic specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any substitutions that can be understood by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A GNSS / INS tightly coupled adaptive anti-spoofing method based on generalized likelihood ratio and sequential decision, characterized in that, Includes the following steps: Step 1: Construct a tightly coupled GNSS / INS model. Combine the INS error state equation with the GNSS error state equation to construct a tightly coupled system state equation. Take the pseudorange and pseudorange rate difference between GNSS and INS as the system measurement values ​​and construct the system measurement equation. Step 2: Construct a GNSS deception jamming model. Generative deception jamming autonomously generates deception signals and applies a controllable offset to their code phase. It artificially constructs pseudorange and pseudorange rate deviations. Based on the deviation change characteristics, it can be divided into step-type and ramp-type deception, thereby inducing the target receiver to smoothly deviate from the real navigation trajectory. Step 3: Propose a multi-satellite deception sequential decision-making method based on generalized likelihood ratio. Quickly eliminate the non-deception case through global chi-square test. For the deception case, calculate the conditional anomaly statistics one by one based on the current set of remaining satellites. Use Cholesky decomposition to ensure numerical stability and remove the most suspicious satellite corresponding to the maximum statistic until all remaining satellites pass the consistency test, so as to achieve accurate isolation between deception signal and normal signal. Step 4: Propose an adaptive filtering method based on generalized likelihood ratio statistics. By constructing equivalent weight factors to dynamically adjust the observation noise covariance, and combining it with global adaptive factors to correct the state covariance update, the standard Kalman filter is maintained under normal conditions, and the observation correction is reduced or cut off under abnormal conditions, thus forming a closed-loop mechanism that integrates detection and suppression, taking into account both anti-spoofing robustness and anti-spoofing filtering accuracy. Step 1 describes the construction of a tightly coupled GNSS / INS model, which involves constructing a tightly coupled system state equation by combining the INS error state equation with the GNSS error state equation. The pseudorange and pseudorange rate difference between GNSS and INS are taken as system measurement values, and the system measurement equation is constructed. The specific steps are as follows: Step 1-1: In a tightly coupled GNSS / INS navigation system, construct the tightly coupled system state equations from the INS error state equations and the GNSS error state equations: （1） Right now: （2） In the formula, the system state vector is: （3） In the formula, For attitude error, For speed error, For position error, For zero bias of the gyroscope, For accelerometer zero bias, For receiver clock bias, For the deviations between each satellite system relative to the GPS system, For receiver clock drift, , , , and These represent the inter-system biases of GLONASS, Galileo, BDS, and QZSS relative to GPS, respectively. Steps 1-2: In a tightly coupled GNSS / INS navigation system, the pseudorange and pseudorange rate difference between GNSS and INS are taken as system measurement values, and the system measurement equations are constructed as follows: （4） In the formula, Represents the observation matrix; The measurement noise vector is represented by the following formula: ; Observation vector It can be represented as: （5） （6） In the formula, and These refer to the original pseudorange and Doppler observations, respectively, indicated by the superscript. Indicates frequency, This refers to satellite systems, including GPS, GLONASS, GALILEO, BDS, and QZSS; and These represent the distance from the receiver to the satellite predicted by INS and the rate of change of that distance, respectively. and These are the sum of error corrections related to the receiver clock for pseudorange and Doppler, respectively; and The observation matrix in the measurement equation is represented as follows: (The original text contains several grammatical errors and inconsistencies, which have been omitted from the translation.) （7） In the formula, This represents the line-of-sight vector from the receiver to the satellite; It is the transformation matrix that converts position disturbance errors from the navigation coordinate system to the Earth coordinate system; It is the transformation matrix that converts the velocity error from the navigation coordinate system to the Earth coordinate system; Step 2 describes the construction of a GNSS deception jamming model, which autonomously generates deception signals through generative deception jamming, applies a controllable offset to its code phase, and artificially constructs pseudorange and pseudorange rate deviations. Based on the deviation change characteristics, it can be divided into step-type and ramp-type deception, thereby inducing the target receiver to smoothly deviate from the real navigation trajectory. The specific steps are as follows: Step 2-1: The GNSS receiver provides the real satellite signal; the detection module provides the target's position and velocity in real time; the deception generation module generates a corresponding deception signal according to the deception strategy, and the transmission power is adjusted to the target antenna by the deception signal transmission module; at the RF front end of the GNSS receiver, the received signal contains the real signal, the deception signal, and noise, and its expression is as follows: （8） In the formula, the subscript and These respectively represent identifiers for real satellite signals and deceptive satellite signals; and These represent the sets of real satellite signals and spoofed satellite signals, respectively. , , , , These represent the power, navigation message, code delay, carrier phase, and Doppler frequency of the actual satellite signal, respectively. , , , , These represent the power of the deception satellite signal, the navigation message, the code delay, the carrier phase, and the Doppler frequency, respectively. It has a mean of zero and a variance of 0, with a variance of 0. Gaussian white noise; Step 2-2: The actual signal received by the target receiver is : （9） In the formula, The nominal carrier frequency of the GNSS signal; Ignoring the internal frequency conversion error of the deception device, the frequency of the deception signal received by the target is: : （10） In the formula, For the interference source relative to the satellite Doppler frequency shift; The offset of the deceptive signal frequency relative to the real signal frequency is: （11） Multiplying both sides of the above equation by the carrier wavelength and rearranging the terms, we obtain the speed deception mathematical model: （12） In the formula, For the deception of the first The pseudorange rate of a single satellite; The pseudorange rate is the actual measurement rate of the satellite signal. To achieve speed deception against the first The carrier frequency offset applied by the satellite signal; based on the characteristics of step spoofing and ramp spoofing, the model is established as follows: （13） In the formula, To deceive and interfere with the slope; The deviation between the true pseudorange rate and the deceptive pseudorange rate; when At that time, it represents a ramp-type pseudo-range rate deception; At this time, it represents a step-like pseudo-range rate deception; Steps 2-3: The receiver measures the pseudorange of multiple satellites. Solve its own position and clock difference Its expression is: （14） When the target receives a GNSS spoofing signal, the spoofing signal guides the target to follow a spoofed navigation trajectory by modifying pseudorange observation information; assuming Deception at all times causes the first pseudorange of a satellite There is a deviation Then the first The pseudorange of the satellite after being deceived is: （15） make , The code phase delay of the deception signal is calculated based on the characteristics of step deception and ramp deception, and the model is established as follows: （16） In the formula, To deceive and interfere with the slope; The deviation between the true pseudorange and the deceptive pseudorange; when At that time, it represents a ramp-type pseudo-distance deception; At this time, it represents a step-like pseudo-distance deception.

2. The GNSS / INS tightly coupled adaptive anti-spoofing method based on generalized likelihood ratio and sequential decision-making as described in claim 1, characterized in that, Step 3 proposes a multi-satellite deception sequential decision-making method based on generalized likelihood ratio. It quickly eliminates the non-deception case through global chi-square test. For the deception case, it calculates the conditional anomaly statistics based on the current set of remaining satellites one by one, uses Cholesky decomposition to ensure numerical stability, and removes the most suspicious satellite corresponding to the maximum statistic until all remaining satellites pass the consistency test, thus achieving accurate isolation between deception signals and normal signals. The specific steps are as follows: Step 3-1: The tightly coupled GNSS / INS system fuses the original satellite measurements with the predicted values ​​based on INS solutions, improving the accuracy of the navigation system; the discrete-time dynamic model can be written in the following form: （17） Considering tightly coupled GNSS / INS systems The Kalman filter update at time step 1 makes This is the pseudorange observation vector; The observation matrix; Predict the state in one step; To predict state covariance; To observe the noise covariance matrix; Define the innovation vector as: （18） In the absence of deception, the innovation follows a zero-mean Gaussian distribution: （19） In the formula, The information covariance matrix represents the uncertainty between prediction and observation; When the When a satellite is subjected to deception interference, its pseudorange observations and pseudorange rate observations contain an unknown bias. This causes the new information to shift on that component; at this point, the new information can be expressed as: （20） In the formula, To avoid deceiving the new information, For the first One standard basis vector; if multiple satellites are deceived and interfered with, then , For the deception set; Step 3-2: When a single satellite is subjected to deception interference, assume that the first... The satellite has a deviation. All other observation satellites are functioning normally; therefore, the null and alternative hypotheses are: （21） In the formula, To provide an interference-free environment; To avoid disturbing the environment; Below, the innovation vector follows a Gaussian distribution. To detect this bias, a generalized likelihood ratio statistic is constructed: （22） According to the probability density function of the multivariate Gaussian distribution: （23） After taking the logarithm, the bias caused by deception To maximize; let ,have to: （24） Substituting the likelihood ratio and simplifying, we obtain the test statistic: （25） exist Down, ,therefore This refers to a chi-square distribution with 1 degree of freedom; this distribution characteristic originates from the classic conclusion of Gaussian quadratic forms, for... ,have ;and Consider the quadratic form in a given direction The degrees of freedom of the chi-square distribution of the projection on the surface are determined by the constraint dimension; To further reveal the physical meaning of this statistic, Divide into blocks, let （26） In the formula, Indicates the first The variance of the information of each observation; Indicates the first The covariance of one observation with the rest of the observations; This means removing the first... After one observation, the covariance submatrix among the remaining observations; Then, according to the formula for finding the inverse of a block matrix, we can obtain: （27） therefore, （28） Given other observations, The conditional distribution is ,therefore It is the first The square of the conditionally standardized residual of the nth observation represents the... This statistic measures the degree of deviation between an observation and a predicted value based on other observations, while fully preserving the correlation information between observations; this statistic is obtained through conditional mean. The influence of other observations was eliminated, thus achieving optimal detection performance in the single-fault scenario; a significance level was set. Calculate the upper quantile of the chi-square distribution. ;like If so, then refuse. Determine the first The satellite is subject to deception and interference; Step 3-3: When multiple satellites are involved in deception, directly applying the generalized likelihood ratio test for single-satellite deception to each pseudorange channel independently will lead to misjudgment, because the deception interference will pass through the information covariance matrix. The off-diagonal elements affect the conditional mean of other pseudorange channels, causing normal satellites to... It also gets bigger; Therefore, the multi-fault identification problem is transformed into a series of sequential hypothesis tests. At each step, the most likely spoofing satellites are identified and separated based on the current remaining set until the statistics of the remaining satellites all pass the consistency test. First, calculate the global chi-square statistic: （29） In a deception-free environment ;like If there is no fault at the current moment and all satellites are fault-free, then the filtering calculation is performed directly. This global check can quickly eliminate fault-free cases and reduce computational complexity; If the global check fails, it indicates that at least one source of deception exists in the current observation set, and the sequential decision-making process begins; let the current set of remaining satellite indexes be denoted as . ,initial Deceiving the collection ; in the Step, based on the observed subvectors of the current remaining set Covariance Submatrix For each Calculate the statistic: （30） In the formula, yes China's corresponding satellite Standard basis vectors; It measures the degree of conditional anomaly of each satellite relative to the other remaining satellites in the current remaining set; To further ensure numerical stability, Cholesky decomposition is adopted; let... ,but: （31） Expanding it, we get: （32） In the formula, The statistic can be written as: （33） According to sequential decision theory, at each step, the satellite with the greatest impact on the current global anomaly should be removed; this decision is achieved by the following maximization criterion: （34） From the perspective of likelihood ratio, The corresponding observed value causes the generalized likelihood function to reach its maximum value among the candidate hypotheses, thus making it statistically the most likely source of the fault. Therefore, it is considered the most likely source to deceive the satellite and is added to the deception set. And remove from the remaining set: ; The updated residual set should be used to recalculate the statistics, but to simplify the calculation, the following identity can be used to avoid recalculating the inverse: （35） In the formula, Is it removal? The remaining set before; when the remaining set All satellites in China If the remaining satellites are deemed to be functioning normally, the iteration stops. In the sequential decision-making process, each iteration iterates through the set of remaining satellites. All satellites are examined simultaneously, and the observations of the deceitful satellites are isolated from those of the normal satellites. A locally optimal choice is made, ultimately achieving accurate identification of multi-satellite deception.

3. The GNSS / INS tightly coupled adaptive anti-spoofing method based on generalized likelihood ratio and sequential decision-making as described in claim 1, characterized in that, Step 4 proposes an adaptive filtering method based on generalized likelihood ratio statistics. This method constructs equivalent weighting factors to dynamically adjust the observation noise covariance and combines it with global adaptive factors to correct the state covariance update. Under normal conditions, it maintains the standard Kalman filter and reduces the weighting or cuts off the observation correction under abnormal conditions, thus forming a closed-loop mechanism that integrates detection and suppression, taking into account both anti-spoofing robustness and anti-spoofing filtering accuracy. The specific steps are as follows: Step 4-1: Based on the generalized likelihood ratio statistic, construct the first... Equivalent weighting factors for each observation: （36） It can be seen from equation (36) that The larger the value, the more significant the deviation between observations and model predictions; while IMUs possess short-term high-precision characteristics, GNSS observation noise is significant; when hour, Normal observation weights remain unchanged; when hour, And follow Increase the monotonically decreasing weight to reduce the weight of abnormal observations; Construct the equivalent observation noise covariance matrix using equivalent weight factors: （37） In the formula, This is equivalent to reducing the variance of the original observation noise. In the Kalman filter framework, the observation noise covariance is inversely proportional to the gain matrix, therefore... The smaller the value, the lower the weight of the corresponding observation in the state update; when When the value approaches 0, the corresponding observation can be considered to have been completely eliminated; Step 4-2: To address the overall change in deception intensity, a global adaptive factor is introduced. Dynamically adjust the prediction covariance matrix: （38） In the formula, This is the global chi-square statistic; This is a preset lower threshold value; For degrees of freedom The upper quantile of the chi-square distribution, For another significance level; when At that time, the formula is reduced to the covariance update of the standard Kalman filter. GNSS observations showed no abnormalities, and the filter was functioning normally; when When the correction of covariance by the observations is partially weakened, the filter's confidence in the current observations decreases, but it still retains a certain correction capability, balancing anti-spoofing and convergence speed under normal observation conditions; when At this point, the overall information significantly exceeds the chi-square threshold, indicating strong deception, and the covariance update formula degenerates into... At this point, the filter updates its state solely through time propagation, effectively preventing the covariance from being pulled toward an incorrect value by deceiving the observations and preventing the filter from exhibiting "false convergence". global adaptive factor Substituting into the covariance update formula, we get: （39） The equivalent weighting factors and global adaptive metric constructed through equations (36)-(39) essentially dynamically adjust the observation noise matrix and the state covariance matrix by deceiving the detection statistic. When the system is normal, the filter performs a standard Kalman filter update to maintain optimal estimation performance. When there are weak anomalies, the observation values ​​affect the observation noise matrix. and covariance matrix Dynamic adjustments are made to avoid over-response of the filter due to slight disturbances; when strong spoofing is detected, the observations are completely cut off from the covariance. The correction retains only time propagation, while also incorporating the observation noise matrix. The adjustment allows the filter to maintain its state through inertial recursion, thereby isolating the influence of deception interference on the state uncertainty and effectively balancing the robustness against deception with the filtering accuracy under deception-free conditions.

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