Gps spoofing detection and positioning recovery method and system for vehicle safety positioning
By constructing an exponentially weighted moving average discriminant statistic and a GPS-IMU fusion extended Kalman filter, the problem of insufficient adaptability of GPS spoofing detection methods to covert attacks is solved, achieving stable positioning recovery in complex environments and improving the continuity and accuracy of vehicle positioning.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHEASTERN UNIV CHINA
- Filing Date
- 2026-04-30
- Publication Date
- 2026-07-28
AI Technical Summary
Existing GPS spoofing detection methods are not adaptable to covert attacks, and positioning recovery methods have poor accuracy and stability under strong spoofing conditions, making it difficult to achieve stable and continuous vehicle positioning in complex environments.
By constructing an exponentially weighted moving average (EWMA) discriminant statistic based on residual statistics and combining it with a GPS-IMU fusion extended Kalman filter, we can detect and recover GPS spoofing attacks. We can also use the fusion weight relationship and Kalman gain trace for information extraction and error correction.
It improves the ability to identify concealed deception signals, reduces the probability of missed detection and false alarm rate, achieves positioning continuity and robustness in complex environments, reduces error accumulation, and improves positioning accuracy and reliability.
Smart Images
Figure CN122469372A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of vehicle positioning security technology, and in particular to a GPS spoofing detection and positioning recovery method and system for vehicle security positioning. Background Technology
[0002] With the rapid development of intelligent vehicles and autonomous driving technologies, the Global Positioning System (GPS) is widely used in vehicle positioning and navigation systems due to its wide coverage and high positioning accuracy. However, GPS signals have relatively weak power during transmission, making them susceptible to external interference and malicious attacks, especially GPS spoofing attacks. Attackers can forge or replay satellite signals, causing the receiver to output incorrect positioning results. These erroneous results are often consistent and continuous in form, posing a serious threat to vehicle navigation safety and driving reliability. Particularly in autonomous driving and advanced driver assistance systems, GPS spoofing attacks can lead to incorrect vehicle decisions, posing significant safety risks.
[0003] To address the threat of GPS spoofing attacks, existing research has proposed various detection methods, mainly including signal feature analysis-based methods, statistical detection methods, and machine learning-based methods. Statistical detection methods typically utilize information such as positioning residuals, pseudorange consistency, or filtering innovation, setting fixed or empirical thresholds to determine the presence of anomalies. Machine learning methods rely on large amounts of prior data for model training. However, these methods often struggle to detect sophisticated, progressive GPS spoofing attacks in a timely manner, and their detection performance is highly dependent on parameter selection and attack patterns, indicating that their adaptability and stability still need improvement.
[0004] After detecting a GPS spoofing attack, effectively recovering the vehicle's location is a key focus of existing technologies. Some methods directly discard GPS measurements upon detecting the anomaly, relying solely on inertial measurement units (IMUs) or other sensors for short-term positioning; others re-estimate the vehicle's position through multi-sensor fusion. However, completely discarding GPS information can lead to rapid error accumulation, while directly using the attacked GPS measurements under strong spoofing conditions may introduce significant system bias. Existing recovery methods struggle to balance positioning accuracy and robustness.
[0005] In summary, existing GPS spoofing protection technologies are insufficiently adaptable to covert attacks during the detection phase, and their utilization of attacked measurements during the recovery phase is relatively limited, making it difficult to achieve stable and continuous vehicle positioning in complex attack scenarios. Therefore, there is an urgent need for a GPS spoofing detection and positioning recovery method that can balance detection sensitivity and positioning recovery robustness to improve the positioning security and reliability of vehicles in complex environments and under attack conditions. Summary of the Invention
[0006] To address the shortcomings of existing technologies, this application provides a GPS spoofing detection and positioning recovery method and system for vehicle security positioning, in order to solve the problems of insufficient adaptability of existing GPS spoofing detection methods to covert attacks, and poor positioning accuracy and stability of existing positioning recovery methods under strong spoofing conditions.
[0007] The technical solution of this invention is as follows:
[0008] On the one hand, the present invention provides a GPS spoofing detection and location recovery method for vehicle safety positioning, comprising the following steps:
[0009] Collect GPS sensor data and inertial measurement unit sensor data of the target vehicle, and perform fusion estimation on the GPS sensor data and inertial measurement unit sensor data to obtain the fusion state estimation result and the corresponding filtering residual;
[0010] Based on the filtered residuals, an exponentially weighted moving average method is used to obtain an exponentially weighted moving average discrimination statistic for GPS spoofing attack detection.
[0011] After detecting a GPS spoofing attack, a first-stage rough estimate of the target vehicle's true location is obtained based on the fused state estimation results before the GPS spoofing attack and the global satellite navigation system sensor data acquired under the GPS spoofing attack.
[0012] Based on the coarse estimation results of the first stage and the sensor data of the inertial measurement unit, a fine estimation result of the true position of the target vehicle is obtained, realizing positioning recovery under GPS spoofing attack conditions.
[0013] Furthermore, the process of collecting GPS sensor data and inertial measurement unit (IMU) sensor data from the target vehicle, and fusing and estimating the GPS sensor data and IMU sensor data to obtain the fused state estimation result and the corresponding filtering residual, specifically includes the following steps:
[0014] A1: Collect GPS sensor data and inertial measurement unit sensor data of the target vehicle;
[0015] First, a model of a vehicle multi-sensor fusion positioning system is constructed. The vehicle multi-sensor fusion positioning system consists of a global satellite navigation system receiver and an inertial measurement unit, which are used to acquire global satellite navigation system sensor data and inertial measurement unit sensor data, respectively.
[0016] The discrete state equation of the vehicle multi-sensor fusion localization system, i.e., the model of the vehicle multi-sensor fusion localization system, is shown below:
[0017] (1);
[0018] in, Represents the discrete time step. This represents the state vector of the target vehicle. Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in velocity in direction, Indicates the target vehicle is in velocity in direction, Indicates the target vehicle is in velocity in direction, Indicates clock offset, It is the clock drift rate, which refers to the first derivative of the clock offset with respect to time; Indicates transpose;
[0019] A first-order autoregressive process is used to characterize clock skew and clock drift rate, i.e.:
[0020] (2);
[0021] (3);
[0022] in, Indicates time interval, Additive white Gaussian noise representing the clock drift rate;
[0023] Therefore, the measurement equations characterizing the target vehicle that acquires both global navigation satellite system sensor data and inertial measurement unit sensor data are as follows:
[0024] (4);
[0025] in, It is a set of measured values and , These are the measured values of the inertial measurement unit sensor data. These are measurements from sensor data of the global satellite navigation system. It is a set of measurement functions, and , For the inertial measurement unit measurement function, Measurement functions for global satellite navigation systems; Representing all measurement noise, following a zero-mean Gaussian distribution, its covariance matrix is: , Construct operators for block diagonal matrices. For the noise covariance of the inertial measurement unit, For the noise covariance of global satellite navigation systems;
[0026] A2: The GPS-IMU fusion extended Kalman filter is used to fuse and estimate the sensor data of the global satellite navigation system and the sensor data of the inertial measurement unit to obtain the fusion state estimation result; the GPS-IMU fusion extended Kalman filter is an extended Kalman filter;
[0027] First, construct the linear state transition equation:
[0028] (5);
[0029] in, Here is the state transition matrix. The process noise is represented by the following formula: ;
[0030] The state transition matrix is defined as follows:
[0031] (6);
[0032] in, for The identity matrix, for The zero matrix, Let be the row number of the matrix. is the number of columns in the matrix;
[0033] The covariance matrix of the process noise is:
[0034] (7);
[0035] (8);
[0036] (9);
[0037] in, for The identity matrix, It is the standard deviation of the target vehicle speed noise. The standard deviation of clock drift rate noise;
[0038] Then, the implementation of the GPS-IMU fusion extended Kalman filter includes a prediction stage and a measurement update stage. The prediction stage is used to predict the fusion state estimation result, and the output of the measurement update stage is used for the next prediction stage.
[0039] The prediction phase is given by the following formula:
[0040] (10);
[0041] (11);
[0042] The measurement update phase is given by the following formula:
[0043] (12);
[0044] (13);
[0045] (14);
[0046] in, This is the prior state vector, i.e., the fused state estimation result; For the posterior state vector, To estimate the covariance matrix a priori, To estimate the covariance matrix posteriorly, Let be the covariance matrix of the process noise. The Kalman gain matrix of the extended Kalman filter for GPS-IMU fusion. The Jacobian matrix of the GPS-IMU fused extended Kalman filter is defined as follows: , The Jacobian matrix of the inertial measurement unit. For the Jacobian matrix of global satellite navigation systems, For measurement functions;
[0047] A3: Calculate the filtering residuals based on the fusion state estimation results;
[0048] (15);
[0049] in, This represents the filtering residual.
[0050] Furthermore, the method of using exponentially weighted moving average based on filtered residuals to obtain an exponentially weighted moving average discrimination statistic for GPS spoofing attack detection specifically includes the following steps:
[0051] B1: Calculate residual statistics based on the filtered residuals, including the square norm and covariance of the filtered residuals;
[0052] (16);
[0053] in, It is the filter residual. The covariance matrix, It is the square norm of the filter residual.
[0054] (17);
[0055] in, Let be the covariance matrix of the filtered residuals;
[0056] B2: Calculate the index-weighted moving average discriminant statistic based on the residual statistic;
[0057] The discriminant statistic of the exponentially weighted moving average is calculated as follows:
[0058] (18);
[0059] (19);
[0060] (20);
[0061] in, This is an exponentially weighted moving average statistic. This is the exponentially weighted moving average statistic from the previous time step. It is the coefficient of the exponentially weighted moving average, which is related to the offset. Proportional It is the sample mean. For sample covariance, For offset estimation; The covariance of the exponentially weighted moving average statistic. This is the discriminant statistic for the exponentially weighted moving average. It is the inverse of the covariance of the exponentially weighted moving average statistic;
[0062] (twenty one);
[0063] B3: Compare the exponentially weighted moving average discrimination statistic with the preset detection threshold. When the discrimination condition is met, it is determined that a GPS spoofing attack has occurred.
[0064] The discrimination criteria are as follows:
[0065] (twenty two);
[0066] in, This is the preset detection threshold.
[0067] Furthermore, after detecting a GPS spoofing attack, the first-stage coarse estimation result of the target vehicle's true location is obtained based on the fused state estimation result before the GPS spoofing attack and the global satellite navigation system sensor data acquired under the GPS spoofing attack. This specifically includes the following steps:
[0068] C1: Calculate the Kalman gain matrix for the global satellite navigation system and the inertial measurement unit, respectively;
[0069] Set the inertial measurement unit sensor data as Global Navigation Satellite System sensor data is Then the Kalman gain ,Measurement And Jacobi matrix It can be represented in the form of a partitioned matrix, as follows: , and , Kalman gain corresponding to the inertial measurement unit, The Kalman gain corresponding to the global satellite navigation system; This is the Jacobian matrix corresponding to the inertial measurement unit. The Jacobian matrix corresponding to the global satellite navigation system;
[0070] The steady-state expectation of the posterior state estimate of the GPS-IMU fused extended Kalman filter is:
[0071] (twenty three);
[0072] in, The Kalman gain matrix of the GPS-IMU fused extended Kalman filter after steady state. This is the Kalman gain matrix corresponding to the inertial measurement unit. The Kalman gain matrix corresponding to the global satellite navigation system; For the reason A definite state, For the reason A definite state; For posterior state estimation;
[0073] C2: Calculate the trace values corresponding to the Kalman gain matrices of the global navigation satellite system sensor data and the inertial measurement unit sensor data;
[0074] C3: Construct the weighting coefficients of the global navigation satellite system and the inertial measurement unit based on the trace values corresponding to the Kalman gain matrices of the sensor data of the global navigation satellite system and the sensor data of the inertial measurement unit;
[0075] The state vector of the target vehicle There are 8 variables, including the position of the target vehicle. and clock offset It is the observed state variable; velocity and clock drift rate These are hidden state variables, calculated from the observed state variables;
[0076] Kalman gain matrix Follow the following format:
[0077] (twenty four);
[0078] in, for Medium component right Medium component The weights;
[0079] set up , and ,in , , for , , The corresponding position; , , for , , Substituting the corresponding clock offset into formula (23) yields:
[0080] (25);
[0081] let Represents the set of observed state variables, i.e. Then, formula (23) simplifies to include only the set of observed state variables. Format:
[0082] (26);
[0083] in, for The corresponding extended Kalman filter's Kalman gain matrix after steady state. for Posterior state estimation, for The Kalman gain matrix corresponding to the inertial measurement unit. for The Kalman gain matrix corresponding to the Chinese global satellite navigation system; For the reason Determined observed state variables, For the reason Determined observed state variables;
[0084] Further simplifying formula (26):
[0085] (27);
[0086] in, Represents the trace value;
[0087] The weighting coefficient of the inertial measurement unit is:
[0088] (29);
[0089] The weighting coefficient for global satellite navigation systems is:
[0090] (30);
[0091] in, For inertial measurement units, weighting coefficients. For global satellite navigation systems, Discrete time step time , Discrete time step time ;
[0092] C4: The fusion state estimation results and the global satellite navigation system sensor data obtained under GPS spoofing attack are weighted and fused according to the weight coefficients of the global satellite navigation system and the weight coefficients of the inertial measurement unit to obtain the first-stage rough estimation results of the true position of the target vehicle.
[0093] The first-stage rough estimation result of the target vehicle's true location The formula is:
[0094] (32);
[0095] in, Discrete time step The fusion state estimation results at that time This is the first-stage rough estimate of the target vehicle's true location. This refers to sensor data from the Global Navigation Satellite System obtained under a GPS spoofing attack.
[0096] Furthermore, the detailed estimation of the target vehicle's true position based on the coarse estimation result from the first stage and the sensor data from the inertial measurement unit, thereby achieving positioning recovery under GPS spoofing attack conditions, specifically involves:
[0097] A newly designed extended Kalman filter with refined predictions is used to fuse the coarse estimation results from the first stage with the sensor data from the inertial measurement unit to generate a refined estimation result. The set of measurements used in this stage It includes two parts, namely ;
[0098] The extended Kalman filter with fine prediction includes a prediction phase and a measurement update phase;
[0099] The prediction phase is represented as:
[0100] (33);
[0101] (34);
[0102] The measurement update phase is written as:
[0103] (35);
[0104] (36);
[0105] (37);
[0106] in, This represents the prior state estimate, i.e., the detailed estimate of the true position of the target vehicle; Represents the state transition matrix. This represents the posterior state estimate. Denotes the prior covariance matrix. Denotes the posterior covariance matrix. Indicates the noise covariance; Indicates Kalman gain, Represents the observation matrix. Represents the observation noise covariance. Represents the observation vector. Represents the observation function;
[0107] definition , Covariance of the first-stage rough estimate results:
[0108] (39);
[0109] in, The standard deviation of a single-point positioning solution of a global navigation satellite system without GPS spoofing attacks is represented by the symbol. Represents the Hadamah altar;
[0110] The detailed estimate of the target vehicle's true location is then input into the global satellite navigation system to help reconstruct its true location.
[0111] On the other hand, the present invention also provides a GPS spoofing detection and location recovery system for vehicle safety positioning, which implements a GPS spoofing detection and location recovery method for vehicle safety positioning, including:
[0112] The data acquisition module is used to collect global satellite navigation system sensor data and inertial measurement unit sensor data of the target vehicle;
[0113] The fusion estimation module is used to perform fusion estimation on sensor data from the Global Navigation Satellite System and sensor data from the Inertial Measurement Unit to obtain the fusion state estimation result and the corresponding filtering residual.
[0114] The deception detection module is used to detect GPS deception attacks by using the exponentially weighted moving average method based on the filtered residuals to obtain the exponentially weighted moving average discrimination statistic.
[0115] The first positioning recovery module is used to obtain a first-stage rough estimate of the target vehicle's true location based on the fused state estimation results before the GPS spoofing attack and the global satellite navigation system sensor data obtained under the GPS spoofing attack.
[0116] The second positioning recovery module is used to obtain a fine estimate of the target vehicle's true position based on the coarse estimation result of the first stage and the sensor data of the inertial measurement unit, thereby realizing positioning recovery under GPS spoofing attack conditions.
[0117] Thirdly, this application proposes an electronic device, including: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to perform the GPS spoofing detection and positioning recovery method for vehicle safety positioning.
[0118] Fourthly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the GPS spoofing detection and location recovery method for vehicle safety positioning.
[0119] Fifthly, this application proposes a computer program product, including a computer program or instructions that, when executed by a processor, implement the aforementioned GPS spoofing detection and positioning recovery method for vehicle safety positioning.
[0120] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0121] This invention constructs an exponentially weighted moving average (EWMA) discriminant statistic based on residual statistics and introduces an EWMA coefficient related to the attack offset. This allows for dynamic adjustment of the weighting of historical information and current observations according to the magnitude of residual changes. When the offset is small in the early stages of an attack, a smaller EWMA coefficient is used to enhance the cumulative sensitivity to small changes; as the offset gradually increases, the EWMA coefficient is increased to accelerate the response. Therefore, compared to fixed-parameter detection methods, this invention can effectively identify slowly changing, covert deception signals without relying on prior attack models, reducing the probability of missed detections while suppressing false alarms caused by random noise.
[0122] Unlike existing technologies that directly remove anomalous GPS measurements, this invention establishes an analytical model based on the intrinsic relationship between the fused EKF output and the observations of each sensor. The fusion result can be represented as a weighted combination of the true and spoofed states. Furthermore, it utilizes the Kalman gain trace as an approximate weight index to achieve online weight estimation. This mechanism theoretically reveals the composition ratio of true and spoofed information in the fused positioning result, enabling the extraction of effective motion trend information from contaminated data even under GPS attacks, thus improving information utilization.
[0123] In the recovery phase, this invention first uses the fusion weight relationship to invert the true location and obtain a coarse estimate. Then, a new extended Kalman filter is constructed to fuse the coarse estimate with unattacked IMU data, thereby correcting the error and achieving convergence. This two-stage structure has the following advantages: the first stage achieves rapid decoupling from the attack's impact, providing initial recovery capability; the second stage utilizes the short-term high-precision characteristics of the IMU to suppress model errors and residual biases. Therefore, compared to single filtering or direct replacement strategies, this invention can significantly reduce the cumulative error caused by attacks, achieving rapid convergence and accuracy recovery of the positioning results. Attached Figure Description
[0124] Figure 1This is a flowchart of a GPS spoofing detection and positioning recovery method for vehicle safety positioning in an embodiment of the present invention. Detailed Implementation
[0125] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0126] Example 1:
[0127] This application combines an adaptive EWMA detection mechanism with two-stage fusion estimation to effectively detect and recover the location of progressive and covert GPS spoofing attacks without directly discarding the attacked GPS measurement information. This improves the continuity, robustness, and reliability of vehicle positioning in complex attack environments, making it well-suited for real-time positioning security tasks in autonomous driving and advanced driver assistance systems. Thus, it addresses the shortcomings of existing GPS spoofing detection methods in their insufficient sensitivity to covert attacks, and the serious error accumulation and poor positioning stability of existing positioning recovery methods under strong spoofing conditions.
[0128] This embodiment provides a GPS spoofing detection and location recovery method for vehicle security positioning, such as... Figure 1 As shown, it includes the following steps:
[0129] S1: Collect GPS sensor data and IMU sensor data of the target vehicle, and perform fusion estimation on the GPS sensor data and IMU sensor data to obtain the fusion state estimation result and the corresponding filtering residual;
[0130] S1.1: Collect GPS sensor data and IMU sensor data from the target vehicle;
[0131] In this embodiment, a vehicle multi-sensor fusion positioning system model is first constructed. The vehicle multi-sensor fusion positioning system mainly consists of a Global Navigation Satellite System (GPS) receiver and an Inertial Measurement Unit (IMU), which are used to acquire GPS sensor data and IMU sensor data, respectively.
[0132] The discrete state equation of the vehicle multi-sensor fusion localization system, i.e., the model of the vehicle multi-sensor fusion localization system, is shown below:
[0133] (1);
[0134] in, Represents the discrete time step. This represents the state vector of the target vehicle. Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in velocity in direction, Indicates the target vehicle is in velocity in direction, Indicates the target vehicle is in velocity in direction, Indicates clock offset, It is the clock drift rate, which refers to the first derivative of the clock offset with respect to time; Indicates transpose;
[0135] Because GPS sensor data and IMU sensor data need to be fused, and it is assumed that the GPS and IMU sensor data are synchronized, only the clock offset of the target vehicle is unknown. A first-order autoregressive process is used to characterize the clock offset and clock drift rate, i.e.:
[0136] (2);
[0137] (3);
[0138] in, Indicates time interval, The additive white Gaussian noise represents the clock drift rate. In addition, the speed of the target vehicle here is only an auxiliary variable in the extended Kalman filter (EKF) when estimating the position of the target vehicle, and can be determined based on the vehicle position.
[0139] In practical applications, the position and orientation of the target vehicle can be observed using a Global Navigation Satellite System (GPS) receiver and an Inertial Measurement Unit (IMU), therefore the measurement equation can be:
[0140] (4);
[0141] in, It is a set of measured values and , These are the measured values of the inertial measurement unit (IMU) sensor data. Measurements from GPS sensor data; It is a set of measurement functions, and , For inertial measurement unit (IMU) measurement functions, Measurement functions for the Global Navigation Satellite System (GPS); Representing all measurement noise, following a zero-mean Gaussian distribution, its covariance matrix is: , Construct operators for block diagonal matrices. For the noise covariance of the inertial measurement unit (IMU), The noise covariance of the Global Navigation Satellite System (GPS);
[0142] S1.2: In order to accurately estimate the attitude of the target vehicle, a GPS-IMU fusion extended Kalman filter is used to fuse and estimate the Global Navigation Satellite System (GPS) sensor data and Inertial Measurement Unit (IMU) sensor data to obtain the fusion state estimation result;
[0143] This method leverages the advantages of the extended Kalman filter (EKF) to effectively integrate multiple measurements under nonlinear conditions, thereby improving estimation accuracy.
[0144] First, construct the linear state transition equations for the constant-rate model:
[0145] (5);
[0146] in, Here is the state transition matrix. Let represent process noise, which is Gaussian distributed, and its covariance matrix is . ;
[0147] The state transition matrix is defined as follows:
[0148] (6);
[0149] in, for The identity matrix, for The zero matrix, Let be the row number of the matrix. is the number of columns in the matrix;
[0150] The covariance matrix of the process noise is:
[0151] (7);
[0152] (8);
[0153] (9);
[0154] in, for The identity matrix, It is the standard deviation (STD) of the target vehicle speed noise. The standard deviation (STD) of clock drift rate noise; and These are the process noise covariance matrices of the state subsystem and the clock subsystem, respectively.
[0155] Then, the implementation of the GPS-IMU fusion extended Kalman filter includes a prediction stage and a measurement update stage. The prediction stage is used to predict the fusion state estimation result, and the output of the measurement update stage is used for the next prediction stage.
[0156] The prediction phase is given by the following formula:
[0157] (10);
[0158] (11);
[0159] The measurement update phase is given by the following formula:
[0160] (12);
[0161] (13);
[0162] (14);
[0163] in, This is the prior state vector, i.e., the fused state estimation result; For the posterior state vector, To estimate the covariance matrix a priori, To estimate the covariance matrix posteriorly, Let be the covariance matrix of the process noise. The Kalman gain matrix of the extended Kalman filter for GPS-IMU fusion. The Jacobian matrix of the GPS-IMU fused extended Kalman filter is defined as follows: , The Jacobian matrix of the inertial measurement unit. For the Jacobian matrix of global satellite navigation systems, For measurement functions;
[0164] S1.3: Calculate the filtering residuals based on the fusion state estimation results;
[0165] (15);
[0166] in, This is the filter residual;
[0167] S2: Based on the filtered residuals, the Exponentially Weighted Moving Average (EWMA) method is used to obtain the Exponentially Weighted Moving Average (EWMA) discriminant statistic for GPS spoofing attack detection;
[0168] After obtaining the fusion state estimation results of the target vehicle, in order to identify whether it has been subjected to a GPS spoofing attack, the filter residuals are analyzed and the attack detection is achieved using the exponentially weighted moving average (EWMA) method.
[0169] S2.1: Calculate residual statistics based on the filtered residuals, including the square norm of the filtered residuals and the covariance of the filtered residuals;
[0170] (16);
[0171] in, It is the filter residual. The covariance matrix (statistical significance). This is the square norm of the filtered residuals, i.e., the residual statistic. This indicates a mismatch between the measurement and the prediction, and the filtered residuals can be observed. It is a Gaussian distribution with a mean of zero and a known covariance.
[0172] (17);
[0173] in, Let be the covariance matrix of the filtered residuals;
[0174] S2.2: Calculate the Exponentially Weighted Moving Average (EWMA) discriminant statistic based on the residual statistic;
[0175] The discriminant statistic of Exponentially Weighted Moving Average (EWMA) is calculated as follows:
[0176] (18);
[0177] (19);
[0178] (20);
[0179] in, This is an exponentially weighted moving average (EWMA) statistic. This is the exponentially weighted moving average (EWMA) statistic from the previous time step. It is the coefficient of the Exponentially Weighted Moving Average (EWMA), which is related to the offset. Proportional It is the sample mean. For sample covariance, For offset estimation; The covariance of the exponentially weighted moving average (EWMA) statistic. The discriminant statistic for the exponentially weighted moving average (EWMA) is... It is the inverse of the covariance of the exponentially weighted moving average (EWMA) statistic;
[0180] Generally speaking, the Exponentially Weighted Moving Average (EWMA) coefficient The calculation employs Markov chain, Monte Carlo, or checklist methods. In this invention, the exponentially weighted moving average (EWMA) coefficients... The average run length (ARL) profile was calculated and explored with the aid of Monte Carlo simulations. Selecting appropriate exponentially weighted moving average (EWMA) coefficients required offsetting... To estimate the average drift of the unknown process, the estimator for the controlled process is 0. However, the complex noise in the navigation process is difficult to analyze, and the estimation... This becomes challenging, hence the weighted moving average (EWMA) coefficient. It can be represented as follows:
[0181] (twenty one);
[0182] S2.3: Compare the Exponentially Weighted Moving Average (EWMA) discrimination statistic with the preset detection threshold. When the discrimination condition is met, it is determined that a GPS spoofing attack has occurred.
[0183] The discrimination criteria are as follows:
[0184] (twenty two);
[0185] in, The preset detection threshold;
[0186] When the exponentially weighted moving average (EWMA) discrimination statistic exceeds a preset detection threshold, it is determined that there is an anomaly in the current Global Navigation Satellite System (GPS) sensor data, and subsequent attack mitigation and positioning recovery mechanisms are triggered. When the exponentially weighted moving average (EWMA) discrimination statistic is lower than or equal to the preset detection threshold, it is considered to be in normal operation, and the regular fusion positioning process continues. Through the above method, anomalies can be detected in time at the beginning of GPS spoofing attacks, providing a reliable basis for subsequent location recovery, thereby improving the security and robustness of vehicle positioning.
[0187] S3: After detecting a GPS spoofing attack, based on the fusion state estimation results before the GPS spoofing attack and the Global Navigation Satellite System (GPS) sensor data obtained under the GPS spoofing attack, a first-stage rough estimation result of the target vehicle's true location is obtained;
[0188] In the event of a GPS spoofing attack, the true location of the target vehicle and deceptive positioning Inconsistencies may exist between them, such as the position of the target vehicle in the fusion state estimation results. The actual location of the target vehicle and deceptive positioning A compromise is made between them, falling into the area between them, so that the actual position of the target vehicle can be determined. Deceiving position The position of the target vehicle in the fusion state estimation results The quantitative relationship is used to obtain the true position of the target vehicle. Rough estimate ;
[0189] S3.1: Calculate the Kalman gain matrix for the Global Navigation Satellite System (GPS) and the Inertial Measurement Unit, respectively;
[0190] Set the inertial measurement unit (IMU) sensor data as Global Navigation Satellite System (GPS) sensor data is Then the Kalman gain ,Measurement And Jacobi matrix It can be represented in the form of a partitioned matrix, as follows: , and , Kalman gain corresponding to the inertial measurement unit (IMU), The Kalman gain corresponding to the Global Navigation Satellite System (GPS); This is the Jacobian matrix corresponding to the inertial measurement unit (IMU). This is the Jacobian matrix corresponding to the Global Navigation Satellite System (GPS);
[0191] The steady-state expectation of the posterior state estimate of the GPS-IMU fused extended Kalman filter is:
[0192] (twenty three);
[0193] in, The Kalman gain matrix of the GPS-IMU fused extended Kalman filter after steady state. This is the Kalman gain matrix corresponding to the inertial measurement unit (IMU). This is the Kalman gain matrix corresponding to the Global Navigation Satellite System (GPS); For the reason A definite state, For the reason A definite state; For posterior state estimation;
[0194] S3.2: Calculate the trace values corresponding to the Kalman gain matrices of the Global Navigation Satellite System (GPS) sensor data and the Inertial Measurement Unit (IMU) sensor data;
[0195] S3.3: Construct GPS weighting coefficients and IMU weighting coefficients based on the trace values corresponding to the Kalman gain matrices of GPS sensor data and IMU sensor data;
[0196] The state vector of the target vehicle There are 8 variables, including the position of the target vehicle. and clock offset It is the observed state variable; velocity and clock drift rate These are hidden state variables, calculated from the observed state variables;
[0197] Kalman gain matrix Follow the following format:
[0198] (twenty four);
[0199] in, for Medium component right Medium component The weights;
[0200] set up , and ,in , , for , , The corresponding position; , , for , , The corresponding clock offset, when substituted into formula (23), yields:
[0201] (25);
[0202] The above analysis shows that the obtained and , , The hidden state variables in G are irrelevant, although the off-diagonal elements in G with respect to velocity are irrelevant. , and They have large values, but they do not affect the estimation of the observed state variables;
[0203] let Represents the set of observed state variables, i.e. Then, equation (23) can be simplified to include only the set of observed state variables. The form is because this invention primarily observes state variables:
[0204] (26);
[0205] in, for The corresponding extended Kalman filter's Kalman gain matrix after steady state. for Posterior state estimation, for The Kalman gain matrix corresponding to the inertial measurement unit. for The Kalman gain matrix corresponding to the GPS global satellite navigation system; For the reason Determined observed state variables, For the reason Determined observed state variables;
[0206] To reduce computational complexity, equation (26) can be further simplified to the following equation:
[0207] (27);
[0208] in, Represents the trace value;
[0209] and Since they are all scalars, the final position variables follow the following relationship:
[0210] (28);
[0211] in, The results are the fusion state estimation results;
[0212] In addition, the discrete time step Adding it back, the weighting coefficients for the inertial measurement unit (IMU) are then:
[0213] (29);
[0214] The weighting factor for the Global Navigation Satellite System (GPS) is:
[0215] (30);
[0216] in, These are the weighting coefficients for the inertial measurement unit (IMU). The weighting coefficients for the Global Navigation Satellite System (GPS) are as follows: Discrete time step time , Discrete time step time ;
[0217] S3.4: The fusion state estimation result and the GPS sensor data obtained under GPS spoofing attack are weighted and fused according to the weight coefficients of the Global Navigation Satellite System (GPS) and the Inertial Measurement Unit (IMU) to obtain the first-stage rough estimation result of the true position of the target vehicle.
[0218] because and All are scalar values, resulting in:
[0219] (31);
[0220] in, Discrete time step The fusion state estimation results at that time This is the first-stage rough estimate of the target vehicle's true location. This refers to GPS sensor data obtained under a GPS spoofing attack.
[0221] Specifically, when a GPS spoofing attack occurs, and Both contain significant biases. Since inertial measurement unit (IMU) measurements are unaffected by GPS spoofing attacks, the first-stage rough estimate of the target vehicle's true position contains substantial biases. Still near the actual location, in order to obtain the first-stage rough estimate of the target vehicle's actual location. The formula was rewritten as:
[0222] (32);
[0223] S4: Based on the coarse estimation result of the first stage and the sensor data of the inertial measurement unit (IMU), a fine estimation result of the true position of the target vehicle is obtained, realizing the positioning recovery under the condition of GPS spoofing attack;
[0224] In this stage, a newly designed extended Kalman filter with refined predictions is used to fuse the coarse estimation results from the first stage with the inertial measurement unit (IMU) sensor data to generate a refined estimation result. This helps reduce errors in coarse estimations, and the set of measurements used at this stage... It includes two parts, namely ;
[0225] The extended Kalman filter with fine prediction also includes a prediction phase and a measurement update phase;
[0226] The prediction phase is represented as:
[0227] (33);
[0228] (34);
[0229] The measurement update phase is written as:
[0230] (35);
[0231] (36);
[0232] (37);
[0233] in, This represents the prior state estimate, i.e., the detailed estimate of the true position of the target vehicle; Represents the state transition matrix. This represents the posterior state estimate. Denotes the prior covariance matrix. Denotes the posterior covariance matrix. Indicates the noise covariance; Indicates Kalman gain, Represents the observation matrix. Represents the observation noise covariance. Represents the observation vector. Represents the observation function;
[0234] Specifically, the detailed estimation results of the target vehicle's true location. The initial value can be determined based on the initial value of the GPS-IMU fused extended Kalman filter. This setup means running both the GPS-IMU fusion extended Kalman filter and the proposed fine-prediction extended Kalman filter simultaneously. A major advantage is that a fine estimate of the location can be obtained immediately once spoofing is detected, but at the cost of a certain computational load.
[0235] definition , The covariance of the first-stage rough estimate determines the confidence level of the first-stage rough estimate. It is given by the following formula:
[0236] (38);
[0237] in, For variance, For covariance;
[0238] Among them, considering and The positioning uncertainties are not independent of each other, covariance Cov(p + [n],p spoof [n]) is not zero, therefore after simplification Written as:
[0239] (39);
[0240] in, The standard deviation of a single-point positioning solution of the Global Navigation Satellite System (GPS) without GPS spoofing attacks is represented by the sign. Represents the Hadamard.
[0241] The obtained precise location estimate is then input into the Global Navigation Satellite System (GPS) to help reconstruct the true location.
[0242] Example 2:
[0243] A GPS spoofing detection and location recovery system for vehicle safety positioning, comprising:
[0244] The data acquisition module is used to collect global satellite navigation system sensor data and inertial measurement unit sensor data of the target vehicle;
[0245] The fusion estimation module is used to perform fusion estimation on sensor data from the Global Navigation Satellite System and sensor data from the Inertial Measurement Unit to obtain the fusion state estimation result and the corresponding filtering residual.
[0246] The deception detection module is used to detect GPS deception attacks by using the exponentially weighted moving average method based on the filtered residuals to obtain the exponentially weighted moving average discrimination statistic.
[0247] The first positioning recovery module is used to obtain a first-stage rough estimate of the target vehicle's true location based on the fused state estimation results before the GPS spoofing attack and the global satellite navigation system sensor data obtained under the GPS spoofing attack.
[0248] The second positioning recovery module is used to obtain a fine estimate of the target vehicle's true position based on the coarse estimation result of the first stage and the sensor data of the inertial measurement unit, thereby realizing positioning recovery under GPS spoofing attack conditions.
[0249] Example 3:
[0250] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the GPS spoofing detection and positioning recovery method for vehicle safety positioning.
[0251] The electronic device may be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the GPS spoofing detection and location recovery method for vehicle safety positioning as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.
[0252] The processor is used to execute all or part of the steps in the GPS spoofing detection and location recovery method for vehicle safety positioning as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.
[0253] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the GPS spoofing detection and positioning recovery method for vehicle safety positioning described in the above embodiments.
[0254] Example 4:
[0255] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.
[0256] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the GPS spoofing detection and positioning recovery method for vehicle security positioning described in the various embodiments of this application.
[0257] The aforementioned storage media include: flash memory, hard disk, multimedia card, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disk, optical disk, server, APP (Application) application store, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned GPS spoofing detection and positioning recovery method for vehicle safety positioning.
[0258] Example 5:
[0259] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned GPS spoofing detection and positioning recovery method for vehicle safety positioning.
[0260] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.
[0261] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.
[0262] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.
[0263] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
[0264] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection 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 GPS spoofing detection and location recovery method for vehicle safety positioning, characterized in that, Includes the following steps: Collect GPS sensor data and inertial measurement unit sensor data of the target vehicle, and perform fusion estimation on the GPS sensor data and inertial measurement unit sensor data to obtain the fusion state estimation result and the corresponding filtering residual; Based on the filtered residuals, an exponentially weighted moving average method is used to obtain an exponentially weighted moving average discrimination statistic for GPS spoofing attack detection. After detecting a GPS spoofing attack, a first-stage rough estimate of the target vehicle's true location is obtained based on the fused state estimation results before the GPS spoofing attack and the global satellite navigation system sensor data acquired under the GPS spoofing attack. Based on the coarse estimation results of the first stage and the sensor data of the inertial measurement unit, a fine estimation result of the true position of the target vehicle is obtained, realizing positioning recovery under GPS spoofing attack conditions.
2. The GPS spoofing detection and positioning recovery method for vehicle safety positioning according to claim 1, characterized in that, The process of collecting GPS sensor data and inertial measurement unit (IMU) sensor data from the target vehicle, and fusing and estimating the GPS sensor data and IMU sensor data to obtain the fused state estimation result and the corresponding filtering residual, specifically includes the following steps: A1: Collect GPS sensor data and inertial measurement unit sensor data of the target vehicle; First, a model of a vehicle multi-sensor fusion positioning system is constructed. The vehicle multi-sensor fusion positioning system consists of a global satellite navigation system receiver and an inertial measurement unit, which are used to acquire global satellite navigation system sensor data and inertial measurement unit sensor data, respectively. The discrete state equation of the vehicle multi-sensor fusion localization system, i.e., the model of the vehicle multi-sensor fusion localization system, is shown below: （1）； in, Represents the discrete time step. This represents the state vector of the target vehicle. Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in The position of direction, Indicates the target vehicle is in velocity in direction, Indicates the target vehicle is in velocity in direction, Indicates the target vehicle is in velocity in direction, Indicates clock offset, It is the clock drift rate, which refers to the first derivative of the clock offset with respect to time; Indicates transpose; A first-order autoregressive process is used to characterize clock skew and clock drift rate, i.e.: （2）； （3）； in, Indicates time interval, Additive white Gaussian noise representing the clock drift rate; Therefore, the measurement equations characterizing the target vehicle that acquires both global navigation satellite system sensor data and inertial measurement unit sensor data are as follows: （4）； in, It is a set of measured values and , These are the measured values of the inertial measurement unit sensor data. These are measurements from sensor data of the global satellite navigation system. It is a set of measurement functions, and , For the inertial measurement unit measurement function, Measurement functions for global satellite navigation systems; Representing all measurement noise, following a zero-mean Gaussian distribution, its covariance matrix is: , Construct operators for block diagonal matrices. For the noise covariance of the inertial measurement unit, For the noise covariance of global satellite navigation systems; A2: The GPS-IMU fusion extended Kalman filter is used to fuse and estimate the sensor data of the global satellite navigation system and the sensor data of the inertial measurement unit to obtain the fusion state estimation result; the GPS-IMU fusion extended Kalman filter is an extended Kalman filter; First, construct the linear state transition equation: （5）； in, Here is the state transition matrix. The process noise is represented by the following formula: ; The state transition matrix is defined as follows: （6）； in, for The identity matrix, for The zero matrix, Let be the row number of the matrix. is the number of columns in the matrix; The covariance matrix of the process noise is: （7）； （8）； （9）； in, for The identity matrix, It is the standard deviation of the target vehicle speed noise. The standard deviation of clock drift rate noise; Then, the implementation of the GPS-IMU fusion extended Kalman filter includes a prediction stage and a measurement update stage. The prediction stage is used to predict the fusion state estimation result, and the output of the measurement update stage is used for the next prediction stage. The prediction phase is given by the following formula: （10）； （11）； The measurement update phase is given by the following formula: （12）； （13）； （14）； in, This is the prior state vector, i.e., the fused state estimation result; For the posterior state vector, To estimate the covariance matrix a priori, To estimate the covariance matrix posteriorly, Let be the covariance matrix of the process noise. The Kalman gain matrix of the extended Kalman filter for GPS-IMU fusion. The Jacobian matrix of the GPS-IMU fused extended Kalman filter is defined as follows: , The Jacobian matrix of the inertial measurement unit. For the Jacobian matrix of global satellite navigation systems, For measurement functions; A3: Calculate the filtering residuals based on the fusion state estimation results; （15）； in, This represents the filtering residual.
3. The GPS spoofing detection and positioning recovery method for vehicle safety positioning according to claim 1, characterized in that, The method of using exponentially weighted moving average based on filtered residuals to obtain an exponentially weighted moving average discrimination statistic for GPS spoofing attack detection specifically includes the following steps: B1: Calculate residual statistics based on the filtered residuals, including the square norm and covariance of the filtered residuals; （16）； in, It is the filter residual. The covariance matrix, It is the square norm of the filter residual. （17）； in, Let be the covariance matrix of the filtered residuals; B2: Calculate the index-weighted moving average discriminant statistic based on the residual statistic; The discriminant statistic of the exponentially weighted moving average is calculated as follows: （18）； （19）； （20）； in, This is an exponentially weighted moving average statistic. This is the exponentially weighted moving average statistic from the previous time step. It is the coefficient of the exponentially weighted moving average, which is related to the offset. Proportional It is the sample mean. For sample covariance, For offset estimation; The covariance of the exponentially weighted moving average statistic. This is the discriminant statistic for the exponentially weighted moving average. It is the inverse of the covariance of the exponentially weighted moving average statistic; （21）； B3: Compare the exponentially weighted moving average discrimination statistic with the preset detection threshold. When the discrimination condition is met, it is determined that a GPS spoofing attack has occurred. The discrimination criteria are as follows: （22）； in, This is the preset detection threshold.
4. The GPS spoofing detection and positioning recovery method for vehicle safety positioning according to claim 1, characterized in that, After detecting a GPS spoofing attack, the first-stage rough estimate of the target vehicle's true location is obtained based on the fused state estimation result before the GPS spoofing attack and the global satellite navigation system sensor data acquired under the GPS spoofing attack. This specifically includes the following steps: C1: Calculate the Kalman gain matrix for the global satellite navigation system and the inertial measurement unit, respectively; Set the inertial measurement unit sensor data as Global Navigation Satellite System sensor data is Then the Kalman gain ,Measurement And Jacobi matrix It can be represented in the form of a partitioned matrix, as follows: , and , Kalman gain corresponding to the inertial measurement unit, The Kalman gain corresponding to the global satellite navigation system; This is the Jacobian matrix corresponding to the inertial measurement unit. The Jacobian matrix corresponding to the global satellite navigation system; The steady-state expectation of the posterior state estimate of the GPS-IMU fused extended Kalman filter is: （23）； in, The Kalman gain matrix of the GPS-IMU fused extended Kalman filter after steady state. This is the Kalman gain matrix corresponding to the inertial measurement unit. The Kalman gain matrix corresponding to the global satellite navigation system; For the reason A definite state, For the reason A definite state; For posterior state estimation; C2: Calculate the trace values corresponding to the Kalman gain matrices of the global navigation satellite system sensor data and the inertial measurement unit sensor data; C3: Construct the weighting coefficients of the global navigation satellite system and the inertial measurement unit based on the trace values corresponding to the Kalman gain matrices of the sensor data of the global navigation satellite system and the sensor data of the inertial measurement unit; The state vector of the target vehicle There are 8 variables, including the position of the target vehicle. and clock offset It is the observed state variable; velocity and clock drift rate These are hidden state variables, calculated from the observed state variables; Kalman gain matrix Follow the following format: （24）； in, for Medium component right Medium component The weights; set up , and ,in , , for , , The corresponding position; , , for , , Substituting the corresponding clock offset into formula (23) yields: （25）； let Represents the set of observed state variables, i.e. Then, formula (23) simplifies to include only the set of observed state variables. Format: （26）； in, for The corresponding extended Kalman filter's Kalman gain matrix after steady state. for Posterior state estimation, for The Kalman gain matrix corresponding to the inertial measurement unit. for The Kalman gain matrix corresponding to the Chinese global satellite navigation system; For the reason Determined observed state variables, For the reason Determined observed state variables; Further simplifying formula (26): （27）； in, Represents the trace value; The weighting coefficient of the inertial measurement unit is: （29）； The weighting coefficient for global satellite navigation systems is: （30）； in, For inertial measurement units, weighting coefficients. For global satellite navigation systems, Discrete time step time , Discrete time step time ; C4: The fusion state estimation results and the global satellite navigation system sensor data obtained under GPS spoofing attack are weighted and fused according to the weight coefficients of the global satellite navigation system and the weight coefficients of the inertial measurement unit to obtain the first-stage rough estimation results of the true position of the target vehicle. The first-stage rough estimation result of the target vehicle's true location The formula is: （32）； in, Discrete time step The fusion state estimation results at that time This is the first-stage rough estimate of the target vehicle's true location. This refers to sensor data from the Global Navigation Satellite System obtained under a GPS spoofing attack.
5. The GPS spoofing detection and positioning recovery method for vehicle safety positioning according to claim 1, characterized in that, The detailed estimation of the target vehicle's true position, based on the coarse estimation result from the first stage and the sensor data from the inertial measurement unit, is obtained to achieve positioning recovery under GPS spoofing attack conditions. Specifically: A newly designed extended Kalman filter with refined predictions is used to fuse the coarse estimation results from the first stage with the sensor data from the inertial measurement unit to generate a refined estimation result. The set of measurements used in this stage It includes two parts, namely ; The extended Kalman filter with fine prediction includes a prediction phase and a measurement update phase; The prediction phase is represented as: （33）； （34）； The measurement update phase is written as: （35）； （36）； （37）； in, This represents the prior state estimate, i.e., the detailed estimate of the true position of the target vehicle; Represents the state transition matrix. This represents the posterior state estimate. Denotes the prior covariance matrix. Denotes the posterior covariance matrix. Indicates the noise covariance; Indicates Kalman gain, Represents the observation matrix. Represents the observation noise covariance. Represents the observation vector. Represents the observation function; definition , Covariance of the first-stage rough estimate results: （39）； in, The standard deviation of a single-point positioning solution of a global navigation satellite system without GPS spoofing attacks is represented by the symbol. Represents the Hadamah altar; The detailed estimate of the target vehicle's true location is then input into the global satellite navigation system to help reconstruct its true location.
6. A GPS spoofing detection and location recovery system for vehicle safety positioning, used to implement the GPS spoofing detection and location recovery method for vehicle safety positioning as described in any one of claims 1-5, characterized in that, include: The data acquisition module is used to collect global satellite navigation system sensor data and inertial measurement unit sensor data of the target vehicle; The fusion estimation module is used to perform fusion estimation on sensor data from the Global Navigation Satellite System and sensor data from the Inertial Measurement Unit to obtain the fusion state estimation result and the corresponding filtering residual. The deception detection module is used to detect GPS deception attacks by using the exponentially weighted moving average method based on the filtered residuals to obtain the exponentially weighted moving average discrimination statistic. The first positioning recovery module is used to obtain a first-stage rough estimate of the target vehicle's true location based on the fused state estimation results before the GPS spoofing attack and the global satellite navigation system sensor data obtained under the GPS spoofing attack. The second positioning recovery module is used to obtain a fine estimate of the target vehicle's true position based on the coarse estimation result of the first stage and the sensor data of the inertial measurement unit, thereby realizing positioning recovery under GPS spoofing attack conditions.
7. An electronic device, characterized in that, include: One or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the GPS spoofing detection and location recovery method for vehicle safety positioning as described in any one of claims 1-5.
8. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed, cause the processor to perform the GPS spoofing detection and location recovery method for vehicle safety positioning as described in any one of claims 1-5.
9. A computer program product, characterized in that, Includes a computer program or instructions that, when executed by a processor, implement the GPS spoofing detection and location recovery method for vehicle safety positioning as described in any one of claims 1-5.