A GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization

Abstract

The application provides a GNSS / MIMU spoofing detection and suppression method based on a regression model and a fading factor optimization, and the method comprises the following steps: first, position, velocity and attitude of a GNSS / MIMU combined system are initialized, and GNSS and MIMU data are collected in real time; second, time synchronization of the GNSS and MIMU data is performed by using a time synchronization module, and ARKF is solved; third, whether the system is subjected to GNSS spoofing interference is detected by setting a detection threshold and a normalized innovation ratio; fourth, if the spoofing interference is detected, a measurement innovation time sequence formed by short-term high-confidence MIMU data and GNSS spoofing data is used to fit a mathematical model, GNSS spoofing errors at the current time are predicted and fed back, and ARKF is solved again; and fifth, a combined filtering system based on a fading factor is constructed, and the fading factor is used to adjust the weight of system observation values, so that the reliability and robustness of the combined system are further improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of combined navigation of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS), and particularly relates to a GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization. BACKGROUND

[0002] GNSS and INS have been widely used in both civil and military fields. GNSS / INS integrated navigation system can provide users with all-weather, high-precision, continuous and real-time position, velocity and attitude information. While GNSS brings convenience and high-precision position information to human beings, its security problem has great hidden dangers. Since the navigation satellite is 20000-36000km away from the ground, the satellite signal is very weak in the propagation process, and GNSS navigation terminal is easy to be interfered by malicious interference. GNSS spoofing interference can be divided into step spoofing (Meaconing Attacks, MEAC) and ramp spoofing (Lift-off-aligned Attacks, LOA) according to the adjustment mode of parameters. Both of them send spoofing signals to the navigation terminal by changing the parameters of the spoofing signals. MEAC adjusts the code phase or carrier frequency of the signal to produce a large offset from the real signal; LOA adjusts the code phase or carrier frequency of the signal to gradually deviate from the real signal, and compared with MEAC, LOA has higher concealment.

[0003] Currently, Inertial Measurement Unit (IMU) aided recognition is the mainstream solution in the field of GNSS spoofing detection using multi-sensor fusion technology. Wu et al. proposed a GNSS / INS spoofing detection method based on combined epoch innovation robustness, designed a multi-epoch equivalent weight factor to weaken the influence of spoofing, constructed a statistical quantity to test the spoofing type and classified the processing. For the slope spoofing, the normal measurement value is used to reset the filter, so that the position error quickly recovers to the normal level. Zhang et al. proposed a GNSS / INS integrated navigation system spoofing detection algorithm based on innovation rate robust estimation. To solve the problem of long detection time, high false alarm rate and high miss alarm rate of synchronous spoofing interference, the innovation rate is used as the detection quantity, and the influence of spoofing interference on innovation sequence is weakened by using robust estimation method. By adjusting the parameters, the detection ability is improved. Xu et al. studied the influence of spoofing interference on GNSS / INS loose combination zero estimation. According to the different spoofing strategies, the spoofing interference is divided into MEAC and LOA. First, the influence of the two types of spoofing on the position and velocity of GNSS output is analyzed. According to the change rule of the position and velocity deviation of GNSS output, the influence of the two types of spoofing interference on the IMU zero bias estimation of GNSS / INS loose combination filter output is analyzed, which is used as the index of spoofing detection. In the same year, Xu Rui et al. analyzed the influence of LOA spoofing on the position state of GNSS / INS loose combination filter output. It is pointed out that when the system is interfered by spoofing, the positioning result of the inertial navigation system and the difference between the spoofing position increase. In order to avoid the divergence of the filter, the positioning of the inertial navigation system is modified by adjusting the position error estimation, so as to tend to the spoofing position. Although these methods can suppress the spoofing interference in the integrated system to some extent, with the prolongation of the spoofing interference time or the use of miniature inertial measurement unit (MIMU), the integrated system cannot fundamentally solve the influence of GNSS spoofing on the positioning result, and cannot effectively suppress the spoofing interference. This patent proposes a GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization, which can realize real-time spoofing detection and suppression of integrated system under the condition of GNSS spoofing interference while ensuring low cost.

[0004] Regression Model is a mathematical model that quantitatively describes the statistical relationship, which is a predictive modeling technique. It studies the relationship between dependent variables (targets) and independent variables (predictors). This technique is commonly used for predictive analysis, time series modeling, and discovering causal relationships between variables.

[0005] Exponentially Weighted Moving Average (EWMA) is a method used to estimate the local mean of a variable, where the update of the variable is related to the historical values over a period of time. It involves assigning different weights to each observation, calculating the moving average based on these weights, and using the last moving average as the basis for predicting future values. The reason for using EWMA is that recent observations have a greater impact on the prediction, as they better reflect the current trends. Exponential moving weighted average is a method where the weights of each value decrease exponentially over time, with the weights of more recent values being larger.

[0006] Decaying Factor Filter is a filtering method commonly used in data processing of dynamic systems, especially when filtering and estimating system states or signals. It has the characteristic of gradually reducing the weight. The main purpose is to gradually reduce the dependence on old data over time, so as to pay more attention to current and future observation data. This characteristic makes the decaying factor filter adapt to the dynamic changes of the system and effectively suppress the long-term cumulative error. SUMMARY

[0007] To overcome the shortcomings of the prior art, the present application provides a GNSS / MIMU spoofing detection and suppression method based on regression model and decaying factor optimization. The method sets a test threshold by combining the false alarm rate and the probability distribution function with the normalized innovation ratio to detect whether the system is disturbed. Based on the spoofing detection, the short-term high-precision characteristics of MIMU are used to provide a highly confident measurement innovation time series, and an exponentially moving weighted average regression model is designed to stabilize the prediction and feedback of the filter measurement innovation sequence. The decaying factor is used to adjust the ARKF adaptive factor to enhance the robustness of the filter.

[0008] A GNSS / MIMU spoofing detection and suppression method based on regression model and decaying factor optimization includes the following steps:

[0009] Step 1, using the initial position information of GNSS, the initial attitude information of MIMU, and the lever arm information, the position, velocity and attitude information of the MIMU measurement center are calculated as the initialization information of the GNSS / MIMU integrated system, and the GNSS and MIMU sensor data are collected in real time;

[0010] Step 2, for the real-time collected GNSS and MIMU data, time synchronization module is used to realize the time synchronization between the two types of sensor data and ARKF is used to solve;

[0011] Step 3, based on step 2, when GNSS is subjected to external spoofing interference, based on the ARKF-GNSS / MIMU standardized measurement innovation, by setting the test threshold and the normalized innovation ratio double parameters, detecting whether the GNSS / MIMU combined system is subjected to spoofing interference;

[0012] Step 4, based on step 3, if the combined system detects that it is subjected to spoofing interference, effectively suppressing the spoofing interference by using the regression model and the fading factor optimized ARKF-GNSS / MIMU spoofing suppression method, based on the measurement innovation time series composed of the short-term highly confident MIMU data and the GNSS spoofing data, storing the measurement innovation time series into the regression window fitting the GNSS spoofing data into a mathematical model, predicting and feeding back the GNSS spoofing error at the current time, and then performing ARKF solving on the feedback measurement innovation; if the combined system is not subjected to spoofing interference, the measurement innovation time series does not need to be regressed, predicted and fed back, and ARKF solving can be directly performed;

[0013] Step 5, when the GNSS spoofing ends, the combined filtering system based on the fading factor is constructed, on the one hand, the fading factor is used to reduce the adaptive factor weight of ARKF, to weaken the influence of the predicted value on the estimation of the current filtering system under the spoofing condition, and to accelerate the convergence speed of the filtering system after the spoofing ends, on the other hand, the fading factor is used to determine whether the filter of the combined system converges, when the filter converges, the adaptive factor weight of ARKF is adjusted again, and then the spoofing interference is continuously detected, and the reliability and anti-interference ability of the combined system are further improved.

[0014] Step 2, the GNSS / MIMU combined positioning method based on ARKF is solved;

[0015] The specific steps are as follows:

[0016] Step 2-1, the state vector of the GNSS / MIMU loose combined positioning model is the position error , the velocity error , the attitude error , the gyro zero offset , the accelerometer zero offset , that is,

[0017] (1)

[0018] Step 2-2, the state equation of the Kalman filter can be expressed as follows:

[0019] (2)

[0020] Wherein, the state transition matrix , the noise distribution matrix and system noise matrix The expression is as follows:

[0021] (3)

[0022] where, is the attitude matrix; is the specific force; and respectively represent the measurement white noise of the accelerometer and the gyroscope;

[0023] Step 2-3, the measurement equation of the GNSS / MIMU loose combination is as follows:

[0024] (4)

[0025] where, represents the observation matrix; represents the measurement noise vector, and the covariance matrix thereof is The expression of each matrix is as follows:

[0026] The observation vector can be represented as:

[0027] (5)

[0028] where, represents the rod arm vector from the center of the MIMU to the phase center of the GNSS receiver antenna in the carrier coordinate system, , respectively represent the position and velocity of the MIMU in the navigation coordinate system calculated by the inertial navigation; , respectively represent the position and velocity of the antenna phase center calculated by the GNSS in the coordinate system; the observation matrix in the measurement equation is represented as:

[0029] (6)

[0030] Step 2-4, the ARKF is used to adjust the measurement noise matrix in real time in the measurement update process, so as to obtain more accurate positioning results. The filtering method introduces a robustness factor , The calculation formula is as follows:

[0031] (7)

[0032] where, and represent empirical constant values; represents the The information value of a measurement is expressed as follows:

[0033] (8)

[0034] When the absolute value of the new value is less than At that time, the measured value is considered normal, robustness factor The value is 1; when the absolute value of the innovation value is between and between, robustness factor The value will increase, and the corresponding weight of the measurement value will decrease; when the absolute value of the innovation value is greater than... When it is considered that the measured value has a large measurement error, the robustness factor is set to infinity.

[0035] Robustness factor Substitute into Adjusting the elements within the array yields the following formula:

[0036] (9)

[0037] In the formula, This represents the measurement noise matrix after adaptive adjustment, and

[0038] (10)

[0039] and Represent matrices respectively The Line 1 After the above adjustments, the gain matrix is ​​then calculated. Then, the optimal estimate of the state parameters at that moment can be obtained. and its variance-covariance matrix .

[0040] Step 3 describes how, when GNSS is subjected to external deception interference, the GNSS / MIMU combined system is detected to be subjected to deception interference based on the standardized measurement innovation of ARKF-GNSS / MIMU by setting two parameters: a test threshold and a normalized innovation ratio.

[0041] The specific steps are as follows:

[0042] Step 3-1: Construct new measurement information for the current epoch. :

[0043] (11)

[0044] According to probability and statistics, measuring innovation The white noise sequence is subject to a normal distribution with a mean of zero:

[0045] (12)

[0046] In the full closed loop ARKF, the system model error is controlled in a small range through feedback correction, so the influence of the system model can be ignored, and the measurement innovation can reflect whether the observation is abnormal;

[0047] When the system is not subject to deceptive interference, the measurement innovation is a white noise sequence with a mean of zero, and when the system fails, the mean of the measurement innovation is no longer subject to a white noise sequence with a mean of zero, so the fault detection condition is converted into a hypothesis testing problem:

[0048] (13)

[0049] Step 3-2, according to the standard normal distribution theory of mathematical statistics, construct a test statistic through the measurement innovation, and set a test threshold through the false alarm rate and the probability distribution function:

[0050] Standardize the measurement innovation:

[0051] (14)

[0052] wherein, ; is the three-dimensional position measurement innovation; is the first row and the first column of the measurement noise covariance matrix; , a binary hypothesis is made on , and under the condition of a given false alarm probability , the required test threshold is derived using the probability density function of the normal distribution;

[0053] (15)

[0054] The system is subjected to deception detection by comparing the test innovation value with the test threshold If , the system is subjected to deceptive attack; if , the system is not subjected to deceptive attack.

[0055] Step 3-3, the ratio of the current time standardized innovation value to the previous time standardized innovation value is taken as a feature for determining the time when the deception ends:

[0056] (16)

[0057] In the formula, is the test parameter of the end time of deception; the normalized innovation value on the left side of the fraction is the innovation value at the current time; the normalized innovation value on the right side of the fraction is the innovation value at the previous time; is the end time of deception.

[0058] The combined system of step 4 detects that it is disturbed by deception, and the ARKF-GNSS / MIMU deception suppression method optimized by the regression model and the fading factor effectively suppresses the deception disturbance. Based on the measurement innovation time sequence composed of the short-term highly confident MIMU data and the GNSS deception data, the measurement innovation time sequence is stored in the regression window, the GNSS deception data is fitted into a mathematical model, the GNSS deception error at the current time is predicted and fed back, and then the measurement innovation after the feedback is solved by the ARKF;

[0059] The specific steps are as follows:

[0060] Step 4-1, construct the measurement innovation under the deception environment by using the measurement equation of the GNSS / MIMU combination:

[0061] (17)

[0062] In the formula, represents the actual position of the IMU measurement center; represents the actual position of the GNSS antenna phase center; is the projection of the vector from the IMU measurement center to the GNSS antenna phase center in ; The expression of

[0063] (18)

[0064] When the GNSS is attacked by external deception, the system measurement innovation is written as:

[0065] (19)

[0066] In the formula, represents a random error, which is a random variable satisfying and ;

[0067] Step 4-2, assuming that there are highly confident positioning results of MIMU after the GNSS is attacked by deception, which are constructed into time sequence data as: , , … , then:

[0068] (20)

[0069] Step 4-3: Analyze each time series data point and its regression value. To minimize the deviation, a least squares model is established:

[0070] (twenty one)

[0071] in, , , , , ;

[0072] Step 4-4: Use the exponentially moving weighted average model to find the optimal regression value. and Assign weights that change over time:

[0073] (twenty two)

[0074] in, for The regression coefficient at time point; for The regression coefficient at time point; The attenuation coefficient is... ;

[0075] Using the optimal regression coefficients to predict and compensate for measurement innovation, the corrected for:

[0076] (twenty three)

[0077] The corrected Introduce a filter loop.

[0078] Step 5 describes the construction of a combined filtering system based on the fading factor. The fading factor is used to adjust the adaptive factor, which weakens the influence of the predicted value on the current filtering system estimation under the deception condition and accelerates the convergence speed of the filtering system after the deception ends.

[0079] The specific steps are as follows:

[0080] Step 5-1: Reduce the impact of deceptive data and suppress filter divergence. Assume the prediction error covariance and the innovation covariance are related as follows:

[0081] (twenty four)

[0082] (25)

[0083] In the formula, It is a gradually diminishing factor; is a scalar factor; and are the estimated values calculated according to the fading factor and the scalar factor respectively, and the new gain matrix is obtained as:

[0084] (26)

[0085] Step 5-2, obtaining the optimal fading factor and the scalar factor to make the gain matrix optimal:

[0086] (27)

[0087] Substitute formula (27) into formula (25), and the optimal fading factor is obtained as:

[0088] (28)

[0089] The current estimated innovation covariance can also be expressed as:

[0090] (29)

[0091] Write formula (29) as:

[0092] (30)

[0093] From the expression it can be seen that is a value close to 1, so is close to 0 and can be ignored, and then is approximately equal to , and is set as , so the fading factor obtained is expressed as:

[0094] (31)

[0095] Step 5-3, using the fading factor to control the robust factor in the ARKF filter as:

[0096] (32)

[0097] When , it is considered that the combined system filter does not converge, and even if the innovation value is greater than , the value of the robust factor must be set to 1 to make the filtering system gradually converge; when , it is considered that the combined system filter converges, and at this time, the robust factor is calculated by using formula (7).

[0098] Advantages of the present application:

[0099] 1、The application can effectively identify the cheating interference of the system by constructing a double-parameter detection combination system and assisting in cheating detection through MIMU, and the false alarm rates of the north, east and high directions under the MEAC and LOA models are 0.411%, 0.308% and 1.129% respectively, the average missed alarm rate is 0%, the average false alarm rate is 0.616%, and the cheating interference can be effectively detected.

[0100] 2、The long and continuous cheating interference is effectively suppressed by MIMU, and the combination system is verified by experiments, and when the MEAC and LOA are subjected to the north deviation of 500m, the east deviation of-200m for 200s, and the north and east cheating rate of 1m / s for 300s, there is no filter divergence phenomenon and the cheating interference is effectively suppressed, the maximum errors of the north and east directions are 2.551m and 1.817m respectively, and the maximum positioning error is 2.677m, so that the system has higher stability and reliability, and the ability to cope with cheating interference is improved.

[0101] 3、The application introduces a fading factor to adjust the adaptive factor of ARKF to form a combination filtering system, which can reduce the adaptive factor weight of ARKF by using the fading factor, weaken the influence of the predicted value on the current filtering system estimation under the cheating condition, increase the weight of GNSS, and accelerate the convergence speed of the filtering system after the cheating ends, and on the other hand, the fading factor can determine whether the filter of the combination system converges, and when the filter converges, the adaptive factor weight of ARKF is adjusted again, and then the continuous detection of the cheating interference is carried out. BRIEF DESCRIPTION OF DRAWINGS

[0102] Fig. 1 is a flow chart of a GNSS / MIMU cheating detection and suppression method based on a regression model and a fading factor optimization according to the application;

[0103] Fig. 2 is a specific flow chart of step 2 of an embodiment of the application;

[0104] Fig. 3 is a specific flow chart of step 3 of an embodiment of the application;

[0105] Fig. 4 is a specific flow chart of step 4 of an embodiment of the application;

[0106] Fig. 5 is a specific flow chart of step 5 of an embodiment of the application;

[0107] Fig. 6 is a summary flow chart of an embodiment of the application;

[0108] Fig. 7 is a track diagram of an experiment and a cheating track using the application;

[0109] Figure 8 is a north, east and high direction spoofing interference situation detected by the present application;

[0110] Figure 9 is a positioning result of MEAC and LOA spoofing suppression by the present application, and comparison of EKF and ARKF algorithms;

[0111] Figure 10 is a north, east and position error curve diagram of different algorithms by the present application for MEAC and LOA spoofing suppression; DETAILED DESCRIPTION

[0112] An embodiment of the present application will be further described below in combination with the drawings.

[0113] In the embodiment of the present application, the GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization comprises the following steps, as shown in the figure: Figure 1

[0114] Step 1, the initial position information and speed information of GNSS, the initial attitude information of MIMU and the lever arm information are used to calculate the position, speed and attitude information of the MIMU measurement center as the initialization information of the GNSS / MIMU integrated system, and the GNSS and MIMU sensor data are collected in real time;

[0115] Step 2, for the real-time collected GNSS and MIMU data, the time synchronization module is used to realize the time synchronization between the two types of sensor data, and the ARKF is used to solve, as shown in the figure: Figure 2

[0116] Step 2-1, the state vector of the GNSS / MIMU loose integrated positioning model is position error , speed error , attitude error , gyro zero offset , accelerometer zero offset , that is:

[0117] (1)

[0118] Step 2-2, the state equation of Kalman filter can be expressed as follows:

[0119] (2)

[0120] Wherein, the state transition matrix , the noise distribution matrix and the system noise matrix are expressed as follows:

[0121] (3) ​​

[0122] where, is the attitude matrix; is the specific force; and denote the measurement white noise of accelerometer and gyroscope, respectively;

[0123] Step 2-3, the measurement equation of GNSS / MIMU loose combination is as follows:

[0124] (4)

[0125] where, denotes the observation matrix; denotes the measurement noise vector, and the covariance matrix thereof is The expressions of respective matrices are as follows:

[0126] The observation vector can be expressed as:

[0127] (5)

[0128] where, denotes the rod vector from the center of MIMU to the phase center of GNSS receiver antenna in the carrier coordinate system, , denote the position and velocity of MIMU in the navigation coordinate system calculated by inertial navigation, , denote the position and velocity of the antenna phase center calculated by GNSS in the coordinate system; the observation matrix in the measurement equation is expressed as:

[0129] (6)

[0130] Step 2-4, the ARKF is used to adjust the measurement noise matrix in real time in the measurement update process, so as to obtain more accurate positioning results. The filtering method introduces a robustness factor , The calculation formula of the robustness factor is as follows:

[0131] (7)

[0132] where, and denote empirical constant; denotes the innovation value of the i-th measurement value at a certain epoch, and the expression thereof is as follows:

[0133] (8)

[0134] ​When the absolute value of the new value is less than At that time, the measured value is considered normal, robustness factor The value is 1; when the absolute value of the innovation value is between and between, robustness factor The value will increase, and the corresponding weight of the measurement value will decrease; when the absolute value of the innovation value is greater than... When it is considered that the measured value has a large measurement error, the robustness factor is set to infinity.

[0135] Robustness factor Substitute into Adjusting the elements within the array yields the following formula:

[0136] (9)

[0137] In the formula, This represents the measurement noise matrix after adaptive adjustment, and

[0138] (10)

[0139] and Represent matrices respectively The Line 1 After the above adjustments, the gain matrix is ​​then calculated. Then, the optimal estimate of the state parameters at that moment can be obtained. and its variance-covariance matrix .

[0140] Step 3: Based on Step 2, when GNSS is subjected to external deception interference, the ARKF-GNSS / MIMU standardized measurement innovation is used to detect whether the GNSS / MIMU combined system is subjected to deception interference by setting two dual parameters: a verification threshold and a normalized innovation ratio. Figure 3 As shown;

[0141] Step 3-1: Construct new measurement information for the current epoch. :

[0142] (11)

[0143] According to probability and statistics, measuring new information The sequence is white noise and follows a normal distribution with a mean of zero.

[0144] (12)

[0145] In a fully closed-loop ARKF, the system model error is controlled within a small range through feedback correction, thus the influence of the system model can be ignored. Therefore, by measuring the innovation... This can reflect whether the observed values ​​are abnormal;

[0146] When the system is free from deception interference, the measurement innovation is a sequence of white noise with a mean of zero. However, when a fault occurs in the system, the mean of the measurement innovation no longer follows a sequence of white noise with a mean of zero, transforming the fault detection condition into a hypothesis testing problem.

[0147] (13)

[0148] Step 3-2: Based on the standard normal distribution theory of mathematical statistics, construct the test statistic by measuring the innovation, and set the test threshold using the false alarm rate and probability distribution function:

[0149] Standardize the measurement of new information:

[0150] (14)

[0151] In the formula, ; For new information on three-dimensional position measurement; To measure the first of the noise covariance matrix Line 1 List; ,right Make a binary hypothesis, given the false alarm probability Under the given conditions, the required test threshold is derived using the probability density function of the normal distribution. ;

[0152] (15)

[0153] By examining the statistical new value With test threshold Perform spoofing detection on the system, if The system was subjected to a deception attack; if The system is immune to deception attacks;

[0154] Step 3-3: Use the ratio of the standardized innovation value at the current time to the standardized innovation value at the previous time as a feature to determine the end time of the deception.

[0155] (16)

[0156] In the formula, The test parameters are used to deceive the end time; the standardized innovation value on the left side of the fraction is the innovation value at the current time; the standardized innovation value on the right side of the fraction is the innovation value at the previous time. To deceive the end time.

[0157] Step 4, based on step 3, if the combined system detects that it is disturbed by spoofing, the ARKF-GNSS / MIMU spoofing suppression method optimized by regression model and fading factor effectively suppresses the spoofing disturbance, based on the measurement innovation time series composed of short-term highly confident MIMU data and GNSS spoofing data, the measurement innovation time series is stored in the regression window, the GNSS spoofing data is fitted into a mathematical model, and the GNSS spoofing error at the current time is predicted and fed back, and then the ARKF is solved based on the feedback measurement innovation; if the combined system is not disturbed by spoofing, the measurement innovation time series does not need to be regressed, predicted and fed back, and ARKF can be directly solved, as shown in Figure 4

[0158] Step 4-1, construct the measurement innovation under spoofing environment by using the measurement equation of GNSS / MIMU combination:

[0159] (17)

[0160] In the formula, represents the actual position of the IMU measurement center; represents the actual position of the GNSS antenna phase center; is the projection of the vector from the IMU measurement center to the GNSS antenna phase center in the system; The expression of is:

[0161] (18)

[0162] When GNSS is attacked by external spoofing, the system measurement innovation is written as:

[0163] (19)

[0164] In the formula, represents a random error, which is a random variable satisfying and

[0165] Step 4-2, assuming that there are highly confident positioning results of MIMU after GNSS is attacked by spoofing, which are constructed into time series data as: , , ,

[0166] (20)

[0167] ​​Step 4-3: Analyze each time series data point and its regression value. To minimize the deviation, a least squares model is established:

[0168] (twenty one)

[0169] in, , , , , ;

[0170] Step 4-4: Use the exponentially moving weighted average model to find the optimal regression value. and Assign weights that change over time:

[0171] (twenty two)

[0172] in, for The regression coefficient at time point; for The regression coefficient at time point; The attenuation coefficient is... ;

[0173] Using the optimal regression coefficients to predict and compensate for measurement innovation, the corrected for:

[0174] (twenty three)

[0175] The corrected Introduce a filter loop.

[0176] Step 5: When the GNSS deception ends, such as Figure 5 As shown, a combined filtering system based on the fading factor is constructed. On the one hand, the fading factor is used to reduce the adaptive factor weight of ARKF, weaken the influence of the predicted value on the current filtering system estimation under the deception condition, and accelerate the convergence speed of the filtering system after the deception ends. On the other hand, the fading factor is used to determine whether the filter of the combined system has converged. When the filter converges, the adaptive factor weight of ARKF is readjusted, and then the deception interference is continuously detected, further improving the reliability and anti-interference capability of the combined system.

[0177] Step 5-1: Reduce the impact of deceptive data and suppress filter divergence. Assume the prediction error covariance and the innovation covariance are related as follows:

[0178] (twenty four)

[0179] (25)

[0180] In the formula, It is a gradually diminishing factor; Scalar factor; and The estimated values ​​are obtained from the fading factor and the scalar factor, respectively, resulting in the new gain matrix:

[0181] (26)

[0182] Step 5-2: Find the optimal fading factor and scalar factor To optimize the gain matrix:

[0183] (27)

[0184] Substituting equation (27) into equation (25), we can obtain... for:

[0185] (28)

[0186] The current estimate of the new information covariance can also be expressed as follows:

[0187] (29)

[0188] Equation (29) can be written as:

[0189] (30)

[0190] from The expression shows It is a value very close to 1, therefore Approaching 0, it can be ignored, thus yielding and They are approximately equal, let's assume Therefore, the fading factor is expressed as:

[0191] (31)

[0192] Step 5-3: Use the fading factor to control the robustness factor in ARKF filtering as follows:

[0193] (32)

[0194] when At that time, it is considered that the combined system filter has not converged, even if the innovation value is greater than Robustness factor must also be included. Setting the value to 1 allows the filtering system to gradually converge; when When the combined system filter is considered to have converged, the robustness factor is calculated using formula (7). Numerical value.

[0195] In this invention example, the experimental simulation of the vehicle's driving trajectory is as follows: Figure 7 As shown in the figure, the "pentagram" shape represents the starting point of the carrier, with coordinates (30°27'37.557", 114°28'21.017", 23.000m), and the "circle" shape represents the ending point of the carrier, with coordinates (30°30'42.084", 114°31'50.322", 23.000m). The entire simulation lasted 985 seconds, and the motion process included acceleration, deceleration, and turning. The GNSS northward and eastward errors were 1cm, the altitude error was 2cm, and the MIMU gyro zero bias was... Adding zero bias to the table The random walk of the gyroscope is Adding a random walk to the table Between 200s and 399s, the GNSS northward position was subjected to a 500m MEAC, and the GNSS eastward position was subjected to a -200m MEAC. The MEAC caused a sudden change in the GNSS positioning result and lasted for 200s. Between 600s and 899s, the GNSS northward and eastward positions were subjected to a 1m / s LOA, with a deception time of 300s. During the period when the GNSS was subjected to LOA interference, the position of the carrier was gradually pulled off course and eventually deviated from the reference trajectory.

[0196] Depend on Figure 8 It can be seen that the integrated navigation system is susceptible to deception interference within the timeframes of 200s-399s and 600s-899s. Under the MEAC and LOA models, the false alarm rates for northbound, eastbound, and altitude directions are 0.411%, 0.308%, and 1.129%, respectively, with an average false alarm rate of 0% and an average false alarm rate of 0.616%. Although the algorithm exhibits a small number of false alarms, these false alarms are random and sporadic, rather than persistent, thus achieving effective detection of deception interference.

[0197] like Figure 9As shown, the EKF is an extended Kalman filter solution, the ARKF is an adaptive robust Kalman filter solution, and the ARKF-RMW is a GNSS / MIMU spoofing suppression algorithm solution based on a regression model and a fading factor optimization; the positioning result of the EKF algorithm is greatly affected by the GNSS positioning result, and there is a phenomenon of filter divergence at the beginning and end of GNSS spoofing, and the filter system gradually converges when the GNSS positioning result gradually stabilizes; the ARKF algorithm adaptively adjusts the weight between the GNSS positioning result and the MIMU positioning result at the beginning of spoofing, and continues to calculate by using the short-term high-precision characteristics of the MIMU, and with the error drift of the MIMU, the filter of the integrated system rapidly diverges, and after the GNSS spoofing ends, the unstable innovation value caused by the divergent filter leads to the instability of the robust factor, and the filter is difficult to converge; the ARKF-RMW algorithm is closer to the reference trajectory compared with the EKF algorithm and the ARKF algorithm, and there is no filter divergence at the beginning and end of spoofing, and the ARKF-RMW algorithm suppresses the span error caused by MEAC and the error accumulation caused by LOA during the GNSS suffers from MEAC and LOA, and has higher reliability and stability.

[0198] As shown in Figure 10 When the GNSS suffers from spoofing attacks, the positioning results of the EKF and ARKF algorithms that fuse MIMU data and GNSS data are unreliable, and the positioning results are severely distorted; in terms of reliability and stability of the system, the ARKF-RMW algorithm quickly adapts at the beginning of the spoofing attack, and the filter does not diverge at the beginning and end of the spoofing attack, and returns to the normal state after the attack ends, showing good anti-interference ability and stability, and improving the reliability and robustness of the positioning system when suffering from spoofing attacks; in terms of positioning accuracy of the system, under the attack of MEAC with a duration of 200s and a maximum span of 500m and LOA with a duration of 300s and a maximum deviation of 300m, the maximum errors in the north and east directions are 2.551m and 1.817m respectively, and the maximum positioning error is 2.677m.

[0199] The above is only the most basic specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can understand the replacement within the technical scope disclosed by the present application, which should be covered within the scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A GNSS / MIMU spoofing detection and mitigation method based on regression model and fading factor optimization, characterized in that, The method comprises the following steps: Step 1, initial position information, speed information of GNSS, initial attitude information of MIMU and lever arm information are used to calculate the position, speed and attitude information of the MIMU measurement center as the initialization information of the GNSS / MIMU combined system, and GNSS and MIMU sensor data are collected in real time; Step 2, for the real-time collected GNSS and MIMU data, time synchronization between the two types of sensor data is realized by using a time synchronization module and ARKF is solved; Step 3, based on step 2, when GNSS is subjected to external deception interference, based on the standardized measurement innovation of ARKF-GNSS / MIMU, two double parameters of setting a detection threshold and a normalized innovation ratio are used to detect whether the GNSS / MIMU combined system is subjected to deception interference; Step 4, based on step 3, if the combined system is detected to be subjected to deception interference, the ARKF-GNSS / MIMU deception suppression method using a regression model and a fading factor is used to effectively suppress the deception interference, a measurement innovation time series is formed based on short-term highly confident MIMU data and GNSS deception data, the measurement innovation time series is stored in a regression window, GNSS deception data is fitted into a mathematical model, GNSS deception errors at the current time are predicted and fed back, and the measurement innovation after the feedback is solved by ARKF; if the combined system is not subjected to deception interference, the measurement innovation time series does not need to be regressed, predicted and fed back, and ARKF can be directly solved; Step 5, when the GNSS deception ends, a combined filtering system based on a fading factor is constructed, on the one hand, the fading factor is used to reduce the adaptive factor weight of ARKF, to weaken the influence of the predicted value on the estimation of the current filtering system under the deception condition, and to accelerate the convergence speed of the filtering system after the deception ends, on the other hand, the fading factor is used to determine whether the filter of the combined system converges, when the filter converges, the adaptive factor weight of ARKF is adjusted, and then the deception interference is continuously detected, and the reliability and anti-interference ability of the combined system are further improved.

2. The GNSS / MIMU spoofing detection and mitigation method based on regression model and fading factor optimization according to claim 1, characterized in that, The ARKF-based GNSS / MIMU combined positioning method of step 2; The specific steps are as follows: Step 2-1, the state vector of the GNSS / MIMU loose combination positioning model is position error , velocity error , attitude error , gyro zero bias , accelerometer zero bias , that is: （1） Step 2-2, the state equation of Kalman filtering can be expressed as follows: （2） where the state transition matrix , the noise allocation matrix , and the system noise matrix are expressed as follows: （3） wherein is the attitude matrix; is the specific force; and denote the measurement white noise of the accelerometer and the gyroscope, respectively; Step 2-3, the measurement equation of GNSS / MIMU loose combination is as follows: （4） wherein represents an observation matrix; represents a measurement noise vector, the covariance matrix of which is The expressions of the respective matrices are as follows: Observation vector may be represented as: （5） In the formula, The lever arm vector representing the distance from the MIMU center to the GNSS receiver antenna phase center in the carrier coordinate system. , These represent the position and velocity of the MIMU in the navigation coordinate system calculated by the inertial navigation system, respectively. , These represent the antenna phase centers calculated by GNSS at... Position and velocity within the system; the observation matrix in the measurement equation is represented as: （6） Step 2-4, Update the measurement noise matrix in the measurement update process with ARKF The filtering method introduces a robustness factor to obtain more accurate positioning results by adjusting in real time , The calculation formula is as follows: （7） wherein and represents an empirical constant; represents the innovation of the measurement value at an epoch The expression of the innovation is as follows: （8） When the absolute value of the innovation is less than , the measurement is considered normal, and the value of the robustness factor is 1; when the absolute value of the innovation is between and , the value of the robustness factor increases, and the corresponding weight of the measurement decreases; when the absolute value of the innovation is greater than , the measurement is considered to have a large measurement error, and the robustness factor is set to infinity. The robustness factor is substituted into the matrix, the elements of which are adjusted, the following equation applies: （9） wherein denotes the adapted measurement noise matrix, and （10） and denote the element in the i-th row and j-th column of matrix .​​​​​ 3. The GNSS / MIMU spoofing detection and mitigation method based on regression model and fading factor optimization according to claim 2, characterized in that, The two double parameters of step 3 are used to detect whether the system is subjected to deception interference; The specific steps are as follows: Step 3-1, construct the measurement innovation at the current epoch : （11） According to probability statistics, the measurement innovation is a white noise sequence, which is normally distributed with mean zero: （12） In the full closed loop ARKF, the system model error is controlled in a small range by feedback correction, so the influence of the system model can be ignored, and the measurement innovation can reflect whether the observation is abnormal. When the system is not subjected to deception interference, the measurement innovation is a white noise sequence with a mean value of zero, when the system fails, the mean value of the measurement innovation no longer obeys the white noise sequence with a mean value of zero, and the fault detection condition is converted into a hypothesis testing problem: （13） Step 3-2, according to the standard normal distribution theory of mathematical statistics, a test statistic is constructed by using the measurement innovation, and a detection threshold is set by using the false alarm rate and the probability distribution function: The measurement innovation is standardized: （14） In the formula, ; For new information on three-dimensional position measurement; To measure the first of the noise covariance matrix Line 1 List; ,right Make a binary hypothesis, given the false alarm probability Under the given conditions, the required test threshold is derived using the probability density function of the normal distribution. ; （15） by examining the new information value against the examination threshold fraud detection is performed on the system, and if the system is under a fraudulent attack; and if the system is free of a fraudulent attack Step 3-3, the ratio of the current time standardized innovation value to the last time standardized innovation value is used as a feature for judging the end time of deception: （16） In the formula, is the test parameter at the end of the fraud; the standardized innovation value on the left side of the fraction is the innovation value at the current time; The partial right side normalized innovation value is the innovation value at the last time; is the end time of the fraud.

4. The GNSS / MIMU spoofing detection and mitigation method based on regression model and fading factor optimization according to claim 1, characterized in that, The ARKF-GNSS / MIMU spoofing suppression method using the regression model and the fading factor optimization of step 4 effectively suppresses spoofing interference; The specific steps are as follows: Step 4-1, the measurement innovation under the spoofing environment is constructed by using the measurement equation of GNSS / MIMU combination: （17） wherein represents the actual position of the IMU measurement center; represents the actual position of the GNSS antenna phase center; is the projection of the vector pointing from the IMU measurement center to the GNSS antenna phase center in the direction of ; and The expression for is （18） When GNSS is subjected to external spoofing attack, the system measurement innovation is written as: （19） wherein represents a random error, which is a random variable satisfying and ; Step 4-2, assuming there is one MIMU highly confident positioning result after GNSS suffers from spoofing attack, construct it into time series data as: , , , , then: （20） Step 4-3, by each time series data and regression value Minimizing the degree of deviation, establishing a least squares model: （21） wherein , , , , ; Step 4-4, applying an exponentially moving weighted average model to the optimal regression values and Impose time-varying weights: （22） wherein is the regression coefficient for the time of day; is the regression coefficient for the time of day; is a decay coefficient, ; The optimal regression coefficient is used to predict and compensate the measurement innovation, and the corrected is: （23） Corrected Introduce filter loop.

5. The GNSS / MIMU spoofing detection and mitigation method based on regression model and fading factor optimization according to claim 1, characterized in that, Step 5, the combined filtering system based on the fading factor is constructed, the fading factor is used to adjust the adaptive factor, the influence of the predicted value on the current filtering system estimation under the spoofing condition is weakened, and the convergence speed of the filtering system after the end of the spoofing is accelerated; The specific steps are as follows: Step 5-1, the influence of the spoofing data is reduced, and the filtering divergence is suppressed; assuming that the prediction error covariance and the innovation covariance, their relationship is: （24） （25） wherein is an evanescent factor; is a scalar factor; and are estimates calculated from the evanescent factor and the scalar factor, respectively, resulting in a new gain matrix （26） Step 5-2, find optimal fading factor and a scalar factor Optimize gain matrix: （27） Substituting equation (27) into equation (25), we can obtain is: （28） The current estimated innovation covariance can also be expressed as follows: （29） Equation (29) is written as: （30） From The expression can be seen is a value very close to 1, so close to 0, negligible, and thus and approximately equal, set Thus the evanescent factor is expressed as: （31） Step 5-3, the robust factor in the ARKF filtering is controlled by using the fading factor: （32） When , the combined system filter is considered not to converge, even if the innovation value is greater than , the value of the robustness factor must be set to 1, so that the filtering system gradually converges; when , the combined system filter is considered to converge, and the numerical value of the robustness factor is calculated using equation (7).

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