GNSS / MIMU deception detection and inhibition method based on regression model and fading factor optimization

Abstract

The invention provides a GNSS / MIMU deception detection and inhibition method based on regression model and fading factor optimization, and the method comprises the following steps: 1, carrying out the position, speed and attitude initialization of a GNSS / MIMU combined system, and collecting the GNSS and MIMU data in real time; 2, performing time synchronization on GNSS and MIMU data by using a time synchronization module, and resolving through ARKF; 3, detecting whether the system suffers from GNSS deception interference or not by setting an inspection threshold and a normalized innovation ratio; 4, if deception jamming is detected, fitting a measurement information time sequence into a mathematical model by using the measurement information time sequence formed by the MIMU data with short-term high confidence and the GNSS deception data, predicting and feeding back a GNSS deception error at the current moment, and then carrying out ARKF calculation; and 5, constructing a combined filtering system based on the fading factor, and adjusting the weight of the observation value of the system by using the fading factor to further improve the reliability and robustness of the combined system.

Description

Technical Field

[0001] The present invention belongs to the field of combined navigation of a global satellite navigation system (GNSS) and an inertial navigation system (INS), and specifically relates to a GNSS / MIMU deception detection and suppression method based on a regression model and fading factor optimization. Background Art

[0002] GNSS and INS have been widely used in both civil and military fields. The GNSS / INS integrated navigation system can provide users with all-weather, high-precision, continuous, and real-time position, speed, and attitude information. While GNSS brings convenience and high-precision location information to humans, its security issues pose huge risks. Since navigation satellites are 20,000 to 36,000 km from the ground, satellite signals are very weak during propagation, and GNSS navigation terminals are susceptible to malicious interference. GNSS spoofing interference can be divided into step spoofing (Meaconing Attacks, MEAC) and slope spoofing (Lift-off-aligned Attacks, LOA) according to the parameter adjustment method. Both send spoofing signals to navigation terminals by changing the spoofing signal parameters. 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. Compared with MEAC, LOA has higher concealment.

[0003] At present, inertial measurement unit (IMU) assisted identification 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 multi-epoch equivalent weight factors to weaken the impact of spoofing, constructed statistics to test the spoofing type and classified it. For slope spoofing, the filter is reset using normal measurement values ​​to quickly restore the position error to a normal level. Zhang et al. proposed a GNSS / INS integrated navigation system spoofing detection algorithm based on innovation rate robust estimation. In order to solve the problems of long detection time, high missed alarm rate and false alarm rate of synchronous spoofing interference, the rate of change of the new information is used as the detection quantity, and the robust estimation method is used to weaken the impact of spoofing interference on the new information sequence. By adjusting parameters, the detection capability is improved. Xu et al. studied the impact of deception interference on the zero bias estimation of the loose combination of GNSS / INS. According to different deception strategies, the deception interference was divided into MEAC and LOA. First, the impact of these two types of deception on the position and velocity output of GNSS was analyzed. According to the change law of the position and velocity deviation of GNSS output, the impact of the two types of deception interference on the IMU zero bias estimation output by the loose combination filter of GNSS / INS was analyzed, and it was used as an indicator of deception detection. In the same year, Xu Rui et al. analyzed the impact of LOA deception on the position state output by the loose combination filter of GNSS / INS. The analysis pointed out that when the system is subjected to deception interference, the difference between the positioning result of the inertial navigation system and the deception position increases. In order to avoid filter divergence, the system corrects the positioning of the inertial navigation system by adjusting the position error estimate to make it tend to the deception position. Although these methods can suppress deception interference in the combined system to a certain extent, with the extension of the deception interference time or the use of Miniature Inertial Measurement Unit (MIMU), the combined system fails to fundamentally solve the impact of GNSS deception on the positioning results and cannot effectively suppress deception interference. This patent proposes a GNSS / MIMU deception detection and suppression method based on regression model and fading factor optimization. In the case of GNSS deception interference, it can detect and suppress deception of the combined system in real time while ensuring low cost.

[0004] A regression model is a mathematical model that quantitatively describes statistical relationships. It is a predictive modeling technique that studies the relationship between dependent variables (targets) and independent variables (predictors). This technique is often used in predictive analysis, time series models, and discovering causal relationships between variables.

[0005] The Exponentially Weighted Moving Average method can be used to estimate the local mean of a variable so that the update of the variable is related to the historical value over a period of time. It is a method that gives different weights to the observed values, obtains the moving average according to the different weights, and determines the predicted value based on the final moving average. The weighted moving average method is used because the recent observed values ​​in the observation period have a greater impact on the predicted value, and it can better reflect the trend of recent changes. The exponential moving weighted average method means that the weighting coefficient of each value decreases exponentially over time, and the closer the value is to the current moment, the greater the weighting coefficient.

[0006] Decaying Factor Filter is a filtering method commonly used in data processing in dynamic systems, especially when filtering and estimating system states or signals, with the characteristic of gradually reducing weights. Its main purpose is to gradually reduce the reliance on old data over time, so as to pay more attention to current and future observation data. This characteristic enables the Decaying Factor Filter to adapt to system dynamic changes and effectively suppress long-term accumulated errors. Summary of the invention

[0007] In view of the shortcomings of the prior art, the present invention proposes a GNSS / MIMU deception detection and suppression method based on regression model and fading factor optimization. The method sets the test threshold by the false alarm rate and probability distribution function and combines the normalized new information ratio to detect whether the system is interfered. On the basis of deception detection, the short-term high-precision characteristics of MIMU are used to provide a highly confident measurement new information time series, and an exponential moving weighted average regression model is designed to perform stable prediction and feedback on the filtered measurement new information sequence. The ARKF adaptive factor is adjusted in combination with the fading factor to enhance the robustness of the filter.

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

[0009] Step 1: Use the initial position information, speed information of GNSS, the initial attitude information of MIMU and the arm information to calculate the position, speed and attitude information of the MIMU measurement center as the initialization information of the GNSS / MIMU combined system, and collect the GNSS and MIMU sensor data in real time;

[0010] Step 2: For the real-time collected GNSS and MIMU data, the time synchronization module is used to achieve time synchronization between the two types of sensor data and the ARKF solution is used;

[0011] Step 3, based on step 2, when the GNSS is subjected to external deception interference, based on the standardized measurement information of ARKF-GNSS / MIMU, by setting the double parameters of the inspection threshold and the normalized information ratio, detect whether the GNSS / MIMU combination system is subjected to deception interference;

[0012] Step 4: Based on step 3, if the combined system detects that it is interfered by spoofing, the measurement innovation time series composed of short-term highly confident MIMU data and GNSS spoofing data is used, and the measurement innovation time series is stored in the regression window to fit the GNSS spoofing data into a mathematical model, and the GNSS spoofing error at the current moment is predicted and fed back, and then the feedback measurement innovation is solved by ARKF; if the combined system is not interfered by spoofing, there is no need to regress, predict and feedback the measurement innovation time series, and the ARKF solution can be directly used;

[0013] Step 5. When the GNSS spoofing ends, 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 under the spoofing condition on the current filtering system estimation, and 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 has converged. When the filter converges, the adaptive factor weight of ARKF is readjusted, and the spoofing interference is continuously detected to further improve the reliability and anti-interference ability of the combined system.

[0014] The solution described in step 2 is performed by using the GNSS / MIMU combined positioning method based on ARKF;

[0015] The specific steps are as follows:

[0016] Step 2-1: The state vector of the GNSS / MIMU loose combination positioning model is the position error δr n , speed error δv n , attitude error φ, gyro bias b g 、Accelerometer bias b a , that is:

[0017] X=[δr n δv n φb g b a ] (1)

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

[0019]

[0020] Among them, the state transfer matrix F, the noise allocation matrix G and the system noise matrix W bThe expression is as follows:

[0021]

[0022] In the formula, is the posture matrix; f b For comparison; w ab and w gb represent the measurement white noise of accelerometer and gyroscope respectively;

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

[0024] Z k =H k X k +V k (4)

[0025] In the formula, H k represents the observation matrix; V k represents the measurement noise vector, whose covariance matrix is ​​R k , the expressions of each matrix are as follows:

[0026] Observation vector Z k It can be expressed as:

[0027]

[0028] In the formula, represents the arm vector from the MIMU center to the GNSS receiver antenna phase center in the carrier coordinate system, They represent the position and velocity of MIMU in the navigation coordinate system obtained by inertial navigation respectively; They represent the position and velocity of the antenna phase center in the n-frame calculated by GNSS respectively. The observation matrix in the measurement equation is expressed as:

[0029]

[0030] Step 2-4: Use ARKF to update the measurement noise matrix R k Real-time adjustment is performed to obtain more accurate positioning results. This filtering method introduces a robustness factor γ ii , γ ii The calculation formula is as follows:

[0031]

[0032] Where k0 and k1 represent empirical constants; v k,i It represents the innovation value of the i-th measurement value of a certain epoch, and its expression is as follows:

[0033]

[0034] When the absolute value of the new information value is less than k0, the measured value is considered normal and the robustness factor γ ii The value of is 1; when the absolute value of the new information value is between k0 and k1, the robustness factor γ ii The value of will become larger, and the weight of the corresponding measurement value will decrease; when the absolute value of the new information value is greater than k1, it is considered that there is a large measurement error in the measurement value, and the robustness factor is set to infinity;

[0035] The robustness factor γ ii Substituting it into the R matrix and adjusting its elements, we have the following formula:

[0036]

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

[0038]

[0039] i and j represent the matrix R k After the above adjustment, the gain matrix K is calculated. k , and then obtain the optimal estimate of the state parameters at that moment and its variance-covariance matrix P.

[0040] When the GNSS is subjected to external deception interference as described in step 3, based on the standardized measurement innovation of ARKF-GNSS / MIMU, by setting the double parameters of the inspection threshold and the normalized innovation ratio, it is detected whether the GNSS / MIMU combined system is subjected to deception interference;

[0041] The specific steps are as follows:

[0042] Step 3-1: Construct the measurement innovation δr at the current epoch k :

[0043]

[0044] According to probability statistics, measure the new information δr k is a white noise sequence that follows a normal distribution with a mean of zero:

[0045]

[0046] In the fully closed-loop ARKF, the system model error is controlled within a small range through feedback correction, so the influence of the system model can be ignored. k It can reflect whether the observed value is abnormal;

[0047] When the system has no deceptive interference, the measured new information is a white noise sequence with a mean of zero. When the system fails, the mean of the measured new information no longer obeys the white noise sequence with a mean of zero, which transforms the above fault detection condition into a hypothesis testing problem:

[0048]

[0049] Step 3-2: According to the standard normal distribution theory of mathematical statistics, construct the test statistic by measuring the new information, and set the test threshold by the false alarm rate and probability distribution function:

[0050] Normalize the measurement innovations:

[0051]

[0052] Where, i = 1, 2, 3; δr i Measuring innovation for three-dimensional position; is the i-th row and i-th column of the measurement noise covariance matrix; Right i Make a binary hypothesis, given the false alarm probability P FA Under the condition of , the probability density function of the normal distribution can be used to derive the required test threshold T lse ;

[0053]

[0054] By checking the value of the innovation i With the test threshold T lse Perform deception detection on the system. If d i >T lse , the system is under spoofing attack; if d i <T lse ,The system has no deception attack;

[0055] Step 3-3: The ratio of the standardized novelty value at the current moment to the standardized novelty value at the previous moment is used as a feature for determining the moment when the deception ends:

[0056]

[0057] In the formula, is the test parameter at the end of the deception; the standardized new value on the left side of the fraction is the new value at the current moment; the standardized new value on the right side of the fraction is the new value at the previous moment; t e Time for the deception to end.

[0058] The combined system described in step 4 detects that it is interfered by spoofing, uses the measurement innovation time series composed of short-term highly confident MIMU data and GNSS spoofing data, stores the measurement innovation time series in the regression window, fits the GNSS spoofing data into a mathematical model, and predicts and feedbacks the GNSS spoofing error at the current moment, and then performs ARKF solution on the feedback measurement innovation;

[0059] The specific steps are as follows:

[0060] Step 4-1: Use the measurement equation of the GNSS / MIMU combination to construct measurement information in a deceptive environment:

[0061]

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

[0063]

[0064] When GNSS is attacked by external spoofing, the system measurement information is written as follows according to equations (17) and (18):

[0065]

[0066] In the formula, ε represents the random error, which is a random variable that satisfies E(ε) = 0 and

[0067]

[0068] Step 4-2: Assume that there are n MIMU highly confident positioning results after the GNSS is spoofed, and construct them into time series data as follows: but:

[0069]

[0070] Step 4-3: Through each time series data and regression value Minimize the degree of deviation and establish the least squares model:

[0071]

[0072] in,

[0073] Step 4-4: Use the exponential moving weighted average model to assign time-varying weights to the optimal regression values ​​β0 and β1:

[0074]

[0075] in, t k The regression coefficient of time; t k-1 The regression coefficient at the moment; α is the attenuation coefficient, α∈

[01] ;

[0076] Use the optimal regression coefficient to predict and compensate for the measurement information, and convert the corrected The filter loop introduced is:

[0077]

[0078] Step 5 constructs a combined filtering system based on a fading factor, uses the fading factor to adjust the adaptive factor, weakens the influence of the predicted value under deception conditions on the current filtering system estimation, 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 that the prediction error covariance and the innovation covariance have the following relationship:

[0081]

[0082] In the formula, λ k is the fading factor; α k is a scalar factor; and are the estimated values ​​calculated based on the fading factor and the scalar factor, respectively, and the new gain matrix is:

[0083]

[0084] Step 5-2: Obtain the optimal fading factor λ k and the scalar factor α k Make the gain matrix optimal:

[0085]

[0086] Substituting equation (27) into equation (25), we can obtain α k for:

[0087]

[0088] The current estimated innovation covariance can also be expressed as follows:

[0089]

[0090] Rewrite equation (29) as:

[0091]

[0092] From α k The expression shows that α k is very close to 1, so (1-α k )R k Close to 0, it can be ignored, and then we get α k With λ k Approximately equal, let α k =λ k , so the fading factor is expressed as:

[0093]

[0094] Step 5-3: Use the fading factor to control the robust factor in the ARKF filter:

[0095]

[0096] When k > 1, the combined system filter is considered not to have converged, even if the innovation value is greater than T lse , the robustness factor γ ij The value of is set to 1, so that the filtering system gradually converges; when λ k = 1, the combined system filter is considered to be converged, and the robustness factor γ is calculated using formula (7) ij Numeric value.

[0097] Advantages of the present invention:

[0098] 1. The present invention uses MIMU-assisted deception detection to mainly construct a dual-parameter detection combination system to determine whether it is deceiving. Experimental verification shows that it can effectively identify the deception interference of the system. Under the MEAC and LOA models, the false alarm rates in the north, east and high directions are 0.411%, 0.308% and 1.129% respectively, the average missed alarm rate is 0%, and the average false alarm rate is 0.616%, thus achieving effective detection of deception interference.

[0099] 2. MIMU is used to effectively suppress long-term and continuous deception interference. Experiments have verified that when the combined system is subjected to MEAC with a duration of 200s, a north deviation of 500m, an east deviation of -200m, and a LOA with a duration of 300s and a north-east deception rate of 1m / s, there is no filter divergence and the deception interference is effectively suppressed. The maximum errors in the north and east directions are 2.551m and 1.817m respectively, and the maximum positioning error is 2.677m. It has higher stability and reliability, and improves the system's ability to deal with deception interference.

[0100] 3. The present invention introduces a fading factor to adjust the adaptive factor of ARKF to form a combined filtering system based on ARKF. On the one hand, the fading factor is used to reduce the adaptive factor weight of ARKF, weaken the influence of the predicted value under the deception condition on the current filtering system estimation, increase the weight of GNSS, 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 converges. When the filter converges, the adaptive factor weight of ARKF is readjusted to continuously detect deception interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 A flow chart of a GNSS / MIMU spoofing detection and suppression method based on a regression model and fading factor optimization according to the present invention;

[0102] Figure 2 A specific flow chart of step 2 of an embodiment of the present invention;

[0103] Figure 3 A specific flow chart of step 3 of an embodiment of the present invention;

[0104] Figure 4 A specific flow chart of step 4 of an embodiment of the present invention;

[0105] Figure 5 A specific flow chart of step 5 of an embodiment of the present invention;

[0106] Figure 6 A summary flow chart of one embodiment of the present invention;

[0107] Figure 7 Experimental trajectory and deception trajectory diagram for utilizing the present invention;

[0108] Figure 8 To utilize the present invention to detect the north, east and high direction deception interference situation;

[0109] Fig. 9 In order to use the present invention to suppress the deception of MEAC and LOA, the positioning results of EKF and ARKF algorithms are compared;

[0110] Fig.10 In order to utilize the present invention to suppress the deception of MEAC and LOA, the northing, easting and position error curves of different algorithms are plotted; DETAILED DESCRIPTION

[0111] An embodiment of the present invention is further described below with reference to the accompanying drawings.

[0112] In an embodiment of the present invention, a GNSS / MIMU spoofing detection and suppression method based on a regression model and fading factor optimization is provided. Figure 1 As shown, the following steps are included:

[0113] Step 1: Use the initial position information, speed information of GNSS, the initial attitude information of MIMU and the arm information to calculate the position, speed and attitude information of the MIMU measurement center as the initialization information of the GNSS / MIMU combined system, and collect the GNSS and MIMU sensor data in real time;

[0114] Step 2: For the real-time collected GNSS and MIMU data, the time synchronization module is used to achieve time synchronization between the two types of sensor data and the ARKF solution is used, such as Figure 2 As shown;

[0115] Step 2-1: The state vector of the GNSS / MIMU loose combination positioning model is the position error δr n , speed error δv n , attitude error φ, gyro bias b g 、Accelerometer bias b a , that is:

[0116] X=[δr n δv n φb g b a ] (1)

[0117] Step 2-2, the state equation of Kalman filtering can be expressed as follows:

[0118]

[0119] Among them, the state transfer matrix F, the noise allocation matrix G and the system noise matrix W b The expression is as follows:

[0120]

[0121] In the formula, is the posture matrix; f b For comparison; w ab and w gbrepresent the measurement white noise of accelerometer and gyroscope respectively;

[0122] Step 2-3, the measurement equation for the GNSS / MIMU loose combination is as follows:

[0123] Z k =H k X k +V k (4)

[0124] In the formula, H k represents the observation matrix; V k represents the measurement noise vector, whose covariance matrix is ​​R k , the expressions of each matrix are as follows:

[0125] Observation vector Z k It can be expressed as:

[0126]

[0127] In the formula, represents the arm vector from the MIMU center to the GNSS receiver antenna phase center in the carrier coordinate system, They represent the position and velocity of MIMU in the navigation coordinate system obtained by inertial navigation respectively; They represent the position and velocity of the antenna phase center in the n-frame calculated by GNSS respectively. The observation matrix in the measurement equation is expressed as:

[0128]

[0129] Step 2-4: Use ARKF to update the measurement noise matrix R k Real-time adjustment is performed to obtain more accurate positioning results. This filtering method introduces a robustness factor γ ii , γ ii The calculation formula is as follows:

[0130]

[0131] Where k0 and k1 represent empirical constants; v k,i It represents the innovation value of the i-th measurement value of a certain epoch, and its expression is as follows:

[0132]

[0133] When the absolute value of the new information value is less than k0, the measured value is considered normal and the robustness factor γ ii The value of is 1; when the absolute value of the new information value is between k0 and k1, the robustness factor γ iiThe value of will become larger, and the weight of the corresponding measurement value will decrease; when the absolute value of the new information value is greater than k1, it is considered that there is a large measurement error in the measurement value, and the robustness factor is set to infinity;

[0134] The robustness factor γ ii Substituting it into the R matrix and adjusting its elements, we have the following formula:

[0135]

[0136] In the formula, represents the measurement noise matrix after adaptive adjustment, and

[0137]

[0138] i and j represent the matrix R k After the above adjustment, the gain matrix K is calculated. k , and then obtain the optimal estimate of the state parameters at that moment and its variance-covariance matrix P.

[0139] Step 3: Based on step 2, when GNSS is subjected to external deception interference, based on the standardized measurement information of ARKF-GNSS / MIMU, by setting two dual parameters, the test threshold and the normalized information ratio, it is detected whether the GNSS / MIMU combination system is subjected to deception interference, such as Figure 3 As shown;

[0140] Step 3-1: Construct the measurement innovation δr at the current epoch k :

[0141]

[0142] According to probability statistics, measure the new information δr k is a white noise sequence that follows a normal distribution with a mean of zero:

[0143]

[0144] In the fully closed-loop ARKF, the system model error is controlled within a small range through feedback correction, so the influence of the system model can be ignored. k It can reflect whether the observed value is abnormal;

[0145] When the system has no deceptive interference, the measured new information is a white noise sequence with a mean of zero. When the system fails, the mean of the measured new information no longer obeys the white noise sequence with a mean of zero, which transforms the above fault detection condition into a hypothesis testing problem:

[0146]

[0147] Step 3-2: According to the standard normal distribution theory of mathematical statistics, construct the test statistic by measuring the new information, and set the test threshold by the false alarm rate and probability distribution function:

[0148] Normalize the measurement innovations:

[0149]

[0150] Where, i = 1, 2, 3; δr i Measuring innovation for three-dimensional position; is the i-th row and i-th column of the measurement noise covariance matrix; Right i Make a binary hypothesis, given the false alarm probability P FA Under the condition of , the probability density function of the normal distribution can be used to derive the required test threshold T lse ;

[0151]

[0152] By checking the value of the innovation i With the test threshold T lse Perform deception detection on the system. If d i >T lse , the system is under spoofing attack; if d i <T lse ,The system has no deception attack;

[0153] Step 3-3: The ratio of the standardized novelty value at the current moment to the standardized novelty value at the previous moment is used as a feature for determining the moment when the deception ends:

[0154]

[0155] In the formula, Q te is the test parameter at the end of the deception; the standardized new value on the left side of the fraction is the new value at the current moment; the standardized new value on the right side of the fraction is the new value at the previous moment; t e Time for the deception to end.

[0156] Step 4: Based on step 3, if the combined system detects that it is interfered by spoofing, the measurement innovation time series composed of short-term highly confident MIMU data and GNSS spoofing data is used to store the measurement innovation time series in the regression window to fit the GNSS spoofing data into a mathematical model, and the GNSS spoofing error at the current moment is predicted and fed back, and then the feedback measurement innovation is solved by ARKF; if the combined system is not interfered by spoofing, there is no need to regress, predict and feedback the measurement innovation time series, and the ARKF solution can be directly used, such as Figure 4As shown;

[0157] Step 4-1: Use the measurement equation of the GNSS / MIMU combination to construct measurement information in a deceptive environment:

[0158]

[0159] In the formula, Indicates the actual position of the IMU measurement center; Indicates the actual position of the GNSS antenna phase center; b It is the projection of the vector from the IMU measurement center to the GNSS antenna phase center in the b system; The expression is:

[0160]

[0161] When GNSS is attacked by external spoofing, the system measurement information is written as follows according to equations (17) and (18):

[0162]

[0163] In the formula, ε represents the random error, which is a random variable that satisfies E(ε) = 0 and

[0164]

[0165] Step 4-2: Assume that there are n MIMU highly confident positioning results after the GNSS is spoofed, and construct them into time series data as follows: but:

[0166]

[0167] Step 4-3: Through each time series data and regression value Minimize the degree of deviation and establish the least squares model:

[0168]

[0169] in,

[0170] Step 4-4: Use the exponential moving weighted average model to assign time-varying weights to the optimal regression values ​​β0 and β1:

[0171]

[0172] in, t k The regression coefficient of time; t k-1The regression coefficient at the moment; α is the attenuation coefficient, α∈

[01] ;

[0173] Use the optimal regression coefficient to predict and compensate for the measurement information, and convert the corrected The filter loop introduced is:

[0174]

[0175] Step 5: When GNSS spoofing ends, Figure 5 As shown in the figure, a combined filtering system based on fading factors is constructed. On the one hand, the fading factors are used to reduce the adaptive factor weight of ARKF, weaken the influence of the predicted value under deception conditions on the current filtering system estimation, and accelerate the convergence speed of the filtering system after the deception ends. On the other hand, the fading factors are used to determine whether the filter of the combined system converges. 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 ability of the combined system.

[0176] Step 5-1: Reduce the impact of deceptive data and suppress filter divergence. Assume that the prediction error covariance and the innovation covariance have the following relationship:

[0177]

[0178] In the formula, λ k is the fading factor; α k is a scalar factor; and are the estimated values ​​calculated based on the fading factor and the scalar factor, respectively, and the new gain matrix is:

[0179]

[0180] Step 5-2: Obtain the optimal fading factor λ k and the scalar factor α k Make the gain matrix optimal:

[0181]

[0182] Substituting equation (27) into equation (25), we can obtain α k for:

[0183]

[0184] The current estimated innovation covariance can also be expressed as follows:

[0185]

[0186] Rewrite equation (29) as:

[0187]

[0188] From α k The expression shows that α k is very close to 1, so (1-α k )R k Close to 0, it can be ignored, and then we get α k With λ k Approximately equal, let α k =λ k , so the fading factor is expressed as:

[0189]

[0190] Step 5-3: Use the fading factor to control the robust factor in the ARKF filter:

[0191]

[0192] When k > 1, the combined system filter is considered not to have converged, even if the innovation value is greater than T lse , the robustness factor γ ij The value of is set to 1, so that the filtering system gradually converges; when λ k = 1, the combined system filter is considered to be converged, and the robustness factor γ is calculated using formula (7) ij Numeric value.

[0193] In the present invention, the experimental simulation vehicle driving trajectory is as follows Figure 7 As shown in the figure, the "five-pointed star" shape represents the starting point of the carrier, with coordinates of (30°27'37.557", 114°28'21.017", 23.000m), and the "circle" shape represents the end point of the carrier, with coordinates of (30°30'42.084", 114°31'50.322", 23.000m). The entire experimental simulation lasts 985s, and the experimental motion process includes acceleration, deceleration, and turning. The north and east errors of GNSS are 1cm, the height error is 2cm, the MIMU gyro bias is 15° / hr, the table bias is 100μg, and the gyro random walk is The random walk of the added table is During the period of 200s-399s, the GNSS north position suffered a MEAC of 500m, and the GNSS east position suffered a MEAC of -200m. The MEAC caused a sudden change in the position of the GNSS positioning result and lasted for 200s. During the period of 600s-899s, the GNSS north and east positions suffered a LOA of 1m / s, and the deception time was as long as 300s. During the period when the GNSS was interfered by the LOA, the position of the carrier was gradually pulled away and eventually deviated from the reference trajectory.

[0194] Depend on Figure 8 It can be seen that the integrated navigation system was interfered with by deception during the time of 200s-399s and 600s-899s. Under the MEAC and LOA models, the false alarm rates of north, east and high directions were 0.411%, 0.308% and 1.129% respectively, the average missed alarm rate was 0%, and the average false alarm rate was 0.616%. Although there were a small number of false alarms in the algorithm, these false alarms were random and sporadic, not continuous false alarms, and effective detection of deception interference was achieved.

[0195] like Fig. 9 As shown in the figure, EKF is the solution result of the extended Kalman filter, ARKF is the solution result of the adaptive robust Kalman filter, and ARKF-RMW is the solution result of the GNSS / MIMU deception suppression algorithm based on the regression model and the optimization of the fading factor; 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 the GNSS deception. When the GNSS positioning result gradually stabilizes, the filter system gradually converges; the ARKF algorithm adaptively adjusts the weight between the GNSS positioning result and the MIMU positioning result at the beginning of the deception, and uses the MIMU The short-term high-precision characteristics continue to be extrapolated. As the error of MIMU drifts, the filter of the combined system diverges rapidly. When the GNSS deception ends, the divergent filter will cause the new information value to be unstable, which in turn leads to the instability of the robust factor and the filter is difficult to converge. Compared with the EKF algorithm and the ARKF algorithm, the ARKF-RMW algorithm is closer to the reference trajectory. There is no filter divergence at the starting point and the end point of the deception. When the GNSS is subjected to MEAC and LOA, the span error caused by MEAC and the error accumulation caused by LOA are suppressed, and it has higher reliability and stability.

[0196] like Fig.10 As shown in the figure, when GNSS is subjected to a spoofing attack, the positioning result obtained by fusing MIMU data with GNSS data using the EKF and ARKF algorithms is not reliable, and its positioning result has been seriously distorted; in terms of system reliability and stability, 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, and returns to normal after the attack, showing good anti-interference ability and stability, which improves the reliability and robustness of the positioning system when subjected to a spoofing attack; in terms of the positioning accuracy of the system, when the ARKF-RMW algorithm is attacked by a MEAC with a maximum span of 500m for 200s and a LOA with a maximum deviation of 300m for 300s, the maximum errors in the north and east directions are 2.551m and 1.817m respectively, and the maximum positioning error is 2.677m.

[0197] The above is only the most basic specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any replacement that can be understood by a person skilled in the art within the technical scope disclosed by the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization, characterized in that: The following steps are involved: Step 1: Use the initial position information, speed information of GNSS, the initial attitude information of MIMU and the arm information to calculate the position, speed and attitude information of the MIMU measurement center as the initialization information of the GNSS / MIMU combined system, and collect the GNSS and MIMU sensor data in real time; Step 2: For the real-time collected GNSS and MIMU data, the time synchronization module is used to achieve time synchronization between the two types of sensor data and the ARKF solution is used; Step 3, based on step 2, when the GNSS is subjected to external deception interference, based on the standardized measurement information of ARKF-GNSS / MIMU, by setting two dual parameters of the inspection threshold and the normalized information ratio, whether the GNSS / MIMU combination system is subjected to deception interference; Step 4: Based on step 3, if the combined system detects that it is interfered by spoofing, the measurement innovation time series composed of short-term highly confident MIMU data and GNSS spoofing data is used, and the measurement innovation time series is stored in the regression window to fit the GNSS spoofing data into a mathematical model, and the GNSS spoofing error at the current moment is predicted and fed back, and then the feedback measurement innovation is solved by ARKF; if the combined system is not interfered by spoofing, there is no need to regress, predict and feedback the measurement innovation time series, and the ARKF solution can be directly used; Step 5. When the GNSS spoofing ends, 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 under the spoofing condition on the current filtering system estimation, and 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 has converged. When the filter converges, the adaptive factor weight of ARKF is readjusted, and the spoofing interference is continuously detected to further improve the reliability and anti-interference ability of the combined system.

2. A GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization according to claim 1, characterized in that: The GNSS / MIMU combined positioning method based on ARKF described in step 2; The specific steps are as follows: Step 2-1: The state vector of the GNSS / MIMU loose combination positioning model is the position error δr n , speed error δv n , attitude error φ, gyro bias b g 、Accelerometer bias b a , that is: X=[δr n δv n φb g b a ] (1) Step 2-2, the state equation of Kalman filtering can be expressed as follows: Among them, the state transfer matrix F, the noise allocation matrix G and the system noise matrix W b The expression is as follows: In the formula, is the posture matrix; f b For comparison; w ab and w gb represent the measurement white noise of accelerometer and gyroscope respectively; Step 2-3, the measurement equation for the GNSS / MIMU loose combination is as follows: Z k =H k X k +V k (4) In the formula, H k represents the observation matrix; V k represents the measurement noise vector, whose covariance matrix is ​​R k , the expressions of each matrix are as follows: Observation vector Z k It can be expressed as: In the formula, represents the arm vector from the MIMU center to the GNSS receiver antenna phase center in the carrier coordinate system, They represent the position and velocity of MIMU in the navigation coordinate system obtained by inertial navigation respectively; They represent the position and velocity of the antenna phase center in the n-frame calculated by GNSS respectively. The observation matrix in the measurement equation is expressed as: Step 2-4: Use ARKF to update the measurement noise matrix R k Real-time adjustment is performed to obtain more accurate positioning results. This filtering method introduces a robustness factor γ ii , γ ii The calculation formula is as follows: Where k0 and k1 represent empirical constants; v k,i It represents the innovation value of the i-th measurement value of a certain epoch, and its expression is as follows: When the absolute value of the new information value is less than k0, the measured value is considered normal and the robustness factor γ ii The value of is 1; when the absolute value of the new information value is between k0 and k1, the robustness factor γ ii The value of will become larger, and the weight of the corresponding measurement value will decrease; when the absolute value of the new information value is greater than k1, it is considered that there is a large measurement error in the measurement value, and the robustness factor is set to infinity; The robustness factor γ ii Substituting it into the R matrix and adjusting its elements, we have the following formula: In the formula, represents the measurement noise matrix after adaptive adjustment, and i and j represent the matrix R k After the above adjustment, the gain matrix K is calculated. k , and then obtain the optimal estimate of the state parameters at that moment and its variance-covariance matrix P.

3. The GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization according to claim 1, characterized in that: Step 3 uses two dual parameters, namely, the test threshold and the normalized new information ratio, to detect whether the system is subject to fraudulent interference; The specific steps are as follows: Step 3-1: Construct the measurement innovation δr at the current epoch k : According to probability statistics, measure the new information δr k is a white noise sequence that follows a normal distribution with a mean of zero: In the fully closed-loop ARKF, the system model error is controlled within a small range through feedback correction, so the influence of the system model can be ignored. k It can reflect whether the observed value is abnormal; When the system has no deceptive interference, the measured new information is a white noise sequence with a mean of zero. When the system fails, the mean of the measured new information no longer obeys the white noise sequence with a mean of zero, which transforms the above fault detection condition into a hypothesis testing problem: Step 3-2: According to the standard normal distribution theory of mathematical statistics, construct the test statistic by measuring the new information, and set the test threshold by the false alarm rate and probability distribution function: Normalize the measurement innovations: Where, i = 1, 2, 3; δr i Measuring innovation for three-dimensional position; is the i-th row and i-th column of the measurement noise covariance matrix; d i N(0,1), for d i Make a binary hypothesis, given the false alarm probability P FA Under the condition of , the probability density function of the normal distribution can be used to derive the required test threshold T lse ; By checking the value of the innovation i With the test threshold T lse Perform deception detection on the system. If d i >T lse , the system is under spoofing attack; if d i <T lse ,The system has no deception attack; Step 3-3: The ratio of the standardized novelty value at the current moment to the standardized novelty value at the previous moment is used as a feature for determining the moment when the deception ends: In the formula, Q te is the test parameter at the end of the deception; the standardized new value on the left side of the fraction is the new value at the current moment; the standardized new value on the right side of the fraction is the new value at the previous moment; t e Time for the deception to end.

4. The GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization according to claim 1, characterized in that: The ARKF-GNSS / MIMU spoofing suppression algorithm optimized by using the regression model and the fading factor described in step 4 effectively suppresses spoofing interference, improves the spoofing suppression capability of the system in complex environments, and thus enhances the anti-spoofing performance and stability of the overall system; The specific steps are as follows: Step 4-1: Use the measurement equation of the GNSS / MIMU combination to construct measurement information in a deceptive environment: In the formula, Indicates the actual position of the IMU measurement center; Indicates the actual position of the GNSS antenna phase center; b It is the projection of the vector from the IMU measurement center to the GNSS antenna phase center in the b system; The expression is: When GNSS is attacked by external spoofing, the system measurement information is written as follows according to equations (17) and (18): In the formula, ε represents the random error, which is a random variable that satisfies E(ε) = 0 and Step 4-2: Assume that there are n MIMU highly confident positioning results after the GNSS is spoofed, and construct them into time series data as follows: but: Step 4-3: Through each time series data and regression value Minimize the degree of deviation and establish the least squares model: in, Step 4-4: Use the exponential moving weighted average model to assign time-varying weights to the optimal regression values ​​β0 and β1: in, t k The regression coefficient of time; t k-1 The regression coefficient at the moment; α is the attenuation coefficient, α∈[0 1]; Use the optimal regression coefficient to predict and compensate for the measurement information, and convert the corrected The filter loop introduced is:

5. The GNSS / MIMU spoofing detection and suppression method based on regression model and fading factor optimization according to claim 1, characterized in that: Step 5 constructs a combined filtering system based on a fading factor, uses the fading factor to adjust the adaptive factor, weakens the influence of the predicted value under deception conditions on the current filtering system estimation, and accelerates the convergence speed of the filtering system after the deception ends; The specific steps are as follows: Step 5-1, reduce the impact of deceptive data and suppress filter divergence; assume that the prediction error covariance and the innovation covariance have the following relationship: In the formula, λ k is the fading factor; α k is a scalar factor; and are the estimated values ​​calculated based on the fading factor and the scalar factor, respectively, and the new gain matrix is: Step 5-2: Obtain the optimal fading factor λ k and the scalar factor α k Make the gain matrix optimal: Substituting equation (27) into equation (25), we can obtain α k for: The current estimated innovation covariance can also be expressed as follows: Rewrite equation (29) as: From α k The expression shows that α k is very close to 1, so (1-α k )R k Close to 0, it can be ignored, and then we get α k With λ k Approximately equal, let α k =λ k , so the fading factor is expressed as: Step 5-3: Use the fading factor to control the robust factor in the ARKF filter: When k > 1, the combined system filter is considered not to have converged, even if the innovation value is greater than T lse , the robustness factor γ ij The value of is set to 1, so that the filtering system gradually converges; when λ k = 1, the combined system filter is considered to be converged, and the robustness factor γ is calculated using formula (7) ij Numeric value.

Images