A GNSS / INS Tightly Coupled Spoofing Detection Method Based on Innovation Robust Estimation

Abstract

The present invention provides a GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation, belonging to the technical field of spoofing detection in navigation systems. Existing spoofing detection algorithms, when detecting slowly growing ramp-type spoofing interference, due to the small rate of spoofing growth, it takes a long time to accumulate to reach the preset detection threshold and then be detected, resulting in too long detection time. When it is difficult to judge whether spoofing exists in the present invention, an equivalent weight matrix is calculated according to the average normalized innovation vector and the upper and lower limit detection thresholds, and then weight reduction processing is carried out through the equivalent weight matrix to obtain a new gain matrix. The prior estimated state vector and the prior covariance estimated vector are optimized through the gain matrix, so as to amplify the undetected spoofing interference at the k+1 moment, so that the spoofing interference can reach the preset detection threshold through short-time accumulation, thereby judging whether spoofing exists and shortening the spoofing detection time.

Description

Technical Field

[0001] The present invention relates to a GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation, belonging to the technical field of spoofing detection of navigation systems. Background Art

[0002] In the prior art, unmanned aerial vehicles (UAVs) generally adopt an integrated navigation system combining the Global Navigation Satellite System and the Inertial Navigation System for navigation control. The integrated navigation system of the Global Navigation Satellite System (GNSS) and the Inertial Navigation System (INS) has the complementary error characteristics of the two. GNSS can provide all-weather continuous Position, Velocity & Time (PVT) services globally, while INS has the advantages of being independent, continuously working, and providing short-term anti-interference ability. The combination of the two increases the redundancy and reliability of the system. GNSS / INS integrated navigation can be divided into three combination modes: loose coupling, tight coupling, and deep coupling. Tight coupling is to combine the pseudorange, pseudorange rate and other observables output by the GNSS receiver with the pseudorange and pseudorange rate obtained by inverse calculation of the ephemeris in combination with INS.

[0003] However, due to the low power and open structure of GNSS signals, GNSS services are vulnerable to spoofing interference. A third party may interfere with the movement of the UAV by applying spoofing interference. At this time, the flight trajectory of the UAV deviates from the normal flight trajectory. However, when the flight trajectory of the UAV deviates, it is difficult to determine whether it is caused by problems existing in the UAV itself or by spoofing interference applied by a third party. Therefore, it is necessary to perform real-time, fast, and accurate spoofing detection to ensure the reliability and integrity of the integrated navigation system.

[0004] Spoofing interference refers to the interference source generating spoofing signals highly similar to the real signals or relaying the real signals to deceive the target receiver, forcing it to generate incorrect and possibly dangerous information. In the GNSS / INS integrated navigation system, the GNSS module locks the spoofing signal and outputs incorrect information, which in turn affects the estimated value of the state error in the measurement update stage of the Kalman filter and outputs incorrect navigation results. At the same time, the incorrect estimated value of the state error is fed back to INS through information fusion, ultimately affecting the GNSS / INS integrated navigation system, causing a large deviation in the trajectory of the unmanned control device and possibly affecting the safety of the device.

[0005] The GNSS / INS tightly coupled spoofing detection method mainly uses the Kalman filter innovation vector as the detection statistic. It has the advantages of low cost, high efficiency, and small computational complexity, and is a widely used hypothesis testing method. This method can be divided into the "snapshot method" and the "continuous method". The "snapshot method" uses the innovation vector at the current moment to form the test statistic, which is sensitive to step-type spoofing interference but cannot identify incorrect measurements. The "continuous method" forms the test statistic with the innovation vectors within a period of time and is sensitive to ramp-type spoofing interference. However, both of these methods have limitations. When one channel is affected by spoofing interference, the closed-loop correction mechanism will cause other channels to deviate from the normal innovation values, resulting in missed alarms or false alarms. Therefore, the difficulties in GNSS / INS integrated navigation system spoofing interference detection are the closed-loop correction mechanism of integrated navigation and the time delay problem of slowly growing ramp-type spoofing detection.

[0006] Regarding the problem of the integrated navigation closed-loop correction mechanism, ZHANG Chuang et al. proposed an improved detection algorithm based on robust estimation and the "detection window". The core idea is to select two appropriate thresholds to calculate the weight median factor and adaptively adjust the measurement noise covariance matrix to reduce the weight of the spoofed measurement value, thereby adaptively adjusting the gain matrix. When a single-channel is affected by a 0.5 m / s ramp-type interference, the improved algorithm shortens the detection time by 10 s compared with the traditional algorithm, and the missed alarm rate is reduced by 9%. Zhang Chao et al. proposed an innovation rate robust estimation detection algorithm, which can effectively suppress the influence of spoofing interference on the state vector, improve the data utilization rate and the reliability of the algorithm. The missed alarm rate and false alarm rate of the slowly growing ramp-type spoofing interference with a slope of 0.1 m / s in a single-channel are maintained within 4%. However, both of these algorithms have too long detection times or are insensitive to slowly growing ramp-type spoofing interference, especially spoofing interference with a slope less than 0.1 m / s.

[0007] Regarding the time delay problem of slowly growing ramp-type spoofing detection, Bhatti et al. proposed using the innovation rate to judge whether there are abnormalities in GNSS measurement values, and then using the Kalman filter to estimate the normalized innovation rate in real time. This method effectively improves the detection time, but affected by the integrated navigation closed-loop correction, the innovation rates of the remaining normal channels are also affected. When a single-channel is affected by a slowly growing interference of 0.1 m / s, the detection time is 110 s. At the same time, this method designs a two-layer filter mechanism, increasing the complexity of actual operation. Xu Rui et al. proposed a spoofing signal detection method of MEDLL, which can successfully detect and identify a 2 m / s ramp-type spoofing, but its ramp slope is relatively large and it is difficult to apply to slowly growing ramp-type spoofing interference with a slope of 0.1 m / s. In the past five years, some scholars have studied spoofing detection algorithms such as neural networks and support vector machines, but they have problems such as high computational complexity, weak compatibility, and high cost.

[0008] In summary, when the existing deception interference detection algorithms detect slow-growing ramp-type deception interference, the detection time is too long, and there is even a phenomenon of insensitive detection, with a high missed detection rate and false alarm rate. As a result, it takes a relatively long distance for the drone to fly before it can accurately determine whether there is deception interference imposed by a third party, seriously affecting the safety of the drone flight process. Summary of the Invention

[0009] The purpose of the present invention is to provide a GNSS / INS tightly coupled deception detection method based on innovation robust estimation, which is used to solve the problem of long detection time when the existing deception interference detection algorithms detect slow-growing ramp-type deception interference.

[0010] To achieve the above purpose, the present invention provides a GNSS / INS tightly coupled deception detection method based on innovation robust estimation, including the following steps:

[0011] S1. Set a detection window with a time length of L, and observe the GNSS / INS tightly coupled system through an observation model within the detection window to obtain the average normalized innovation vector from the (k - L + 1)-th moment to the k-th moment and the innovation vector r at the k-th moment k ; i = 1, 2,..., n, where n is the number of visible satellites;

[0012] S2. If the absolute value of the i-th element in the average normalized innovation vector is greater than the preset upper detection threshold T d2 , then the GNSS measurement value corresponding to the i-th element in the average normalized innovation vector is deceived; if is less than the preset lower detection threshold T d1 , then the GNSS measurement value corresponding to the i-th element in the average normalized innovation vector is not deceived; if is greater than T d1 and less than T d2 , then according to T d1 、T d2 and the observation noise covariance matrix R of the observation model k , calculate the equivalent weight matrix W k ;

[0013] S3. According to the observation model H at the k-th moment k 、the prior covariance estimation vector P k - and the equivalent weight matrix W k calculate the gain matrix According to the gain matrix at the k-th moment innovation vector rk and the prior estimated state vector Calculate the posterior estimated state vector at time k According to the observation model H at time k k , the gain matrix and the prior covariance estimation vector P k - , calculate the posterior estimated covariance vector P at time k k + ;

[0014] S4. At time k + 1, according to the posterior estimated state vector at time k and the posterior estimated covariance vector P k + , calculate the prior estimated state vector at time k + 1 and the prior covariance estimation vector According to the prior estimated state vector at time k + 1 and the prior covariance estimation vector Combined with the observation vector Z at time k + 1 k+1 , calculate the average normalized innovation vector from time k - L to k + 1, and then according to T d1 and T d2 Perform spoofing detection at time k + 1

[0015] Existing spoofing detection algorithms, when detecting slowly growing ramp-style spoofing interference, due to the small rate of spoofing growth, it takes a long time to accumulate to reach the preset detection threshold and then be detected, resulting in too long detection time. The present invention designs a detection window with a time length of L, and within this detection window, observes the GNSS / INS tightly coupled navigation system through the observation model to obtain the average normalized innovation vector from time k - L + 1 to k and the innovation vector at time k. Combined with the preset upper and lower limit detection thresholds, it is judged whether there is spoofing. When it is difficult to judge whether there is spoofing, calculate the equivalent weight matrix according to the average normalized innovation vector and the upper and lower limit detection thresholds. Perform weight reduction processing through the equivalent weight matrix to obtain a new gain matrix, and perform posterior estimation on the prior estimated state vector and the prior covariance estimation vector at time k through the gain matrix to obtain the posterior estimated state vector and the posterior covariance estimation vector. At time k + 1, calculate the prior estimated state vector and the prior covariance estimation vector at time k + 1 through the posterior estimated state vector and the posterior covariance estimation vector at time k, combined with the observation vector at time k + 1, and the average normalized innovation vector from time k - L to k + 1, and then according to T d1 and T d2Perform deception detection at the (k + 1)-th moment until the deception detection is completed. For the slowly increasing ramp-type deception, the present invention performs weight reduction processing through an equivalent weight matrix, amplifies the undetected deception interference, so that the deception interference can reach the preset detection threshold through short-time accumulation, thereby determining whether there is deception and shortening the deception detection time.

[0016] Further, in the above method, the gain matrix is calculated by the following formula in step S2:

[0017]

[0018] In the formula, represents the gain matrix, H k represents the observation model, P k - represents the prior covariance estimation vector, W k represents the equivalent weight matrix.

[0019] Providing a set of specific formulas to calculate the gain matrix according to the equivalent weight matrix facilitates the implementation of the present invention.

[0020] Further, in the above method, the equivalent weight matrix W is calculated by the following formula in step S2 k :

[0021]

[0022]

[0023] In the formula, represents the i-th element of the equivalent weight matrix W k of, represents the i-th element of the observation noise covariance matrix R k of, w i is an intermediate variable, represents the i-th element in the average normalized innovation vector T d1 represents the preset lower detection threshold, T d2 represents the preset upper detection threshold.

[0024] Providing a set of specific formulas to calculate the intermediate variable according to the average normalized innovation vector and the upper and lower detection thresholds, and then calculating the equivalent weight matrix according to the intermediate variable and the observation noise covariance matrix facilitates the implementation of the present invention.

[0025] Further, in the above method, the posterior estimation state vector is calculated by the following formula in step S2

[0026]

[0027] In the formula, represents the prior estimated state vector, represents the gain matrix, r k represents the innovation vector.

[0028] A set of specific formulas are provided to optimize the prior estimated state vector according to the gain matrix, so as to obtain the posterior estimated state vector for deception detection at the next moment. The real-time performance of the state vector is better and it is convenient to implement.

[0029] Furthermore, in the above method, the prior estimated state vector at the (k + 1)-th moment is calculated by the following formula in step S3

[0030]

[0031] In the formula, represents the state transition matrix, represents the posterior estimated state vector at the k-th moment.

[0032] A set of specific formulas are provided to calculate the prior estimated state vector at the (k + 1)-th moment according to the posterior estimated state vector at the k-th moment, which is convenient for the implementation of the present invention.

[0033] Furthermore, in the above method, the posterior estimated covariance vector P is calculated by the following formula in step S2 k + :

[0034]

[0035] In the formula, I represents the identity vector, represents the gain matrix, H k represents the observation model, P k - represents the prior covariance estimation vector.

[0036] A set of specific formulas are provided to optimize the prior covariance estimation vector according to the gain matrix, so as to obtain the posterior estimated covariance vector for deception detection at the next moment. The real-time performance of the covariance vector is better and it is convenient to implement.

[0037] Furthermore, in the above method, the prior covariance estimation vector at the (k + 1)-th moment is calculated by the following formula in step S3

[0038]

[0039] In the formula, represents the state transition matrix, P k+ denotes the posterior estimation covariance vector at time k, q k denotes the system noise covariance matrix.

[0040] Provide a set of specific formulas to calculate the prior estimation covariance vector at time k + 1 based on the posterior estimation covariance vector at time k, which is convenient for the implementation of the present invention.

[0041] Furthermore, in the above method, the innovation vector r is calculated in step S2 through the following formula k and its covariance matrix V k :

[0042]

[0043]

[0044] In the formula, Z k denotes the observation vector, H k denotes the observation model, denotes the prior estimation state vector at time k, P k - denotes the prior covariance estimation vector at time k, R k denotes the observation noise covariance matrix.

[0045] Provide a set of formulas to calculate the innovation vector and its covariance matrix, which is simple to calculate and convenient for the implementation of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flowchart of the GNSS / INS tight integration spoofing detection method based on innovation robust estimation in the method embodiment of the present invention;

[0047] Figure 2 is a schematic diagram of the simulated flight trajectory in the method embodiment of the present invention;

[0048] FIG. 3(a) is the simulation result of the snapshot method under step spoofing in the method embodiment of the present invention;

[0049] FIG. 3(b) is the simulation result of the continuous method under step spoofing in the method embodiment of the present invention;

[0050] FIG. 4(a) is the simulation result of the snapshot method under ramp spoofing in the method embodiment of the present invention;

[0051] FIG. 4(b) is the simulation result of the continuous method under ramp spoofing in the method embodiment of the present invention;

[0052] FIG. 5(a) is the simulation result of the continuous method under ramp spoofing of 0.1 m / s in the method embodiment of the present invention;

[0053] Figure 5(b) shows the simulation results of the continuous method based on innovation robust estimation under ramp deception of 0.1 m / s in the method embodiment of the present invention;

[0054] Figure 6(a) shows the simulation results of the continuous method based on innovation robust estimation under ramp deception of 0.1 m / s in the method embodiment of the present invention;

[0055] Figure 6(b) shows the simulation results of the GNSS / INS tightly coupled deception detection method based on innovation robust estimation under ramp deception of 0.1 m / s in the method embodiment of the present invention;

[0056] Figure 7 It is a schematic diagram for comparing the simulation results of the continuous method based on innovation robust estimation and the GNSS / INS tightly coupled deception detection method based on innovation robust estimation under ramp deception of 0.1 m / s applied to channel 6 in the method embodiment of the present invention. Detailed implementation manners

[0057] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0058] Method embodiment:

[0059] The GNSS / INS tightly coupled deception detection method based on innovation robust estimation of the present invention is as Figure 1 shown and includes the following steps:

[0060] 1. The GNSS / INS tightly coupled navigation system uses GNSS pseudorange and pseudorange rate as inputs. In the closed-loop correction, the estimated position, velocity and attitude errors are fed back to the INS processor in each filtering iteration to correct the solution of the INS. The 17-dimensional state vector X of the error state extended Kalman filter (EKF) is expressed as:

[0061]

[0062] where δv and δr are respectively the attitude, velocity and position vectors of the INS estimation error, b a and b g are respectively the accelerometer and gyro zero biases of the inertial sensors, b clk and are respectively the GNSS clock error and clock drift.

[0063] At time k, the observation vector Z k obtained by subtracting the GNSS observation value from the INS prediction value is obtained. The observation vector Z k can be expressed as:

[0064]

[0065] Wherein, and respectively represent the GNSS observed pseudorange and the observed pseudorange rate, and respectively represent the INS predicted pseudorange and the predicted pseudorange rate, and n represents the number of visible satellites.

[0066] 2. In the real-time update stage of the Kalman filter, the observation vector is updated in real time. The real-time update includes a time update stage and a measurement update stage.

[0067] In the time update stage, through the prior estimation of the state vector and covariance of the GNSS / INS tightly coupled system, the prior estimated state vector and the prior covariance estimation vector P k - .

[0068]

[0069]

[0070] Wherein, the symbol "∧" represents the estimated value, the superscript "-" represents the prior estimation, the "+" represents the posterior estimation, and the superscript "T" represents the transpose of the matrix. represents the prior estimated state vector at time k, represents the posterior estimated state vector at time k-1, represents the state transition matrix; P k - represents the prior error covariance matrix at time k, represents the posterior error covariance matrix at time k-1, q k-1 represents the system noise covariance matrix. The prior estimated state vector and the prior covariance estimation vector P k - The initial values of will be obtained according to the 17-dimensional state vector X at the initial moment. Generally, the initial velocity is taken as 0, that is, the initial velocities in the north, east, and ground directions are all taken as 0. In the simulation experiment, the values of position, attitude, accelerometer, and gyroscope are generally also taken as 0. In other different scenarios, they will be determined according to the actual situation on site. The remaining states are also determined according to the actual situation on site.

[0071] Then, through the observation matrix H k , the prior estimated state vector the prior covariance estimation vector P k - and the observation noise covariance matrix R k, the innovation vector r is calculated k and its covariance matrix V k .

[0072] The innovation vector r k and its covariance matrix V k can be expressed as:

[0073]

[0074]

[0075] Then, based on the innovation vector r k and its covariance matrix V k , the normalized innovation vector ω i is calculated. The i-th element in the normalized innovation vector ω i is calculated through the following formula:

[0076]

[0077] where is the i-th value of the innovation vector at time k (i = 1, …, n, n is the number of visible satellites), is the covariance at time k, and ω i represents the i-th normalized innovation value at time k, which can reflect the error of the i-th GNSS measurement value.

[0078] 3. Define the detection window as L. By averaging the normalized innovation vectors at each time within the detection window, the average normalized innovation from time k - L + 1 to time k is obtained The i-th element in it is calculated through the following formula:

[0079]

[0080] 4. Based on the average normalized innovation, determine whether there is spoofing in the GNSS measurement values. Set T d2 as the test threshold, and T d1 = 0.5T d2 .

[0081] The detection criterion for spoofing interference is:

[0082]

[0083] When the average normalized innovation satisfies , it is difficult to determine whether there is spoofing. At this time, by updating the gain matrix K k , and then using the updated gain matrix for spoofing detection.

[0084] 5. In the measurement update phase, according to the average normalized innovation, using the IGG-3 equivalent weight function, perform downweighting processing to calculate the equivalent weight matrix W k . The equivalent weight matrix can be expressed as:

[0085]

[0086] where, represents the i-th element of the equivalent weight matrix W k , represents the i-th element of the observation noise covariance matrix R k .

[0087] Calculate w through the IGG-3 equivalent weight function i , and the IGG-3 equivalent weight function is:

[0088]

[0089] where, is the average normalized innovation corresponding to the i-th GNSS measurement value, w i is the equivalent weight corresponding to the i-th GNSS measurement value, w i is a non-zero value.

[0090] 6. Calculate the new gain matrix according to the equivalent weight matrix W k so as to update the gain matrix K . The calculation formula is: k

[0091]

[0092]

[0092] According to the gain matrix innovation vector r k and the updated gain matrix calculate the posterior estimation state vector at time k

[0093]

[0094] Also calculate the posterior estimation covariance vector P at time k k + .

[0095]

[0096] where I is the identity vector.

[0097] So far, the spoofing detection process at time k is completed. At time k + 1, return to step 1 and according to the posterior estimation state vector at time k and the posterior estimation covariance vector P k + Calculate the prior estimation state vector at time k + 1 respectively and the prior covariance estimation vector Combine the observation vector Z at time k + 1 k+1 Perform spoofing detection, so as to amplify the undetected spoofing interference at time k + 1, and achieve the purpose of fast detection and reduced detection time.

[0098] Calculate the prior estimation state vector at time k + 1 through the following formula

[0099]

[0100] In the formula, represents the state transition matrix, represents the posterior estimation state vector at time k.

[0101] Calculate the prior covariance estimation vector at time k + 1 through the following formula

[0102]

[0103] In the formula, represents the state transition matrix, P k + represents the posterior estimation covariance vector at time k, q k represents the system noise covariance matrix.

[0104] In order to verify the beneficial effects of the present invention, compare four methods: the snapshot method (M1), the continuous method (M2), the continuous method based on innovation robust estimation (M3), and the GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation (M4).

[0105] Design 3 GNSS / INS integrated navigation spoofing detection experimental scenarios. (1) When there are pseudo-range biases of different degrees of step and ramp types in one channel, compare the detection effects of M1 and M2; (2) When there is a ramp-type pseudo-range bias in one channel, compare the detection effects of M2 and M3; (3) When there is a ramp-type pseudo-range bias in one channel, compare the detection effects of M3 and M4.

[0106] 1. Parameter settings. The experimental parameter settings of GNSS / INS tight coupling include: simulated flight trajectory data, spoofing scenarios, and parameters of the three major sensors of GNSS, IMU, and Kalman. Respectively as Figure 2 and shown in Table 1 and Table 2.

[0107] Table 1 Spoofing scenario settings

[0108]

[0109]

[0110] Table 2 Simulation Parameters

[0111]

[0112] 2. Result Analysis. (1) Scenario 1: The channel 1 is subjected to spoofing interference with step or ramp pseudorange deviation values of different degrees to compare the detection capabilities of M1 and M2.

[0113] Two groups of experiments are set up. Step pseudorange deviation values of 50 m, 20 m, and 10 m are respectively applied to channel 1 (i.e., visible satellite 1) in the first group of experiments, and the spoofing duration is from 350 s to 550 s. Fig. 3(a) is the simulation result graph of M1, and Fig. 3(b) is the simulation result graph of M2. It can be seen from Fig. 3(a) and Fig. 3(b) that: 1) Fig. 3(a) shows that M1 can immediately detect the step spoofing of 50 m and 20 m applied to channel 1, and the detection time is 0 s for both, while the detection of the 10-m step spoofing is invalid; 2) Fig. 3(b) shows that when M2 detects the step spoofing of 50 m, 20 m, and 10 m applied to channel 1, the detection times are 10 s, 10 s, and 10 s respectively. By comparing Fig. 3(a) and Fig. 3(b), it can be seen that the detection time of M2 is on average 10 s longer than that of M1, but M2 can detect all spoofing cases, proving that the detection performance of M2 is better than that of M1.

[0114] Ramp pseudorange deviation values of 0.5 m / s, 0.2 m / s, and 0.1 m / s are respectively applied to channel 1 (i.e., visible satellite 1) in the second group of experiments. Fig. 4(a) is the simulation result graph of M1, and Fig. 4(b) is the simulation result graph of M2. It can be seen from Fig. 4(a) and Fig. 4(b) that: 1) Fig. 4(a) shows that when M1 detects the ramp spoofing of 0.5 m / s and 0.2 m / s applied to channel 1, the detection times are 44 s and 135 s respectively, while the detection of the 0.1-m / s ramp spoofing is invalid; 2) Fig. 4(b) shows that when M2 detects the ramp spoofing of 0.5 m / s, 0.2 m / s, and 0.1 m / s applied to channel 1, the detection times are 20 s, 50 s, and 100 s respectively. By comparing Fig. 4(a) and Fig. 4(b), it can be seen that the detection time of M2 is shortened by 24 s, 85 s, and 100 s respectively compared with that of M1, with an average shortening of 67 s. Thus, it is concluded that M2 has better detection efficiency and detection performance in dealing with ramp spoofing.

[0115] Based on the above comparison results, it can be obtained that when Roadcom 1 is subjected to step deception, the detection time of M2 is on average extended by 10 s compared to M1, but the detection performance of M2 is better; when Channel 1 is subjected to ramp deception, the detection times of M2 are shortened by 54.5%, 63% and 100% respectively compared to M1, with an average shortening of 72.5%, and the detection performance of M2 is better. Therefore, the detection efficiency and detection performance of M2 are relatively better than those of M1.

[0116] (2) Scenario 2: Set Channel 1 to be deceived and interfered with by a ramp pseudorange deviation value of 0.1 m / s to compare the detection capabilities of M2 and M3, so as to verify the effect of robust estimation in suppressing the deviation of a normal channel from the normal value due to deception interference.

[0117] Apply a ramp deception pseudorange deviation of 0.1 m / s to Channel 1. Figure 5(a) is the simulation result diagram of M1, and Figure 5(b) is the simulation result diagram of M2. It can be seen from Figure 5(a) and Figure 5(b) that: 1) Figure 5(a) shows that the detection time of M2 when detecting that Channel 1 is deceived is 100 s, but Channels 3, 4 and 5 are all affected by deception interference to different degrees, resulting in the deviation of their innovations from the normal values, and the innovation of Channel 4 even exceeds the threshold T d2 , resulting in a false alarm situation; 2) Figure 5(b) shows that the detection time of M3 when detecting that Channel 1 is deceived is 100 s, and the innovation values of the remaining channels do not deviate, proving that the robust estimation effectively weakens the influence of deception interference on other roadcoms. However, it can also be seen that the M3 method cannot shorten the detection time.

[0118] To further illustrate the advantages of M3, Table 3 shows the Monte Carlo simulation of 100 cycles in Scenario 2. Among them, "*" indicates the channel affected by deception interference, and will not be elaborated later.

[0119] Table 3 Monte Carlo simulation results of Experiment 2

[0120]

[0121] (3) Scenario 3: Aiming at the limitations of M3 in detecting small ramp deceptions in Scenario 2, especially the problem of long detection time for slope deceptions less than 0.1 m / s, two groups of experiments are set up in Scenario 3 to compare the detection capabilities of M3 and M4.

[0122] The first group of experiments: Apply a ramp pseudorange deviation value of 0.1 m / s to Channel 1. Figure 6(a) is the simulation result diagram of M3, and Figure 6(b) is the simulation result diagram of M4. It can be seen from Figure 6(a) and Figure 6(b) that: 1) Figure 6(a) shows that the detection time of M3 when detecting that Channel 1 is deceived is 100 s, and the remaining channels are normal; 2) Figure 6 shows that the detection time of M4 when detecting that Channel 1 is deceived is 70 s, which is 30 s shorter than the detection time of M3.

[0123] The second group of experiments: Apply a ramp - type pseudorange deviation value of 0.1 m / s to channel 6. Starting from Figure 7 It can be seen that: The detection time of M3 when detecting deception in channel 6 is 110 s, while the detection time of M4 when detecting deception in channel 6 is 60 s. The detection time of M4 is 50 s shorter than that of M3. Through the two groups of experiments, it shows that when dealing with slowly increasing ramp - type deception detection, the detection algorithm of M4 is superior to that of M3.

[0124] To better illustrate that M4 is superior to M3, Table 4 shows the Monte Carlo simulation results for 100 cycles in Scenario 3.

[0125] Table 4 Monte Carlo simulation results of Experiment 3

[0126]

[0127] Combined with Figure 6(a), Figure 6(b), Figure 7 and Table 4, it can be seen that: 1) When applying a ramp - type deception of 0.1 m / s to channel 1, the detection time of M4 is 30% shorter than that of M3; when applying a ramp - type deception of 0.1 m / s to channel 6, the detection time is shortened by 45.5%. Combining the deception detection situations of channel 1 and channel 6, it can be seen that: The detection time of M4 is on average 37.8% shorter than that of M3. 2) For the missed detection rate, both M3 and M4 are 0%. For channels 3, 4, and 5, the false alarm rates of M3 are 8%, 6%, and 0 respectively; the false alarm rates of M4 are 2%, 0, and 0 respectively. The false alarm rates of M4 compared to M3 are reduced by 6%, 6%, and 0 respectively, with an average reduction of 4%. Thus, it can be verified that when dealing with slowly increasing ramp - type deception interference, M4 can shorten the detection time and improve the detection performance.

[0128] In summary, the present invention optimizes the innovation detection quantity by adjusting the pseudorange parameters, and further improves the detection and processing ability of slowly increasing deception interference. The simulation results show that when detecting slowly increasing deception interference, the present invention shortens the detection time by an average of 37.8%, maintains the missed detection rate at 0, and maintains the false alarm rate within 0.7% on average. Compared with the traditional algorithm, when detecting slowly increasing ramp - type deception interference, it has the advantages of fast detection and low false alarm rate, which is of great significance in the application fields of civil and military unmanned aerial vehicles.

Claims

1. A GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation, characterized in that The method includes the following steps: S1. Set a detection window with a time length of L. Observe the GNSS / INS tightly coupled system through the observation model within the detection window to obtain the average normalized innovation vector from time k - L + 1 to time k and the innovation vector r at time k k ; i = 1, 2,..., n, where n is the number of visible satellites; S2. If the absolute value of the i-th element in the average normalized innovation vector is greater than the preset upper limit detection threshold T , then the GNSS measurement value corresponding to the i-th element in the average normalized innovation vector d2 is spoofed; ​ If is less than the preset lower detection threshold T d1 , then the GNSS measurement value corresponding to the i-th element in the average normalized innovation vector is not spoofed; if is greater than T d1 and less than T d2 , then according to T d1 , T d2 and the observation noise covariance matrix R of the observation model k , calculate the equivalent weight matrix W k ; S3. Calculate the gain matrix according to the observation model H at time k k , the prior covariance estimation vector and the equivalent weight matrix W k Calculate the gain matrix According to the gain matrix at time k the innovation vector r k and the prior estimated state vector Calculate the posterior estimated state vector at time k According to the observation model H at time k k , the gain matrix and the prior covariance estimation vector Calculate the posterior estimated covariance vector at time k S4. At time k + 1, according to the posterior estimated state vector at time k and the posterior estimated covariance vector calculate the prior estimated state vector at time k + 1 and the prior covariance estimated vector According to the prior estimated state vector at time k + 1 and the prior covariance estimated vector Combine with the observation vector Z at time k + 1 k+1 , calculate the average normalized innovation vector from time k - L to time k + 1, and then perform spoofing detection at time k + 1 according to T d1 and T d2 .

2. The GNSS / INS tightly-coupled spoofing detection method based on innovation robust estimation according to claim 1, characterized in that, In step S2, the gain matrix is calculated by the following formula: In the formula, represents the gain matrix, H k represents the observation model, represents the prior covariance estimation vector, W k represents the equivalent weight matrix.

3. The GNSS / INS tightly-coupled spoofing detection method based on innovation robust estimation according to claim 2, wherein In step S2, the equivalent weight matrix W is calculated by the following formula k :[[]]END]] In the formula, represents the \(i\)-th element of the equivalent weight matrix \(W\) k , represents the \(i\)-th element of the observation noise covariance matrix \(R\) k , \(w\) i is an intermediate variable, represents the \(i\)-th element in the average normalized innovation vector , \(T\) d1 represents a preset lower detection threshold, \(T\) d2 represents a preset upper detection threshold.

4. The GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation according to claim 1 or 2, characterized in that, In step S2, the posterior estimated state vector is calculated by the following formula In the formula, represents the prior estimated state vector, represents the gain matrix, r k represents the innovation vector.

5. The GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation according to claim 4, characterized in that, In step S3, the prior estimated state vector at the (k + 1)-th moment is calculated by the following formula In the formula, represents the state transition matrix, represents the posterior estimation state vector at time k.

6. The GNSS / INS tightly coupled spoofing detection method based on innovation robust estimation according to claim 1 or 2, characterized in that, In step S2, the posterior estimation covariance vector is calculated by the following formula Where, I represents a unit vector, represents the gain matrix, H k represents the observation model, represents the prior covariance estimation vector.

7. The GNSS / INS tightly-coupled spoofing detection method based on innovation robust estimation according to claim 6, characterized in that In step S3, the prior covariance estimation vector at the (k + 1)-th moment is calculated by the following formula In the formula, represents the state transition matrix, represents the posterior estimation covariance vector at time k, and q k represents the system noise covariance matrix.

8. The GNSS / INS tightly-coupled spoofing detection method based on innovation robust estimation according to claim 1 or 2, characterized in that In step S2, the innovation vector r is calculated by the following formula k and its covariance matrix V k : Where, Z k represents the observation vector, H k represents the observation model, represents the prior estimated state vector at time k, represents the prior covariance estimation vector at time k, R k represents the observation noise covariance matrix.

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