GNSS / INS Tight Integration Spoofing Detection Method Based on Innovation Rate Optimization and Robust Estimation

Abstract

The present invention relates to a GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and robust estimation, belonging to the technical field of spoofing detection for navigation systems. For step spoofing with minute mutations or slope spoofing with slow growth, compared with the existing solution that directly calculates the innovation rate through the innovation vector and covariance and then makes a judgment, the present invention first obtains the normalized innovation vector and then updates the normalized innovation vector in real time through a Kalman filter. In the time update stage, the prior estimated state vector is obtained through prior estimation; in the measurement update stage, the innovation vector is updated according to the normalized innovation vector and the prior estimated state vector, and the posterior estimated state vector is calculated according to the updated innovation vector and the gain matrix. The innovation rate is calculated according to the posterior estimated state vector and the innovation rate matrix, and then combined with the preset upper and lower limit detection thresholds to determine whether there is spoofing, and the time used for spoofing detection is shorter and the detection efficiency is improved.

Description

Technical Field

[0001] The present invention relates to a GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and 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 a combined navigation system of a global satellite navigation system and an inertial navigation system for navigation control. The combined navigation system of the Global Navigation Satellite System (GNSS) and the Inertial Navigation System (INS) has the complementary error characteristics of the two. GNSS has the advantages of providing 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 capabilities. The combination of the two increases the redundancy and reliability of the system. GNSS / INS combined 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 combined navigation system.

[0004] Spoofing interference refers to the interference source generating spoofing signals highly similar to the real signals or retransmitting the real signals to deceive the target receiver, forcing it to generate incorrect and possibly dangerous information. In the GNSS / INS combined 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 combined navigation system, causing a large deviation in the trajectory of the unmanned control device and possibly affecting the safety of the device.

[0005] GNSS / INS integrated navigation system spoofing detection can be divided into two categories. The first category is the method based on measurement values. Common methods include the chi-square detection method based on innovation or residual, the Autonomous Integrity Monitored Extrapolation (AIME), the Extended Receiver Autonomous Integrity Monitoring (ERAIM), and the rate detection method, etc. The second category is the method based on conclusions, such as the Multiple Solution Separation (MSS). The chi-square detection method based on innovation uses the Kalman filter innovation as the detection statistic, which has the advantages of low cost, high efficiency, and small computational complexity, and is a widely used detection method. This method can be further divided into the "snapshot method" and the "continuous method". The "snapshot method" uses the innovation vector and its covariance matrix at the current moment to form the test statistic, which is suitable for detecting step-like errors in GNSS measurement values. The "continuous method" uses all the innovation vectors and their covariance matrices from a past moment to the current moment to form the test statistic, which is suitable for detecting slowly growing errors. Some literature specifically introduces the classification and models of step-like and slowly growing errors, and at the same time classifies the error characteristics of GNSS spoofing interference into synchronous spoofing and asynchronous spoofing. The synchronous spoofing signal remains synchronized with the real signal in the initial stage. When the receiver tracking loop locks on the spoofing signal, in order to prevent the receiver from autonomous integrity monitoring, it adopts a step-by-step induction method to gradually deviate the pseudorange measurement value from the real value, which is equivalent to applying a slope-like spoofing to the measurement value of the real pseudorange. The code of the asynchronous spoofing signal cannot be synchronized with the real signal in terms of phase and carrier frequency, so its pseudorange measurement value is arbitrary, which is equivalent to applying a step-like spoofing to the real pseudorange, indicating that this error characteristic is similar to the step-like and ramp-like spoofing in integrity analysis.

[0006] The difficulties in detecting spoofing interference in GNSS / INS integrated navigation systems are: the time delay problem in detecting step spoofing with small mutations and ramp spoofing with slow growth. To address this difficulty, WANG ShiZhuang et al. proposed an algorithm for detecting step spoofing with small mutations, namely "normalized small mutation amplitude", which divides the spoofing influence value of the actual small mutation by the normalized innovation covariance value. When a single-channel is interfered by a small mutation of 5 m, the detection time using robust estimation is 28 s. The algorithm for detecting ramp spoofing with slow growth is "normalized sliding window ramp amplitude", which divides the spoofing influence value of the actual slow growth within the detection window by the normalized innovation covariance value. When a single-channel is interfered by a slow growth of 0.1 m / s, the detection time using robust estimation is shortened by about 30 s. ZHANG Chuang et al. proposed an improved detection algorithm based on robust estimation and sliding window. For ramp spoofing with slow growth, two appropriate thresholds are selected to calculate the weight factor and the gain matrix is adaptively adjusted. When a single-channel is interfered by a ramp of 0.5 m / s, the false alarm rate is 28%. The drawback of the above algorithms is that a reasonable detection window needs to be set. That is, within a certain detection time, the length without incorrect measurements becomes the "wasted window", which has a negative impact on both the detection time and performance. Therefore, the detection window needs to be determined according to specific situations.

[0007] Regarding the problem that a detection window needs to be set for spoofing detection in GNSS / INS integrated navigation systems, Bhatti et al. proposed an innovation rate detection algorithm. By normalizing the change rate of the innovation, it is determined whether there is an abnormality in the GNSS measurement value, and then the Kalman filter is used to estimate the normalized innovation rate in real time. This method effectively improves the detection efficiency. However, affected by the closed-loop correction in the integrated navigation system, the innovation rates of the other normal channels are also affected. When a single-channel is interfered by a slow growth of 0.1 m / s, the detection time is 110 s. 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 algorithm reliability. When detecting a slow growth interference of 0.1 m / s in a single-channel, the detection time is shortened by 60%, and the false alarm rate and missed alarm rate are maintained within 4%. However, when detecting step spoofing with small mutations and ramp spoofing with slow growth, both of these algorithms still have the problems of too long detection time and even insensitive detection.

[0008] In summary, the existing spoofing interference detection algorithms have too long detection time and even insensitive detection when detecting step spoofing with small mutations and ramp spoofing with slow growth, resulting in that after the unmanned aerial vehicle has flown a long distance, it can accurately judge whether there is spoofing interference imposed by a third party, seriously affecting the safety of the unmanned aerial vehicle during flight. Summary of the Invention

[0009] The object of the present invention is to provide a GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and robust estimation, which is used to solve the problem of too long detection time of existing spoofing detection interference algorithms when detecting small mutations and slowly increasing spoofing interference.

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

[0011] S1. Observe the GNSS / INS tightly coupled system through the observation model H k to obtain the normalized innovation vector ω at time k i , where i = 1, 2,..., n, and n is the number of visible satellites;

[0012] S2. Update the normalized innovation vector ω i in real time through the Kalman filter. The real-time update includes time update and measurement update;

[0013] In the time update stage, perform a priori estimation on the state vector of the GNSS / INS tightly coupled system to obtain the a priori estimated state vector at time k

[0014] In the measurement update stage, subtract the product of the normalized innovation vector ω i from the observation model H k and the a priori estimated state vector to obtain the updated innovation vector r k ; According to the observation model H k , the updated innovation vector r k and the pre-obtained gain matrix K k , calculate the posteriori estimated state vector According to the posteriori estimated state vector and the pre-obtained innovation rate matrix C, calculate the innovation rate vector

[0015] S3. If the absolute value of the i-th element in the innovation rate vector is greater than the preset upper detection threshold k1, the GNSS measurement value corresponding to the i-th element in the innovation rate vector is spoofed. If is less than the preset lower detection threshold k0, the GNSS measurement value corresponding to the i-th element in the innovation rate vector is not spoofed; If is greater than k0 and less than k1, then for the gain matrix K in step S2 kUpdate and perform spoofing detection again based on the updated gain matrix.

[0016] When observing the GNSS / INS tightly coupled navigation system in the present invention, first obtain the normalized innovation vector, and then update the normalized innovation vector in real time through a Kalman filter. In the time update stage, obtain the prior estimated state vector through prior estimation; in the measurement update stage, update the innovation vector according to the normalized innovation vector and the prior estimated state vector, calculate the posterior estimated state vector according to the updated innovation vector and the previously obtained gain matrix, and then calculate the innovation rate according to the posterior estimated state vector and the previously obtained innovation rate matrix, and further combine the preset upper and lower detection thresholds to determine whether spoofing exists. For step spoofing with small mutations or slope spoofing with slow growth, compared with the existing method of directly calculating the innovation rate through the innovation vector and covariance and then making a judgment, the present invention first updates the innovation vector using the normalized innovation vector, and then uses the updated innovation vector, combines the gain matrix, calculates the posterior estimated state vector, and then calculates the innovation rate based on this, so that the time used to detect spoofing is shorter and the detection efficiency is improved.

[0017] Further, in the above method, in step S3, according to k0 and k1, calculate the equivalent weight matrix W, and update the gain matrix K according to the equivalent weight matrix W k for update.

[0018] For the situation where it is impossible to accurately determine whether spoofing exists, robust estimation is introduced to weaken the influence of spoofing interference. During robust estimation, calculate the weight corresponding to the i-th measurement value by combining the innovation rate with the upper and lower detection thresholds, and then update the gain matrix through the weight, which can improve the sensitivity of spoofing detection.

[0019] Further, in the above method, the gain matrix K k is updated through the following formula:

[0020] K R = K k ·W

[0021] In the formula, K R represents the updated gain matrix.

[0022] Provide a relatively simple way to update the gain matrix, which is convenient for the implementation of the present invention.

[0023] Further, in the above method, the equivalent weight matrix is expressed as W = diag(w1 … w i … w n ), and the i-th element w of the equivalent weight matrix is calculated through the following formulai :

[0024]

[0025] In the formula, represents the innovation rate vector the absolute value of the i-th element in, k1 represents the upper limit detection threshold, and k0 represents the lower limit detection threshold.

[0026] Provide a set of relatively simple formulas to calculate the elements in the equivalent weight matrix, which is convenient for the implementation of the present invention.

[0027] Furthermore, in the above method, in step S2, a priori covariance estimation vector is also obtained in the time update stage. The gain matrix K is calculated through the following formula k :

[0028]

[0029] In the formula, H k represents the observation model, represents the a priori covariance estimation vector, and R k represents the observation noise covariance of the observation model.

[0030] By performing a priori estimation on the covariance in the time update stage, an a priori covariance estimation vector is obtained. On this basis, a relatively simple method for calculating the gain matrix is provided, which is convenient for the implementation of the present invention.

[0031] Furthermore, in the above method, in step S2, the posterior estimation state vector is calculated through the following formula

[0032]

[0033] In the formula, represents the a priori estimation state vector, K k represents the gain matrix, and r k represents the updated innovation vector.

[0034] The updated innovation vector is weighted by the gain matrix, and then the a priori estimation state vector is optimized to obtain the posterior estimation state vector, which is simple to calculate and convenient for implementation.

[0035] Furthermore, in the above method, in step S2, the a priori covariance estimation vector is calculated through the following formula

[0036]

[0037] In the formula, denotes the state transition matrix, denotes the posterior error covariance matrix at time k-1, q k-1 denotes the system noise covariance matrix.

[0038] Furthermore, in the above method, in step S2, the prior estimated state vector is calculated by the following formula

[0039]

[0040] wherein, denotes the state transition matrix, denotes the posterior estimated state vector at time k-1.

[0041] Two specific formulas are provided for calculating the prior estimated state vector and the prior covariance estimated vector in the time update stage, which are simple to calculate and convenient to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flowchart of the GNSS / INS tight integration spoofing detection method based on innovation rate optimization and robust estimation in the embodiment of the method of the present invention;

[0043] Figure 2 is a schematic diagram of the target receiver being spoofed and interfered in the embodiment of the method of the present invention;

[0044] Figure 3 is a schematic diagram of the influence analysis of spoofing interference during Kalman filtering in the embodiment of the method of the present invention;

[0045] Figure 4 is a schematic diagram of the simulated flight trajectory in the embodiment of the method of the present invention;

[0046] FIG. 5(a) is the simulation result of the innovation rate spoofing detection algorithm under step spoofing in the embodiment of the method of the present invention;

[0047] FIG. 5(b) is the simulation result of the innovation rate robust estimation spoofing detection algorithm under step spoofing in the embodiment of the method of the present invention;

[0048] FIG. 6(a) is the simulation result of the innovation rate spoofing detection algorithm under ramp spoofing in the embodiment of the method of the present invention;

[0049] FIG. 6(b) is the simulation result of the innovation rate robust estimation spoofing detection algorithm under ramp spoofing in the embodiment of the method of the present invention;

[0050] FIG. 7(a) is the simulation result of the innovation rate robust estimation spoofing detection algorithm under step spoofing with a 5m small mutation in the embodiment of the method of the present invention;

[0051] Figure 7(b) shows the simulation results of the robust estimation deception detection algorithm for the innovation rate under a slowly increasing ramp - type deception in the method embodiment of the present invention;

[0052] Figure 8(a) is a schematic diagram comparing the simulation results of the robust estimation deception detection algorithm for the innovation rate and the step - type deception detection algorithm for small mutations under step - type deception in the method embodiment of the present invention;

[0053] Figure 8(b) is a schematic diagram showing the influence effect of step - type deception with small mutations on the position error in the method embodiment of the present invention;

[0054] Figure 9(a) is a schematic diagram comparing the simulation results of the robust estimation deception detection algorithm for the innovation rate and the ramp - type deception detection algorithm for slowly increasing ramps under ramp - type deception in the method embodiment of the present invention;

[0055] Figure 9(b) is a schematic diagram showing the influence effect of slowly increasing ramp - type deception on the position error in the method embodiment of the present invention. Specific Embodiment

[0056] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0057] Method Embodiment:

[0058] During the flight of an unmanned aerial vehicle (UAV), when it is determined that there is spoofing interference imposed by a third party, it is necessary to verify quickly and accurately. The present invention first establishes a spoofing interference model for the GNSS / INS integrated navigation system and analyzes the influence brought by the spoofing interference.

[0059] To construct a spoofing interference simulation environment for the GNSS / INS integrated navigation system and establish a spoofing interference model at the GNSS measurement level, the spoofing model at the complex signal level is first analyzed. As Figure 1 shown, it represents the spoofing interference received by the target receiver.

[0060] The original pseudorange model of the i - th satellite R (i) at time t is:

[0061] R (i) (t) = cτ (i) + c((t + δt r ) - (t + δt (i) ))

[0062] In the formula, c is the speed of light, τ (i) is the signal propagation delay, δt r and δt (i) are the receiver clock error and the satellite clock error.

[0063] For a real signal, the propagation delay is composed of the geometric distance ionospheric effects and tropospheric effects and is expressed by the following formula:

[0064]

[0065] Considering the receiver noise the true pseudorange is:

[0066]

[0067] For a spoofing signal, the propagation delay is:

[0068]

[0069] In the formula, is the geometric distance from the spoofing device to the satellite, is the geometric distance from the spoofing device to the target receiver. Assuming that the spoofing device and the target receiver do not consider external factors and errors, the above formula can be changed to:

[0070]

[0071] In the formula, ▽τ s (i) is the additional signal delay introduced by the spoofing device at the target receiver, and the relationship between the spoofed pseudorange and the true pseudorange is:

[0072]

[0073] Therefore, according to the spoofed pseudorange measurement value and the true pseudorange measurement value of the i-th channel, they are respectively and The spoofing interference model at the measurement level is derived as:

[0074]

[0075] In the formula, t Lock is the moment when the spoofing signal locks the tracking loop of the target receiver, a(t - t Lock ) + b is the additional pseudorange value of the spoofing interference, a is the slope, and b is the pseudorange deviation between the spoofed pseudorange and the true pseudorange. When a ≠ 0 and b = 0, it represents step spoofing; when a = 0 and b ≠ 0, it represents ramp spoofing.

[0076] The tightly coupled navigation system based on GNSS / INS 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 at each filter iteration to correct the INS solution. The 17-dimensional state vector X of the error state Extended Kalman Filter (EKF) is expressed as:

[0077]

[0078] where, δv and δr are the attitude, velocity, and position vectors of the INS estimation error, b a and b g are the accelerometer and gyro bias of the inertial sensor respectively, b clk and are the GNSS clock error and clock drift respectively. Let Z k be the observation vector obtained by subtracting the INS predicted value from the GNSS observation value, H k be the observation matrix, be the one-step predicted state vector, be the covariance matrix of the one-step predicted state vector, R k be the observation noise covariance matrix, then the observed quantity Z k , the innovation vector r k and its covariance matrix V k can be expressed as:

[0079]

[0080]

[0081]

[0082] In the formula, and represent the GNSS observed pseudorange and observed pseudorange rate respectively, and represent the INS predicted pseudorange and predicted pseudorange rate respectively, n represents the number of visible satellites. Then the normalized innovation is

[0083]

[0084] In the formula, is the i-th value of the innovation vector at time k (i = 1, …, n, n is the number of visible satellites), is the variance of at time k. ω i represents the i-th normalized innovation value at time k, which can reflect the error of the i-th GNSS measurement value. The innovation vector It reflects the magnitude of the additional pseudorange value affected by spoofing interference, which is called spoofing innovation. However, due to the influence of spoofing interference and the closed-loop correction effect in the prediction and update stages of the Kalman filter, the true innovation is not equal to the spoofing innovation. The analysis of the influence of spoofing interference is as follows Figure 2 As shown, when spoofing interference is applied at time k, in the state filtering loop, the GNSS observation value changes, resulting in the influence of spoofing interference, which in turn affects the innovation vector r k , leading to the influence on the state filtering loop at time k + 1. The specific derivation is as follows.

[0085] Assume that at time k, the i-th measurement has a spoofing interference with an additional pseudorange value of μ, and its vector Λ is expressed as:

[0086] Λ = [0 0 … μ … 0] T

[0087] All elements except the i-th element are 0. According to the Kalman filter theory, we can obtain:

[0088]

[0089]

[0090] Among them, represents the estimated value of spoofing interference occurring at time k, represents the value after measurement update. At time k + 1,

[0091]

[0092]

[0093]

[0094]

[0095] In the formula, Φ k+1 is the transition matrix, and K k is the gain matrix. Therefore, the innovation at time k + 1 can reflect the spoofing innovation r k+1,s , which is expressed as:

[0096] r k+1,s = r k+1 - H k+1 Φ k+1 K k Λ

[0097] It can be seen from the formula that the spoofing innovation r k+1,s differs from the true innovation r k+1 by an additional pseudorange value. Therefore, the influence of spoofing interference on the innovation Δr is defined as:

[0098] Δr = -H k+1 Φ k+1 K k Λ

[0099] Since the deception innovation reduces by Δr, the values of other innovations increase by |Δr|. Therefore, the deception interference will cause a difference between the true innovation and the deception innovation, thus reducing the performance of deception interference detection. For small mutations and slowly growing deception interference, its impact is not obvious and relatively concealed. However, due to the detection time delay, during this detection time, the innovation is also affected to a certain extent, ultimately affecting the GNSS / INS integrated navigation system.

[0100] Therefore, the GNSS / INS tight integration deception detection method provided by the present invention based on innovation rate optimization and robust estimation is as Figure 3 shown, and includes the following steps:

[0101] 1. At time k, obtain the observation vector Z obtained by subtracting the GNSS observation value from the INS predicted value k , and then through the observation matrix H k , the one-step predicted state vector the one-step predicted state vector covariance matrix and the observation noise covariance matrix R k , calculate the innovation vector r k and its covariance matrix V k .

[0102]

[0103]

[0104] Then, according to the innovation vector r k and its covariance matrix V k , calculate the normalized innovation vector ω i . The i-th element in the normalized innovation vector ω i is calculated by the following formula:

[0105]

[0106] In the formula, is the i-th value of the innovation vector at time k (i = 1,..., n, n is the number of visible satellites), is the normalized variance 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.

[0107] 2. The Kalman filter is used for real-time update, and the update process includes time update and measurement update.

[0108] Define the state vector as where is the estimated value of ω i , v i is the innovation rate of ω i , a i is the innovation acceleration of ω i , p i is the constant bias of ω i .

[0109] During the real-time update process of the Kalman filter, noise needs to be considered. Therefore, define the system model as:

[0110]

[0111] where the improved innovation rate is defined as a random process related to time. Different values of β will result in different noise values. β is the correlation coefficient, generally taking values from 0.5 to 0.9; ε is the noise, generally taking values from 10 -7 to 10 -9 .

[0112] Define the observation model as:

[0113]

[0114] In the formula, υ i is the observation noise.

[0115] Use the normalized innovation vector ω i obtained in step 1 as the input to the Kalman filter for cyclic update.

[0116] In the time update stage, through the prior estimation of the state vector and covariance of the GNSS / INS tightly coupled system, obtain the prior estimated state vector and the prior covariance estimation vector

[0117]

[0118]

[0119] In the formula, 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; 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 The initial values are obtained from the 17-dimensional state vector X at the initial time. 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.

[0120] In the measurement update stage, subtract the normalized innovation vector ω i from the product of the observation matrix H k and the prior estimated state vector to obtain the updated innovation vector r k .

[0121]

[0122] According to the observation matrix H k , the prior covariance estimation vector and the observation noise covariance matrix R of the observation model k , calculate the gain matrix K k .

[0123]

[0124] According to the observation matrix H k , the updated innovation vector r k and the gain matrix K k , calculate the posterior estimated state vector

[0125]

[0126] Also calculate the posterior estimated covariance vector

[0127]

[0128] where R k is the observation noise covariance matrix and I is the unit vector.

[0129] According to the posterior estimated state vector and the previously obtained innovation rate matrix C, calculate the improved innovation rate

[0130]

[0131] where \(C = [0\ 1\ 0\ 0]\).

[0132] 3. Determine whether there is spoofing in the GNSS measurement values according to the improved innovation rate.

[0133] Assuming that there is no spoofing, the null hypothesis is Then the alternative hypothesis is where follows a normal distribution, and \(\delta\) is the non-central parameter. According to the integrity requirements of the navigation system, let the false alarm rate be \(P\) fa , and \(n\) is the number of visible satellites. Then the false alarm rate corresponding to the \(i\)-th GNSS measurement value is:

[0134]

[0135] Then corresponding to the detection threshold is:

[0136]

[0137] In the formula, \(N\) -1 is the inverse of the Gaussian distribution, is the variance of the covariance matrix of.

[0138] Therefore, the detection criterion for spoofing interference is:

[0139]

[0140] In the formula, \(k_0 = 0.5k_1\). When the innovation rate 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.

[0141] 4. Calculate the equivalent weight matrix \(W\) according to the innovation rate by using the IGG-3 equivalent weight function. The equivalent weight matrix can be expressed as: \(W=\text{diag}(w_1\ \cdots\ w i \ \cdots\ w n ). The calculation formula is:

[0142]

[0143] In the formula, is the innovation rate corresponding to the \(i\)-th GNSS measurement value, and \(w i is the equivalent weight corresponding to the \(i\)-th GNSS measurement value.

[0144] 5. Calculate the new gain matrix \(K\) according to the equivalent weight matrix \(W\) R, thus realizing the update of the gain matrix K k The update formula is as follows:

[0145] K R = K k ·W

[0146] Perform calculations using the new gain matrix K R to obtain the updated state vector Then, through the innovation rate matrix C and the updated calculate the optimized innovation rate Furthermore, conduct spoofing detection through the spoofing interference detection criterion until it is determined whether there is spoofing in the GNSS measurement value.

[0147] Based on the process of analyzing the impact of spoofing interference previously, it is determined that: the existence of Δr between the spoofed innovation and the true innovation is the direct cause of the decrease in the spoofed innovation. Therefore, reducing Δr is an effective way to improve the spoofing detection ability. By adaptively adjusting the equivalent weight to reduce the weight of spoofing interference, that is, by replacing the gain matrix K k for calculating Δr with the new gain matrix K R , thus weakening the abnormal impact and effectively improving the detection ability of the navigation system.

[0148] Δr = -H k Φ k K R Λ = -H k Φ k (K k ·W)Λ

[0149] Next, taking the slowly increasing ramp spoofing and the step spoofing with tiny mutations as examples, verify the effect of the present invention. By constructing a spoofing interference model of the GNSS / INS integrated navigation system, simulate the slowly increasing ramp spoofing and the step spoofing with tiny mutations, and then use the present invention for spoofing detection to verify the detection effect of the present invention.

[0150] 1. Select a spoofing detection algorithm according to the spoofing type and calculate the improved normalized innovation. If it is slowly increasing ramp spoofing, select the slowly increasing ramp spoofing detection algorithm; if it is step spoofing with tiny mutations, select the step spoofing with tiny mutations detection algorithm.

[0151] In the slowly increasing ramp spoofing detection algorithm, assume that a ramp spoofing interference with a slowly increasing pseudorange additional value of A is applied. When performing the i-th measurement, the improved normalized innovation is calculated by the following formula:

[0152]

[0153] Wherein, A is the slowly increasing additional pseudorange value, is the i-th value of the innovation vector at time k (i = 1, …, n, where n is the number of visible satellites), is the normalized variance at time k, a(t - t Lock ) represents the actual slow growth from time t to t Lock time, a' represents the result of dividing the actual slow growth a(t - t Lock ) by the normalized variance, ω i represents the i-th normalized innovation value at time k, which can reflect the error of the i-th GNSS measurement value.

[0154] In the step-by-step deception detection algorithm for small mutations, assume that a step-by-step deception interference with an additional pseudorange value of B for small mutations is applied. When the i-th measurement is performed, the improved normalized innovation is calculated by the following formula:

[0155]

[0156] Wherein, B is the additional pseudorange value for small mutations, is the i-th value of the innovation vector at time k (i = 1, …, n, where n is the number of visible satellites), is the normalized variance at time k, b is the result of dividing the additional pseudorange value B by the normalized variance, ω i represents the i-th normalized innovation value at time k, which can reflect the error of the i-th GNSS measurement value.

[0157] 2. In the slowly increasing ramp-style deception detection algorithm, the improved normalized innovation is updated in real time through a Kalman filter to obtain the slowly increasing innovation rate In the step-by-step deception detection algorithm for small mutations, the improved normalized innovation is updated in real time through a Kalman filter to obtain the small mutation innovation rate

[0158] Taking the step-by-step deception detection algorithm for small mutations as an example, the update process is described as follows:

[0159] Define the state vector as Wherein, is the estimated value, is the innovation rate, is the innovation acceleration, is the constant deviation.

[0160] Define the system model as:

[0161]

[0162] Define the observation model as:

[0163]

[0164] In the time update stage, obtain the prior estimated state vector at time k and the prior covariance estimated vector

[0165]

[0166]

[0167] In the measurement update stage, subtract the product of the normalized innovation vector and the observation matrix H k and the prior estimated state vector to obtain the updated innovation vector

[0168]

[0169] According to the observation matrix H k , the prior covariance estimated vector and the observation noise covariance matrix R of the observation model k , calculate the gain matrix K k .

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[0171] According to the observation matrix H k , the updated innovation vector and the gain matrix K k , calculate the posterior estimated state vector

[0172]

[0173] Also calculate the posterior estimated covariance vector

[0174]

[0175] Then, according to the posterior estimated state vector and the previously obtained innovation rate matrix C, calculate the improved innovation rate

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[0177] 3. Perform spoofing detection according to the detection criteria of spoofing jamming.

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[0179] When the innovation rate satisfies , update the gain matrix through Steps 4 and 5, and then perform spoofing detection.

[0180] In the slow-growing ramp-type spoofing detection algorithm, use the same method to calculate the slow-growing innovation rate and then perform spoofing detection according to the interference criteria of spoofing detection.

[0181] To verify the beneficial effects of the spoofing detection algorithm with optimized pseudorange added value, compare four algorithms: the innovation rate spoofing detection algorithm (M1), the innovation rate robust estimation spoofing detection algorithm (M2), the step-type spoofing detection algorithm with minute mutations (M3), and the slow-growing ramp-type spoofing detection algorithm (M4).

[0182] Design 4 GNSS / INS tightly coupled spoofing jamming detection experimental scenarios to compare the detection capabilities of different algorithms. (1) When the step-type spoofing and ramp-type spoofing with the same pseudorange added value occur in 3 channels, compare the detection capabilities of M1 and M2; (2) When the step-type spoofing and ramp-type spoofing with different pseudorange added values occur in 1 channel, verify the detection capability of M2; (3) When the step-type spoofing with minute mutations occurs in 1 channel, compare the detection capabilities of M2 and M3; (4) When the slow-growing ramp-type spoofing occurs in 1 channel, compare the detection capabilities of M2 and M4.

[0183] 1. Parameter settings. The experimental parameter settings of GNSS / INS tight coupling include: simulated flight trajectory data, spoofing scenarios, and the parameters of GNSS and IMU sensors, as shown in Figure 4 and Tables 1 and 2 respectively.

[0184] Table 1 Spoofing scenario settings

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[0187] Table 2 Simulation parameters

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[0189] 2. Result analysis

[0190] (1) Scenario 1. M2 can suppress the effect of the innovation rate deviating from the normal value, that is, the normal channel is not affected by the spoofed channel and deviates abnormally, and compare the detection capabilities of M2 and M1.

[0191] The simulation results of step deception are shown in Figure 5. During the time period from 350 s to 550 s, step deception with a pseudorange deviation of 30 m was applied to channels 1, 2, and 3. The data shows that: (1) Figure 5(a) is the simulation result of M1, showing that the detection times of channels 1, 2, and 3 are 10 s, 9 s, and 10 s respectively. However, the other 5 channels were all affected by deception interference to varying degrees, resulting in the deviation of their corresponding innovation rates from the normal values and false alarm situations. (2) Figure 5(b) is the simulation result of M2, showing that the detection times of channels 1, 2, and 3 are 9 s, 8 s, and 9 s respectively. Compared with Figure 5(a), the detection times of the three deceived channels are shortened by 1 s, 2 s, and 1 s respectively, and the innovation rates of the other channels are normal. Therefore, it can be seen that when applying step deception with a relatively large pseudorange deviation, the detection efficiency of M2 relative to M1 is not significantly improved, but M2 can suppress the deviation of the innovation rate from the normal value, increasing the fault tolerance and robustness of the system.

[0192] The simulation results of ramp deception are shown in Figure 6. During the time period from 350 s to 550 s, ramp deception with a slope of 0.3 m / s was applied to channels 1, 2, and 3. The data shows that: (1) Figure 6(a) is the simulation result of M1, showing that the detection times of channels 1, 2, and 3 are 59 s, 50 s, and 64 s respectively. Similar to step deception, the other channels were all affected by deception interference to varying degrees, resulting in false alarm situations. (2) Figure 6(b) is the simulation result of M2, showing that the detection times of channels 1, 2, and 3 are 47 s, 43 s, and 49 s respectively. Compared with Figure 6(a), the detection times of the three deceived channels are shortened by 12 s, 7 s, and 15 s respectively, and the innovation rates of the other channels are normal.

[0193] Combining the data in Figure 5 and Figure 6, it can be obtained that when subjected to step deception, the detection times of M2 compared to M1 are shortened by 10%, 22.2%, and 10% respectively, with an average shortening of 35.5%. When subjected to ramp deception, the detection times of M2 compared to M1 are shortened by 20.3%, 14%, and 64.2% respectively, with an average shortening of 32.8%. It can be concluded that the average detection efficiency of M2 is improved by about one-third compared to M1. This shows that the robust estimation of M2 well suppresses the deviation of the innovation rate of the normal channels from the normal value, reduces the false alarm rate, and the detection efficiency and detection performance are superior to M1.

[0194] (2) Scenario 2. Scenario 2 sets up a scenario where different deception types correspond to different pseudorange additional values to verify that M2 has limitations for step deception with a small mutation (5 m) or ramp deception with a slow growth rate (0.05 m / s), that is, the detection time is too long or the detection is insensitive.

[0195] The simulation results are shown in Figure 7. The data indicate that: (1) Figure 7(a) shows the simulation results of step deception of M2. During the time period from 350 s to 550 s, step deceptions with pseudo-range biases of 40 m, 30 m, 20 m, 10 m, and 5 m are applied to Channel 3. The detection times for the corresponding pseudo-range biases are shown to be 4 s, 6 s, 10 s, 25 s, respectively, and the step deception of 5 m is not detected effectively. (2) Figure 7(b) shows the simulation results of ramp deception of M2. During the time period from 350 s to 550 s, ramp deceptions with pseudo-range biases of 0.4 m / s, 0.3 m / s, 0.2 m / s, 0.1 m / s, and 0.05 m / s are applied to Channel 3. The detection times for the corresponding ramp deceptions with additional values are shown to be 36 s, 44 s, 57 s, 92 s, and 157 s, respectively. It can be seen from this that it is verified that as the stepwise application of pseudo-range bias (from 40 m to 5 m) and the ramp application slope (from 0.4 m / s to 0.05 m / s) of M2 decrease, the detection time increases and even the detection becomes insensitive. Among them, the maximum detection time for ramp deception (0.05 m / s) is 157 s; the detection of small mutation deception (5 m) is ineffective.

[0196] (3) Scenario 3. Aiming at the limitation of the step deception detection of M2 for small mutations in Scenario 2, a step deception scenario 3 for small mutations is set up to compare the detection capabilities of M2 and M3.

[0197] The simulation results are shown in Figure 8. During the time period from 350 s to 550 s, step deceptions with pseudo-range biases of 10 m and 5 m are applied to Channel 3. The data indicate that: (1) Figure 8(a) shows the simulation results of small mutation deception by M2 and M3. For a pseudo-range bias of 10 m, the detection times of M2 and M3 are 25 s and 9 s respectively; for a pseudo-range bias of 5 m, the detection of M2 is ineffective, while the detection of M3 is effective and its detection time is 22 s. It can be seen from this that in the detection of small mutation deception, M3 is more sensitive than M2. (2) Figure 8(b) shows the influence of small mutation deception on position error. When deceptions of 10 m and 5 m are applied, the maximum northward errors are 1.041 m and 1.042 m respectively, the maximum eastward errors are 1.305 m and 1.398 m respectively, and there are slight changes in the height error, indicating that small mutation deception is very concealed and the errors meet the accuracy requirements. Generally, it is very difficult to detect, but it is very harmful to applications with high-precision positioning, such as missile precision guidance, intelligent driving, and unmanned aerial vehicles, etc.

[0198] Combining Scenario 2 and Scenario 3, it can be concluded that: when Channel 3 is subjected to a deception interference of 10 m, the detection time of M3 is shortened by 64% compared with that of M2; when subjected to a deception interference of 5 m, the detection of M3 is effective and the detection of M2 is insensitive. It can be concluded from this that M3 can detect step deceptions of small mutations with strong concealment.

[0199] (4) Scenario 4. Aiming at the limitations of M2 in the detection of slow-growing ramp deception in Scenario 2, a slow-growing ramp deception scenario 4 is set up to compare the detection capabilities of M2 and M4.

[0200] The simulation results are shown in Figure 9. During the time period from 350 s to 550 s, ramp deceptions with slopes of 0.1 m / s and 0.05 m / s are applied to Channel 3. The data shows that: (1) Figure 9(a) is the simulation results of M2 and M4 for slow-growing deception, showing that for the ramp deception with a slope of 0.1 m / s, the detection times of M2 and M4 are 92 s and 57 s respectively; for 0.05 m / s, the detection times of M2h and M3 are 147 s and 86 s respectively. It can be seen that in the detection of slow-growing ramp deception, M3 has a higher detection efficiency than M2. (2) Figure 9(b) is the influence of slow-growing deception on the position error. When deceptions of 0.1 m / s and 0.05 m / s are applied, the maximum northward errors are 1.213 m and 1.173 m respectively, the maximum eastward errors are 1.316 m and 1.344 m respectively, and there are slight changes in the height error, indicating that the smaller the slope of slow growth, the longer the time to reach the maximum error.

[0201] Combining Scenario 2 and Scenario 4, it can be concluded that when Channel 3 is deceived by slow growth of 0.1 m / s and 0.05 m / s, the detection times of M4 are shortened by 38% and 41.5% respectively compared with M2, with an average shortening of 39.8%. In this regard, it is verified that M4 can detect slow-growing ramp deceptions with strong concealment and great harm.

Claims

1. A GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and robust estimation, characterized in that, Comprising the following steps: S1. Observe the GNSS / INS tightly coupled system through the observation model H k to obtain the normalized innovation vector ω at time k i , where i = 1, 2,..., n and n is the number of visible satellites; S2. Update the normalized innovation vector ω in real time through a Kalman filter i The real-time update includes time update and measurement update; In the time update phase, a prior estimate of the state vector of the GNSS / INS tightly coupled system is made to obtain the prior estimated state vector at time k. In the measurement update phase, the normalized innovation vector ω i is subtracted from the observation model H k multiplied by the prior estimated state vector to obtain the updated innovation vector r k ; According to the observation model H k , the updated innovation vector r k and the pre-obtained gain matrix K k , the posterior estimated state vector is calculated. According to the posterior estimated state vector and the pre-obtained innovation rate matrix C, the innovation rate vector C = [0 1 0 0]; The gain matrix K k has the following calculation formula: where, H k represents the observation model, represents the prior covariance estimation vector, and R k represents the observation noise covariance of the observation model; S3, if the innovation rate vector The absolute value of the i-th element in If it is greater than the preset upper detection threshold k1, then the new information rate vector The GNSS measurement value corresponding to the i-th element in is deceptive if If it is less than the preset lower detection threshold k0, then the new information rate vector The GNSS measurement value corresponding to the i-th element in does not contain deception; if is greater than k0 and less than k1, then the gain matrix K in step S2 k The update is performed and the deception detection is re-performed according to the updated gain matrix.

2. The GNSS / INS tight integration spoofing detection method based on innovation rate optimization and robust estimation according to claim 1, wherein In step S3, according to k0 and k1, calculate the equivalent weight matrix W, and update the gain matrix K according to the equivalent weight matrix W k for updating.

3. The GNSS / INS tightly-coupled spoofing detection method based on innovation rate optimization and robust estimation according to claim 2, characterized in that The gain matrix K is updated by the following formula: k as follows: K R = K k ·W where K R represents the updated gain matrix.

4. The GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and robust estimation according to claim 2, characterized in that The equivalent weight matrix is expressed as W = diag(w1…w i …w n ). The i-th element wi in the equivalent weight matrix is calculated through the following formula i : In the formula, represents the innovation rate vector the absolute value of the i-th element in, k1 represents the upper limit detection threshold, and k0 represents the lower limit detection threshold.

5. The GNSS / INS tightly-coupled spoofing detection method based on innovation rate optimization and robust estimation according to claim 1, characterized in that In step S2, the posterior estimation state vector is calculated by the following formula wherein, represents the prior estimated state vector, K k represents the gain matrix, r k represents the updated innovation vector.

6. The GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and robust estimation according to claim 1, wherein In step S2, the prior covariance estimation vector is calculated through the following formula In the formula, represents the state transition matrix, represents the posterior error covariance matrix at time k-1, and q k-1 represents the system noise covariance matrix.

7. The GNSS / INS tightly coupled spoofing detection method based on innovation rate optimization and robust estimation according to claim 1, characterized in that, In step S2, the prior estimated state vector is calculated by the following formula In the formula, represents the state transition matrix, represents the posterior estimation state vector at the (k - 1)th moment.

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