An Adaptive Robust Estimation Method for GNSS Spoofers

Abstract

The present invention relates to an adaptive robust estimation method for a GNSS spoofing device, belonging to the technical field of GNSS navigation. The present invention uses the error discrimination statistic of the GNSS spoofing device to determine the adaptive factor and the equivalent measurement noise matrix, constructs an adaptive robust Kalman gain matrix according to the adaptive factor and the equivalent measurement noise matrix, and uses the constructed adaptive robust Kalman gain matrix as the Kalman gain matrix of the state estimator of the GNSS spoofing device, which can enable the estimator of the GNSS spoofing device to reliably estimate the UAV state information in real time, improve the robustness of the estimator in the face of observation errors, and accelerate the convergence speed of error control. And through simulation experiments, it is further verified that the present invention can shorten the convergence time of the true trajectory error of the UAV, shorten the convergence time of the estimated trajectory error of the UAV, shorten the convergence time of the estimated trajectory error of the GNSS spoofing device, and shorten the convergence time of the broadcast trajectory error of the GNSS spoofing device, and can effectively and more covertly deviate the UAV from the preset trajectory to the spoofing trajectory.

Description

Technical Field

[0001] The present invention relates to an adaptive robust estimation method for a GNSS spoofing device, belonging to the technical field of GNSS navigation. Background Art

[0002] Unmanned Aerial Vehicles (UAVs) have the advantages of strong stealth, long endurance, and low cost, and fly at a relatively low altitude, with higher optical resolution than reconnaissance satellites. UAVs generally use a Global Navigation Satellite System (GNSS)-aided Inertial Navigation System (INS) to achieve navigation and positioning. Their defense capabilities are relatively poor. Implementing satellite navigation spoofing interference on the UAV navigation system can have a significant impact on its positioning results. Conducting research on satellite navigation spoofing interference technology for UAVs has very profound practical significance and is also one of the research hotspots in the field of navigation countermeasure. Moreover, with the increasing maturity of inertial navigation technology, many UAVs are equipped with inertial navigation systems. How to effectively use satellite navigation spoofing interference technology to deceive UAVs is an urgent problem to be solved in the field of navigation countermeasure.

[0003] First, there are two representative events in the development of GNSS spoofing devices as follows: In 2002, Jon S. Warner et al. deceived the GPS receiver of a freight truck using a simple GPS signal simulator in an experiment, demonstrating that civilian GPS receivers are vulnerable to simple spoofing attacks. In 2008, Todd E. Humphreys of the University of Texas at Austin had developed a generally recognized GPS spoofing attack system (GPS GNSS spoofer) in the industry.

[0004] The Shepard team et al. demonstrated that GNSS spoofers can effectively implement wireless air spoofing against UAVs. The experiment was conducted at the White Sands Missile Range under the supervision of the US Department of Homeland Security in June 2012. In this test, the simulated GPS signals were transmitted through the air from a distance of approximately 620 m. When the GNSS spoofer captured its navigation system, the UAV hovered at about 12 m above the ground. Then, the GNSS spoofer induced the captured GPS receiver to generate positions and velocities, falsely indicating the UAV to move upward. As a result, the UAV moved downward to correct its apparent deviation from the commanded hover position. The same Shepard team also conducted a new experiment near Austin, Texas in June 2013. In the new experiment, the GPS receiver and state estimator of the target UAV continuously recorded data. To avoid unauthorized radio transmissions in the protected GPS frequency band, indirect signals were directly injected into the UAV's GPS antenna through a lightweight coaxial cable, where they were combined with the real GPS signals from the satellites. In both the previous air trial and the subsequent wired experiment, the GNSS spoofer showed open-loop control for the UAV. In 2019, Liu Yachuan developed a miniaturized synchronous GPS spoofing interference source, which can cause a certain type of commercial receiver and a certain type of civilian rotor UAV to gradually deviate from the normal positioning and velocity measurement results and generate controlled positioning and velocity measurement results.

[0005] In 2012, the Todd E. Humphreys team used a civilian signal GNSS spoofer with a hardware cost of less than $1,000 to transmit signals, causing an unmanned helicopter that should have maintained a fixed altitude to continuously descend. In this GPS spoofing experiment, the UAV was modeled as a double-integral dynamics model. The UAV used a Kalman filter to estimate the state and a Proportional-differential (PD) algorithm to generate control commands. They further established the interconnection models between the controllers, estimators, and devices of the UAV and the GNSS spoofer respectively. However, in Todd Humphreys' experiment, many parameters were set, and it was assumed that the GNSS spoofer was not affected by errors, which was actually very difficult to achieve.

[0006] In fact, there are errors in each observation of the UAV state by the GNSS spoofing device. Therefore, each estimation of the GNSS spoofing device state estimator contains new state errors. Only studying the influence of the initial state error does not conform to the actual scenario. To sum up, there is little discussion on the influence of the state estimation error of the GNSS spoofing device on the spoofing effect and error convergence under the condition that the GNSS spoofing device has continuous observation errors for the UAV. At present, only by adjusting the parameters of the GNSS spoofing device to control the state estimation error. When the GNSS spoofing device has continuous observation errors for the UAV, only by adjusting the original parameters of the GNSS spoofing device, the error cannot be effectively controlled to converge to meet the threshold condition. Summary of the Invention

[0007] The object of the present invention is to provide an adaptive robust estimation method for a GNSS spoofing device to solve the problem that the current GNSS spoofing device cannot effectively control error convergence.

[0008] The present invention provides an adaptive robust estimation method for a GNSS spoofing device to solve the above technical problems. The estimation method includes the following steps:

[0009] 1) Construct an adaptive robust Kalman gain matrix according to the adaptive factor and the equivalent measurement noise matrix, where the adaptive factor and the equivalent measurement noise matrix are determined by the error discrimination statistic;

[0010] 2) Use the constructed adaptive robust Kalman gain matrix as the Kalman gain matrix of the state estimator of the GNSS spoofing device, re-model the state estimator of the GNSS spoofing device, and control the GNSS spoofing device according to the re-modeled state estimator of the GNSS spoofing device.

[0011] The present invention considers the influence of continuous observation errors, determines the adaptive factor and the equivalent measurement noise matrix by using the error discrimination statistic of the GNSS spoofing device, constructs an adaptive robust Kalman gain matrix according to the adaptive factor and the equivalent measurement noise matrix, and uses the constructed adaptive robust Kalman gain matrix as the Kalman gain matrix of the state estimator of the GNSS spoofing device, which can enable the estimator of the GNSS spoofing device to reliably estimate the UAV state information in real time, improve the robustness of the estimator in the face of observation errors, and accelerate the convergence speed of error control.

[0012] Furthermore, the constructed adaptive robust gain matrix is:

[0013]

[0014] is a gain matrix with adaptive robust function, α is the adaptive factor, is the inverse matrix of the equivalent measurement noise matrix, C T is the transpose of the measurement matrix C, P s is the steady-state estimation error covariance matrix of the GNSS spoofing device.

[0015] Furthermore, to accurately determine the adaptive factor, the calculation formula of the adaptive factor is:

[0016]

[0017] where c 0 is the first threshold, c 1 is the second threshold, represents the error discrimination statistic.

[0018] Furthermore, the c 0 is 1.25, c 1 is 5.25.

[0019] Furthermore, the inverse matrix of the equivalent measurement noise matrix is a diagonal matrix, and the diagonal components in this diagonal matrix are calculated as follows:

[0020]

[0021] where p i is the i-th diagonal component of the inverse matrix of the measurement noise matrix and, is the i-th diagonal component of the inverse matrix of the equivalent measurement noise matrix and w i is the equivalent weight, which is determined by the error discrimination statistic.

[0022] Furthermore, the determination process of the equivalent weight is:

[0023]

[0024] where k 0 is the first set value, k 1 is the second set value, and v is the observation residual.

[0025] Furthermore, the k 0 is 1.25, k 1 is 5.25.

[0026] Furthermore, the error discrimination statistic is characterized by the prediction residual statistic, that is:

[0027]

[0028] where, represents the prediction residual statistic, that is, the error discrimination statistic, represents the predicted residual vector, and tr represents the trace of a matrix. Description of the Drawings

[0029] Figure 1 is a schematic diagram of the closed-loop control system of the current UAV-GNSS spoofing device;

[0030] Figure 2 is a flowchart of the adaptive robust estimation method of the GNSS spoofing device of the present invention;

[0031] Figure 3 is a schematic diagram of the estimated trajectory and broadcast trajectory of the GNSS spoofing device in Experiment 1;

[0032] Figure 4 is a schematic diagram of the estimated trajectory of the UAV and the true trajectory in Experiment 1;

[0033] Figure 5 is a schematic diagram of the NIS value distribution of the UAV system in Experiment 1;

[0034] Figure 6 is a distribution diagram of the estimated value of the acceleration measurement deviation in Experiment 1;

[0035] Figure 7 is a schematic diagram of the estimated trajectory and broadcast trajectory of the NSS spoofing device in Experiment 2;

[0036] Figure 8 is a schematic diagram of the estimated trajectory of the UAV and the true trajectory in Experiment 2;

[0037] Figure 9 is a schematic diagram of the NIS value distribution of the UAV system in Experiment 2;

[0038] Figure 10 is a distribution diagram of the estimated value of the acceleration measurement deviation in Experiment 2;

[0039] Figure 11 is a schematic diagram of the comparison of the UAV true trajectory errors obtained from Experiment 1 and Experiment 2;

[0040] Figure 12 is a schematic diagram of the comparison of the UAV estimated trajectory errors obtained from Experiment 1 and Experiment 2;

[0041] Figure 13 is a comparison diagram of the estimated trajectory errors of the GNSS spoofing device in Experiment 1 and Experiment 2;

[0042] Figure 14 is a comparison diagram of the broadcast trajectory errors of the GNSS spoofing device in Experiment 1 and Experiment 2. Detailed Embodiments

[0043] The following further describes the detailed embodiments of the present invention with reference to the accompanying drawings.

[0044] By analyzing the influence of the state estimation error of the GNSS spoofing device on the spoofing effect and the error convergence under the condition of continuous observation error of the GNSS spoofing device, the present invention proposes an adaptive robust estimation algorithm applicable to a steady-state linear quadratic estimator to enable the estimator of the GNSS spoofing device to reliably estimate the UAV state information in real time. The implementation process of this method is as Figure 2 shown.

[0045] Before describing the solution of the present invention, the GNSS spoofing device and the UAV model are introduced first.

[0046] If the UAV is the spoofing target, it is assumed that the target UAV is a rotary-wing aircraft and the navigation system of the target UAV is based on the configuration of a traditional GNSS-aided IMU. Generally, the UAV is composed of three parts: an aircraft, an estimator, and a controller. It is assumed that the state vector of the UAV is x = [r, v] T , where the UAV position is r, the speed is v, and the acceleration is a, and r, v, and a are all three-dimensional vectors. The above parameters are given by the double-integral dynamics model. The preset trajectory of the UAV is The dynamic model of the UAV is:

[0047]

[0048] Among them,

[0049]

[0050] Let the acceleration measurement value with deviation be a m = a - b, where b is the acceleration measurement deviation, and the observation value broadcast by the GNSS spoofing device to the UAV is x * = [r * , v * T , which is given by the double-integral dynamics model , and are the estimated values of the UAV's position, velocity, and acceleration measurement deviation given by the UAV state estimator respectively. The UAV state estimator is modeled as a steady-state linear quadratic estimation model:

[0051]

[0052] Among them, L is the Kalman gain matrix,

[0053] In addition, and are the variance of the GNSS position and velocity measurement noise respectively, is the corresponding position and velocity measurement noise covariance,​ is the measurement noise variance of the IMU acceleration, is the process noise variance of the IMU acceleration measurement deviation.

[0054] The controller of the UAV is modeled as a PD compensator:

[0055]

[0056] The purpose of the GNSS spoofing device is to make the UAV move along the spoofing path and are the estimated values of the UAV's position, velocity, and acceleration given by the GNSS spoofing device state estimator, respectively. The estimator of the GNSS spoofing device is modeled as a steady-state linear quadratic estimator:

[0057]

[0058] where the Kalman gain matrix of the GNSS spoofing device is Let and be the measurement noise variances of the position and velocity of the GNSS spoofing device state estimator, respectively, is the corresponding measurement noise covariance of the position and velocity, is the acceleration process noise variance. Therefore, the measurement noise matrix R and the process noise matrix of the GNSS spoofing device state estimator are respectively expressed as:

[0059]

[0060] Let the measurement matrix be C = [I 0], and the steady-state estimation error covariance matrix P s of the GNSS spoofing device is the solution of the same continuous Riccati algebraic equation:

[0061]

[0062] The Kalman gain matrix L s is obtained from

[0063] Its controller is modeled as a PD compensator:

[0064]

[0065] where the gain matrix is obtained from the above formula as a * After that, through x * = Ax * + Ba * calculate x * = [r * ,v​* T 。

[0066] Therefore, the complete dynamic model of the GNSS spoofing device is as follows:

[0067]

[0068] From Eqs. (3), (4), and (9), the coupled dynamics mathematical model of the closed-loop system formed by the UAV and the GNSS spoofing device is expressed by the following equation:

[0069]

[0070] where represents the estimation error of the acceleration measurement deviation.

[0071] A closed-loop system is formed by the UAV and the GNSS spoofing device, and the overall modeling of the closed-loop system is as Figure 1 shown. The state estimator of the GNSS spoofing device calculates the estimated values and by obtaining the state parameters x of the UAV. Usually, x is considered observable and error-free. However, in reality, the x obtained by the GNSS spoofing device through lidar or photovoltaic tracker always contains errors, and the errors will have a certain impact on the GNSS spoofing device to spoof the UAV. This part will analyze the error characteristics according to the characteristics of the closed-loop system.

[0072] Assume that each input x of the state estimator of the GNSS spoofing device will contain an error ξ, that is

[0073] χ = x + ξ (11)

[0074] where χ represents the state parameter x containing the error ξ. Substituting Eq. (11) into Eq. (10), we get:

[0075]

[0076] where and represent the estimation error of the measurement deviation affected by ξ and the acceleration estimated by the GNSS spoofing device, respectively.

[0077] Subtracting the above equation from Eq. (10), we get

[0078]

[0079] Eq. (13) shows that the error term ξ not only causes an error Aξ to , but also causes errors to and which are and ​

[0080] According to Equation (10), we can obtain:

[0081]

[0082] Therefore, the error term will also affect x * and cause an impact.

[0083] According to the dynamic characteristics of a Linear Time-Invariant (LTI) system, the state parameters of the UAV estimated by the state estimator of the GNSS spoofing device can be expressed as:

[0084]

[0085] The state parameter containing the error term ξ can be expressed as:

[0086]

[0087] where ξ' represents the error term of. Let Equation (16) minus Equation (1), we get:

[0088]

[0089] It can be seen that the error term ξ affects both the non-integral term and the integral term in Equation (17). For the non-integral term in Equation (17), the convergence study can be divided into two cases. The first case: the eigenvalues of the matrix are distinct; the second case: the eigenvalues of the matrix satisfy the multiplicity condition.

[0090]

[0091] And the integral term in Equation (17) can be transformed into According to the conclusion of Equation (2.8), we can obtain:

[0092]

[0093] Therefore, when t → ∞, the following conclusion will be satisfied:

[0094]

[0095] The above derivation shows that when the true state parameter x of the UAV obtained by the estimator of the GNSS spoofing device each time contains the error term ξ, the final estimated parameter will converge to The magnitude of the final error convergence value is related to ξ.

[0096] Therefore, based on the above analysis, the present invention provides an adaptive robust estimation method for a GNSS spoofing device. This method uses an adaptive robust estimation algorithm applicable to a steady-state linear quadratic estimator to improve the robustness of the estimator in the face of observation errors and make the estimation results more reliable.

[0097] Specifically, the present invention modifies the Kalman gain matrix of the state estimator of the GNSS spoofing device from to:

[0098]

[0099] where is the gain matrix with adaptive robust function, and α is the adaptive factor, aiming to control the influence of the dynamic model error; is the equivalent measurement noise matrix, aiming to resist the influence of the observation error.

[0100] According to the modified Kalman gain matrix, the state estimator of the GNSS spoofing device is re-modeled as:

[0101]

[0102] Both the adaptive factor and the equivalent measurement noise matrix are determined according to the error discrimination statistic, and the error discrimination statistic is characterized by the prediction residual statistic, that is:

[0103]

[0104] where tr represents the trace of the matrix, represents the prediction residual statistic, represents the prediction residual vector.

[0105] The adaptive factor α is determined according to the error discrimination statistic (prediction residual statistic). The present invention uses the IGG3 scheme to determine the adaptive factor, that is, when the model error statistic is less than the first threshold, the adaptive factor is set equal to 1; when the model error is greater than the second threshold, the adaptive factor is set equal to 0; when the model error is between the first threshold and the second threshold, the adaptive factor is greater than 0 and less than. Among them, the first threshold is less than the second threshold. The specific calculation formula used is as follows:

[0106]

[0107] where c 0 is the first threshold, c 1 is the second threshold. For this embodiment, c 0 = 1.25, c 1 = 5.25.

[0108] Determine the inverse of the equivalent measurement noise matrix according to the error discrimination statistic (prediction residual statistic). Both the equivalent measurement noise matrix and the measurement noise matrix are diagonal matrices, and their corresponding inverse matrices are also diagonal matrices. For a diagonal matrix, as long as its diagonal components are calculated, the matrix itself can be obtained. There is the following relationship between the diagonal components of the inverse matrix of the equivalent measurement noise matrix and the diagonal components of the inverse matrix of the measurement noise matrix. According to this relationship, the inverse matrix of the equivalent measurement noise matrix can be determined.

[0109]

[0110] where p i is the i-th diagonal component of the inverse matrix of the measurement noise matrix and is the i-th diagonal component of the inverse matrix of the equivalent measurement noise matrix , and w i is the equivalent weight.

[0111] The equivalent weight w i is determined according to the error discrimination statistic. The present invention adopts the IGG3 scheme to determine the adaptive factor, that is, when the model error statistic is less than the first set value, the adaptive factor is set equal to 1; when the model error is greater than the second set value, the adaptive factor is set equal to 0; when the model error is between the first set value and the second set value, the adaptive factor is set greater than 0 and less than. Among them, the first set value is less than the second set value. The specific calculation formula adopted is as follows:

[0112]

[0113] where v is the observation residual, k 0 is the first set value, k 1 is the second set value. In this embodiment, k 0 = 1.25 and k 1 = 5.25.

[0114] Using the improved Kalman gain matrix as the Kalman gain matrix of the state estimator of the GNSS spoofing device can enable the estimator of the GNSS spoofing device to reliably estimate the UAV state information in real time, improve the robustness of the estimator in the face of observation errors, and accelerate the convergence speed of error control.

[0115] Experimental verification

[0116] To verify the effect of the present invention, a simulation experiment is first designed for verification. The GNSS spoofing device can accurately obtain the position estimation value of the UAV speed estimation value and It is the premise for implementing deception on the UAV. Assume that the GNSS spoofing device generates spoofing signals, causing the measurement value of the UAV to be equal to the output of the GNSS spoofing device. Assume that the processing delay in the GNSS spoofing device is 0, and the update frequency of the GNSS spoofing device is 1 Hz, synchronized with the 1 Hz update of the UAV controller.

[0117] The parameter settings of the UAV are shown in Table 1, and the parameter settings of the state estimator of the GNSS spoofing device are shown in Table 2.

[0118] Table 1

[0119]

[0120] Table 2

[0121]

[0122] To simulate the process of a rotary-wing UAV taking off vertically from the ground and then completing maneuvering actions, the three-dimensional components of the acceleration of the UAV's preset trajectory and spoofing trajectory (unit: m / s 2 ) are as follows, and the total simulation duration t ∈ [0, 2400] s.

[0123] ① When t ∈ [0, 400] s, it is the vertical takeoff stage of the UAV.

[0124]

[0125] ② When t ∈ [400, 1000] s, it is the first side of the UAV's flight trajectory.

[0126]

[0127]

[0128]

[0129] ③ When t ∈ [1000, 1400] s, it is the second side of the UAV's flight trajectory.

[0130]

[0131]

[0132] ④ When t ∈ [1400, 2000] s, it is the third side of the UAV's flight trajectory.

[0133]

[0134]

[0135]

[0136] ⑤ When t ∈ [2000, 2400] s, it is the fourth side of the UAV flight trajectory.

[0137]

[0138]

[0139] Assume that there is a constant position error of 10 m and a constant velocity error of 1 m / s when the GNSS spoofing device first estimates the state of the UAV, and then there is a position error of 0.1 m and a constant velocity error of 0.01 m / s when estimating the state of the UAV each time.

[0140] Experiment 1: Trajectory spoofing experiment of the GNSS spoofing device on the UAV when the state estimator of the GNSS spoofing device does not use the improved algorithm.

[0141] The experimental results are as Figure 3 and Figure 4 shown, where Figure 3 shows the changes in the estimated trajectory and the broadcast trajectory of the state estimator of the GNSS spoofing device when the state estimator of the GNSS spoofing device does not use the improved algorithm. Since there are observation errors in the state estimator of the GNSS spoofing device at each moment, when the UAV is on the first side and the second side of the flight path, the estimated trajectory has large fluctuations. When the UAV is on the third side and the fourth side of the flight path, the estimated trajectory gradually converges to the spoofing trajectory.

[0142] Figure 4 shows the changes in the estimated trajectory of the UAV estimator and the true trajectory of the UAV. During the flight of the UAV, the estimated trajectory basically coincides with the preset trajectory, that is, the estimated state output by the UAV still remains consistent with the preset trajectory. However, when the UAV is on the first side and the second side of the flight path, the true trajectory has large fluctuations near the spoofing trajectory. When the UAV is on the third side and the fourth side of the flight path, the true trajectory gradually converges to the spoofing trajectory. The results show that when the estimator of the GNSS spoofing device does not use the improved algorithm, there are large fluctuations in the estimated trajectory of the estimator of the GNSS spoofing device and the true trajectory of the UAV in the early stage of the flight process, which may lead to the failure of the spoofing behavior.

[0143] During the control period after the GNSS spoofing device captures the UAV, the spoofing signal has captured the tracking loop of the target GNSS receiving chip, and the concealment during the control period after capture is only determined by the NIS value in the UAV navigation state estimator. NIS is defined as:

[0144]

[0145] In the formula, Z(k) is the measurement vector at time k, and H(k) is the measurement matrix at time k. is the one-step prediction of X calculated, where S(k) is the prediction error covariance matrix, k and is the innovation vector of the measurement. S(k) represents the covariance of the innovation and is the sum of the measurement noise covariance and the error covariance of the state estimate transformed into the measurement space, that is

[0146] S(k) = HP k / k-1 H T + R (27)

[0147] where R is the measurement noise variance matrix, and the alarm judgment criterion is:

[0148]

[0149] In the formula, T In represents the set NIS alarm threshold. When NIS remains below the threshold value T In , it is considered that the spoofing behavior is concealed; when NIS is greater than the threshold value T In , it is considered that the navigation system detects spoofing and gives an alarm, and at this time the spoofing behavior has poor concealment. Therefore, to make the spoofing have good concealment, NIS(k) < T In should be satisfied. Here, the NIS detection threshold is set to 0.2.

[0150] Figure 5 shows the NIS values of the UAV system in this experiment. The black dots represent the NIS values, and the black line represents the threshold of 0.2. After statistics, the average value of the NIS values in the time period of 0 - 2400 s is 0.26. In the time period of 0 - 718 s, there are a large number of moments when the NIS values are greater than the threshold, and the threshold condition cannot be met. The spoofing behavior may fail during this time period; after 718 s, the NIS values are all less than the threshold. Therefore, the NIS value convergence time is 718 s. Figure 6 shows the estimated acceleration measurement deviation values given by the estimator of the UAV and the estimated values in the three-dimensional directions can all converge.

[0151] Experiment 2: Trajectory spoofing experiment of the state estimator of the GNSS spoofing device using the improved method of the present invention.

[0152] The experimental results are as shown in Figure 7 , 8 and 9. Figure 7 shows the changes in the estimated trajectory and the broadcast trajectory of the state estimator of the GNSS spoofing device when the state estimator of the GNSS spoofing device uses the improved algorithm of the present invention. Since there are observation errors in the state estimator of the GNSS spoofing device at each moment, compared with Experiment 1, the UAV only has a small fluctuation in the estimated trajectory when flying along the first side of the flight path, and the fluctuation amplitude is significantly smaller than​Figure 3 The fluctuations of the estimated trajectory. When the UAV is on the second, third, and fourth sides of the flight path, the estimated trajectory converges to the spoofing trajectory.

[0153] Figure 8 Shows the changes in the estimated trajectory of the UAV estimator and the true trajectory of the UAV. During the flight of the UAV, the estimated trajectory basically coincides with the preset trajectory, that is, the estimated state output by the UAV still remains consistent with the preset trajectory; but when the UAV is on the first and second sides of the flight path, compared with Experiment 1, there are small fluctuations in the true trajectory near the spoofing trajectory, but this fluctuation is significantly smaller than Figure 4 the fluctuations of the true trajectory in Experiment 1. When the UAV is on the third and fourth sides of the flight path, the true trajectory converges to the spoofing trajectory. The results show that when the improved algorithm is used in the estimator of the GNSS spoofing device, there are small fluctuations in the estimated trajectory of the estimator of the GNSS spoofing device and the true trajectory of the UAV in the short term during the flight process, and this fluctuation is significantly smaller than that when the improved algorithm is not used in the estimator of the GNSS spoofing device.

[0154] Figure 9 Shows the NIS values of the UAV system in this experiment. The black dots represent the NIS values, and the black line represents the threshold of 0.2. After statistics, the average value of the NIS values in the time period of 0 - 2400 s is 0.03. Within 0 - 170 s, there are a large number of moments when the NIS values are greater than the threshold. After 170 s, the NIS values are all less than the threshold, and the convergence time of the NIS value is 170 s. Therefore, compared with Experiment 1, when the state estimator of the GNSS spoofing device uses the improved algorithm, the average value of the NIS value decreases by 0.23, that is, the average value of the NIS value decreases by 88.5%; the convergence time of the NIS value is shortened by 548 s, that is, the convergence time of the NIS value is shortened by 76.3%, so the concealment of the spoofing behavior is greatly improved. Figure 10 Shows the estimated value of the acceleration measurement deviation given by the estimator of the UAV Compared with Experiment 1, its estimated values in the three-dimensional directions are smaller and can all converge quickly.

[0155] Therefore, the GNSS spoofing device adopting the adaptive robust estimation method of the present invention can make the UAV deviate from the preset trajectory to the spoofing trajectory, and greatly improve the concealment of the spoofing behavior.

[0156] To better illustrate the effect of the present invention, the following four types of results of Experiment 1 and Experiment 2 are compared, and the results are as Figure 11 , Figure 12 , Figure 13 and Figure 14As shown in it. It can be seen that the UAV true trajectory error, UAV estimated trajectory error, GNSS spoofing device estimated trajectory error, and GNSS spoofing device broadcast trajectory error. The above various errors refer to the differences between various trajectory results when the estimated error is set in the GNSS spoofing device including NIS and when there is no estimated error. The solid line represents the result of Experiment 1, and the double dashed line represents the result of Experiment 2. When the estimator of the GNSS spoofing device uses the improved algorithm of the present invention, the UAV true trajectory error, UAV estimated trajectory error, GNSS spoofing device estimated trajectory error, and GNSS spoofing device broadcast trajectory error are all smaller than the case when the estimator of the GNSS spoofing device does not use the improved algorithm. The convergence time is defined as: if the error is less than the convergence threshold after a certain moment, then that moment is the convergence time. The statistical results of the convergence thresholds and convergence times of various errors are shown in Table 3, and the convergence shortening times and shortening time percentages of various errors are shown in Table 4.

[0157] Table 3

[0158]

[0159] Table 4

[0160]

[0161] As can be seen from Table 4, when the estimator of the GNSS spoofing device uses the improved algorithm of the present invention, compared with the case when the estimator of the GNSS spoofing device does not use the improved algorithm, the convergence time of the UAV true trajectory error is shortened by 42.3%, the convergence time of the UAV estimated trajectory error is shortened by 67.4%, the convergence time of the GNSS spoofing device estimated trajectory error is shortened by 33.7%, and the convergence time of the GNSS spoofing device broadcast trajectory error is shortened by 54.8%. The results show that the designed GNSS spoofing device can significantly shorten the convergence times of the above four types of errors, and can effectively and more covertly deviate the UAV from the preset trajectory to the spoofing trajectory, thereby achieving the covert spoofing of the UAV.

Claims

1. An adaptive robust estimation method for a GNSS spoofing device, characterized in that, the estimation method comprises the following steps: 1) Construct an adaptive robust Kalman gain matrix based on an adaptive factor and an equivalent measurement noise matrix, wherein the adaptive factor and the equivalent measurement noise matrix are determined by an error discrimination statistic; 2) Use the constructed adaptive robust Kalman gain matrix as the Kalman gain matrix of the state estimator of the GNSS spoofing device, re-model the state estimator of the GNSS spoofing device, and control the GNSS spoofing device according to the re-modeled state estimator of the GNSS spoofing device.

2. The adaptive robust estimation method for a GNSS spoofing device according to claim 1, characterized in that, the constructed adaptive robust gain matrix is: is the gain matrix with an adaptive robust function, α is the adaptive factor, is the inverse matrix of the equivalent measurement noise matrix, C T is the transpose of the measurement matrix C, P s is the steady-state estimation error covariance matrix of the GNSS spoofing device.

3. The adaptive robust estimation method for a GNSS spoofing device according to claim 2, characterized in that, the calculation formula of the said adaptive factor is: where c 0 is the first threshold, and c 1 is the second threshold, represents an error discrimination statistic.

4. The adaptive robust estimation method for a GNSS spoofing device according to claim 3, characterized in that, The described c 0 is 1.25, and c 1 is 5.

25.

5. The adaptive robust estimation method for a GNSS spoofing device according to claim 2, characterized in that, the inverse matrix of the equivalent measurement noise matrix is a diagonal matrix, and the diagonal components in this diagonal matrix adopt the following calculation method: where p i is the inverse matrix of the measurement noise matrix of the i-th diagonal component, is the inverse matrix of the equivalent measurement noise matrix of the i-th diagonal component, w i is the equivalent weight, which is determined by the error discrimination statistic.

6. The adaptive robust estimation method for a GNSS spoofing device according to claim 5, characterized in that, the determination process of the said equivalent weight is: where k 0 is the first set value, k 1 is the second set value, and v is the observation residual.

7. The adaptive robust estimation method for a GNSS spoofing device according to claim 6, characterized in that, The said k 0 is 1.25, and k 1 is 5.

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8. The adaptive robust estimation method for a GNSS spoofing device according to any one of claims 1-7, characterized in that, the said error discrimination statistic is characterized by a prediction residual statistic, that is: Among them, represents the prediction residual statistic, that is, the error discrimination statistic, represents the prediction residual vector, and tr represents the trace of the matrix.

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