UAV trajectory deception method based on cumulative sum

Abstract

The present invention proposes a UAV trajectory deception method based on cumulative sum CUSUM, which belongs to the field of UAV technology. The implementation steps are as follows: initializing the cumulative sum of the position deviation of the UAV at time T0 to zero; making the UAV track and capture the deception signal of the real speed and position, n=1; T n At this moment, the real position and speed of the drone are obtained using radar, the preset position at the current moment is calculated using the parallelogram law, and its distance from the real position is calculated as the position deviation of the drone at the current moment; the cumulative sum of the position deviation at the current moment is calculated; the spoofed position and speed are calculated based on the relationship between the cumulative sum and the preset threshold; a spoofing signal is generated based on the spoofed position and speed for amplification and forwarding; in this way, the deviation between the spoofed position of the drone at the current moment and the preset position can be limited to within the preset threshold, thereby evading detection by the drone's flight control system and achieving the requirement of covert deception.

Description

Technical Field

[0001] The present invention belongs to the technical field of drones and relates to a drone trajectory deception method, in particular to a drone trajectory deception method based on CUSUM, which can be applied to drone GPS security testing. Background Art

[0002] With the development and advancement of science and technology, drone technology has become increasingly sophisticated, and drones are gradually becoming integrated into people's daily lives. While drones bring various conveniences to people's lives, they also face security issues. Because GPS systems have low power and weak signals, and are susceptible to electromagnetic interference, attackers can forge GPS jamming signals based on the characteristics of satellite signals that a target drone can receive and forward them to the target drone's signal reception area. This causes the target drone's GPS receiver to receive the fake GPS signal, allowing the attacker to spoof the target drone's GPS receiver's output, such as its position and speed, and thereby control the target drone's trajectory.

[0003] Therefore, it is necessary to test the GPS security of drones and identify any security vulnerabilities. Specifically, an attacker can deploy GPS attack equipment near a drone to perform GPS spoofing. This equipment consists of an embedded computer, a signal generator, and a GPS transmitting antenna. The embedded computer generates the GPS spoofing signal and configures the signal generator's parameters, adjusting the signal generator's transmission frequency. The signal generator, connected to the embedded computer, converts the GPS spoofing signal to a specified frequency band. The transmitting antenna, connected to the signal generator's transmitting end, transmits the GPS signal to the target drone's GPS receiver. During this process, it is crucial to control the GPS spoofing signal so that the drone's flight control system cannot detect the trajectory deviation, which is known as covert spoofing. The key factors affecting the success of covert spoofing are the performance of the detection system deployed on the drone and the magnitude of the trajectory deviation caused by the spoofing. Therefore, a common approach is for the attacker to analyze the spoofing method based on the detection system deployed on the drone, so as to make the trajectory deviation caused by the spoofing undetectable by the detection system while maximizing the deviation.

[0004] The patent application with the publication number CN111650620A, titled “A trajectory deception method based on GPS navigation”, discloses a trajectory deception method for drones based on GPS navigation. The method first uses radar to obtain the flight speed and position of the target drone, and then derives T according to the parallelogram law. nAt this moment, if the offset rate is greater than a set value, the offset rate is adjusted based on whether the spoofed position differs from the preset position by less than a threshold. This invention ensures that the spoofed position and speed are closely aligned with the target drone's preset trajectory, thereby deceiving the target drone's navigation system and making the spoofing attack somewhat stealthy. However, by simply limiting the deviation between the spoofed position and the preset position to a larger preset value, if the target drone's flight control system deploys a detection system with stronger detection capabilities, the trajectory deviation will exceed the detection threshold of the detection system, causing the trajectory spoofing to be detected, reducing the stealth of the deception. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a drone trajectory deception method based on , aiming to solve the technical problem of poor concealment of trajectory deception in the prior art.

[0006] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Initialization parameters:

[0008] The duration of initializing the drone trajectory deception includes N moments T = {T n |0≤n<N}, the time interval between adjacent moments is Δt, T n Momentary drone position deviation error n The cumulative sum is S(n), T n The deceptive position, real position, deceptive speed and real speed of the drone at the moment are P n ′、P n 、V n ′ and V n , the cumulative sum of the position deviations of the UAV at time T0 is S(0)=0, where N≥2;

[0009] (2) The attacker makes the drone track the GPS spoofing signal:

[0010] The attacker uses radar to obtain the drone's true position P0 and true speed V0 at time T0, and uses P0 and V0 as the drone's spoofed position P0' and spoofed speed V0', respectively. Based on P0' and V0', the attacker generates a GPS spoofing signal, amplifies it, and then forwards it, jamming the drone's GPS so that the drone captures and tracks the attacker's GPS spoofing signal. Set n = 1;

[0011] (3) The attacker calculates T n The cumulative sum of the drone's position deviation at each moment:

[0012] (3a) The attacker uses radar to obtain the drone T nThe actual position P at the moment n , true speed V n , and using the parallelogram law, the drone T n-1 The actual position P at the moment n-1 To drone T n The actual position P at the moment n The connection, and the drone T n-1 The actual position P at the moment n-1 to T n-1 Always deceiving position P n-1 ′ are adjacent edges, and the UAV T is calculated. n The preset trajectory position P at the moment n ″;

[0013] (3b) The attacker sends the drone T n The actual position P at the moment n With the preset trajectory position P n ″ distance error n As a drone T n The position deviation at the moment, and judge whether S(n-1)>0 is established. If so, according to T n-1 Time error n-1 The cumulative sum S(n-1), T n The position deviation error of the drone at the moment n and the positioning error b of the drone GPS sensor within Δt, calculate T n Time error n The cumulative sum S(n) = S(n-1) + error n -b; otherwise, according to T n The position deviation error of the drone at this moment n and the positioning error b of the drone GPS sensor within Δt, calculate T n Time error n The cumulative sum S(n) = error n -b;

[0014] (4) Determine whether S(n) and the preset threshold th satisfy S(n)<th. If so, execute step (5); otherwise, set T n Moment drone's deceptive speed V n ′=V n , spoofed position P n ′=P n , and execute step (6);

[0015] (5) The attacker calculates T n The deceptive position of the drone at the moment P n ′ and deceptive speed Vn ′:

[0016] The attacker calculates the actual speed of the drone based on its velocity V n and the real position of the drone P n Spoofing position of drone P n ′ distance calculation T n The deceptive position of the drone at the moment P n ′, and according to any point Q(x,y) on the UAV trajectory within Δt to P n The distance between the drone and the time Δt is constant speed V n The relationship between the distance traveled and the slope of the tangent line on the drone trajectory at point Q(x,y) is established. n ′ and V n The differential equation of , and then solve the differential equation to get T n Time cheat speed V n ′The component V on the X-axis, Y-axis and Z-axis of the drone body coordinate system nx ′、V ny ′、V nz ', and execute step (6), wherein:

[0017]

[0018]

[0019] V nx ′=V nx

[0020]

[0021]

[0022]

[0023]

[0024] Among them, x and y represent T n The horizontal and vertical coordinates of any point Q on the UAV trajectory at time Δt, where |·| represents the modulo operation;

[0025] (6) Obtaining the drone’s deceptive trajectory:

[0026] The attacker uses T n The deceptive position of the drone at the moment P n ′ and deceptive speed V n Generate a GPS spoofing signal, amplify it and forward it, and judge whether n=N. If so, connect the spoofing positions of the drones at N moments in sequence.

[0027] , get the deceptive trajectory of the drone; otherwise, set n = n + 1 and execute step (3). Compared with the existing technology, the present invention has the following advantages:

[0028] (1) The present invention calculates the cumulative sum of the drone's position deviation at each moment and compares the cumulative sum with the cumulative sum threshold. When the cumulative sum is greater than the threshold, the drone's current true position and true speed are used as the deceptive position and deceptive speed. This can avoid the defect of large drone trajectory deviation in the prior art, thereby effectively deceiving the drone's detection system and achieving better concealment. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart for implementing the present invention.

[0030] Figure 2 Schematic diagram of the structure of the UAV deviation induction model of the present invention. DETAILED DESCRIPTION

[0031] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] Reference Figure 1 , the present invention comprises the following steps:

[0033] Step 1a) In the simulation environment, the attacker lets the drone fly a flight path that includes as many flight postures as possible, and the time is T = {T k |1≤k≤K}, let k=1, T k The deceptive position and real position of the drone at the moment are P k ′、P k , initialize P k ′ and P k The distance is the positioning error b of the GPS sensor of the drone within Δt, S max =0, where T K is the moment when the UAV stops flying, and K is the total number of moments;

[0034] Step 1b) In the UAV flight control software, obtain T k The distance between the target position of the UAV and the position output by the GPS sensor at the moment is T k The position deviation error of the drone at this moment k ;

[0035] Step 1c) Determine whether S(k-1)>0 is true. If so, according to T k-1 Time error k-1 The cumulative sum S(k-1), T kThe position deviation error of the drone at this moment k and the positioning error b of the drone GPS sensor within Δt, calculate T k Time error k The cumulative sum S(k)=S(k-1)+error k -b; otherwise, according to T k The position deviation error of the drone at this moment k and the positioning error b of the drone GPS sensor within Δt, calculate T k Time error k The cumulative sum S(k) = error k -b;

[0036] Step 1d) Determine if S(k)>S max Is it true? If so, then S max = S(k), go to step 1f); otherwise, S max =S max , proceed to step 1f);

[0037] Step 1e) If k=K, then output S max ; Otherwise, k=k+1, go to step 1b);

[0038] Step 1f) Initialize threshold th = S max ;

[0039] Step 1g) Initialize the duration of the drone trajectory deception, which includes N moments T = {T n |0≤n<N}, the time interval between adjacent moments is Δt, T n Momentary drone position deviation error n The cumulative sum is S(n), T n The deceptive position, real position, deceptive speed and real speed of the drone at the moment are P n ′、P n 、V n ′ and V n , the cumulative sum of the position deviations of the UAV at time T0 is S(0)=0, where N≥2;

[0040] Step 2) The attacker makes the drone track the GPS spoofing signal:

[0041] The attacker uses radar to obtain the drone's true position P0 and true speed V0 at time T0, and uses P0 and V0 as the drone's spoofed position P0' and spoofed speed V0', respectively. Based on P0' and V0', the attacker generates a GPS spoofing signal, amplifies it, and then forwards it, jamming the drone's GPS so that the drone captures and tracks the attacker's GPS spoofing signal. Set n = 1;

[0042] Step 3) The attacker calculates T n The cumulative sum of the drone's position deviation at each moment:

[0043] (3a) The attacker uses radar to obtain the drone T n The actual position P at the moment n , true speed V n , and using the parallelogram law, the drone T n-1 The actual position P at the moment n-1 To drone T n The actual position P at the moment n The connection, and the drone T n-1 The actual position P at the moment n-1 to T n-1 Always deceiving position P n-1 ′ are adjacent edges, and the UAV T is calculated. n The preset trajectory position P at the moment n ″;

[0044] (3b) The attacker sends the drone T n The actual position P at the moment n With the preset trajectory position P n ″ distance error n As a drone T n The position deviation at the moment, and judge whether S(n-1)>0 is established. If so, according to T n-1 Time error n-1 The cumulative sum S(n-1), T n The position deviation error of the drone at this moment n and the positioning error b of the drone GPS sensor within Δt, calculate T n Time error n The cumulative sum S(n) = S(n-1) + error n -b; otherwise, according to T n The position deviation error of the drone at this moment n and the positioning error b of the drone GPS sensor within Δt, calculate T n Time error n The cumulative sum S(n) = error n -b;

[0045] Step 4) Determine whether S(n) and the preset threshold th satisfy S(n)<th. If so, execute step (5); otherwise, set T n Moment drone's deceptive speed V n ′=V n , spoofed position Pn ′=P n , and execute step (6);

[0046] Step 5) The attacker n Time to T n+1 At this moment, according to the actual speed V of the UAV nx 、V ny , the real position of the drone P n Spoofing position of drone P n ′ is calculated to get T n The deceptive position of the drone at the moment P n The coordinates of ′ are

[0047]

[0048] like Figure 2 As shown, to simplify the calculation, we establish n The body coordinate system has only the X-axis and Y-axis as the origin.

[0049] According to the UAV deviation induction model, the curve of the UAV flight trajectory in unit time Δt is P n P n ′, let its equation be y=f(x), let Q(x,y) be the flight trajectory curve P of the drone n P n ′, then point Q(x,y) to the origin P n The distance between the drone and the time Δt is constant speed V n The distance traveled is equal; and the flight trajectory curve P of the drone n P n The slope of the tangent line at point Q(x,y) can be found in Figure 2 The triangle inside is obtained as shown below:

[0050]

[0051] Eliminate Δt in Equation (1-1) first, then add the initial conditions to convert it into a second-order differential equation, as shown in Equation (1-2):

[0052]

[0053] Where m=|V ny ′| / Δt. Let Solving the differential equation (1-2), we can get the UAV flight trajectory P n P n The equation of ′ is as follows

[0054]

[0055] When x=x1, Let y = y1, solve the quadratic function with respect to m, and we get:

[0056]

[0057] in After removing the negative solutions, we can get

[0058]

[0059] From formula (1-5), we can see that when the coordinates of the deceptive position are determined, the flight speed V of the drone is obtained. n , we can derive a definite and unique offset rate V ny ',Right now:

[0060]

[0061] in:

[0062]

[0063] The above discussion is about the UAV offset induction model in two-dimensional space. The three-dimensional space is similar to the two-dimensional space. It only needs to add an offset on the Z axis to complete the expansion to the three-dimensional space, that is,

[0064]

[0065] in:

[0066]

[0067] The deceptive speed V on the X axis nx ′=V nx , proceed to step 8);

[0068] Step 6) Get the drone’s spoofing trajectory:

[0069] The attacker based on V n ′ and P n Generate GPS spoofing signal to amplify and forward, and judge whether n=N is established. If so, connect T1 to T in sequence. n The deceptive position of the drone at time P1′ to P n ′, and obtain the deceptive trajectory of the drone; otherwise, set n=n+1 and execute step 3).

Claims

1. A drone trajectory deception method based on cumulative sum, characterized in that: The steps include: (1) Initialization parameters: Initialize the duration of the UAV trajectory deception to include N moments \(T = \{T n |0\leq n < N\}\), the time interval between adjacent moments is \(\Delta t\), and the cumulative sum of the UAV position deviation error n at moment \(T n is \(S(n)\). The spoofing position, true position, spoofing speed, and true speed of the UAV at moment \(T n are \(P n '\), \(P n \), \(V n '\) and \(V n respectively. The cumulative sum of the UAV position deviation at moment \(T_0\) is \(S(0)=0\), where \(N\geq2\). (2) The attacker makes the drone track the GPS spoofing signal: The attacker uses radar to obtain the drone's true position P0 and true speed V0 at time T0, and uses P0 and V0 as the drone's spoofed position P0' and spoofed speed V0', respectively. Based on P0' and V0', the attacker generates a GPS spoofing signal, amplifies it, and then forwards it, jamming the drone's GPS so that the drone captures and tracks the attacker's GPS spoofing signal. Set n = 1; (3) The attacker calculates T n The cumulative sum of the drone's position deviation at each moment: (3a) The attacker uses radar to obtain the drone T n The actual position P at the moment n , true speed V n , and using the parallelogram law, the drone T n-1 The actual position P at the moment n-1 To drone T n The actual position P at the moment n The connection, and the drone T n-1 The actual position P at the moment n-1 to T n-1 Always deceiving position P n-1 ′ are adjacent edges, and the UAV T is calculated. n The preset trajectory position P at the moment n ″; (3b) The attacker sends the drone T n The actual position P at the moment n With the preset trajectory position P n ″The deviation error n As a drone T n The position deviation at the moment, and judge whether S(n-1)>0 is established. If so, according to T n-1 Time error n-1 The cumulative sum S(n-1), T n The position deviation error of the drone at this moment n and the positioning error b of the drone GPS sensor within △t, calculate T n Time error n The cumulative sum S(n) = S(n-1) + error n -b; otherwise, according to T n The position deviation error of the drone at this moment n and the positioning error b of the drone GPS sensor within △t, calculate T n Time error n The cumulative sum S(n) = error n -b; (4) Determine whether S(n) and a pre-set threshold th satisfy S(n) < th. If so, execute step (5); otherwise, let the spoofing speed V n of the UAV at time n ' = V n , and the spoofing position P n ' = P n , and execute step (6); (5) The attacker calculates T n The deceptive position of the drone at the moment P n ′ and deceptive speed V n ′: The attacker calculates the actual speed of the drone based on its velocity V n and the real position of the drone P n Spoofing position of drone P n ′ distance calculation T n The deceptive position of the drone at the moment P n ′, and according to any point Q(x,y) on the drone trajectory within △t to P n The distance between the drone and the real speed V in time △t n The relationship between the distance traveled and the slope of the tangent line on the drone trajectory at point Q(x,y) is established. n ′ and V n The differential equation of , and then solve the differential equation to get T n Time cheat speed V n ′The component V on the X-axis, Y-axis and Z-axis of the drone body coordinate system nx ′、V ny ′、V nz ', and execute step (6), wherein: V nx ′=V nx Among them, x and y represent T n The horizontal and vertical coordinates of any point Q on the UAV trajectory at time △t, |·| represents the modulo operation; (6) Obtaining the drone’s deceptive trajectory: The attacker uses T n The deceptive position of the drone at the moment P n ′ and deceptive speed V n 'After generating the GPS spoofing signal, amplify and forward it, and determine whether n = N. If so, sequentially connect the spoofing positions of the drone at N moments to obtain the spoofing trajectory of the drone; otherwise, set n = n + 1 and execute step (3).

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