Unmanned aerial vehicle cooperative positioning method and system in satellite denial environment

Abstract

The invention belongs to the technical field of navigation and positioning, and particularly discloses an unmanned aerial vehicle cooperative positioning method and system in a satellite denial environment. According to the invention, relative distance information between cluster unmanned aerial vehicles is utilized to design a cluster unmanned aerial vehicle cooperative positioning system architecture based on relative information assistance, and through the architecture, communication between an inertial navigation system and an unmanned aerial vehicle group can provide more reliable positioning service; and the positioning precision is optimized in combination with a selective correction adaptive particle filter algorithm. According to the method, the inertial navigation system is used for obtaining the position of each auxiliary unmanned aerial vehicle, the external source relative distance sensor is used for measuring the relative distance relative to the to-be-assisted unmanned aerial vehicle, then the observation position of the to-be-assisted unmanned aerial vehicle is obtained, and the result is substituted into the improved particle filter for filtering. The method is used for correcting the drift error of the inertial navigation system, so that the positioning precision of cooperative positioning in the denial environment is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of navigation and positioning, and relates to a method and system for collaborative positioning of unmanned aerial vehicles in a satellite denial environment. Background Art

[0002] In recent years, cooperative navigation technology of unmanned aerial vehicles has been applied in different fields. As a small, low-cost self-organizing intelligent agent that can interact with surrounding individuals, unmanned aerial vehicles are widely used in agriculture, rescue, military and other fields to perform detection, tracking, commercial performance and other tasks. Cooperative navigation is a navigation technology in a multi-agent system, which aims to improve the navigation accuracy, robustness and task execution efficiency of the overall system through information sharing, data fusion and collaboration among multiple agents (such as unmanned aerial vehicles, robots, etc.). Compared with single-machine navigation, cooperative navigation can achieve higher-precision positioning, path planning and cooperative task execution in complex environments (such as limited GPS signals, interference or dynamic obstacles, etc.) through inter-machine communication, distributed computing and environmental perception.

[0003] Collaborative positioning is the core of collaborative navigation. It enables multiple intelligent agents to accurately determine their relative positions, providing a key foundation for collaborative navigation. Collaborative positioning algorithms are the key technical means to achieve collaborative positioning and complete subsequent navigation tasks. Current algorithms include Kalman filter algorithms, particle filter algorithms, factor graphs, machine learning, and so on.

[0004] Kalman filtering is an optimal estimation method based on the state space model of a linear system. It continuously estimates and corrects state variables by using the system's dynamic equations and observation equations through two steps: prediction and update. However, the algorithm has high requirements on the accuracy of the system model. When there is a large deviation between the actual system and the model, the filtering performance will deteriorate.

[0005] Particle filtering is a nonlinear filtering algorithm based on Monte Carlo simulation. It represents the probability distribution by randomly sampling a large number of particles in the state space, updates the weights of the particles according to the sensor measurement values, and then obtains the estimated value of the state through operations such as resampling. However, this algorithm requires a large number of particles to ensure the accuracy of the estimation, and its real-time performance is relatively poor. When applied in high-dimensional state space, particle degradation problems may occur.

[0006] In an environment where the global navigation satellite system is denied, it is difficult to meet the high-precision positioning requirements by relying solely on the inertial navigation system. Summary of the invention

[0007] The purpose of the present invention is to propose a method for collaborative positioning of UAVs in a satellite denial environment. The method obtains prediction information and observation information of the UAV to be assisted by using endogenous inertial and exogenous relative distance sensors onboard the UAV group, and performs filtering processing by a selectively modified adaptive particle filtering algorithm, thereby improving the collaborative positioning accuracy.

[0008] In order to achieve the above object, the present invention adopts the following technical scheme: A method for cooperative positioning of unmanned aerial vehicles in a satellite denial environment comprises the following steps: Step 1. For each drone to be assisted in the drone group, obtain its initial position. The process is as follows: Firstly, three auxiliary UAVs are selected and the position of each auxiliary UAV is obtained respectively; then the distance between each auxiliary UAV and the UAV to be assisted is measured, and the position of the UAV to be assisted is calculated by the least square method; The drone group includes at least three auxiliary drones with a first precision inertial navigation system and at least one drone to be assisted with a second precision inertial navigation system, and a distance sensor is arranged on the auxiliary drone; Step 2. After obtaining the position of the UAV to be assisted in step 1, its flight trajectory is obtained; the flight trajectory of the UAV to be assisted is used as observation information, and its own inertial navigation predicted trajectory is filtered based on the selective correction adaptive particle filter algorithm, and the inertial navigation error is corrected by feedback, so as to finally realize the collaborative positioning of the UAV to be assisted; The accuracy of the first-precision inertial navigation system is higher than the accuracy of the second-precision inertial navigation system.

[0009] In step 2, the selectively modified adaptive particle filter algorithm introduces a high-weight particle fine-tuning strategy between the weight calculation and resampling steps to improve the estimation accuracy, alleviate the particle degradation and impoverishment problems, and optimize the computational efficiency.

[0010] The process of fine-tuning the high-weight particle strategy is as follows: I. First, give the screening threshold R and adjustment factor of high-weight particles ; II. After the weight calculation step to update the particle state weight, perform the following operations: II.1. Screening high-weight particles. Particles that meet the following conditions are considered high-weight particles: ; Set the high weight particle index set for: ;in, is the particle weight; II.2. Calculating the center position of high-weight particles , the formula is as follows: ; in, represents the particle state, is the number of high-weight particles; II.3. Setting the low-weight particle index set for: ; The low-weight particles move closer to the high-weight center position, and the calculation formula for updating the particle state is as follows: , ; in, is the updated particle state; When the algorithm is repeated next time, the updated particle state will be used as the initial value for state propagation.

[0011] In addition, based on the above-mentioned UAV collaborative positioning method in a satellite denial environment, the present invention also proposes a corresponding UAV collaborative positioning system in a satellite denial environment, which adopts the following technical solutions: A UAV collaborative positioning system in a satellite-denied environment, including a ground control center and a group of UAVs; The drone group includes at least three auxiliary drones with a first precision inertial navigation system and at least one drone to be assisted with a second precision inertial navigation system, and a distance sensor is arranged on the auxiliary drone; A computer device is provided at the ground control center; wherein the position information of the assisting UAV measured by the assisting UAV and the distance information between the assisting UAV and the UAV to be assisted are transmitted to the computer device at the ground control center; The computer device includes a memory and one or more processors; the memory stores executable code, and when the processor executes the executable code, it is used to implement the steps of the UAV collaborative positioning method in a satellite denial environment as described above.

[0012] The present invention has the following advantages: As described above, the present invention relates to a method and system for cooperative positioning of unmanned aerial vehicles in a satellite denial environment. The cooperative positioning method uses the relative distance information between clustered unmanned aerial vehicles to design a clustered unmanned aerial vehicle cooperative positioning system architecture based on relative information assistance. Through this architecture, the communication between the inertial navigation system and the unmanned aerial vehicle group can provide more reliable positioning services, and combine the selective correction adaptive particle filter algorithm (SCA-PF) to optimize the positioning accuracy. The method of the present invention uses the inertial navigation system to obtain the own position of each unmanned aerial vehicle, and uses an exogenous relative distance sensor to measure the relative distance relative to the unmanned aerial vehicle to be assisted, and then obtains the observed position of the unmanned aerial vehicle to be assisted, and brings the observation result into the improved particle filter for filtering, which is used to correct the drift error of the inertial navigation system, thereby improving the positioning accuracy of cooperative positioning in a denial environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a schematic diagram of the position of a drone in an embodiment of the present invention; Figure 2 It is a processing flow chart of the UAV collaborative positioning method in a satellite denial environment according to an embodiment of the present invention; Figure 3 The three actual flight trajectory diagrams of the assisting UAV and the UAV to be assisted shown in the embodiment of the present invention; Figure 4 This is a three-dimensional distance error analysis diagram after the observation trajectory is filtered by SCA-PF to improve the positioning accuracy in an embodiment of the present invention; Figure 5 This is a comparison diagram of the root mean square error of the observed trajectory after the SCA-PF filtering improves the positioning accuracy in the embodiment of the present invention. DETAILED DESCRIPTION

[0014] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment 1 describes a method for cooperative positioning of UAVs in a satellite denial environment, which obtains prediction information and observation information based on the perception mechanism of the inertial and relative distance sensors on the UAV group, and performs cooperative positioning of UAVs in combination with an improved particle filter. Among them, the improved particle filter is based on the Selectively Corrected Adaptive-Particle Filter (SCA-PF) algorithm, which significantly improves the estimation accuracy, alleviates the particle degradation and impoverishment problems, and optimizes the calculation efficiency, making the filtering process more robust and accurate.

[0015] like Figure 2 As shown, the UAV collaborative positioning method in a satellite denial environment in this embodiment includes the following steps: Step 1. For each drone to be assisted in the drone group, obtain its initial position. The process is as follows: Firstly, three auxiliary UAVs are selected and the position of each auxiliary UAV is obtained respectively; then the distance between each auxiliary UAV and the UAV to be assisted is measured, and the position of the UAV to be assisted is calculated by the least square method.

[0016] The drone group includes at least three auxiliary drones with a first-precision inertial navigation system and at least one drone to be assisted with a second-precision inertial navigation system, and a distance sensor is arranged on the auxiliary drone.

[0017] The accuracy of the first precision inertial navigation system is higher than that of the second precision inertial navigation system. In this embodiment, the first precision inertial navigation system is a high precision inertial navigation system, and the second precision inertial navigation system is a low precision inertial navigation system.

[0018] by Figure 1 Take the three high-precision inertial navigation system-assisted drones shown in the figure as an example.

[0019] In order to improve the positioning accuracy of the low-precision inertial navigation system to be assisted by the UAV, the high-precision autonomous positioning of the assisted UAV is used to obtain its own position, and the distance sensor is used to measure the distance information between it and the UAV to be assisted. .

[0020] Take auxiliary drone 1 as an example, its position is known And the distance between it and the drone to be assisted , the positions of auxiliary UAV 2 and auxiliary UAV 3 and their distances to the UAV to be assisted can be obtained similarly.

[0021] By bringing this information into the three-dimensional coordinate system, the position coordinates of the drone to be assisted can be calculated through mathematical models. Then, SCA-PF is used to filter feedback to correct the inertial navigation error. The overall steps are as follows: Figure 2 shown.

[0022] In three-dimensional space, the actual position of the UAV to be assisted is , but the location is unknown.

[0023] In order to estimate the position of the UAV to be assisted, three high-precision positioning auxiliary UAVs are used to measure the distance and calculate their positions by the least squares method. The positions of the three auxiliary UAVs are known, which are: , , .

[0024] The steps for distance sensor to calculate distance based on signal arrival time (TOA) are as follows: Step a1. Record the signal sending and receiving time. The signal sending time is , the signal receiving time is .

[0025] Step a2. Calculate the time difference: .

[0026] Step a3. Determine the signal propagation speed, define the signal speed as c, usually the speed of light .

[0027] Step a4. Calculate the distance .

[0028] Through the above steps a1 to a4, the relative distance between the assisting UAV and the UAV to be assisted can be calculated. .

[0029] Next, according to the Euclidean distance formula, the distance from the auxiliary drone to the three auxiliary drones is: .

[0030] in is the actual measured distance, i.e. the distance from the assisted UAV to the i-th assisted UAV, i=1,2,3, is the ranging noise, which can be solved by the least squares method: .

[0031] Finally, the position of the UAV to be assisted is calculated. After obtaining the flight trajectory of the UAV to be assisted, it is used as observation information for filtering to improve the positioning accuracy and correct the error information of the inertial navigation system.

[0032] Step 2. After obtaining the position of the UAV to be assisted in step 1, its flight trajectory is obtained.

[0033] The flight trajectory of the UAV to be assisted is used as observation information, and its own inertial navigation prediction trajectory is filtered based on the selective correction adaptive particle filter algorithm. The inertial navigation error is corrected by feedback to achieve collaborative positioning of the UAV to be assisted.

[0034] Particle Filter (PF) is a nonlinear filtering algorithm based on the Monte Carlo method, which is suitable for state estimation problems in non-Gaussian noise environments. The core idea of ​​the PF algorithm is to approximate the posterior probability distribution of the system through a group of weighted particles. However, during the update process, the number of high-weight particles will gradually decrease, and eventually most of the weights will be concentrated on a few particles, which will reduce the diversity of the particle group and cause distortion of the estimation results.

[0035] The improved particle filter algorithm in this embodiment (i.e., the selectively modified adaptive particle filter algorithm) significantly improves the estimation accuracy by introducing a high-weight particle fine-tuning strategy between the weight calculation and resampling steps, effectively alleviates the particle degradation and impoverishment problems, and optimizes the computational efficiency, making the filtering process more robust and accurate.

[0036] Specifically, the processing process of the selectively corrected adaptive particle filter algorithm in this embodiment is as follows: Step 2.1. Initialization.

[0037] At the initial time t=0, N particles are randomly selected from the prior distribution and each particle is given the same weight to represent the various position states of the drone, where N is a natural number.

[0038] Know the actual position of the drone to be assisted for: .

[0039] The initial state of each particle is generated by adding random variables around its true position.

[0040] For the i-th particle, the three components of its initial position along the x, y, and z directions are: .

[0041] in is a random variable, , , Indicates the position of the UAV to be assisted at the first time. Represents the position of the ith particle in three dimensions at the first time.

[0042] Step 2.2. Prediction (state propagation).

[0043] For each time step , according to the state of the system, the state of each particle is propagated, that is, the next flight positioning is inferred based on the previous position information and the current motion state. The process is as follows: .

[0044] in, is the position of the ith particle in three dimensions at time t; , , is the position of the ith particle in three dimensions at time t-1; , , is the speed information at time t-1.

[0045] Step 2.3. Update (weight calculation).

[0046] Step 2.3. Update the weight of each particle according to the obtained observation value of the UAV to be assisted and the state of each particle, and then normalize the updated weight of each particle.

[0047] Assume that the observation value obtained by the auxiliary UAV is , the particle is .

[0048] Update the weight formula for each particle. The calculation formula is as follows: .

[0049] in, is the weight, is the similarity between the observed value and the particle, where Calculate using Euclidean distance and The distance between is the standard deviation of the measurement noise.

[0050] Then the weights are normalized, and the normalization formula is as follows: .

[0051] Step 2.4. Particle fine-tuning.

[0052] Introduce high-weight particle fine-tuning strategy to fine-tune particle status.

[0053] During the update process, the number of high-weight particles will gradually decrease, and eventually most of the weights will be concentrated on a few particles, which will reduce the diversity of the particle group and cause distortion of the estimation results. Innovative improvements are introduced after the weight update to alleviate this problem. The weight update step is to update the weight of each particle according to the measurement value at the current moment. The obtained weight reflects the degree of match between the particle and the current measurement value. If optimization is performed before the weight is updated, the optimization operation may not accurately guide the particles to the true state because the weight has not yet reflected the information of the current measurement value. The resampling operation will copy and delete particles according to their weights, causing the distribution of particles to change. If low-weight particle adjustments are performed after resampling, the diversity of particles has been reduced at this time, which may lead to insignificant fine-tuning effects, and even cause more concentration effects, resulting in reduced exploration capabilities. The improved particle filter algorithm significantly improves the estimation accuracy by introducing a high-weight particle fine-tuning strategy after weight calculation, alleviates the problems of particle degradation and impoverishment, and optimizes the computational efficiency, making the filtering process more robust and accurate.

[0054] The process of fine-tuning the high-weight particle strategy is as follows: I. First, give the screening threshold R and adjustment factor of high-weight particles .

[0055] II. After the weight calculation step to update the particle state weight, perform the following operations: II.1. Screening high-weight particles. Particles that meet the following conditions are considered high-weight particles: ; Set the high weight particle index set for: ;in, is the particle weight.

[0056] II.2. Calculating the center position of high-weight particles , the formula is as follows: .

[0057] in, represents the particle state, is the number of high-weight particles.

[0058] II.3. Setting the low-weight particle index set for: ; The low-weight particles move closer to the high-weight center position, and the calculation formula for updating the particle state is as follows: , .

[0059] in, is the updated particle state.

[0060] The next time the algorithm is repeated, the updated particle state will be used as the initial value for state propagation.

[0061] Step 2.5. Resampling.

[0062] Resample the particles after the state fine-tuning in step 2.4, and re-extract N particles according to the weights of the particles, so that particles with large weights are copied multiple times and particles with small weights are eliminated.

[0063] In order to avoid the problem of particle degradation (i.e. the weights of most particles approach zero), resampling is required. N particles are re-extracted according to the weights of the particles, so that particles with larger weights are replicated multiple times and particles with smaller weights are eliminated.

[0064] Step 2.6. State estimation.

[0065] According to the updated particle set after resampling in step 2.5, the state estimation value of the system is calculated by weighted average, and the most likely location of the drone is deduced. The formula obtained by weighted average is as follows: ;

[0066] in, represents the weight of the i-th particle at time t, is the estimated value of the system state.

[0067] Step 2.7. Increase t by 1 and repeat steps 2.2 to 2.6 until all time steps are completed, and the accurate position after filtering of each time step is obtained, and then the flight trajectory of the UAV to be assisted is obtained.

[0068] The improved SCA-PF in this embodiment has the following advantages: 1. Effectively overcome the problem of distorted estimation results caused by reduced diversity of particle swarms, avoid misleading caused by abnormalities of single particles when calculating the center position, and enhance the convergence and estimation accuracy on the basis of classic PF to make it more robust.

[0069] 2. Different from the conventional improvement steps, the present invention performs fine-tuning after the weight update and before resampling, which not only avoids the problem that the optimization operation may not accurately guide the particles to the true state because the weight has not yet reflected the information of the current measurement value, but also prevents the fine-tuning effect from being unclear due to the reduction of particle diversity after resampling.

[0070] 3. The improvement of the common weight approach strategy is to move low-weight particles closer to high-weight particles, which inevitably causes the particles to be too concentrated and lose diversity, which reduces the particle exploration ability and cannot adapt to the changes in the trajectory in time. The SCA-PF proposed in the present invention retains the high-weight particles above the threshold and only adjusts the low-weight particles, which not only optimizes the distribution of particles, but also maintains the particle diversity, improves the estimation accuracy and alleviates the problem of lack of particle diversity.

[0071] In addition, in order to verify the effectiveness of the method of the present invention, the following simulated flight trajectory experiment is also given.

[0072] In the simulated flight trajectory experiment, the assisted UAV is equipped with a low-precision inertial navigation system, resulting in low positioning accuracy; while the assisting UAV is equipped with a high-precision inertial navigation system, which has a higher positioning accuracy. Figure 3 shows the real trajectories of the three assisting UAVs and the assisted UAV. The observed trajectory is obtained by measuring the distance using the least squares method. After the SCA-PF filter improves the positioning accuracy, the three-dimensional distance error and the mean square error are shown in Figure 4 and Figure 5, respectively. Figure 5 shown.

[0073] Table 1 Comparison of RMS filtering errors

[0074] Table 1 shows the observation values ​​of the assisted UAV and the results after filtering by the SCA-PF method of the present invention. Schematic diagram of the comparison of root mean square filtering errors. It can be seen from Table 1 that the improved SCA-PF method of the present invention can reduce the observation value error by about 70%, and its overall filtering accuracy is high, which can effectively reduce the error and has good filtering performance.

[0075] The selectively corrected adaptive particle filter algorithm proposed in the present invention can adaptively adjust according to the weight of the current particle, ensure that the adjusted particle can accurately reflect the current state after the weight is updated, and calculate its center position, correct the low-weight particles, and make them move closer to the center position to improve the filtering effect, avoiding the wrong guidance due to the influence of a single abnormal particle, and then resampling, which can make them converge to the high-weight area without completely discarding the low-weight particles, improve the stability of state estimation, and maintain a certain exploration ability. The algorithm keeps the high-weight particles unchanged and only adjusts the low-weight particles, while enhancing the positioning accuracy, maintaining the diversity of particles.

[0076] The method of the present invention has a wide range of application scenarios, is convenient, and is suitable for cooperative navigation of unmanned aerial vehicles under satellite navigation denial.

[0077] Example 2 Embodiment 2 of the present invention relates to a UAV collaborative positioning system in a satellite denial environment. The UAV collaborative positioning system in a satellite denial environment includes a ground control center and a group of UAVs.

[0078] The drone group includes at least three auxiliary drones with a first-precision inertial navigation system and at least one drone to be assisted with a second-precision inertial navigation system, and a distance sensor is arranged on the auxiliary drone.

[0079] Computer equipment is provided at the ground control center; the position information of the assisting UAV measured by the assisting UAV and the distance information between the assisting UAV and the UAV to be assisted are transmitted to the computer equipment at the ground control center.

[0080] The computer device includes a memory and one or more processors; the memory stores executable code, and when the processor executes the executable code, it is used to implement the steps of the UAV collaborative positioning method in a satellite denial environment in the above-mentioned embodiment 1.

[0081] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A method for cooperative positioning of unmanned aerial vehicles in a satellite denial environment, characterized in that: The steps include: Step 1. For each drone to be assisted in the drone group, obtain its initial position. The process is as follows: Firstly, three auxiliary UAVs are selected and the position of each auxiliary UAV is obtained respectively; then the distance between each auxiliary UAV and the UAV to be assisted is measured, and the position of the UAV to be assisted is calculated by the least square method; The drone group includes at least three auxiliary drones with a first precision inertial navigation system and at least one drone to be assisted with a second precision inertial navigation system, and a distance sensor is arranged on the auxiliary drone; Step 2. After obtaining the position of the UAV to be assisted in step 1, its flight trajectory is obtained; the flight trajectory of the UAV to be assisted is used as observation information, and its own inertial navigation predicted trajectory is filtered based on the selective correction adaptive particle filter algorithm, and the inertial navigation error is corrected by feedback, so as to finally realize the collaborative positioning of the UAV to be assisted; The accuracy of the first-precision inertial navigation system is higher than the accuracy of the second-precision inertial navigation system.

2. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 1, characterized in that: In step 2, the selectively modified adaptive particle filter algorithm introduces a high-weight particle fine-tuning strategy between the weight calculation and resampling steps to improve the estimation accuracy, alleviate the particle degradation and impoverishment problems, and optimize the computational efficiency.

3. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 2, characterized in that: In step 2, the processing process of the high-weight particle fine-tuning strategy is as follows: I. First, give the screening threshold R and adjustment factor of high-weight particles ; II. After the weight calculation step to update the particle state weight, perform the following operations: II.

1. Screening high-weight particles. Particles that meet the following conditions are considered high-weight particles: ; Set the high weight particle index set for: ;in, is the particle weight; II.

2. Calculating the center position of high-weight particles , the formula is as follows: ； in, represents the particle state, is the number of high-weight particles; II.

3. Setting the low-weight particle index set for: ; The low-weight particles move closer to the high-weight center position, and the calculation formula for updating the particle state is as follows: ， ； in, is the updated particle state; When the algorithm is repeated next time, the updated particle state will be used as the initial value for state propagation.

4. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 3, characterized in that: In step 2, the processing process of selectively correcting the adaptive particle filter algorithm is as follows: Step 2.

1. At the initial time t=0, randomly select N particles from the prior distribution and assign the same weight to each particle to represent the various position states where the drone will appear, where N is a natural number; Step 2.

2. For each time step , according to the state of the system, the state of each particle is propagated, that is, the next flight positioning is inferred based on the previous position information and the current motion state; Step 2.

3. Update the weight of each particle according to the obtained observation value of the UAV to be assisted and the state of each particle, and then normalize the updated weight of each particle; Step 2.

4. Introduce high-weight particle fine-tuning strategy to fine-tune particle state; Step 2.

5. Resample the particles after state fine-tuning. According to the weights of the particles, re-extract N particles so that particles with large weights are replicated multiple times and particles with small weights are eliminated. Step 2.

6. State estimation: Based on the updated particle set after resampling in step 2.5, the system state estimation value is calculated by weighted average to deduce the most likely location of the drone. Step 2.

7. Increase t by 1 and repeat steps 2.2 to 2.6 until all time steps are completed, and the accurate position after filtering of each time step is obtained, and then the flight trajectory of the UAV to be assisted is obtained.

5. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 4, characterized in that: In step 2.1, the real position of the UAV to be assisted is known. for: ;The initial state of each particle is generated by adding random variables near its true position; For the i-th particle, the three components of its initial position along the x, y, and z directions are: ； in is a random variable, , , Indicates the position of the UAV to be assisted at the first time. Represents the position of the ith particle in three dimensions at the first time.

6. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 5, characterized in that: In step 2.2, the process of state propagation for each particle is as follows: ； in is the position of the ith particle in three dimensions at time t; , , is the position of the ith particle in three dimensions at time t-1; , , is the speed information at time t-1.

7. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 6, characterized in that: In step 2.3, the observation value obtained by the auxiliary drone is assumed to be , the particle is ; Update the weight formula of each particle. The calculation formula is as follows: ； in, is the weight, is the similarity between the observed value and the particle, where Calculate using Euclidean distance and The distance between is the standard deviation of the measurement noise.

8. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 7, characterized in that: In step 2.6, the calculation formula for obtaining the estimated value of the system state by weighted average is as follows: ； in, represents the weight of the i-th particle at time t, is the estimated value of the system state.

9. The method for cooperative positioning of unmanned aerial vehicles in a satellite-denied environment according to claim 1, characterized in that: In step 1, the distance sensor calculates the distance between each auxiliary UAV and the UAV to be assisted according to the signal arrival time; and obtains the distance between the UAV to be assisted and the three auxiliary UAVs according to the Euclidean distance formula; The least square method is used to solve the problem and finally the position of the UAV to be assisted is calculated.

10. A UAV collaborative positioning system in a satellite denial environment, including a ground control center and a group of UAVs; The drone group includes at least three auxiliary drones with a first precision inertial navigation system and at least one drone to be assisted with a second precision inertial navigation system, and a distance sensor is arranged on the auxiliary drone; in, The accuracy of the first precision inertial navigation system is higher than the accuracy of the second precision inertial navigation system; A computer device is provided at the ground control center; wherein the position information of the assisting UAV measured by the assisting UAV and the distance information between the assisting UAV and the UAV to be assisted are transmitted to the computer device at the ground control center; The computer device includes a memory and one or more processors; The memory stores executable code, wherein when the processor executes the executable code, it is used to implement the steps of the method for collaborative positioning of unmanned aerial vehicles in a satellite denial environment as described in any one of claims 1 to 9 above.

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