A self-correction method for UAV cluster paths based on air-ground multi-dimensional data fusion
Through the multi-dimensional data fusion of air-ground and multi-objective collaborative path optimization algorithm, combined with the improved Bayesian filtering algorithm, the path self-correction of the drone cluster in complex environments is achieved, the problem of path deviation in air-ground collaborative operations is solved, and the flexibility and reliability of task execution are improved.
Patent Information
- Application Number
- CN202510147228.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-11
- Publication Date
- 2025-04-25
- Estimated Expiration
- 2045-02-11
AI Technical Summary
In air-to-ground collaborative operations, the drone cluster faces dynamic changes in ground mobile platforms and uncertainties in complex environmental factors, resulting in flight path deviations, increasing the difficulty of path planning and system complexity.
The self-correction method of drone cluster paths based on air-to-ground multi-dimensional data fusion is adopted. Through the coordinated work of aerial drones and ground mobile platforms, a variety of data is collected in real time, combined with multi-objective collaborative path optimization algorithm and improved Bayesian filtering algorithm, automatically compensate for path deviations and correct flight paths.
It significantly improves the path planning and self-correction capabilities of drone clusters in complex environments, improves the flexibility and reliability of air-to-ground collaborative tasks, and ensures high tracking accuracy.
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Figure CN119618228B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of unmanned aerial vehicle cluster path planning, and in particular to a unmanned aerial vehicle cluster path self-correction method based on air-ground multi-dimensional data fusion. Background Art
[0002] With the rapid development of drone technology, drone swarms are increasingly used in military reconnaissance, disaster relief, logistics and distribution, and other fields. However, in air-ground collaborative operations, drone swarms need to face the dynamic changes of ground mobile platforms and complex and changing environmental factors, which brings huge challenges to the path planning and collaborative control of drones. At present, traditional drone path planning methods usually rely on prior knowledge of the precise motion model of ground mobile targets, which is often difficult to achieve in practical applications because the motion of ground mobile platforms is often affected by many factors, including the environment, operator intentions, obstacles, etc., which makes it difficult to accurately predict the motion model. In addition, even if the motion model can be established, it needs to be continuously updated and maintained to adapt to the ever-changing actual situation, which undoubtedly increases the complexity and cost of the system.
[0003] In air-ground collaborative tasks, the dynamic changes of ground mobile platforms and the uncertainty of environmental factors make it more difficult to accurately track and coordinate drone clusters. The movement of ground mobile platforms may include changes in speed, adjustments in direction, and even sudden turns, which may cause the flight path of the drone cluster to deviate from the actual target. At the same time, environmental factors such as wind direction and terrain will also affect the flight of drones, further increasing the difficulty of path planning. In order to improve the path planning and self-correction capabilities of drone clusters in complex environments, the present invention develops a drone cluster path self-correction method based on air-ground multidimensional data fusion. Summary of the invention
[0004] The purpose of the present invention is to provide a UAV cluster path self-correction method based on air-ground multi-dimensional data fusion, so as to overcome the deviation between the flight path and the actual target when the aerial UAV cluster and the ground mobile platform work together, and improve the flexibility and reliability of task execution under air-ground collaboration.
[0005] To achieve the above object, the present invention provides a method for self-correcting the path of a UAV cluster based on air-ground multi-dimensional data fusion, comprising the following steps:
[0006] Step S1: Collecting open space data, specifically including:
[0007] Acquire image data, target endpoint location information, and drone position and posture information through the image acquisition equipment and sensor detection carried out by the aerial drone cluster;
[0008] The interactive position, speed information, and mission target information between the ground mobile platforms are obtained by carrying sensors on the ground mobile platforms; wherein the mission target information includes the mission target position and the mission type; the sensors include laser sensors, visual sensors, and inertial measurement units;
[0009] Step S2: Based on the mission target information, the ground mobile platform takes the UAV's minimum energy consumption path, the UAV's flight path and the ground mobile platform's rendezvous point as decision variables, and takes minimizing the mission cost and mission completion time as the optimization goal; the flight path of the UAV cluster and the rendezvous point of the UAV and the ground mobile platform are solved through a multi-objective collaborative path optimization algorithm;
[0010] Step S3: Based on the open space data, combined with the information features of the laser sensor and the visual sensor, a sensor uncertainty probability model is established; a three-dimensional octree map is constructed, and the improved Bayesian filter denoising is used to fuse multiple sensor data and iteratively update the occupancy probability of each node in the three-dimensional octree map;
[0011] Step S4: The UAV cluster uses the inertial measurement unit data of the ground mobile platform coordinate system as the conversion of relative position and speed, automatically compensates for the path deviation caused by environmental changes or ground platform movement, and corrects the flight path of the UAV cluster.
[0012] Furthermore, the step S2 specifically includes the following steps:
[0013] S21: Based on the mission target information, the ground mobile platform takes the UAV flight path, the meeting point of the UAV and the ground mobile platform as decision variables, and minimizes the mission cost and mission completion time as the optimization goal to establish the objective function , as follows:
[0014] ;
[0015] In the formula, Indicates the flight path of the drone; It represents the meeting point of the UAV and the ground mobile platform; Represents the flight path of the drone energy consumption costs; Indicates that the ground moving platform moves from the starting point to the meeting point Costs; are the cost coefficients of UAV and ground mobile platform respectively; Indicates the average flight speed of the drone; is the distance between two points on the i-th and i+1-th task paths; It is the distance from the current position of the ground platform to the meeting point distance; is the moving speed of the ground mobile platform; ∑ represents the sum; Indicates minimization of the objective function;
[0016] S22: Through the multi-objective collaborative path optimization algorithm, the proposed flight path of the UAV and the meeting point of the UAV and the ground mobile platform are solved:
[0017] S221: Set the initial solution set:
[0018] Determine the take-off point for the drone and the mission target location , set the average flight speed of the drone and the moving speed of the ground mobile platform , generating an initial solution set, each solution represents a possible UAV flight path and rendezvous point with the ground mobile platform;
[0019] S222: According to the task target location and task type, the initial solution set is divided into multiple subspaces to obtain multiple local solutions; a new global solution is generated based on the multiple local solutions:
[0020] The initial solution set is divided into multiple subspaces according to the task objectives, a reference local search algorithm is set in each subspace, and an appropriate reference local search algorithm is selected according to the task type to obtain multiple local solutions;
[0021] The initial solution set is decomposed into multiple subspaces:
[0022] ;
[0023] In the formula, represents a subspace; is the target vector; is the m-dimensional target space; is a reference point; and is the unit direction vector on the two-dimensional plane; N is the number of unit direction vectors;
[0024] Multiple local solutions are collaboratively aggregated into a new global solution, specifically:
[0025] ;
[0026] In the formula, represents the maximum value of the solutions of each aggregated subspace, indicating the global solution; represents the number of subspaces; represents the reference point of the kth subspace; Represents the minimum of multiple local solutions; represents the unit direction vector of the kth subspace; Represents an aggregate function; No. The solution of a subspace.
[0027] Furthermore, the step S3 specifically includes the following steps:
[0028] S31: Based on the air-ground data, combined with the information features of the laser sensor and the visual sensor, the uncertainty probability models of the laser sensor and the visual sensor are established respectively. The specific expressions are as follows:
[0029] ;
[0030] In the formula, is the uncertainty probability model of the laser sensor; is the uncertainty probability model of the visual sensor; is the status of the UAV system; Represent the observation models of laser sensor and visual sensor respectively; They represent the observation functions of the laser sensor and the visual sensor respectively; Defined as a verticality indicator function and only if hour, is the angle between the sensor and the ground; To set the threshold; Defined as an elevation filter and only hour, is the elevation value observed by the sensor; To set the elevation threshold; represents Gaussian distribution; represent the noise variance of laser sensor and visual sensor respectively;
[0031] in The calculation process is as follows:
[0032] ;
[0033] In the formula, and It is represented as the observation noise of laser sensor and vision sensor;
[0034] S32: Construct a three-dimensional octree map, and use the improved Bayesian filter to denoise and fuse multiple sensor data and update the occupancy probability of each map node in the three-dimensional octree map:
[0035] S321: Initialize the three-dimensional octree map and define an occupancy probability for each map node in the octree. and a free probability ;
[0036] S322: Use the improved Bayesian filter noise to fuse multiple sensor data and update the occupancy probability of each map node in the three-dimensional octree map to obtain the posterior probability; the specific expression is shown in the following formula:
[0037] ;
[0038] In the formula, The nodes are In time The state mean and covariance at time instant; Represents the posterior probability of the occupancy state of the 3D octree map node based on the sensor observation information.
[0039] Furthermore, the step S4 specifically includes the following steps:
[0040] Update the speed and acceleration of the drone based on the inertial measurement unit data of the ground mobile platform coordinate system:
[0041] The speed of the drone relative to the ground platform :
[0042] ;
[0043] In the formula, Represents the correlation matrix between the drone coordinate system and the ground coordinate system; Represents the velocity vector of the UAV relative to the ground mobile platform; Relative velocity vector of the ground mobile platform; The position vector representing the drone relative to the ground mobile platform; is the angular velocity of the ground platform coordinate system;
[0044] The acceleration of the drone relative to the ground mobile platform :
[0045] ;
[0046] In the formula, They represent the relative angular acceleration of the UAV body coordinate system, the world coordinate system, and the ground mobile platform coordinate system respectively.
[0047] Compared with the prior art, the present invention has the following beneficial effects:
[0048] The present invention realizes the collaborative work of aerial drone clusters and ground mobile platforms to obtain real-time spatial environment image information, target endpoint information, drone position and posture information, and interactive position and speed information between ground mobile platforms. The ground platform uses a multi-objective collaborative path optimization algorithm to determine the flight path and convergence point of the drone, and combines laser and visual sensor data to fuse multi-sensor data through an improved Bayesian filtering algorithm to update the occupancy probability of map nodes. The drone automatically compensates for path deviations and corrects the flight path based on the map data analyzed by the ground platform and its own inertial measurement unit data. The present invention significantly enhances the collaborative operation efficiency of drone clusters and ground platforms, improves the flexibility and reliability of task execution, effectively responds to deviations caused by environmental changes or ground platform movement, and maintains high tracking accuracy.
[0049] The present invention updates the speed and acceleration of the UAV through the coordinate system of the ground mobile platform without making assumptions about the movement of the ground mobile platform. The UAV automatically compensates for the path deviation considering the movement of the ground mobile platform. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Figure 1 This is a flow chart of a method for self-correcting the path of a UAV cluster based on air-ground multi-dimensional data fusion according to the present invention;
[0051] Figure 2 Plan a route map for air-to-ground coordinated drone swarms;
[0052] Figure 3 This is the path error diagram. DETAILED DESCRIPTION
[0053] In order to describe the present invention in more detail, the above-mentioned UAV path planning method is verified below in combination with the accompanying drawings and specific implementation cases.
[0054] Example 1
[0055] The present invention provides a method for self-correcting the path of a UAV cluster based on air-ground multi-dimensional data fusion. Figure 1 As shown, the following steps are included:
[0056] Step S1: Collecting open space data, specifically including:
[0057] Acquire image data, target endpoint location information, and drone position and posture information through the image acquisition equipment and sensor detection carried out by the aerial drone cluster;
[0058] The interactive position, speed information, and mission target information between the ground mobile platforms are obtained by carrying sensors on the ground mobile platforms; wherein the mission target information includes the mission target position and the mission type; the sensors include laser sensors, visual sensors, and inertial measurement units;
[0059] Specifically, the drone is equipped with a high-definition camera, and the GPS and IMU sensors obtain image data, target endpoint location information, drone position and posture information, and other information data and transmit it to the ground mobile platform control station; the ground mobile platform uses the built-in radar and laser rangefinder sensors to obtain real-time interactive position and speed information with other mobile platforms and obstacles and transmit it to the ground mobile platform control station.
[0060] Step S2: Based on the mission target information, the ground mobile platform takes the UAV flight path, the UAV flight path and the ground mobile platform rendezvous point as decision variables, and takes minimizing the mission cost and mission completion time as the optimization goal; the flight path of the UAV cluster and the rendezvous point of the UAV and the ground mobile platform are solved through a multi-objective collaborative path optimization algorithm;
[0061] S21: Based on the mission target information, the ground mobile platform takes the UAV flight path, the meeting point of the UAV and the ground mobile platform as decision variables, and minimizes the mission cost and mission completion time as the optimization goal to establish the objective function , as follows:
[0062] ;
[0063] In the formula, Indicates the flight path of the drone; It represents the meeting point of the UAV and the ground mobile platform; Represents the flight path of the drone energy consumption costs; Indicates that the ground moving platform moves from the starting point to the meeting point Costs; are the cost coefficients of UAV and ground mobile platform respectively; Indicates the average flight speed of the drone; is the distance between two points on the i-th and i+1-th task paths; It is the distance from the current position of the ground platform to the meeting point distance; is the moving speed of the ground mobile platform; ∑ represents the sum; Indicates minimization of the objective function;
[0064] S22: Through the multi-objective collaborative path optimization algorithm, the proposed flight path of the UAV and the meeting point of the UAV and the ground mobile platform are solved:
[0065] S221: Set the initial solution set:
[0066] Determine the take-off point for the drone and the mission target location , set the average flight speed of the drone and the moving speed of the ground mobile platform , generating an initial solution set, each solution represents a possible UAV flight path and rendezvous point with the ground mobile platform;
[0067] S222: According to the task target location and task type, the initial solution set is divided into multiple subspaces to obtain multiple local solutions; a new global solution is generated based on the multiple local solutions:
[0068] The initial solution set is divided into multiple subspaces according to the task objectives, a reference local search algorithm is set in each subspace, and an appropriate reference local search algorithm is selected according to the task type to obtain multiple local solutions;
[0069] The initial solution set is decomposed into multiple subspaces:
[0070] ;
[0071] In the formula, represents a subspace; is the target vector; is the m-dimensional target space; is a reference point; and is the unit direction vector on the two-dimensional plane; N is the number of unit direction vectors;
[0072] Multiple local solutions are collaboratively aggregated into a new global solution, specifically:
[0073] ;
[0074] In the formula, represents the maximum value of the solutions of each aggregated subspace, indicating the global solution; represents the number of subspaces; represents the reference point of the kth subspace; Represents the minimum of multiple local solutions; represents the unit direction vector of the kth subspace; Represents an aggregate function; No. The solution of a subspace.
[0075] Furthermore, the step S3 specifically includes the following steps:
[0076] Step S3: Based on the open space data, combined with the information features of the laser sensor and the visual sensor, a sensor uncertainty probability model is established; a three-dimensional octree map is constructed, and the improved Bayesian filter denoising is used to fuse multiple sensor data and iteratively update the occupancy probability of each node in the three-dimensional octree map;
[0077] S31: Based on the air-ground data, combined with the information features of the laser sensor and the visual sensor, the uncertainty probability models of the laser sensor and the visual sensor are established respectively. The specific expressions are as follows:
[0078] ;
[0079] In the formula, is the uncertainty probability model of the laser sensor; is the uncertainty probability model of the visual sensor; is the status of the UAV system; Represent the observation models of laser sensor and visual sensor respectively; They represent the observation functions of the laser sensor and the visual sensor respectively; Defined as a verticality indicator function and only if hour, is the angle between the sensor and the ground; To set the threshold; Defined as an elevation filter and only hour, is the elevation value observed by the sensor; To set the elevation threshold; represents Gaussian distribution; represent the noise variance of laser sensor and visual sensor respectively;
[0080] in The calculation process is as follows:
[0081] ;
[0082] In the formula, and It is represented as the observation noise of laser sensor and vision sensor;
[0083] S32: Construct a three-dimensional octree map, use improved Bayesian filtering to denoise and fuse multiple sensor data, and update the occupancy probability of each map node in the three-dimensional octree map:
[0084] S321: Initialize the three-dimensional octree map and define an occupancy probability for each map node in the octree. and a free probability ;
[0085] S322: Use the improved Bayesian filter noise to fuse multiple sensor data and update the occupancy probability of each map node in the three-dimensional octree map to obtain the posterior probability; the specific expression is shown in the following formula:
[0086] ;
[0087] In the formula, They are the nodes in the three-dimensional octree map In time The state mean and covariance at time instant; Represents the posterior probability of the occupancy probability of the 3D octree map node based on the sensor observation information.
[0088] It should be noted that the octree is a data structure used to represent a three-dimensional space, which recursively divides the space into eight quadrants (or sub-cubes). Each node represents a cubic area, which can be empty, occupied or unknown. The ground mobile platform initializes the three-dimensional octree map based on the sensor data and sets the resolution and size of the map.
[0089] Step S4: The drone cluster uses the inertial measurement unit data of the ground mobile platform coordinate system as the conversion of relative position and speed, automatically compensates for the path deviation caused by environmental changes or ground platform movement, and corrects the flight path of the drone cluster. Specifically, the following steps are included:
[0090] The speed and acceleration of the drone are updated based on the inertial measurement unit data of the ground mobile platform coordinate system. The specific expression is shown in the following formula:
[0091] The speed of the drone relative to the ground platform :
[0092] ;
[0093] In the formula, Represents the correlation matrix between the drone coordinate system and the ground coordinate system; Represents the velocity vector of the UAV relative to the ground mobile platform; Relative velocity vector of the ground mobile platform; The position vector representing the drone relative to the ground mobile platform; is the angular velocity of the ground platform coordinate system;
[0094] The acceleration of the drone relative to the ground mobile platform :
[0095] ;
[0096] In the formula, They represent the relative angular acceleration of the UAV body coordinate system, the world coordinate system, and the ground mobile platform coordinate system respectively.
[0097] Different from the traditional method, the velocity and acceleration of the UAV are updated through the coordinate system of the ground mobile platform without making assumptions about the motion of the ground mobile platform. The UAV automatically compensates for the path deviation considering the movement of the ground mobile platform.
[0098] Taking a 1100×1200 task area as an example, 11 task target locations are defined to verify the feasibility of the path self-correction method.
[0099] like Figure 2 As shown in the figure, the black line represents the moving path of the ground mobile platform, and the red line represents the flight path of the drone. The intersection of the lines represents the meeting point of the drone and the ground mobile platform.
[0100] like Figure 3 As shown in the figure, the blue dots represent the estimated path error of each mission target position caused by environmental factors or ground mobile platforms. Based on the mission target position, the ground platform uses the UAV flight path and the meeting point between the UAV and the ground mobile platform as decision variables. With the minimization of mission cost and mission completion time as the optimization goal, the multi-objective collaborative path optimization algorithm is used to solve the UAV flight path and the meeting point between the UAV and the ground mobile platform, thereby improving the efficiency of air-ground collaborative mission execution. The iterative update mechanism of Bayesian filtering enables the three-dimensional octree map to continuously adapt to environmental changes, maintaining the real-time and accuracy of the map. The path correction based on the ground mobile platform improves the collaborative performance of the UAV with the ground mobile platform.
Claims
1. A method for self-correction of the path of a UAV cluster based on air-ground multi-dimensional data fusion, characterized in that: The following steps are involved: Step S1: Collecting open space data, specifically including: Acquire space environment image information, target endpoint information, and drone position and posture information through aerial drone clusters equipped with image acquisition equipment and sensors; The interactive position, speed information, and mission target information between the ground mobile platforms are obtained by carrying sensors on the ground mobile platforms; wherein the mission target information includes the mission target position and the mission type; the sensors include laser sensors, visual sensors, and inertial measurement units; Step S2: Based on the mission target information, the ground mobile platform uses the UAV flight path and the meeting point of the UAV and the ground mobile platform as decision variables, and minimizes the mission cost and mission completion time as optimization goals. The flight path of the UAV and the meeting point of the UAV and the ground mobile platform are solved through a multi-objective collaborative path optimization algorithm; Step S3: Based on the open space data, combined with the information features of the laser sensor and the visual sensor, a sensor uncertainty probability model is established; a three-dimensional octree map is constructed, and the improved Bayesian filter denoising is used to fuse multiple sensor data and iteratively update the occupancy probability of each node in the three-dimensional octree map; Step S4: The UAV cluster uses the inertial measurement unit data of the ground mobile platform coordinate system as the conversion of relative position and speed, automatically compensates for the path deviation caused by environmental changes or ground platform movement, and corrects the flight path of the UAV cluster.
2. The method for self-correcting the path of a drone cluster based on air-ground multi-dimensional data fusion according to claim 1 is characterized in that: The step S2 specifically includes the following steps: S21: Based on the mission target information, the ground mobile platform takes the UAV flight path, the meeting point of the UAV and the ground mobile platform as decision variables, and minimizes the mission cost and mission completion time as the optimization goal to establish the objective function , as follows: ; In the formula, Indicates the flight path of the drone; It represents the meeting point of the UAV and the ground mobile platform; Represents the flight path of the drone energy consumption costs; Indicates that the ground moving platform moves from the starting point to the meeting point Costs; are the cost coefficients of UAV and ground mobile platform respectively; Indicates the average flight speed of the drone; is the distance between two points on the i-th and i+1-th task paths; It is the distance from the current position of the ground mobile platform to the meeting point distance; is the moving speed of the ground mobile platform; ∑ represents the sum; Indicates minimization of the objective function; S22: Through the multi-objective collaborative path optimization algorithm, the proposed flight path of the UAV and the meeting point of the UAV and the ground mobile platform are solved: S221: Set the initial solution set: Determine the take-off point for the drone and the mission target location , set the average flight speed of the drone and the moving speed of the ground mobile platform , generating an initial set of solutions, each of which represents a possible UAV flight path and rendezvous point with the ground mobile platform; S222: According to the task target location and task type, the initial solution set is divided into multiple subspaces to obtain multiple local solutions; a new global solution is generated based on the multiple local solutions: Divide the initial solution set into multiple subspaces according to the task objectives, and set a reference local search algorithm in each subspace; select a suitable reference local search algorithm according to the task type to obtain multiple local solutions; The initial solution set is decomposed into multiple subspaces: ; In the formula, represents a subspace; is the target vector; is the m-dimensional target space; is a reference point; and is the unit direction vector on the two-dimensional plane; N is the number of unit direction vectors; Multiple local solutions are collaboratively aggregated into a new global solution, specifically: ; In the formula, represents the maximum value of the solutions of each aggregated subspace, indicating the global solution; represents the number of subspaces; represents the reference point of the kth subspace; Represents the minimum of multiple local solutions; represents the unit direction vector of the kth subspace; Represents an aggregate function; No. The solution of a subspace.
3. The method for self-correcting the path of a drone cluster based on air-ground multi-dimensional data fusion according to claim 1 is characterized in that: The step S3 specifically comprises the following steps: S31: Based on the air-ground data, combined with the information characteristics of the laser sensor and the visual sensor, the uncertainty probability model of the laser sensor and the visual sensor is established. The specific expression is as follows: ; In the formula, is the uncertainty probability model of the laser sensor; is the uncertainty probability model of the visual sensor; is the status of the UAV system; Represent the observation models of laser sensor and visual sensor respectively; They represent the observation functions of the laser sensor and the visual sensor respectively; Defined as a verticality indicator function and only when hour, is the angle between the sensor and the ground; To set the threshold; Defined as an elevation filter and only hour, is the elevation value observed by the sensor, To set the elevation threshold; represents Gaussian distribution; represent the noise variance of laser sensor and visual sensor respectively; in The calculation process is as follows: ; In the formula, and It is represented as the observation noise of laser sensor and vision sensor; S32: Construct a three-dimensional octree map, and use improved Bayesian filtering to denoise and fuse multiple sensor data and update the occupancy probability of each map node in the three-dimensional octree map: S321: Initialize the three-dimensional octree map and define an occupancy probability for each map node in the octree. and a free probability ; S322: Use the improved Bayesian filter noise to fuse multiple sensor data and update the occupancy probability of each map node in the three-dimensional octree map to obtain the posterior probability; the specific expression is shown in the following formula: ; In the formula, They are the nodes in the three-dimensional octree map In time The state mean and covariance at time instant; Represents the posterior probability of the occupancy probability of the 3D octree map node based on the sensor observation information.
4. The method for self-correcting the path of a drone cluster based on air-ground multi-dimensional data fusion according to claim 1 is characterized in that: The step S4 specifically comprises the following steps: Update the speed and acceleration of the drone based on the inertial measurement unit data of the ground mobile platform coordinate system: The speed of the drone relative to the ground platform : ; In the formula, Represents the correlation matrix between the drone coordinate system and the ground coordinate system; Represents the velocity vector of the UAV relative to the ground mobile platform; Relative velocity vector of the ground mobile platform; The position vector representing the drone relative to the ground mobile platform; is the angular velocity of the ground platform coordinate system; The acceleration of the drone relative to the ground mobile platform : ; In the formula, They represent the relative angular acceleration of the UAV body coordinate system, the world coordinate system, and the ground mobile platform coordinate system respectively.
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