Aircraft and satellite cluster collaborative navigation positioning accurate control method and system

Abstract

The invention provides an aircraft and satellite cluster collaborative navigation positioning accurate control method and system, and relates to the technical field of aviation, and the method comprises the steps: an aircraft receives a multi-system navigation signal from a satellite cluster, carries out the fusion processing of multi-source navigation information through employing a self-adaptive Kalman filtering algorithm, and carries out the navigation positioning of a satellite cluster based on the fused multi-source navigation information. Calculating the accurate position of the aircraft by adopting a differential positioning technology; and transmitting the optimal control instruction to a flight control system of the aircraft based on the accurate position of the aircraft in combination with a preset flight plan, calculating a correction instruction by using a satellite-ground cooperative trajectory correction algorithm when trajectory deviation is detected, and transmitting the correction instruction to the aircraft through a high-frequency broadband communication system, and closed-loop accurate control of the track of the aircraft is realized.

Description

Technical Field

[0001] The present invention relates to the field of aviation technology, and in particular to a method and system for precise control of collaborative navigation and positioning of an aircraft and a satellite cluster. Background Art

[0002] With the rapid development of aerospace technology, the requirements for aircraft navigation and positioning accuracy are constantly increasing. Traditional aircraft navigation and positioning mainly rely on airborne inertial navigation systems and global satellite navigation systems (GNSS). However, these systems have certain limitations in certain special environments:

[0003] Although the inertial navigation system has the advantages of strong autonomy and strong anti-interference ability, long-term operation will produce cumulative errors and affect positioning accuracy. The global satellite navigation system performs well in open environments, but in complex terrain, urban canyons or electromagnetic interference environments, its signals are easily blocked or interfered with, resulting in reduced positioning accuracy or even failure. In some special mission scenarios, such as low-altitude flight and precision landing, the accuracy of existing navigation and positioning systems is often difficult to meet requirements. For long-duration and long-range aircraft missions, the reliability and sustainability of a single navigation system are insufficient.

[0004] In order to overcome the above problems, researchers have proposed the concept of multi-source fusion navigation, attempting to improve positioning accuracy and reliability by integrating multiple navigation information sources. However, existing multi-source fusion methods mainly focus on the fusion of ground-based or airborne systems, and have not yet fully utilized space satellite resources.

[0005] In recent years, with the advancement of small satellite technology and the rise of satellite clusters, new possibilities have been provided for aircraft navigation and positioning. Satellite clusters have the advantages of wide coverage, flexible networking, and strong anti-destruction capabilities, and can serve as a powerful supplement to aircraft navigation and positioning. However, how to effectively achieve the coordination between aircraft and satellite clusters, and how to perform precise control in dynamic and complex environments, are still technical challenges that need to be solved urgently. Summary of the invention

[0006] The embodiments of the present invention provide a method and system for precise control of collaborative navigation and positioning of an aircraft and a satellite cluster, which can solve the problems in the prior art.

[0007] According to a first aspect of the embodiments of the present invention,

[0008] Provides precise control methods for collaborative navigation and positioning of aircraft and satellite clusters, including:

[0009] A real-time two-way data link is established between the aircraft and the satellite cluster through a high-frequency broadband communication system, wherein the high-frequency broadband communication system adopts adaptive frequency hopping technology to resist interference; a multi-mode multi-frequency receiver is installed on the aircraft, wherein the multi-mode multi-frequency receiver can simultaneously receive signals of the Global Positioning System, the Beidou Satellite Navigation System, and the Galileo Satellite Navigation System; and data exchange within the satellite cluster is realized using inter-satellite link technology;

[0010] The aircraft receives multi-system navigation signals from the satellite cluster and obtains its own motion state information using the airborne inertial navigation system, barometric altimeter and Doppler radar; the multi-source navigation information is fused and processed using an adaptive Kalman filter algorithm, which can dynamically adjust the weights according to the reliability of different information sources; the time between the aircraft and the satellite cluster is synchronized using the onboard atomic clock; based on the fused multi-source navigation information, the precise position of the aircraft is calculated using differential positioning technology;

[0011] Based on the precise position of the aircraft and in combination with a preset flight plan, a model predictive control algorithm is used to generate optimal control instructions for the aircraft, wherein the model predictive control algorithm takes into account the dynamic characteristics and environmental constraints of the aircraft; the optimal control instructions are transmitted to the flight control system of the aircraft, wherein the flight control system adopts an adaptive control strategy to adjust control parameters according to the real-time flight status; the flight trajectory of the aircraft is continuously monitored through a satellite cluster, and when a trajectory deviation is detected, correction instructions are calculated using a satellite-ground coordinated trajectory correction algorithm, wherein the trajectory correction algorithm optimizes the correction strategy based on the minimum energy principle; the correction instructions are transmitted to the aircraft through a high-frequency broadband communication system to achieve closed-loop precise control of the aircraft trajectory.

[0012] In an optional embodiment,

[0013] The aircraft receives multi-system navigation signals from the satellite cluster and uses the onboard inertial navigation system, barometric altimeter and Doppler radar to obtain its own motion state information; the adaptive Kalman filter algorithm is used to fuse the multi-source navigation information, including:

[0014] Establishing an aircraft navigation state model, wherein the aircraft navigation state model includes position, velocity, attitude, gyroscope drift and accelerometer bias; constructing a system state equation and an observation equation, wherein the system state equation represents the relationship between the state vector at a current moment and the state vector at a previous moment, the state transfer matrix and process noise, and the observation equation represents the relationship between the observation value and the state vector, the observation matrix and the observation noise;

[0015] Execution time update, including state prediction and covariance prediction, where the state prediction uses the optimal state estimate and state transfer matrix of the previous moment to calculate the prior state estimate of the current moment, and the covariance prediction uses the posterior covariance matrix, state transfer matrix and process noise covariance matrix of the previous moment to calculate the prior covariance matrix of the current moment;

[0016] Performing measurement updates, including calculating Kalman gain, updating state estimation, and updating covariance, wherein the calculation of Kalman gain involves a prior covariance matrix, an observation matrix, and an observation noise covariance matrix;

[0017] The innovation sequence consistency test method is used to estimate the observation noise covariance in real time, wherein the innovation sequence consistency test method includes calculating the innovation sequence, estimating the innovation sequence covariance and updating the observation noise covariance;

[0018] Dynamically adjusting the process noise covariance using a fading memory index method, wherein the fading memory index method includes calculating a forgetting factor, updating a state estimation error covariance, and adjusting the process noise covariance;

[0019] Fusion of multi-source navigation information, including using satellite navigation system solutions as position and velocity observations, attitude information output by inertial navigation system as direct observations, and barometric altimeter and Doppler radar data as auxiliary observations;

[0020] The fused aircraft navigation state estimation results are output, including three-dimensional position, velocity, attitude and error parameters of the inertial navigation system.

[0021] In an optional embodiment,

[0022] The innovative sequence consistency test method is used to estimate the observation noise covariance in real time, including:

[0023] An observation residual sequence is calculated, where the observation residual sequence is the difference between the actual observation value and the state prediction value; a sample covariance of the observation residual sequence is estimated using a sliding window method, where the sliding window method uses the most recent N observation residual samples; an observation noise covariance estimate is updated, where the update process considers the sample covariance, the observation matrix, and the state prediction covariance matrix; and an exponential smoothing process is performed on the updated observation noise covariance estimate, where the exponential smoothing process uses a smoothing factor to adjust the weights of the new and old estimates.

[0024] In an optional embodiment,

[0025] Dynamically adjusting the process noise covariance using the fading memory index method includes:

[0026] Setting an initial forgetting factor; calculating a filtering error, wherein the filtering error is the difference between an actual observation value and a predicted observation value; calculating an adaptive forgetting factor based on the filtering error and a state prediction covariance matrix; updating a state estimation error covariance using the adaptive forgetting factor; adjusting a process noise covariance based on the updated state estimation error covariance and the adaptive forgetting factor;

[0027] Apply the updated observation noise covariance and process noise covariance to the Kalman filter update process at the next moment;

[0028] The calculation of the adaptive forgetting factor is shown in the following formula:

[0029]

[0030] Wherein, λ(k) represents the adaptive forgetting factor of k at the current time, λ0 represents the initial forgetting factor, e(k) represents the filtering error of k at the current time, tr() represents the trace operation of the matrix, H(k) represents the observation matrix of k at the current time, P(k|k-1) represents the prior state estimation error covariance matrix of k at the current time, and R(k) represents the observation noise covariance matrix of k at the current time;

[0031] The adaptive forgetting factor is used to update the state estimation error covariance as shown in the following formula:

[0032]

[0033] Wherein, P(k|k) represents the posterior state estimation error covariance matrix of the current time k, K(k) represents the Kalman gain matrix of the current time k, and I represents the identity matrix.

[0034] In an optional embodiment,

[0035] Based on the precise position of the aircraft and the preset flight plan, the optimal control instructions for the aircraft are generated using a model predictive control algorithm that takes into account the dynamic characteristics of the aircraft and environmental constraints, including:

[0036] Establishing a six-degree-of-freedom dynamics model of an aircraft, the six-degree-of-freedom dynamics model includes three translation equations and three rotation equations, wherein the translation equation describes the position and velocity changes of the aircraft in three-dimensional space, and the rotation equation describes the attitude angle changes of the aircraft; discretizing the six-degree-of-freedom dynamics model to obtain a discrete time model, wherein the discrete time model is expressed as a functional relationship between a state vector and a control input vector;

[0037] Design a model predictive control objective function, wherein the objective function includes a trajectory tracking error term and a control input cost term, wherein the trajectory tracking error term is used to minimize the state deviation in the prediction time domain, and the control input cost term is used to balance the control effect and energy consumption;

[0038] defining constraints, wherein the constraints include a state constraint, a control input constraint, and a control input change rate constraint, wherein the state constraint ensures that the aircraft state is within a safe range, the control input constraint reflects the physical limitations of the actuator, and the control input change rate constraint ensures the smoothness of the control command;

[0039] The objective function is converted into a quadratic form, the constraint conditions are converted into linear inequality constraints, and a quadratic programming problem is constructed; the quadratic programming problem is solved by an interior point method to obtain an optimal control sequence; the control instructions at the current moment are extracted from the optimal control sequence, and the control instructions are converted into a rudder deflection angle and an engine thrust instruction; the rudder deflection angle and the engine thrust instruction are executed to control the flight of the aircraft.

[0040] In an optional embodiment,

[0041] The flight trajectory of the aircraft is continuously monitored by a satellite cluster. When a trajectory deviation is detected, a trajectory correction algorithm coordinated by the satellite and the ground is used to calculate the correction instruction. The trajectory correction algorithm is based on the minimum energy principle to optimize the correction strategy including:

[0042] Constructing a monitoring network consisting of multiple low-orbit satellites, wherein the satellites in the monitoring network are equipped with optical sensors and radar sensors for obtaining position information, speed information and attitude information of the aircraft;

[0043] When a trajectory deviation is detected, the satellite-ground coordinated data fusion process is initiated, which includes: preprocessing the original satellite observation data, including denoising and outlier removal; using inter-satellite links for distributed data fusion; collecting and integrating ground radar data and ADS-B data; using a time synchronization algorithm to align data from different sources; using a federated Kalman filter algorithm to design sub-filters to process satellite data and ground data respectively; using information fusion criteria to merge sub-filter results to obtain a global optimal estimate; and dynamically adjusting fusion weights according to the reliability of each data source.

[0044] The trajectory correction algorithm is designed based on the minimum energy principle, and the trajectory correction algorithm includes:

[0045] Define an objective function, which includes a deviation term between the actual trajectory and the desired trajectory and a control input energy term; construct an aircraft dynamics constraint equation; consider control input restrictions, state variable restrictions and terminal constraints; use a variational method to derive an optimal control law; use a pseudospectral method to discretize the continuous-time optimal control problem and transform it into a nonlinear programming problem; use a sequential quadratic programming algorithm to solve the nonlinear programming problem;

[0046] According to the optimal control sequence obtained by solving, specific correction instructions are generated, and the correction instructions include attitude adjustment instructions, speed change instructions and heading correction instructions; the model predictive control framework is used to realize closed-loop control, and the following operations are performed in each control cycle:

[0047] Resolve the optimal control problem based on the current state; execute the first control instruction obtained by the solution; update the prediction time domain; adjust the weight matrix; and correct the dynamic model parameters.

[0048] In an optional embodiment,

[0049] The optimal control law derived by the variational method includes:

[0050] Constructing a Hamiltonian function, wherein the Hamiltonian function includes a state deviation term, a control input term, and a dynamic constraint term, wherein the state deviation term represents a weighted difference between an actual state and a desired state, the control input term represents a weighted control energy, and the dynamic constraint term represents a product of a state equation and a co-state variable;

[0051] Introducing co-state variables, wherein the co-state variables are used to characterize the sensitivity of the state variables to the objective function;

[0052] Based on the Pontryagin minimum principle, the partial derivative of the Hamiltonian function with respect to the control input is calculated and set equal to zero to obtain the optimal control condition.

[0053] Solving the optimal control condition and deriving the optimal control input expression, wherein the optimal control input expression includes the inverse matrix of the control weight matrix, the transpose of the control matrix and the co-state variable;

[0054] Calculating a control matrix, the control matrix being the partial derivatives of the dynamics equations with respect to the control input;

[0055] Constructing a co-state equation, wherein the co-state equation is a negative partial derivative of a Hamiltonian function with respect to a state variable;

[0056] Solving the co-state equation to obtain a differential equation of the co-state variable, wherein the differential equation includes a state deviation term and a product term of a state matrix and the co-state variable;

[0057] Calculating a state matrix, wherein the state matrix is ​​the partial derivatives of the dynamics equation with respect to the state variables;

[0058] Substitute the optimal control input expression into the dynamic equation and combine it with the differential equation of the co-state variables to form the Hamiltonian canonical equation system;

[0059] The numerical method is used to solve the Hamiltonian canonical equations to obtain the optimal state trajectory and the optimal control input sequence.

[0060] According to a second aspect of the embodiments of the present invention,

[0061] Provide precise control system for coordinated navigation and positioning of aircraft and satellite clusters, including:

[0062] The first unit is used to establish a real-time two-way data link between the aircraft and the satellite cluster through a high-frequency broadband communication system, wherein the high-frequency broadband communication system adopts an adaptive frequency hopping technology to resist interference; a multi-mode multi-frequency receiver is installed on the aircraft, wherein the multi-mode multi-frequency receiver can simultaneously receive global positioning system signals, Beidou satellite navigation system signals and Galileo satellite navigation system signals; and data exchange within the satellite cluster is realized by using inter-satellite link technology;

[0063] The second unit is used for the aircraft to receive multi-system navigation signals from the satellite cluster, and to obtain its own motion state information using the airborne inertial navigation system, barometric altimeter and Doppler radar; to fuse the multi-source navigation information using an adaptive Kalman filter algorithm, which can dynamically adjust the weights according to the reliability of different information sources; to synchronize the time between the aircraft and the satellite cluster using the onboard atomic clock; and to calculate the precise position of the aircraft based on the fused multi-source navigation information using differential positioning technology;

[0064] The third unit is used to generate optimal control instructions for the aircraft based on the precise position of the aircraft and in combination with a preset flight plan, using a model predictive control algorithm, wherein the model predictive control algorithm takes into account the dynamic characteristics and environmental constraints of the aircraft; transmit the optimal control instructions to the flight control system of the aircraft, wherein the flight control system adopts an adaptive control strategy to adjust control parameters according to real-time flight status; continuously monitor the flight trajectory of the aircraft through a satellite cluster, and when a trajectory deviation is detected, calculate correction instructions using a satellite-ground coordinated trajectory correction algorithm, wherein the trajectory correction algorithm optimizes the correction strategy based on the minimum energy principle; and transmit the correction instructions to the aircraft through a high-frequency broadband communication system to achieve closed-loop precise control of the aircraft trajectory.

[0065] According to a third aspect of the embodiments of the present invention,

[0066] An electronic device is provided, comprising:

[0067] processor;

[0068] a memory for storing processor-executable instructions;

[0069] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0070] A fourth aspect of the embodiments of the present invention is:

[0071] A computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the aforementioned method is implemented.

[0072] This method realizes the collaborative navigation and positioning of aircraft and satellite clusters, and improves the accuracy and robustness of state estimation through the adaptive Kalman filter algorithm. This method can adapt to complex and changeable flight environments and provide a reliable navigation information basis for the precise control of aircraft. By analyzing the filtering error in real time and dynamically adjusting the forgetting factor and process noise covariance, an adaptive noise model is provided for the Kalman filter, thereby improving the accuracy and robustness of aircraft state estimation. This is crucial for achieving high-precision collaborative navigation and positioning of aircraft and satellite clusters.

[0073] By establishing an accurate dynamic model, combining real-time state estimation and preset flight plans, and using model predictive control algorithms to generate optimal control instructions, high-precision control of the aircraft is achieved. This method can effectively cope with complex flight environments and mission requirements, and provides a reliable execution basis for the coordinated navigation and positioning of aircraft and satellite clusters, greatly improving flight safety and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A schematic diagram of a flow chart of a method for precise control of collaborative navigation and positioning of an aircraft and a satellite cluster according to an embodiment of the present invention;

[0075] Figure 2 It is a schematic diagram of the structure of a precise control system for collaborative navigation and positioning between an aircraft and a satellite cluster according to an embodiment of the present invention. DETAILED DESCRIPTION

[0076] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0077] The technical solution of the present invention is described in detail with specific embodiments below. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0078] Figure 1 FIG. 1 is a flow chart of a method for precise control of collaborative navigation and positioning of an aircraft and a satellite cluster according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0079] S101. Establish a real-time two-way data link between the aircraft and the satellite cluster through a high-frequency broadband communication system, wherein the high-frequency broadband communication system adopts adaptive frequency hopping technology to resist interference; install a multi-mode multi-frequency receiver on the aircraft, wherein the multi-mode multi-frequency receiver can simultaneously receive signals from the Global Positioning System, the Beidou Satellite Navigation System, and the Galileo Satellite Navigation System; and use inter-satellite link technology to achieve data exchange within the satellite cluster;

[0080] S102. The aircraft receives multi-system navigation signals from the satellite cluster, and uses the onboard inertial navigation system, barometric altimeter and Doppler radar to obtain its own motion state information; uses an adaptive Kalman filter algorithm to fuse the multi-source navigation information, and the adaptive Kalman filter algorithm can dynamically adjust the weight according to the reliability of different information sources; uses the onboard atomic clock to synchronize the time between the aircraft and the satellite cluster; and uses the differential positioning technology to calculate the precise position of the aircraft based on the fused multi-source navigation information;

[0081] S103. Based on the precise position of the aircraft and in combination with the preset flight plan, the optimal control instructions for the aircraft are generated using a model predictive control algorithm, wherein the model predictive control algorithm takes into account the dynamic characteristics and environmental constraints of the aircraft; the optimal control instructions are transmitted to the flight control system of the aircraft, wherein the flight control system adopts an adaptive control strategy and adjusts control parameters according to the real-time flight status; the flight trajectory of the aircraft is continuously monitored through a satellite cluster, and when a trajectory deviation is detected, the correction instructions are calculated using a satellite-ground coordinated trajectory correction algorithm, wherein the trajectory correction algorithm optimizes the correction strategy based on the minimum energy principle; the correction instructions are transmitted to the aircraft through a high-frequency broadband communication system to achieve closed-loop precise control of the aircraft trajectory.

[0082] In an optional embodiment,

[0083] The aircraft receives multi-system navigation signals from the satellite cluster and uses the onboard inertial navigation system, barometric altimeter and Doppler radar to obtain its own motion state information; the adaptive Kalman filter algorithm is used to fuse the multi-source navigation information, including:

[0084] Establishing an aircraft navigation state model, wherein the aircraft navigation state model includes position, velocity, attitude, gyroscope drift and accelerometer bias; constructing a system state equation and an observation equation, wherein the system state equation represents the relationship between the state vector at a current moment and the state vector at a previous moment, the state transfer matrix and process noise, and the observation equation represents the relationship between the observation value and the state vector, the observation matrix and the observation noise;

[0085] Execution time update, including state prediction and covariance prediction, where the state prediction uses the optimal state estimate and state transfer matrix of the previous moment to calculate the prior state estimate of the current moment, and the covariance prediction uses the posterior covariance matrix, state transfer matrix and process noise covariance matrix of the previous moment to calculate the prior covariance matrix of the current moment;

[0086] Performing measurement updates, including calculating Kalman gain, updating state estimation, and updating covariance, wherein the calculation of Kalman gain involves a prior covariance matrix, an observation matrix, and an observation noise covariance matrix;

[0087] The innovation sequence consistency test method is used to estimate the observation noise covariance in real time, wherein the innovation sequence consistency test method includes calculating the innovation sequence, estimating the innovation sequence covariance and updating the observation noise covariance;

[0088] Dynamically adjusting the process noise covariance using a fading memory index method, wherein the fading memory index method includes calculating a forgetting factor, updating a state estimation error covariance, and adjusting the process noise covariance;

[0089] Fusion of multi-source navigation information, including using satellite navigation system solutions as position and velocity observations, attitude information output by inertial navigation system as direct observations, and barometric altimeter and Doppler radar data as auxiliary observations;

[0090] The fused aircraft navigation state estimation results are output, including three-dimensional position, velocity, attitude and error parameters of the inertial navigation system.

[0091] Exemplarily, the present invention provides a method for precise control of collaborative navigation and positioning of an aircraft and a satellite cluster, which realizes high-precision and real-time aircraft state estimation through multi-source information fusion and adaptive Kalman filter algorithm. The specific implementation steps of the method are described in detail below:

[0092] First, the aircraft receives multi-system navigation signals from satellite clusters. These signals may include signals from global satellite navigation systems such as GPS, GLONASS, BeiDou and Galileo. At the same time, the aircraft uses the onboard inertial navigation system (INS), barometric altimeter and Doppler radar to obtain its own motion status information. INS provides high-frequency attitude, speed and position data; barometric altimeter provides relatively accurate altitude information; Doppler radar provides ground speed information.

[0093] Next, the aircraft navigation state model is established. The model includes 15 state variables: three-dimensional position (longitude, latitude, altitude), three-dimensional velocity (east velocity, north velocity, vertical velocity), three-dimensional attitude (pitch angle, roll angle, heading angle), three gyroscope drifts and three accelerometer biases. These state variables fully describe the aircraft's motion state and main sensor errors.

[0094] Then, construct the system state equation and observation equation. The system state equation describes the relationship between the current state vector and the previous state vector, the state transfer matrix, and the process noise. For example, the current position is equal to the previous position plus the product of the velocity and the time interval, plus random disturbances. The observation equation describes the relationship between the observation value and the state vector, the observation matrix, and the observation noise. For example, the GPS observation value is equal to the true position plus the observation error.

[0095] In the time update phase of the adaptive Kalman filter, the state prediction is first performed. Assuming that the optimal position estimate at the previous moment is (30°N, 120°E, 1000m), the speed estimate is (100m / s, 0m / s, 0m / s), and the time interval is 1 second, the prior position estimate at the current moment is (30.0009°N, 120.0009°E, 1000m). At the same time, the covariance prediction is performed, and the prior covariance matrix at the current moment is calculated using the posterior covariance matrix, state transfer matrix, and process noise covariance matrix at the previous moment to reflect the uncertainty of the state estimate.

[0096] In the measurement update phase, the Kalman gain is first calculated. The Kalman gain determines the degree of influence of the new observation on the state estimate, and its calculation involves the prior covariance matrix, the observation matrix, and the observation noise covariance matrix. Then, the state estimate is updated using the Kalman gain. For example, if the GPS observation is (30.0010°N, 120.0008°E, 1002m) and the Kalman gain is 0.6, the updated position estimate is (30.00096°N, 120.00086°E, 1001.2m). Finally, the covariance matrix is ​​updated to reflect the uncertainty of the new state estimate.

[0097] In order to improve the adaptability of the filter, the innovation sequence consistency test method is used to estimate the observation noise covariance in real time. First, the innovation sequence is calculated, that is, the difference between the observed value and the predicted observation value. Then, the innovation sequence covariance is estimated to reflect the degree of fluctuation of the observation value. Finally, the observation noise covariance is updated based on the estimated innovation sequence covariance. For example, if the GPS position observations fluctuate greatly for multiple consecutive periods, the system will automatically increase the covariance of the GPS observation noise and reduce its weight in the state estimation.

[0098] At the same time, the process noise covariance is dynamically adjusted using the fading memory index method. First, the forgetting factor is calculated, which determines the weight of the historical data. Then, the state estimation error covariance is updated to reflect the credibility of the current state estimate. Finally, the process noise covariance is adjusted according to the state estimation error covariance. For example, if the position estimation error is large for multiple consecutive cycles, the system will automatically increase the process noise covariance of the position state to increase the sensitivity of the filter to new observations.

[0099] In the multi-source navigation information fusion stage, the satellite navigation system solution results are used as position and velocity observations. For example, GPS may provide position observations of (30.0010°N, 120.0008°E, 1002m) and velocity observations of (98m / s, 2m / s, 0.5m / s). The attitude information output by the inertial navigation system is directly used as attitude observations, such as (2°, 1°, 45°) to represent the pitch angle, roll angle, and heading angle, respectively. The barometric altimeter data is used as an auxiliary altitude observation, such as 1001m. The Doppler radar data is used as an auxiliary ground speed observation, such as 99m / s.

[0100] Finally, the fused aircraft navigation state estimation results are output, which include 3D position (30.00096°N, 120.00086°E, 1001.2m), 3D velocity (98.5m / s, 1.5m / s, 0.2m / s), 3D attitude (1.8°, 0.9°, 45.2°), and error parameters of the inertial navigation system, such as gyroscope drift (0.01° / h, -0.02° / h, 0.015° / h) and accelerometer bias (0.001g, -0.0015g, 0.0008g).

[0101] Through the above steps, this method realizes the collaborative navigation and positioning of the aircraft and the satellite cluster, and improves the accuracy and robustness of state estimation through the adaptive Kalman filter algorithm. This method can adapt to complex and changing flight environments and provide a reliable navigation information basis for the precise control of the aircraft.

[0102] In an optional embodiment,

[0103] The innovative sequence consistency test method is used to estimate the observation noise covariance in real time, including:

[0104] An observation residual sequence is calculated, where the observation residual sequence is the difference between the actual observation value and the state prediction value; a sample covariance of the observation residual sequence is estimated using a sliding window method, where the sliding window method uses the most recent N observation residual samples; an observation noise covariance estimate is updated, where the update process considers the sample covariance, the observation matrix, and the state prediction covariance matrix; and an exponential smoothing process is performed on the updated observation noise covariance estimate, where the exponential smoothing process uses a smoothing factor to adjust the weights of the new and old estimates.

[0105] Exemplarily, the present invention provides a method for real-time estimation of observation noise covariance using an innovative sequence consistency test method, which is a key component of a precise control system for collaborative navigation and positioning of aircraft and satellite clusters. The specific implementation steps of the method are described in detail below:

[0106] First, the observation residual sequence is calculated. The observation residual sequence is the difference between the actual observation value and the state prediction value, reflecting the combined effect of observation noise and state prediction error. Taking GPS position observation as an example, assuming that the actual observation value at a certain moment is (30.0010°N, 120.0008°E, 1002m), and the predicted value based on the previous state estimate is (30.0009°N, 120.0009°E, 1000m), then the observation residual is (0.0001°, -0.0001°, 2m). This process is performed for all observations, including position and velocity observations from the satellite navigation system, and attitude, altitude, and ground speed observations from airborne sensors.

[0107] Next, the sliding window method is used to estimate the sample covariance of the observed residual sequence. The sliding window method uses the most recent N observed residual samples to calculate the sample covariance, which can capture the dynamic changes in the observation noise characteristics. The selection of N requires a balance between real-time and statistical reliability, and a value between 10 and 50 can usually be selected. For example, if N = 20 is selected, the sample covariance is estimated using the most recent 20 GPS position observation residuals. Assume that the mean of the north component of these 20 residuals is 0.00005° and the sample variance is 0.00001°2. Similar statistics are also found in the east and height directions.

[0108] Then, the observation noise covariance estimate is updated. This update process needs to take into account the sample covariance, the observation matrix, and the state prediction covariance matrix. The observation matrix describes the mapping relationship between state variables and observations, while the state prediction covariance matrix reflects the uncertainty of state predictions. By combining this information, changes that are purely caused by observation noise can be separated. For example, if the uncertainty of the state prediction is large, then most of the changes in the observation residuals may come from prediction errors rather than observation noise. Assume that the standard deviation of the GPS position observation noise after the update is estimated to be (0.002°, 0.002°, 5m).

[0109] Finally, the updated observation noise covariance estimate is exponentially smoothed. Exponential smoothing uses a smoothing factor to adjust the weights of the new and old estimates, which helps reduce random fluctuations in the estimate while maintaining sensitivity to real changes. The smoothing factor is usually selected between 0.1 and 0.3. Smaller values ​​make the estimate smoother but slower to react, while larger values ​​do the opposite. Assuming that the smoothing factor is selected as 0.2, the GPS position observation noise standard deviation estimate at the current moment is (0.002°, 0.002°, 5m), and the estimate at the previous moment is (0.0018°, 0.0019°, 4.8m), then the smoothed new estimate is (0.00196°, 0.00198°, 4.84m).

[0110] This process is repeated in each observation cycle, continuously updating the estimate of the observation noise covariance. The updated estimate of the observation noise covariance will be used in the measurement update step of the next Kalman filter cycle, affecting the calculation of the Kalman gain, thereby adjusting the filter's trust in different observation sources.

[0111] By estimating and updating the observation noise covariance in real time, the method can adapt to dynamic changes in the observation environment. For example, when an aircraft enters an urban canyon environment, the GPS signal may be affected by multipath effects and the observation noise will increase. At this time, the method will detect the increase in GPS position residuals and increase the estimate of GPS observation noise covariance accordingly. This will cause the Kalman filter to rely less on GPS observations and rely more on other observation sources (such as inertial navigation systems) to estimate the state of the aircraft.

[0112] On the contrary, when the aircraft flies in an open area and the GPS signal is good, the observation residual will decrease, and the method will reduce the estimated value of the GPS observation noise covariance, making the filter trust the GPS observation more. This adaptive mechanism significantly improves the robustness and accuracy of the navigation system in different environments.

[0113] In summary, this method provides an accurate noise model for the Kalman filter by analyzing the observation residual sequence in real time, dynamically estimating and updating the observation noise covariance, thereby improving the accuracy and reliability of aircraft state estimation. This is crucial for achieving high-precision collaborative navigation and positioning between aircraft and satellite clusters, and lays a solid foundation for precise control of aircraft.

[0114] In an optional embodiment,

[0115] Dynamically adjusting the process noise covariance using the fading memory index method includes:

[0116] Setting an initial forgetting factor; calculating a filtering error, wherein the filtering error is the difference between an actual observation value and a predicted observation value; calculating an adaptive forgetting factor based on the filtering error and a state prediction covariance matrix; updating a state estimation error covariance using the adaptive forgetting factor; adjusting a process noise covariance based on the updated state estimation error covariance and the adaptive forgetting factor;

[0117] Apply the updated observation noise covariance and process noise covariance to the Kalman filter update process at the next moment;

[0118] The calculation of the adaptive forgetting factor is shown in the following formula:

[0119]

[0120] Wherein, λ(k) represents the adaptive forgetting factor of k at the current time, λ0 represents the initial forgetting factor, e(k) represents the filtering error of k at the current time, tr() represents the trace operation of the matrix, H(k) represents the observation matrix of k at the current time, P(k|k-1) represents the prior state estimation error covariance matrix of k at the current time, and R(k) represents the observation noise covariance matrix of k at the current time;

[0121] The adaptive forgetting factor is used to update the state estimation error covariance as shown in the following formula:

[0122]

[0123] Wherein, P(k|k) represents the posterior state estimation error covariance matrix of the current time k, K(k) represents the Kalman gain matrix of the current time k, and I represents the identity matrix.

[0124] Exemplarily, the present invention provides a method for dynamically adjusting the process noise covariance using the fading memory index method, which is a key component of the precise control system for collaborative navigation and positioning of aircraft and satellite clusters. The specific implementation steps of the method are described in detail below:

[0125] First, set the initial forgetting factor. The forgetting factor is a value between 0 and 1 that controls the weight of historical data in the estimation process. The selection of the initial forgetting factor requires a trade-off between the system's ability to respond quickly and the stability of the estimate. Usually, a larger initial value, such as 0.95, can be selected to ensure the stability of the estimate in the initial stage. This means that in the calculation, about 95% of the historical information will be retained, while 5% of the weight will be given to the new observation data.

[0126] Next, calculate the filtering error. The filtering error is the difference between the actual observation value and the predicted observation value, reflecting the deviation between the system model and the actual situation. Taking GPS position observation as an example, assuming that the actual observation value at a certain moment is (30.0010°N, 120.0008°E, 1002m), and the predicted observation value based on the previous state estimation is (30.0009°N, 120.0009°E, 1000m), then the filtering error is (0.0001°, -0.0001°, 2m). This process needs to be performed on all observations, including position, velocity, attitude, etc.

[0127] Then, the adaptive forgetting factor is calculated based on the filter error and the state prediction covariance matrix. The state prediction covariance matrix reflects the uncertainty of the state prediction. The calculation process takes into account the size of the filter error and the uncertainty of the state prediction to dynamically adjust the forgetting factor. For example, if the filter error is large and the uncertainty of the state prediction is small, it means that the system model may not be accurate enough. At this time, the forgetting factor should be reduced to adapt to new observations more quickly. Assume that the calculated adaptive forgetting factor is 0.92, which is less than the initial value of 0.95, indicating that the system is paying more attention to new data.

[0128] The state estimation error covariance is updated using an adaptive forgetting factor. The state estimation error covariance reflects the uncertainty of the state estimate. The update process takes into account the previous state estimation error covariance, the state transition matrix, the process noise covariance, and the newly calculated adaptive forgetting factor. A smaller forgetting factor will result in a larger state estimation error covariance, indicating that the system is less certain about the current state estimate. For example, if the previous position estimate error standard deviation is (1m, 1m, 2m), it may become (1.2m, 1.2m, 2.4m) after the update, reflecting the increased uncertainty of the system's position estimate.

[0129] Adjust the process noise covariance based on the updated state estimation error covariance and the adaptive forgetting factor. The process noise covariance describes the uncertainty of the system model. The adjustment process takes into account the changes in the state estimation error covariance and the value of the adaptive forgetting factor. When the forgetting factor decreases, it is usually necessary to increase the process noise covariance to reflect the reduced trust of the system in the model. For example, if the previous position process noise standard deviation is (0.5m / s, 0.5m / s, 1m / s), it may become (0.6m / s, 0.6m / s, 1.2m / s) after adjustment, indicating that the uncertainty of the system model has increased.

[0130] Finally, the updated observation noise covariance and process noise covariance are applied to the Kalman filter update process at the next moment. These updated covariance matrices will affect the calculation of the Kalman gain, thereby affecting the update of the state estimate. For example, an increased process noise covariance will cause the Kalman filter to trust the observations more than the model predictions, while an increased observation noise covariance will reduce the weight of the corresponding observation in the state estimate.

[0131] This process is repeated at each filtering cycle, continuously adjusting the system's trust in different information sources. By dynamically adjusting the process noise covariance, the method can adapt to changes in the aircraft's motion state and environment. For example, when the aircraft performs violent maneuvers, the process noise covariance of position and velocity may increase, reflecting the reduced predictive ability of the system model in this case. At the same time, if the performance of some sensors (such as GPS) degrades due to environmental changes, the observation noise covariance will increase accordingly, and the system will rely more on data from other sensors (such as inertial navigation systems).

[0132] This adaptive mechanism significantly improves the performance of the navigation system in complex and changing environments. For example, when an aircraft flies from an open area into an urban canyon, the GPS signal may become unstable. The system detects the increase in filtering error, resulting in a decrease in the forgetting factor and an increase in the process noise covariance. This allows the filter to quickly adapt to the new environment, reduce reliance on unreliable GPS signals, and make more use of the data from the inertial navigation system, thereby maintaining high navigation accuracy.

[0133] On the contrary, when the aircraft re-enters an area with good signals, the filtering error will decrease, the forgetting factor will increase, and the process noise covariance will decrease. This allows the system to gradually restore trust in high-precision sensors such as GPS and make full use of the precise position information they provide.

[0134] In summary, this method provides an adaptive noise model for the Kalman filter by analyzing the filtering error in real time and dynamically adjusting the forgetting factor and process noise covariance, thereby improving the accuracy and robustness of aircraft state estimation. This is crucial for achieving high-precision collaborative navigation and positioning of aircraft and satellite clusters, and provides a reliable foundation for precise control of aircraft.

[0135] In an optional embodiment,

[0136] Based on the precise position of the aircraft and the preset flight plan, the optimal control instructions for the aircraft are generated using a model predictive control algorithm that takes into account the dynamic characteristics of the aircraft and environmental constraints, including:

[0137] Establishing a six-degree-of-freedom dynamics model of an aircraft, the six-degree-of-freedom dynamics model includes three translation equations and three rotation equations, wherein the translation equation describes the position and velocity changes of the aircraft in three-dimensional space, and the rotation equation describes the attitude angle changes of the aircraft; discretizing the six-degree-of-freedom dynamics model to obtain a discrete time model, wherein the discrete time model is expressed as a functional relationship between a state vector and a control input vector;

[0138] Design a model predictive control objective function, wherein the objective function includes a trajectory tracking error term and a control input cost term, wherein the trajectory tracking error term is used to minimize the state deviation in the prediction time domain, and the control input cost term is used to balance the control effect and energy consumption;

[0139] defining constraints, wherein the constraints include a state constraint, a control input constraint, and a control input change rate constraint, wherein the state constraint ensures that the aircraft state is within a safe range, the control input constraint reflects the physical limitations of the actuator, and the control input change rate constraint ensures the smoothness of the control command;

[0140] The objective function is converted into a quadratic form, the constraint conditions are converted into linear inequality constraints, and a quadratic programming problem is constructed; the quadratic programming problem is solved by an interior point method to obtain an optimal control sequence; the control instructions at the current moment are extracted from the optimal control sequence, and the control instructions are converted into a rudder deflection angle and an engine thrust instruction; the rudder deflection angle and the engine thrust instruction are executed to control the flight of the aircraft.

[0141] Exemplarily, the present invention provides a method for generating optimal control instructions for an aircraft using a model predictive control algorithm based on the precise position of the aircraft and a preset flight plan. This method takes into account the dynamic characteristics and environmental constraints of the aircraft and is a core component of the precise control system for collaborative navigation and positioning of aircraft and satellite clusters. The specific implementation steps of this method are described in detail below:

[0142] First, a six-degree-of-freedom dynamic model of the aircraft is established. The model includes three translation equations and three rotation equations, which fully describe the motion state of the aircraft in three-dimensional space. The translation equation describes the position and velocity changes of the aircraft in the earth coordinate system, including the position and velocity in the north, east and vertical directions. For example, the position of the aircraft at a certain moment is (30.0010°N, 120.0008°E, 1000m) and the velocity is (200m / s, 0m / s, 0m / s). The rotation equation describes the change of the aircraft's attitude angle, including the yaw angle, pitch angle and roll angle. For example, the aircraft's attitude angle is (0°, 2°, 0°), indicating that the aircraft is slightly raised. These equations take into account the influence of factors such as gravity, aerodynamics, thrust, etc., and reflect the dynamic characteristics of the aircraft.

[0143] Next, the six-degree-of-freedom dynamic model is discretized to obtain a discrete-time model. The discretization process converts the continuous-time model into a differential equation with a discrete time step, which is convenient for numerical calculation and controller design. The discrete-time model is expressed as a functional relationship between the state vector and the control input vector. The state vector includes variables such as position, velocity, and attitude angle, and the control input vector includes the rudder deflection angle and engine thrust. For example, assuming a discrete time step of 0.1 seconds, it can be predicted that at the next moment (0.1 seconds later), the position of the aircraft may become (30.0011°N, 120.0008°E, 1000.2m), the speed is (200m / s, 0m / s, 2m / s), and the attitude angle is (0°, 2.1°, 0°).

[0144] Then, the model predictive control objective function is designed. The objective function is the core of the optimization problem, including the trajectory tracking error term and the control input cost term. The trajectory tracking error term is used to minimize the state deviation in the prediction time domain to ensure that the aircraft can accurately follow the preset flight plan. For example, if the preset waypoint is (30.0020°N, 120.0015°E, 1100m), the objective function will try to minimize the distance between the actual position and this point. The control input cost term is used to balance the control effect and energy consumption to avoid overly frequent or drastic control actions. For example, a smaller weight can be given to the change in the deflection angle of the rudder to encourage a smooth control strategy.

[0145] Defining constraints is the next key step. Constraints include state constraints, control input constraints, and control input change rate constraints. State constraints ensure that the aircraft state is within a safe range, such as the speed does not exceed the maximum design speed and the altitude remains within a safe airspace. For example, the upper speed limit can be set to 250m / s and the lower altitude limit can be set to 500m. Control input constraints reflect the physical limitations of the actuator, such as the maximum deflection angle of the control surface and the maximum thrust of the engine. For example, the deflection angle of the elevator can be limited to ±30° and the engine thrust can be between 20kN and 100kN. Control input change rate constraints ensure the smoothness of control instructions and avoid instability caused by sudden control changes. For example, the rate of change of the control surface deflection angle can be limited to no more than 10° per second.

[0146] Next, the objective function is transformed into a quadratic form, and the constraints are transformed into linear inequality constraints to construct a quadratic programming problem. This transformation process allows the optimization problem to be solved using standard numerical optimization methods. The quadratic objective function can be expressed as a weighted sum of the squares of the state deviation and the control input, and the linear inequality constraints directly correspond to the various constraints defined previously.

[0147] The interior point method is used to solve the quadratic programming problem and obtain the optimal control sequence. The interior point method is an efficient optimization algorithm that can quickly find the optimal solution that satisfies all constraints. The solution process considers the state evolution in the prediction time domain (for example, the next 10 seconds) and obtains a series of optimal control inputs. For example, the control surface deflection angle and engine thrust command for the next 10 time steps may be obtained.

[0148] The current control command is extracted from the optimal control sequence and converted into specific control surface deflection angle and engine thrust command. For example, the command of elevator deflection angle 2.5°, rudder deflection angle 0°, aileron deflection angle 1°, and engine thrust 80kN may be obtained.

[0149] Finally, the control surface deflection angle and engine thrust instructions are executed to control the flight of the aircraft. These instructions are transmitted to the corresponding actuators through the flight control system to achieve precise control of the aircraft.

[0150] The whole process is repeated in each control cycle (usually tens to hundreds of milliseconds), and the control instructions are continuously updated to adapt to changes in the aircraft state and environment. This rolling optimization strategy can effectively cope with external disturbances and model errors, ensuring the robustness of control.

[0151] A specific application scenario of this method is the precise path tracking of an aircraft. Assume that the aircraft needs to fly from (30.0000°N, 120.0000°E, 1000m) to (30.0100°N, 120.0100°E, 1500m). The model predictive control algorithm calculates the optimal control sequence in each control cycle to allow the aircraft to approach the target point smoothly. During the flight, if there is crosswind interference, the algorithm will automatically adjust the control strategy, such as increasing aileron deflection to offset the impact of the crosswind, and adjusting the engine thrust to maintain the desired climb rate.

[0152] Another application scenario is the automatic landing of an aircraft. During the final approach phase, the model predictive control algorithm will accurately control the aircraft's descent rate and speed, while taking into account constraints such as runway length and wind direction. For example, when descending to an altitude of 100 meters, the algorithm may instruct the aircraft to maintain a 3° descent angle while gradually reducing the airspeed to 150 km / h to ensure a safe landing in the designated touchdown area.

[0153] In summary, this method achieves high-precision control of the aircraft by establishing an accurate dynamic model, combining real-time state estimation and preset flight plans, and using the model predictive control algorithm to generate optimal control instructions. This method can effectively cope with complex flight environments and mission requirements, and provides a reliable execution basis for the coordinated navigation and positioning of aircraft and satellite clusters, greatly improving flight safety and efficiency.

[0154] In an optional embodiment,

[0155] The flight trajectory of the aircraft is continuously monitored by a satellite cluster. When a trajectory deviation is detected, a trajectory correction algorithm coordinated by the satellite and the ground is used to calculate the correction instruction. The trajectory correction algorithm is based on the minimum energy principle to optimize the correction strategy including:

[0156] Constructing a monitoring network consisting of multiple low-orbit satellites, wherein the satellites in the monitoring network are equipped with optical sensors and radar sensors for obtaining position information, speed information and attitude information of the aircraft;

[0157] When a trajectory deviation is detected, the satellite-ground coordinated data fusion process is initiated, which includes: preprocessing the original satellite observation data, including denoising and outlier removal; using inter-satellite links for distributed data fusion; collecting and integrating ground radar data and ADS-B data; using a time synchronization algorithm to align data from different sources; using a federated Kalman filter algorithm to design sub-filters to process satellite data and ground data respectively; using information fusion criteria to merge sub-filter results to obtain a global optimal estimate; and dynamically adjusting fusion weights according to the reliability of each data source.

[0158] The trajectory correction algorithm is designed based on the minimum energy principle, and the trajectory correction algorithm includes:

[0159] Define an objective function, which includes a deviation term between the actual trajectory and the desired trajectory and a control input energy term; construct an aircraft dynamics constraint equation; consider control input restrictions, state variable restrictions and terminal constraints; use a variational method to derive an optimal control law; use a pseudospectral method to discretize the continuous-time optimal control problem and transform it into a nonlinear programming problem; use a sequential quadratic programming algorithm to solve the nonlinear programming problem;

[0160] According to the optimal control sequence obtained by solving, specific correction instructions are generated, and the correction instructions include attitude adjustment instructions, speed change instructions and heading correction instructions; the model predictive control framework is used to realize closed-loop control, and the following operations are performed in each control cycle:

[0161] Resolve the optimal control problem based on the current state; execute the first control instruction obtained by the solution; update the prediction time domain; adjust the weight matrix; and correct the dynamic model parameters.

[0162] Exemplarily, the present invention provides a method for continuously monitoring the flight trajectory of an aircraft through a satellite cluster, and calculating correction instructions using a satellite-ground coordinated trajectory correction algorithm when a trajectory deviation is detected. The method optimizes the correction strategy based on the minimum energy principle and realizes high-precision trajectory tracking control of the aircraft. The specific implementation steps of the method are described in detail below:

[0163] First, a monitoring network consisting of multiple low-orbit satellites is constructed. The satellites in this network are equipped with optical sensors and radar sensors to obtain the position, speed and attitude information of the aircraft. For example, a typical monitoring network may consist of 30 satellites distributed at an orbital altitude of 600 kilometers. Each satellite is equipped with a high-resolution optical camera and synthetic aperture radar, which can accurately track aircraft both during the day and at night. The resolution of the optical sensor can reach 0.5 meters, and the distance resolution of the radar sensor can reach 1 meter. This configuration enables the monitoring network to capture the motion status of the aircraft with extremely high accuracy and frequency.

[0164] When a trajectory deviation is detected, the system starts the satellite-ground coordinated data fusion process. This process first pre-processes the original satellite observation data, including denoising and outlier removal. For example, median filtering can be used to remove impulse noise, and the 3σ criterion can be used to remove outliers. Then, distributed data fusion is performed using inter-satellite links. The communication bandwidth of the inter-satellite link can reach 1Gbps, and the delay is as low as 1 millisecond, ensuring the real-time and integrity of the data.

[0165] At the same time, the system collects and integrates ground radar data and ADS-B data. Ground radar can usually provide a position update every 10 seconds with an accuracy of 100 meters; while ADS-B data can be updated once a second with an accuracy of about 10 meters. The system uses a time synchronization algorithm to align data from different sources to eliminate errors caused by transmission delays and sampling time differences.

[0166] The data fusion process uses the federated Kalman filter algorithm, and sub-filters are designed to process satellite data and ground data separately. For example, the satellite data sub-filter may use a 6-dimensional state vector (3D position and 3D velocity), while the ground data sub-filter may use a 4-dimensional state vector (2D plane position and velocity). The system uses the information fusion criterion to combine the sub-filter results to obtain the global optimal estimate. The fusion weight is dynamically adjusted according to the reliability of each data source, such as increasing the weight of satellite data when the satellite line of sight is good, and increasing the weight of ground radar data when flying at low altitude.

[0167] The trajectory correction algorithm is designed based on the minimum energy principle. First, the objective function is defined, which includes the deviation term between the actual trajectory and the desired trajectory and the control input energy term. The deviation term can be expressed as the Euclidean distance in three-dimensional space, and the energy term can be the sum of the square of the rudder deflection angle and the engine thrust. For example, if it is detected that the aircraft deviates from the planned route by 100 meters, the objective function will balance the reduction of this 100-meter deviation and the required control energy.

[0168] Construct the aircraft dynamic constraint equations, which describe the kinematic and dynamic characteristics of the aircraft. Consider control input limits, state variable limits, and terminal constraints. Control input limits may include the control surface deflection angle range (such as ±30 degrees) and engine thrust range (such as 20kN to 100kN). State variable limits may include maximum speed (such as 250m / s) and minimum-maximum altitude range (such as 500m to 12000m). Terminal constraints ensure that the aircraft can reach the target position at a specified time.

[0169] The optimal control law is derived using the calculus of variations. This step transforms the continuous-time optimal control problem into a series of algebraic equations. The continuous-time optimal control problem is discretized using the pseudospectral method and transformed into a nonlinear programming problem. The pseudospectral method uses high-order polynomials to approximate continuous functions and can usually discretize the problem into 20-50 time nodes.

[0170] The sequential quadratic programming algorithm is used to solve nonlinear programming problems. The algorithm finds the optimal solution to a nonlinear problem by iteratively solving a series of quadratic programming subproblems. Each iteration updates the linearization point until it converges to a solution that meets the accuracy requirements. Usually 10-20 iterations are required to achieve convergence.

[0171] Generate specific correction instructions based on the optimal control sequence obtained. Correction instructions include attitude adjustment instructions, speed change instructions, and heading correction instructions. For example, if the aircraft deviates from the route to the right by 100 meters, the correction instructions may include: turn left 2 degrees, maintain the current speed, and return to the correct position after 5 seconds. These instructions are transmitted to the aircraft's flight control system through the data link for execution.

[0172] The closed-loop control is implemented using a model predictive control framework. The following operations are performed in each control cycle (usually 0.1 to 1 second): The optimal control problem is re-solved based on the current state. This ensures that the control strategy can adapt to changes in the aircraft state and external disturbances in real time. The first control instruction obtained by the solution is executed. This instruction is the most recent one in the entire optimal control sequence and best reflects the optimal choice for the current situation.

[0173] Update the prediction horizon, which usually shortens as the aircraft approaches the target. For example, a 300-second prediction horizon may be used from takeoff to cruise, but it may be shortened to 60 seconds during landing. Adjust the weight matrix to adjust the relative importance of trajectory tracking accuracy and control energy consumption according to the different flight phases. For example, energy saving may be more important during cruise, while accurate tracking may be more emphasized during landing.

[0174] Finally, the dynamic model parameters are corrected. Based on the actual flight data, the online parameter estimation technology is used to update the uncertain parameters in the dynamic model, such as the aerodynamic coefficients. This ensures that the model can accurately reflect the actual characteristics of the aircraft and improve the control accuracy.

[0175] In summary, this method achieves high-precision control of the aircraft's flight trajectory through continuous monitoring by satellite clusters and data fusion of satellite-ground collaboration, combined with a trajectory correction algorithm based on the minimum energy principle. This method can effectively cope with complex flight environments and mission requirements, greatly improving the safety, reliability and efficiency of air transportation.

[0176] In an optional embodiment,

[0177] The optimal control law derived by the variational method includes:

[0178] Constructing a Hamiltonian function, wherein the Hamiltonian function includes a state deviation term, a control input term, and a dynamic constraint term, wherein the state deviation term represents a weighted difference between an actual state and a desired state, the control input term represents a weighted control energy, and the dynamic constraint term represents a product of a state equation and a co-state variable;

[0179] Introducing co-state variables, wherein the co-state variables are used to characterize the sensitivity of the state variables to the objective function;

[0180] Based on the Pontryagin minimum principle, the partial derivative of the Hamiltonian function with respect to the control input is calculated and set equal to zero to obtain the optimal control condition.

[0181] Solving the optimal control condition and deriving the optimal control input expression, wherein the optimal control input expression includes the inverse matrix of the control weight matrix, the transpose of the control matrix and the co-state variable;

[0182] Calculating a control matrix, the control matrix being the partial derivatives of the dynamics equations with respect to the control input;

[0183] Constructing a co-state equation, wherein the co-state equation is a negative partial derivative of a Hamiltonian function with respect to a state variable;

[0184] Solving the co-state equation to obtain a differential equation of the co-state variable, wherein the differential equation includes a state deviation term and a product term of a state matrix and the co-state variable;

[0185] Calculating a state matrix, wherein the state matrix is ​​the partial derivatives of the dynamics equation with respect to the state variables;

[0186] Substitute the optimal control input expression into the dynamic equation and combine it with the differential equation of the co-state variables to form the Hamiltonian canonical equation system;

[0187] The numerical method is used to solve the Hamiltonian canonical equations to obtain the optimal state trajectory and the optimal control input sequence.

[0188] Exemplarily, the present invention provides a method for deriving an optimal control law using a variational method for aircraft trajectory correction. The method constructs a Hamiltonian function, introduces co-state variables, and solves the optimal control problem based on the Pontryagin minimum principle. The specific implementation steps of the method are described in detail below:

[0189] First, construct the Hamiltonian function. The Hamiltonian function is the core of the optimal control problem, which contains three key parts: state deviation term, control input term and dynamic constraint term. The state deviation term represents the weighted difference between the actual state and the desired state. For example, for the position and speed of the aircraft, the square of the Euclidean distance can be used to measure the deviation and assign different weights. Assuming that the current position of the aircraft is (x, y, z) = (1000m, 2000m, 5000m) and the desired position is (1100m, 2100m, 5100m), the position deviation can be expressed as the sum of the squares of the deviations in the three directions. The control input term represents the weighted control energy. For example, for the deflection of the aircraft's rudder and the engine thrust, their square sum can be used to represent the energy consumption. Assuming that the rudder deflection angle is 5 degrees and the engine thrust is 50kN, the control energy can be expressed as the square sum of these values ​​multiplied by the corresponding weight. The dynamic constraint term represents the product of the state equation and the co-state variable, which introduces the dynamic characteristics of the system into the optimization problem.

[0190] Next, co-state variables are introduced. Co-state variables are used to characterize the sensitivity of state variables to the objective function. For aircraft systems, each state variable (such as position, velocity, attitude angle, etc.) usually corresponds to a co-state variable. For example, if the system has 6 state variables (3D position and 3D velocity), 6 co-state variables need to be introduced. These co-state variables play a vital role in the subsequent optimization process, and they reflect the impact of state changes on the overall performance indicators.

[0191] Based on the Pontryagin minimum principle, the partial derivative of the Hamiltonian function with respect to the control input is taken and set equal to zero to obtain the optimal control condition. This step is actually to find the control input that minimizes the Hamiltonian function. For aircraft systems, the control input may include the deflection angle of the control surface and the engine thrust. By solving these partial derivative equations, we can obtain the relationship between the control input and the covariate variable.

[0192] Solve the optimal control condition and derive the optimal control input expression. This expression usually contains the inverse matrix of the control weight matrix, the transpose of the control matrix, and the co-state variables. For example, for a simplified two-dimensional planar motion model, the optimal control input may be expressed as the co-state variables multiplied by a coefficient matrix. This coefficient matrix is ​​determined by the system parameters and weight factors.

[0193] Compute the control matrix, which is the partial derivatives of the dynamic equations with respect to the control inputs. For aircraft systems, this typically involves calculating how control surface deflections and engine thrust affect the rate of change of the flight state. For example, the control matrix can be constructed by numerically estimating the effect of small changes in control inputs on the rate of change of the state.

[0194] Construct the co-state equation, which is the negative partial derivative of the Hamiltonian function with respect to the state variables. This step describes the evolution of the co-state variables. For aircraft systems, the co-state equation reflects how state changes affect the overall performance indicators. For example, the rate of change of the position co-state variable may be related to the current position deviation and velocity co-state variables.

[0195] Solving the co-state equations, we get the differential equations of the co-state variables. This differential equation usually contains the state deviation term and the product term of the state matrix and the co-state variables. For example, for the position co-state variable, its rate of change may be proportional to the position deviation and affected by the velocity co-state variable.

[0196] Calculate the state matrix, which is the partial derivatives of the dynamic equations with respect to the state variables. This step describes the mutual influence between the system states. For aircraft systems, the state matrix can be constructed by analyzing the aerodynamic model and kinematic relationships. For example, the influence of speed on position, the influence of attitude angle on speed, etc. can all be reflected in this matrix.

[0197] Substituting the optimal control input expression into the dynamic equations and combining it with the differential equations of the co-state variables, the Hamiltonian canonical equations are formed. This system of equations is a boundary value problem that contains differential equations of state variables and co-state variables. For the aircraft system, this system of equations describes the evolution of the entire optimal trajectory.

[0198] Finally, a numerical method is used to solve the Hamiltonian canonical equations to obtain the optimal state trajectory and the optimal control input sequence. Common numerical methods include shooting and gradient methods. For example, the fourth-order Runge-Kutta method is used to numerically integrate the differential equations, combined with an iterative optimization algorithm (such as Newton's method) to meet the boundary conditions.

[0199] Specific application case: Assume that a drone needs to fly from the initial position (0,0,100)m to the target position (1000,1000,200)m, while considering energy minimization. First, a Hamiltonian function is constructed, which includes the square term of position deviation, the square term of velocity (representing energy) and the dynamic constraint term. Six co-state variables are introduced, corresponding to three-dimensional position and three-dimensional velocity respectively. Based on the minimum principle, the optimal control input expression is derived, which is expressed as a linear combination of co-state variables.

[0200] Calculate the control matrix. Assuming that the power system of the drone makes the control input directly affect the acceleration, the non-zero elements of the control matrix mainly appear in the velocity equation. Construct the co-state equation. The change of the position co-state variable is related to the position deviation and the velocity co-state variable, and the change of the velocity co-state variable is related to the position co-state variable. Calculate the state matrix to reflect the relationship between position and velocity.

[0201] All equations are combined into a Hamiltonian canonical system of equations and solved using the shooting method. The initial guess can be a straight trajectory and a uniform motion. Through iterative calculations, a smooth S-shaped trajectory is finally obtained, which not only satisfies the initial and terminal conditions but also minimizes energy consumption. The optimal control input sequence shows that the drone accelerates at takeoff, maintains a relatively constant speed in the middle, and finally decelerates when approaching the target.

[0202] This method can not only generate the optimal trajectory, but also provide the optimal control strategy along the trajectory, so that the UAV can complete the task with the minimum energy consumption. The advantage of this method is that it takes into account the global optimum and can optimize the performance indicators while satisfying various constraints. By adjusting the weights of each term in the Hamiltonian function, different performance requirements can also be flexibly balanced, such as the trade-off between trajectory tracking accuracy and energy consumption.

[0203] Figure 2 FIG. 1 is a schematic diagram of a structure of an aircraft and satellite cluster cooperative navigation and positioning precision control system according to an embodiment of the present invention. Figure 2 As shown, the system comprises:

[0204] The first unit is used to establish a real-time two-way data link between the aircraft and the satellite cluster through a high-frequency broadband communication system, wherein the high-frequency broadband communication system adopts an adaptive frequency hopping technology to resist interference; a multi-mode multi-frequency receiver is installed on the aircraft, wherein the multi-mode multi-frequency receiver can simultaneously receive global positioning system signals, Beidou satellite navigation system signals and Galileo satellite navigation system signals; and data exchange within the satellite cluster is realized by using inter-satellite link technology;

[0205] The second unit is used for the aircraft to receive multi-system navigation signals from the satellite cluster, and to obtain its own motion state information using the airborne inertial navigation system, barometric altimeter and Doppler radar; to fuse the multi-source navigation information using an adaptive Kalman filter algorithm, which can dynamically adjust the weights according to the reliability of different information sources; to synchronize the time between the aircraft and the satellite cluster using the onboard atomic clock; and to calculate the precise position of the aircraft based on the fused multi-source navigation information using differential positioning technology;

[0206] The third unit is used to generate optimal control instructions for the aircraft based on the precise position of the aircraft and in combination with a preset flight plan, using a model predictive control algorithm, wherein the model predictive control algorithm takes into account the dynamic characteristics and environmental constraints of the aircraft; transmit the optimal control instructions to the flight control system of the aircraft, wherein the flight control system adopts an adaptive control strategy to adjust control parameters according to real-time flight status; continuously monitor the flight trajectory of the aircraft through a satellite cluster, and when a trajectory deviation is detected, calculate correction instructions using a satellite-ground coordinated trajectory correction algorithm, wherein the trajectory correction algorithm optimizes the correction strategy based on the minimum energy principle; and transmit the correction instructions to the aircraft through a high-frequency broadband communication system to achieve closed-loop precise control of the aircraft trajectory.

[0207] According to a third aspect of the embodiments of the present invention,

[0208] An electronic device is provided, comprising:

[0209] processor;

[0210] a memory for storing processor-executable instructions;

[0211] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0212] A fourth aspect of the embodiments of the present invention is:

[0213] A computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the aforementioned method is implemented.

[0214] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0215] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A precise control method for collaborative navigation and positioning of an aircraft and a satellite cluster, characterized in that: include: A real-time two-way data link is established between the aircraft and the satellite cluster through a high-frequency broadband communication system, wherein the high-frequency broadband communication system adopts adaptive frequency hopping technology to resist interference; a multi-mode multi-frequency receiver is installed on the aircraft, wherein the multi-mode multi-frequency receiver can simultaneously receive signals of the Global Positioning System, the Beidou Satellite Navigation System, and the Galileo Satellite Navigation System; and data exchange within the satellite cluster is realized using inter-satellite link technology; The aircraft receives multi-system navigation signals from the satellite cluster and uses the onboard inertial navigation system, barometric altimeter and Doppler radar to obtain its own motion status information; the adaptive Kalman filter algorithm is used to fuse the multi-source navigation information, and the adaptive Kalman filter algorithm can dynamically adjust the weight according to the reliability of different information sources; the onboard atomic clock is used to synchronize the time between the aircraft and the satellite cluster; Based on the fused multi-source navigation information, the precise position of the aircraft is calculated using differential positioning technology; Based on the precise position of the aircraft and in combination with a preset flight plan, the optimal control instructions for the aircraft are generated using a model predictive control algorithm, which takes into account the dynamic characteristics and environmental constraints of the aircraft; the optimal control instructions are transmitted to the flight control system of the aircraft, which adopts an adaptive control strategy to adjust control parameters according to the real-time flight status; the flight trajectory of the aircraft is continuously monitored through a satellite cluster, and when a trajectory deviation is detected, the correction instructions are calculated using a satellite-ground coordinated trajectory correction algorithm, which optimizes the correction strategy based on the minimum energy principle; The correction instructions are transmitted to the aircraft through a high-frequency broadband communication system to achieve closed-loop precise control of the aircraft trajectory.

2. The method according to claim 1, characterized in that The aircraft receives multi-system navigation signals from the satellite cluster and uses the onboard inertial navigation system, barometric altimeter and Doppler radar to obtain its own motion state information; the adaptive Kalman filter algorithm is used to fuse the multi-source navigation information, including: Establishing an aircraft navigation state model, wherein the aircraft navigation state model includes position, velocity, attitude, gyroscope drift and accelerometer bias; constructing a system state equation and an observation equation, wherein the system state equation represents the relationship between the state vector at a current moment and the state vector at a previous moment, the state transfer matrix and process noise, and the observation equation represents the relationship between the observation value and the state vector, the observation matrix and the observation noise; Execution time update, including state prediction and covariance prediction, where the state prediction uses the optimal state estimate and state transfer matrix of the previous moment to calculate the prior state estimate of the current moment, and the covariance prediction uses the posterior covariance matrix, state transfer matrix and process noise covariance matrix of the previous moment to calculate the prior covariance matrix of the current moment; Performing measurement updates, including calculating Kalman gain, updating state estimation, and updating covariance, wherein the calculation of Kalman gain involves a prior covariance matrix, an observation matrix, and an observation noise covariance matrix; The innovation sequence consistency test method is used to estimate the observation noise covariance in real time, wherein the innovation sequence consistency test method includes calculating the innovation sequence, estimating the innovation sequence covariance and updating the observation noise covariance; Dynamically adjusting the process noise covariance using a fading memory index method, wherein the fading memory index method includes calculating a forgetting factor, updating a state estimation error covariance, and adjusting the process noise covariance; Fusion of multi-source navigation information, including using satellite navigation system solutions as position and velocity observations, attitude information output by inertial navigation system as direct observations, and barometric altimeter and Doppler radar data as auxiliary observations; The fused aircraft navigation state estimation results are output, including three-dimensional position, velocity, attitude and error parameters of the inertial navigation system.

3. The method according to claim 2, characterized in that The innovative sequence consistency test method is used to estimate the observation noise covariance in real time, including: An observation residual sequence is calculated, where the observation residual sequence is the difference between the actual observation value and the state prediction value; a sample covariance of the observation residual sequence is estimated using a sliding window method, where the sliding window method uses the most recent N observation residual samples; an observation noise covariance estimate is updated, where the update process considers the sample covariance, the observation matrix, and the state prediction covariance matrix; and an exponential smoothing process is performed on the updated observation noise covariance estimate, where the exponential smoothing process uses a smoothing factor to adjust the weights of the new and old estimates.

4. The method according to claim 3, characterized in that Dynamically adjusting the process noise covariance using the fading memory index method includes: Setting an initial forgetting factor; calculating a filtering error, wherein the filtering error is the difference between an actual observation value and a predicted observation value; calculating an adaptive forgetting factor based on the filtering error and a state prediction covariance matrix; updating a state estimation error covariance using the adaptive forgetting factor; adjusting a process noise covariance based on the updated state estimation error covariance and the adaptive forgetting factor; Apply the updated observation noise covariance and process noise covariance to the Kalman filter update process at the next moment; The calculation of the adaptive forgetting factor is shown in the following formula: Wherein, λ(k) represents the adaptive forgetting factor of k at the current time, λ0 represents the initial forgetting factor, e(k) represents the filtering error of k at the current time, tr() represents the trace operation of the matrix, H(k) represents the observation matrix of k at the current time, P(k|k-1) represents the prior state estimation error covariance matrix of k at the current time, and R(k) represents the observation noise covariance matrix of k at the current time; The adaptive forgetting factor is used to update the state estimation error covariance as shown in the following formula: Wherein, P(k|k) represents the posterior state estimation error covariance matrix of the current time k, K(k) represents the Kalman gain matrix of the current time k, and I represents the identity matrix.

5. The method according to claim 1, characterized in that Based on the precise position of the aircraft and the preset flight plan, the optimal control instructions for the aircraft are generated using a model predictive control algorithm that takes into account the dynamic characteristics of the aircraft and environmental constraints, including: Establishing a six-degree-of-freedom dynamics model of an aircraft, the six-degree-of-freedom dynamics model includes three translation equations and three rotation equations, wherein the translation equation describes the position and velocity changes of the aircraft in three-dimensional space, and the rotation equation describes the attitude angle changes of the aircraft; discretizing the six-degree-of-freedom dynamics model to obtain a discrete time model, wherein the discrete time model is expressed as a functional relationship between a state vector and a control input vector; Design a model predictive control objective function, wherein the objective function includes a trajectory tracking error term and a control input cost term, wherein the trajectory tracking error term is used to minimize the state deviation in the prediction time domain, and the control input cost term is used to balance the control effect and energy consumption; defining constraints, wherein the constraints include a state constraint, a control input constraint, and a control input change rate constraint, wherein the state constraint ensures that the aircraft state is within a safe range, the control input constraint reflects the physical limitations of the actuator, and the control input change rate constraint ensures the smoothness of the control command; The objective function is converted into a quadratic form, the constraint conditions are converted into linear inequality constraints, and a quadratic programming problem is constructed; the quadratic programming problem is solved by an interior point method to obtain an optimal control sequence; the control instructions at the current moment are extracted from the optimal control sequence, and the control instructions are converted into a rudder deflection angle and an engine thrust instruction; the rudder deflection angle and the engine thrust instruction are executed to control the flight of the aircraft.

6. The method according to claim 1, characterized in that The flight trajectory of the aircraft is continuously monitored by a satellite cluster. When a trajectory deviation is detected, a trajectory correction algorithm coordinated by the satellite and the ground is used to calculate the correction instruction. The trajectory correction algorithm is based on the minimum energy principle to optimize the correction strategy including: Constructing a monitoring network consisting of multiple low-orbit satellites, wherein the satellites in the monitoring network are equipped with optical sensors and radar sensors for obtaining position information, speed information and attitude information of the aircraft; When a trajectory deviation is detected, the satellite-ground coordinated data fusion process is initiated, which includes: preprocessing the original satellite observation data, including denoising and outlier removal; using inter-satellite links for distributed data fusion; collecting and integrating ground radar data and ADS-B data; using a time synchronization algorithm to align data from different sources; using a federated Kalman filter algorithm to design sub-filters to process satellite data and ground data respectively; using information fusion criteria to merge sub-filter results to obtain a global optimal estimate; and dynamically adjusting fusion weights according to the reliability of each data source. The trajectory correction algorithm is designed based on the minimum energy principle, and the trajectory correction algorithm includes: Define an objective function, which includes a deviation term between the actual trajectory and the desired trajectory and a control input energy term; construct an aircraft dynamics constraint equation; consider control input restrictions, state variable restrictions and terminal constraints; use a variational method to derive an optimal control law; use a pseudospectral method to discretize the continuous-time optimal control problem and transform it into a nonlinear programming problem; use a sequential quadratic programming algorithm to solve the nonlinear programming problem; According to the optimal control sequence obtained by solving, specific correction instructions are generated, and the correction instructions include attitude adjustment instructions, speed change instructions and heading correction instructions; the model predictive control framework is used to realize closed-loop control, and the following operations are performed in each control cycle: Resolve the optimal control problem based on the current state; execute the first control instruction obtained by the solution; update the prediction time domain; adjust the weight matrix; and correct the dynamic model parameters.

7. The method according to claim 6, characterized in that The optimal control law derived by the variational method includes: Constructing a Hamiltonian function, wherein the Hamiltonian function includes a state deviation term, a control input term, and a dynamic constraint term, wherein the state deviation term represents a weighted difference between an actual state and a desired state, the control input term represents a weighted control energy, and the dynamic constraint term represents a product of a state equation and a co-state variable; Introducing co-state variables, wherein the co-state variables are used to characterize the sensitivity of the state variables to the objective function; Based on the Pontryagin minimum principle, the partial derivative of the Hamiltonian function with respect to the control input is calculated and set equal to zero to obtain the optimal control condition. Solving the optimal control condition and deriving the optimal control input expression, wherein the optimal control input expression includes the inverse matrix of the control weight matrix, the transpose of the control matrix and the co-state variable; Calculating a control matrix, the control matrix being the partial derivatives of the dynamics equations with respect to the control input; Constructing a co-state equation, wherein the co-state equation is a negative partial derivative of a Hamiltonian function with respect to a state variable; Solving the co-state equation to obtain a differential equation of the co-state variable, wherein the differential equation includes a state deviation term and a product term of a state matrix and the co-state variable; Calculating a state matrix, wherein the state matrix is ​​the partial derivatives of the dynamics equation with respect to the state variables; Substitute the optimal control input expression into the dynamic equation and combine it with the differential equation of the co-state variables to form the Hamiltonian canonical equation system; The numerical method is used to solve the Hamiltonian canonical equations to obtain the optimal state trajectory and the optimal control input sequence.

8. An aircraft and satellite cluster collaborative navigation and positioning precision control system, used to implement any of the methods of claims 1-7, characterized in that: include: The first unit is used to establish a real-time two-way data link between the aircraft and the satellite cluster through a high-frequency broadband communication system, wherein the high-frequency broadband communication system adopts an adaptive frequency hopping technology to resist interference; a multi-mode multi-frequency receiver is installed on the aircraft, wherein the multi-mode multi-frequency receiver can simultaneously receive global positioning system signals, Beidou satellite navigation system signals and Galileo satellite navigation system signals; and data exchange within the satellite cluster is realized by using inter-satellite link technology; The second unit is used for the aircraft to receive multi-system navigation signals from the satellite cluster, and to obtain its own motion state information using the airborne inertial navigation system, barometric altimeter and Doppler radar; to fuse the multi-source navigation information using an adaptive Kalman filter algorithm, which can dynamically adjust the weights according to the reliability of different information sources; and to synchronize the time between the aircraft and the satellite cluster using the onboard atomic clock; Based on the fused multi-source navigation information, the precise position of the aircraft is calculated using differential positioning technology; The third unit is used to generate optimal control instructions for the aircraft based on the precise position of the aircraft and in combination with a preset flight plan using a model predictive control algorithm, wherein the model predictive control algorithm takes into account the dynamic characteristics and environmental constraints of the aircraft; transmit the optimal control instructions to the flight control system of the aircraft, wherein the flight control system adopts an adaptive control strategy to adjust control parameters according to the real-time flight status; continuously monitor the flight trajectory of the aircraft through a satellite cluster, and when a trajectory deviation is detected, calculate the correction instructions using a satellite-ground coordinated trajectory correction algorithm, wherein the trajectory correction algorithm optimizes the correction strategy based on the minimum energy principle; The correction instructions are transmitted to the aircraft through a high-frequency broadband communication system to achieve closed-loop precise control of the aircraft trajectory.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method described in any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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