Multi-source information fusion positioning method for air refueling

Abstract

The invention provides a multi-source information fusion positioning method for air refueling, which relates to the technical field of information fusion, collects original visual data, global navigation satellite system (GNSS) data and inertial navigation system (INS) data, overcomes the limitation of a single sensor, and improves the positioning accuracy. A differential satellite navigation algorithm based on a mobile base station is used for accurately calculating the relative position and speed between an oiling machine and an oil receiving machine, and the problems that the updating frequency is low and the system is prone to being interfered by the atmosphere are solved. When information fusion is carried out, the difference of output frequencies of different sensors is considered, data of an IMU, a GNSS and a visual sensor are fused at the closest time point, the effectiveness and timeliness of information are guaranteed, and meanwhile, through the mode of automatically adjusting the size of a measured noise variance matrix, the accuracy of information fusion is improved. All observation information is effectively utilized, appropriate weight adjustment measures are taken for suspicious or abnormal data, and the positioning precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of information fusion, in particular to a multi-source information fusion positioning method for aerial refueling. Background Art

[0002] Aerial refueling, a key technology in modern aviation, plays a crucial role in increasing combat radius and loiter time, reducing logistical requirements, and enhancing battlefield survivability. However, aerial refueling operations are complex and highly risky, especially in complex and volatile flight environments. Ensuring precise docking between the tanker and receiver has become a core challenge hindering the development of aerial refueling technology. To address this issue, researchers have proposed various solutions. Among them, Sun Yongrong et al. proposed a relative navigation method based on the fusion of an inertial navigation system (INS), a global navigation satellite system (GNSS), and a visual navigation system (Vision). This scheme utilizes a federated filter structure to fuse the state estimates of each subsystem (INS / GNSS, INS / Vision). A fault-tolerant filter structure is designed, which estimates time-varying measurement noise using a sliding window and assigns information weights using a covariance singular value block method. This method, when GNSS signals experience soft failures due to factors such as occlusion, can supplement visual information to correct INS errors, thereby enabling estimation of the relative position of the tanker and receiver. Li Wei et al. also acquired three-dimensional target position information by integrating laser ranging and binocular vision technology. This method utilizes the advantages of high-precision distance measurement of laser sensors and binocular vision in spatial reconstruction, complementing each other. It can not only make up for the shortcomings of a single vision system in low light or occlusion conditions, but also correct the errors of laser ranging in harsh environments, thereby realizing docking between tanker and receiver aircraft.

[0003] Traditional aerial refueling navigation and positioning methods mainly rely on a single information source. However, a single navigation information source often has limitations. For example, the accuracy and stability of visual sensors are easily affected by weather and ambient light. Visual sensors are also limited by the distance between them and the target, making it difficult to provide high-precision sensor information for distant targets. GNSS updates are not frequent, and their signals may be affected by factors such as the atmosphere, building obstructions, and electromagnetic interference. In addition, if the number of satellites is insufficient or the distribution is uneven, their positioning accuracy and stability will also be affected. Navigation data errors of inertial navigation will continue to accumulate, and the longer the system operates, the greater the drift.

[0004] While the aforementioned fusion navigation scheme has improved navigation accuracy during aerial refueling docking to a certain extent, it still has some shortcomings and limitations. In the INS / GNSS / Vision combination scheme, although federated filtering and adaptive information allocation mechanisms are employed, the weight adjustments of some subsystems may not be timely enough during the fault isolation process, resulting in a certain impact on the overall estimation accuracy in complex environments. Furthermore, this scheme primarily addresses relative navigation in close-range aerial refueling scenarios and does not consider situations where the tanker and receiver are far apart. In the laser ranging and binocular vision fusion scheme, laser ranging technology is sensitive to environmental conditions (such as fog, rain, and target surface reflectivity) and is easily affected by external interference, which can affect measurement accuracy. The binocular vision system relies on image matching and 3D reconstruction algorithms, which have high computational complexity and may lack real-time performance during high-speed dynamic docking. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the present invention aims to propose a multi-source information fusion positioning method for aerial refueling, comprising:

[0006] Step 1: Obtain visual raw data, global navigation satellite system GNSS data and inertial navigation system INS data;

[0007] Step 2: Process the raw visual data at each moment to obtain the coordinates of the cone sleeve center in the camera coordinate system at each moment;

[0008] Step 3: Using Kalman filtering, the GNSS data is calculated to obtain the relative positions of the tanker and receiver at each moment. The GNSS data includes carrier phase double-difference observations and pseudorange double-difference observations.

[0009] Step 4: Using the tanker or receiver as the carrier, the inertial navigation system (INS) data is solved to obtain the target INS data at each moment. The target INS data at each moment includes the rotation matrix representing the attitude of the tanker and receiver in the navigation coordinate system at that moment, the speed of the tanker and receiver relative to the earth in the n-frame at that moment, and the position of the tanker and receiver at that moment.

[0010] Step 5: Fuse the coordinates of the drogue center in the camera coordinate system at each moment obtained in step 2, the relative positions of the tanker and receiver at each moment obtained in step 3, and the target inertial navigation data at each moment obtained in step 4 to obtain a fused positioning result.

[0011] Optionally, step 1 specifically includes:

[0012] Step 1.1: The camera on the receiving aircraft collects images of the drogue on the refueling aircraft and the environment surrounding the drogue at each moment. The images of the drogue and the environment surrounding the drogue constitute the raw visual data.

[0013] Step 1.2: Receive satellite signals from multiple navigation satellites through the GNSS sensors configured on the tanker and the receiving aircraft. The satellite signals from all navigation satellites form the Global Navigation Satellite System (GNSS) data.

[0014] Step 1.3: Use the inertial sensors on the tanker to monitor and record the accelerometer and gyroscope data output by the tanker's inertial navigation system. Calculate the tanker's position, velocity, and attitude based on the accelerometer and gyroscope data. Use the inertial sensors on the receiving aircraft to monitor and record the accelerometer and gyroscope data output by the receiving aircraft's inertial navigation system. Calculate the inertial navigation system (INS) data based on the accelerometer and gyroscope data.

[0015] Optionally, step 2 specifically includes:

[0016] Step 2.1: Use the YOLO v8 algorithm to detect the image in the raw visual data at each moment and obtain the coordinates (u, v) of the tanker drogue center in the pixel coordinate system of the monocular camera model;

[0017] Step 2.2: Convert the coordinates (u, v) of the cone sleeve center in the pixel coordinate system to the coordinates (x, y) of the cone sleeve center in the image coordinate system using the following formula:

[0018]

[0019] Among them, u0 and v0 represent the coordinates of the image center of the cone sleeve in the pixel coordinate system, d x with d y Indicates the actual physical size corresponding to each pixel unit in the image coordinate system;

[0020] Step 2.3: Convert the coordinates (x, y) of the cone sleeve center in the image coordinate system to the coordinates (X C ,Y C ,Z C ), which is specifically achieved through the following formula:

[0021]

[0022] Where f is the focal length of the camera, that is, the difference between the camera coordinate system and the image coordinate system on the Z axis. f is calculated using the following formula:

[0023]

[0024] Where p is the pixel length or width of the cone sleeve, and w is the actual length or actual width of the cone sleeve;

[0025] Thus, the coordinates of the cone sleeve center in the camera coordinate system at each moment are obtained.

[0026] Optionally, step 3 specifically includes:

[0027] Step 3.1: Obtain the GNSS carrier phase and pseudorange double difference observation model, expressed as:

[0028]

[0029] in, The double difference observation values ​​of the carrier phase of satellite p and satellite q for the receiver s configured for the tanker and the receiver r configured for the receiver, is the actual distance from the receiver r to the satellite p; is the actual distance from the receiver s to the satellite p; is the actual distance from the receiver r to the satellite q; is the actual distance from receiver s to satellite q; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite p; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite q; is the double difference noise of receiver r and receiver s with respect to satellite p and satellite q; is the double difference observation value of pseudorange of receiver r and receiver s about satellite p and satellite q;

[0030] Step 3.2: Construct the state equation and measurement equation of the discretized carrier phase and pseudo-range differential positioning model, which can be expressed as:

[0031] X' k =φ k,k-1 X' k-1 +W' k-1 ,W' k-1 ~N(0,Q' k );

[0032] Z' k =H' k X'k+V' k ,V' k ~N(0,R' k );

[0033] Among them, X' k Represents the state vector of carrier phase and pseudorange differential positioning, Φ k,k-1 is the state transfer matrix of carrier phase and pseudorange differential positioning from time k-1 to k; W'k-1 is the system noise matrix of carrier phase and pseudorange differential positioning at time k-1, Q' k is the covariance matrix of the system noise of carrier phase and pseudorange differential positioning at time k; Z' k is the measurement vector of carrier phase and pseudo-range differential positioning at time k; H' k is the measurement matrix of carrier phase and pseudo-range differential positioning at time k; V' k represents the measurement noise matrix of carrier phase and pseudorange differential positioning at time k; R' k is the measurement noise covariance matrix of carrier phase and pseudorange differential positioning at time k;

[0034] Step 3.3: Perform Kalman filtering to solve the state equation and measurement equation of the discretized carrier phase and pseudo-range differential positioning model to obtain the baseline vector at each moment, that is, the relative position of the tanker and receiver at each moment.

[0035] Optional, X' in step 3.2 k , Φ k,k-1 and Z' k Expressed as:

[0036]

[0037] Φ k,k-1 =I 3+m ;

[0038]

[0039] Among them, B k is the baseline vector, and B k =(δx,δy,δz), where δx is the distance between the receiving aircraft and the refueling aircraft in the x-direction, δy is the distance between the receiving aircraft and the refueling aircraft in the y-direction, and δz is the distance between the receiving aircraft and the refueling aircraft in the z-direction; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite 1; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite m, I 3+m is the identity matrix of 3+m dimensions; is the double difference observation value of pseudorange of receiver r and receiver s about satellite 1 and satellite 2; is the double difference observation value of pseudorange of receiver r and receiver s about satellite 1 and satellite m; is the double difference observation value of the carrier phase of satellite 1 and satellite 2 from receiver r and receiver s; are the double-difference observations of the carrier phase of satellite 1 and satellite 2 from receiver r and receiver s.

[0040] Optional, H' in step 3.2 kObtained through:

[0041] Step A1: Process the GNSS data using the pseudo-range single point positioning method to obtain the initial position (x0, y0, z0) of the receiver r;

[0042] Step A2: The actual distance from the receiver r to the satellite p Perform linear expansion to obtain The linear representation of is:

[0043]

[0044] in, represents the distance from the initial position (x0, y0, z0) of the receiver r to the satellite p;

[0045] Similarly, The linear representation of is:

[0046]

[0047] in, represents the distance from the initial position (x0, y0, z0) of the receiver r to the satellite q;

[0048] Step A3: The actual distance from the receiver s to the satellite p Perform linear expansion at the initial position (x0, y0, z0) of the receiver r, and we get The linear representation of is:

[0049]

[0050] in, represents the unit line of sight vector from receiver r to satellite p;

[0051] Similarly, The linear representation of is:

[0052]

[0053] in, represents the unit line of sight vector from receiver r to satellite q;

[0054] Step A4: The linear representation of The linear representation of The linear representation of Substitute the linear representation of into the GNSS carrier phase and pseudorange double difference observation model to obtain H' k , expressed as:

[0055]

[0056] Where λ is the carrier wavelength, and D and E are expressed as:

[0057]

[0058] in, is the unit line of sight vector from receiver r to satellite 1, is the unit line of sight vector from receiver r to satellite 2, is the unit line of sight vector from receiver r to satellite m.

[0059] Optionally, step 4 specifically includes:

[0060] Step 4.1: Using the tanker or receiver as the carrier, perform attitude calculation on the INS data to obtain the rotation matrix representing the attitude of the tanker and receiver in the navigation coordinate system at each moment.

[0061] Step 4.2: Based on the rotation matrix representing the attitude in the navigation coordinate system, the velocity of the inertial navigation system INS data is solved to obtain the motion speed of the tanker and the receiving aircraft relative to the earth in the n-frame at each moment. This is achieved by the following formula:

[0062]

[0063] in, represents the velocity of the carrier relative to the earth in the n-frame at time k, It represents the velocity of the carrier relative to the earth in the n-frame at time k-1, represents the relative force at time k in system b, represents the angular velocity of the Earth's rotation, Indicates the angular velocity of the carrier relative to the earth's rotation in the navigation coordinate system. The inertial navigation system INS data includes g n represents the gravity in the n-system;

[0064] Thus, the velocity of the carrier relative to the earth in the n-frame at each moment is calculated, and then the velocity of the tanker and receiver relative to the earth in the n-frame at each moment is calculated;

[0065] Step 4.3: Based on the speed of the tanker and receiver relative to the Earth in the n-frame at each moment, the position of the tanker and receiver at each moment is calculated using the following formula:

[0066]

[0067] Among them, pk represents the position of the carrier at time k, p k-1 represents the position of the carrier at time k-1, M pv Shows the mapping relationship matrix between position and velocity;

[0068] In this way, the position of the carrier at each moment is calculated, and then the positions of the refueling machine and the receiving machine at each moment are obtained.

[0069] Optionally, step 4.1 specifically includes:

[0070] Step 4.1.1: Calculate the rotation change of the carrier coordinate system (i.e., the b-system) from time k-1 to time k, with the inertial coordinate system (i.e., the i-system) as the reference base. This is achieved specifically through the following formula:

[0071]

[0072] Where I represents the identity matrix, for The vector direction of the corresponding equivalent rotation vector, τ represents the sampling time interval, is the angular velocity of the carrier in the carrier coordinate system relative to the inertial coordinate system. The inertial navigation system INS data contains express The antisymmetric matrix of ;

[0073] Step 4.1.2: Calculate the rotation change of the navigation coordinate system, i.e., the n-system, from time k-1 to time k, with the i-system as the reference base. This is achieved specifically through the following formula:

[0074]

[0075] in, for The vector direction of the corresponding equivalent rotation vector, Indicates the angular velocity of the carrier in the navigation coordinate system relative to the inertial coordinate system. The inertial navigation system INS data contains express The antisymmetric matrix of ;

[0076] Step 4.1.3: According to and Calculate the rotation matrix representing the attitude in the navigation coordinate system at time k This is achieved specifically through the following formula:

[0077]

[0078] in, represents the rotation matrix of system i relative to system n at time k, represents the rotation matrix of system b relative to system i at time k, represents the rotation matrix of system i relative to system n at time k-1, represents the rotation matrix of system b relative to system i at time k-1, Represents the rotation matrix representing the attitude in the navigation coordinate system at time k-1

[0079] Therefore, according to steps 4.1.1 to 4.1.3, the rotation matrix representing the attitude in the navigation coordinate system at each moment is calculated, and then the rotation matrix representing the attitude of the tanker and the receiving aircraft in the navigation coordinate system at each moment is obtained.

[0080] Optionally, step 5 specifically includes:

[0081] Step 5.1: Construct the state space model of the random linear system, expressed as:

[0082]

[0083] Among them, X k is the state vector at time k, Z k is the measurement vector at time k, X k-1 is the state vector at time k-1, W k-1 is the system noise vector at time k-1, V k is the measurement noise vector at time k, Φ k / k-1 represents the state transfer matrix at time k, H k represents the observation matrix at time k;

[0084] Among them, Φ k / k-1 and H k Expressed as:

[0085]

[0086] Among them, F(t) is the inertial navigation error state transfer matrix, [t k ,t k-1 ] is the continuous time interval from time k-1 to time k, I3 represents the 3D identity matrix, 03 represents the 3D zero matrix, l b is the arm vector of the GNSS antenna, l b × is l b The antisymmetric matrix of Represents the attitude matrix of the carrier coordinate system relative to the navigation coordinate system;

[0087] Step 5.2: Based on the soft chi-square Kalman filter, the state space model of the random linear system is improved to obtain the improved model, which is expressed as:

[0088]

[0089] in, represents the prior estimate at time k, represents the posterior estimate of the state at time k-1, Including the target inertial navigation data at time k-1, P k / k-1 represents the prior estimate of the covariance matrix at time k, P k-1 represents the posterior estimate of the covariance matrix at time k-1, Q k-1 represents the process noise covariance matrix at time k-1, r k represents the measurement prediction error, Z k represents the observation information at time k, Z k Including the coordinates of the drogue center in the camera coordinate system at time k and the relative positions of the tanker and receiver at time k, A k is the intermediate variable, R k represents the covariance matrix of observation noise, K k represents the Kalman gain, represents the posterior estimate of the state at time k, P k represents the posterior estimate of the covariance matrix at time k, and I represents the identity matrix;

[0090] Step 5.3: According to A k and r k Calculate the statistic λ at time k k , which is specifically achieved through the following formula:

[0091]

[0092] Step 5.4: Determine λ k Is it greater than the preset threshold T Dm , in λ k Greater than the preset threshold T Dm In this case, and P k As the fusion positioning result, in λ k Less than or equal to the preset threshold T Dm If yes, proceed to step 5.5;

[0093] Step 5.5: and P k Update and get and P' k , which is specifically achieved through the following formula:

[0094]

[0095] Will and P'k As the fusion positioning result.

[0096] The beneficial effects of adopting the above technical solution are:

[0097] This invention collects raw visual data, Global Navigation Satellite System (GNSS) data, and Inertial Navigation System (INS) data, overcoming the limitations of a single sensor. It uses a differential satellite navigation algorithm based on a mobile reference station to accurately calculate the relative position and velocity between the tanker and the receiving aircraft, overcoming issues such as low update frequency and susceptibility to atmospheric interference. When performing information fusion, the invention considers the differences in output frequencies of different sensors and fuses the data from the IMU, GNSS, and visual sensors at the closest possible time point, ensuring the validity and timeliness of the information. Furthermore, the invention effectively utilizes all observation information by automatically adjusting the size of the measurement noise variance matrix and adopts appropriate weighting measures for suspicious or abnormal data, thereby improving positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 1 is a flow chart of a multi-source information fusion positioning method for aerial refueling according to an embodiment of the present invention;

[0099] Figure 2 This figure is a diagram of experimental results of a multi-source information fusion positioning method for aerial refueling in an embodiment of the present invention. DETAILED DESCRIPTION

[0100] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0101] To address the challenges of existing technologies, this paper provides a multi-source information fusion positioning method for aerial refueling, overcoming existing issues such as single sensor signal obstruction, error accumulation, and environmental interference. By integrating machine vision, differential satellite navigation, and inertial navigation, and employing an improved fusion algorithm, this method achieves real-time synchronization and efficient integration of various navigation data, meeting the requirements for high-precision and high-reliability navigation and positioning.

[0102] Combine Figure 1 The invention provides a multi-source information fusion positioning method for aerial refueling, which may include the following steps:

[0103] Step 1: Obtain visual raw data, global navigation satellite system GNSS data and inertial navigation system INS data;

[0104] Step 1.1: The camera on the receiving aircraft collects images of the drogue on the refueling aircraft and the environment surrounding the drogue at each moment. The images of the drogue and the environment surrounding the drogue constitute the raw visual data.

[0105] Step 1.2: Receive satellite signals from multiple navigation satellites through the GNSS sensors configured on the tanker and the receiving aircraft. The satellite signals include carrier waves, ranging codes, navigation messages, and other data. The satellite signals from all navigation satellites constitute the Global Navigation Satellite System (GNSS) data.

[0106] Step 1.3: Monitor and record the accelerometer and gyroscope data output by the tanker's inertial navigation system using the inertial sensors configured on the tanker, and calculate the tanker's position, velocity, and attitude based on the accelerometer and gyroscope data. Monitor and record the accelerometer and gyroscope data output by the receiver's inertial navigation system using the inertial sensors configured on the receiver, and calculate the inertial navigation system (INS) data based on the accelerometer and gyroscope data. Specifically, calculate the receiver's position, velocity, and attitude. The tanker's position, velocity, and attitude, together with the receiver's position, velocity, and attitude, constitute the INS data.

[0107] Step 2: Process the raw visual data at each moment to obtain the coordinates of the cone sleeve center in the camera coordinate system at each moment;

[0108] In the visual data processing part, a geometric visual positioning algorithm based on target detection is adopted. This method closely combines target detection with geometric visual positioning. The target detection algorithm is used to quickly and accurately locate the two-dimensional image position of the target. Subsequently, the geometric visual positioning algorithm based on the principle of similar triangles is used to further estimate the coordinate information and posture of the target in three-dimensional space. The results of target detection provide the subsequent positioning algorithm with accurate candidate areas and the size of the target cone in the image, while the geometric visual positioning is based on these detection results and maps the points on the image to the world coordinate system through the conversion of the coordinate system. The two work together to not only improve the positioning efficiency of the system, but also ensure the accuracy and robustness of positioning in complex environments. This is achieved through the following steps:

[0109] Step 2.1: Use the YOLO v8 (You Only Look Once) algorithm to detect the image in the raw visual data at each moment and obtain the coordinates (u, v) of the tanker drogue center in the pixel coordinate system of the monocular camera model.

[0110] Among them, YOLO v8 is a single-stage, efficient target detection model. The input image or video is processed by the YOLOv8 network, and multi-level features are extracted through the backbone network. The feature fusion is combined with FPN (Feature Pyramid Network) and PANet (Path Aggregation Network), thereby taking into account the detection effect of targets at different scales. After removing redundant detection frames through non-maximum suppression (NMS), the network finally outputs the target's bounding box center position coordinates (u, v), bounding box length and width, category confidence, and other information. In this invention, the output is the coordinates (u, v) of the tanker cone sleeve center in the pixel coordinate system of the monocular camera model. At the same time, the pixel size of the cone sleeve can also be output. Both play a key role in the subsequent geometric vision positioning algorithm.

[0111] Step 2.2: Convert the coordinates (u, v) of the cone sleeve center in the pixel coordinate system to the coordinates (x, y) of the cone sleeve center in the image coordinate system using the following formula:

[0112]

[0113] Among them, u0 and v0 represent the coordinates of the image center of the cone sleeve in the pixel coordinate system, d x with d y Indicates the actual physical size corresponding to each pixel unit in the image coordinate system;

[0114] Step 2.3: Convert the coordinates (x, y) of the cone sleeve center in the image coordinate system to the coordinates (X C ,Y C ,Z C ), which is specifically achieved through the following formula:

[0115]

[0116] Where f is the focal length of the camera, that is, the difference between the camera coordinate system and the image coordinate system on the Z axis. f is calculated using the following formula:

[0117]

[0118] Where p is the pixel length or width of the cone sleeve, and w is the actual length or actual width of the cone sleeve;

[0119] Thus, the coordinates of the cone sleeve center in the camera coordinate system at each moment are obtained.

[0120] Step 3: Using Kalman filtering, the GNSS data is calculated to obtain the relative positions of the tanker and receiver at each moment. The GNSS data includes carrier phase double-difference observations and pseudorange double-difference observations.

[0121] Step 3.1: Obtain the GNSS carrier phase and pseudorange double difference observation model, expressed as:

[0122]

[0123] in, The double difference observation values ​​of the carrier phase of satellite p and satellite q for the receiver s configured for the tanker and the receiver r configured for the receiver, is the actual distance from the receiver r to the satellite p; is the actual distance from the receiver s to the satellite p; is the actual distance from the receiver r to the satellite q; is the actual distance from receiver s to satellite q; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite p; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite q; is the double difference noise of receiver r and receiver s with respect to satellite p and satellite q; is the double difference observation value of pseudorange of receiver r and receiver s about satellite p and satellite q;

[0124] Step 3.2: Construct the state equation and measurement equation of the discretized carrier phase and pseudo-range differential positioning model, which can be expressed as:

[0125] X' k =φ k,k-1 X' k-1 +W' k-1 ,W' k-1 ~N(0,Q' k );

[0126] Z' k =H' k X'k+C' k ,V' k ~N(0,R' k );

[0127] Among them, X' k Represents the state vector of carrier phase and pseudorange differential positioning, Φ k,k-1 is the state transfer matrix of carrier phase and pseudorange differential positioning from time k-1 to k; W' k-1 is the system noise matrix of carrier phase and pseudorange differential positioning at time k-1, Q' k is the covariance matrix of the system noise of carrier phase and pseudorange differential positioning at time k; Z' k is the measurement vector of carrier phase and pseudo-range differential positioning at time k; H' k is the measurement matrix of carrier phase and pseudo-range differential positioning at time k; V'k represents the measurement noise matrix of carrier phase and pseudorange differential positioning at time k; R' k is the measurement noise covariance matrix of carrier phase and pseudorange differential positioning at time k;

[0128] Among them, X' k , Φ k,k-1 and Z' k Expressed as:

[0129]

[0130] φ k,k-1 =I 3+m ;

[0131]

[0132] Among them, B k is the baseline vector, and B k =(δx,δy,δz), where δx is the distance between the receiving aircraft and the refueling aircraft in the x-direction, δy is the distance between the receiving aircraft and the refueling aircraft in the y-direction, and δz is the distance between the receiving aircraft and the refueling aircraft in the z-direction; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite 1; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite m, I 3+m is the identity matrix of 3+m dimensions; is the double difference observation value of pseudorange of receiver r and receiver s about satellite 1 and satellite 2; is the double difference observation value of pseudorange of receiver r and receiver s about satellite 1 and satellite m; is the double difference observation value of the carrier phase of satellite 1 and satellite 2 from receiver r and receiver s; are the double-difference observations of the carrier phase of satellite 1 and satellite 2 from receiver r and receiver s.

[0133] Among them, the state vector X' for carrier phase and pseudorange differential positioning k Before Kalman filtering, the baseline vector B in the figure is obtained by using pseudorange single-point positioning based on the Global Navigation Satellite System (GNSS) data to calculate the relative positions of the tanker and receiver as the prior value of the baseline vector B. For the single-difference integer ambiguity, since the integer ambiguity does not change when a cycle slip does not occur, the state value of the single-difference integer ambiguity between stations is directly inherited from the previous epoch. If a cycle slip is detected, the pseudorange observation value is used to initialize the integer ambiguity. The integer ambiguity of the tanker receiver and the integer ambiguity of the receiver are obtained, and the single-difference integer ambiguity is obtained by subtracting the two.

[0134] Among them, H' k Obtained through:

[0135] Step A1: Process the GNSS data using the pseudo-range single point positioning method to obtain the initial position (x0, y0, z0) of the receiver r;

[0136] Step A2: The actual distance from the receiver r to the satellite p Perform linear expansion, expressed as:

[0137]

[0138] in, is the actual distance from the receiver r to the satellite p; Indicates the distance from (x0, y0, z0) to satellite p, (X p ,Y p ,Z p ) is the three-dimensional coordinate of satellite p. dx, dy, dz represent the distances in three directions between the initial position of receiver r and its precise position. This distance is much smaller than the distance between the satellite and the receiver and can be ignored. Thus, we can get The linear representation of is:

[0139]

[0140] in, represents the distance from the initial position (x0, y0, z0) of the receiver r to the satellite p;

[0141] Similarly, The linear representation of is:

[0142]

[0143] in, represents the distance from the initial position (x0, y0, z0) of the receiver r to the satellite q;

[0144] Step A3: The actual distance from the receiver s to the satellite p Perform linear expansion at the initial position (x0, y0, z0) of the receiver r, and we get The linear representation of is:

[0145]

[0146] in, represents the unit line of sight vector from receiver r to satellite p;

[0147] in, The linear representation of is obtained by the following steps:

[0148] Will Perform linear expansion at the initial position (x0, y0, z0) of the receiver r, expressed as:

[0149]

[0150] make

[0151] Combining the above two formulas, we can get Linear representation of .

[0152] Similarly, The linear representation of is:

[0153]

[0154] in, represents the unit line of sight vector from receiver r to satellite q;

[0155] Step A4: The linear representation of The linear representation of The linear representation of Substitute the linear representation of into the GNSS carrier phase and pseudorange double difference observation model to obtain H' k , expressed as:

[0156]

[0157] Where λ is the carrier wavelength, and D and E are expressed as:

[0158]

[0159] in, is the unit line of sight vector from receiver r to satellite 1, is the unit line of sight vector from receiver r to satellite 2, is the unit line of sight vector from receiver r to satellite m.

[0160] Step 3.3: Perform Kalman filtering to solve the state equation and measurement equation of the discretized carrier phase and pseudo-range differential positioning model to obtain the baseline vector at each moment, that is, the relative position of the tanker and receiver at each moment.

[0161] Specifically, a Kalman filter is used to calculate the relative position of the two aircraft, obtaining a real-number estimate of the single-difference integer ambiguity. However, integer ambiguities are integer-valued. To improve the accuracy of the position solution, the real-number solution obtained by the Kalman filter is fixed to an exact integer solution using the integer ambiguity fixing algorithm, the LAMBDA algorithm.

[0162] Step 4: Using the tanker or receiver as the carrier, the inertial navigation system (INS) data is solved to obtain the target INS data at each moment. The target INS data at each moment includes the rotation matrix representing the attitude of the tanker and receiver in the navigation coordinate system at that moment, the speed of the tanker and receiver relative to the earth in the n-frame at that moment, and the position of the tanker and receiver at that moment.

[0163] Step 4.1: Using the tanker or receiver as the carrier, perform attitude calculation on the INS data to obtain the rotation matrix representing the attitude of the tanker and receiver in the navigation coordinate system at each moment.

[0164] Step 4.1.1: Calculate the rotation change of the carrier coordinate system (i.e., the b-system) from time k-1 to time k, with the inertial coordinate system (i.e., the i-system) as the reference base. This is achieved specifically through the following formula:

[0165]

[0166] Where I represents the identity matrix, for The vector direction of the corresponding equivalent rotation vector, τ represents the sampling time interval, is the angular velocity of the carrier in the carrier coordinate system relative to the inertial coordinate system. The inertial navigation system INS data contains express The antisymmetric matrix of ;

[0167] in, The calculation formula can be derived from the following formula:

[0168] The attitude differential equation of system b relative to system n is expressed as:

[0169]

[0170] in, It is the attitude matrix of the carrier coordinate system relative to the navigation coordinate system, and also the rotation matrix from the navigation coordinate system to the carrier coordinate system. for The first derivative of is the angular velocity of the carrier coordinate system relative to the navigation coordinate system, express The component on the z axis, the same goes for x and y. express The antisymmetric matrix of

[0171]

[0172] There are two ways to deal with the attitude differential equation. First, we can get the differential equation And similarly, we can get:

[0173]

[0174] in, is the attitude matrix of the inertial coordinate system relative to the navigation coordinate system, is the attitude matrix of the navigation coordinate system relative to the inertial coordinate system, for The first derivative of for The first derivative of is the angular velocity of the navigation coordinate system relative to the inertial coordinate system;

[0175] From the two differential equations we can get

[0176]

[0177] in, represents the rotation matrix of system b relative to system i at time k, Indicates that system i is equivalent to the rotation matrix of system n at time k, It represents the rotation change of b system from time k-1 to time k when i system is used as reference base. Obtain:

[0178]

[0179] Here θ is used to represent the modulus of the equivalent rotation vector, yes The vector direction of the corresponding equivalent rotation vector. At this time, assuming that the rotation angle θ within the sampling time interval τ is a small amount, then approximately sinθ=θ, cosθ=1, and we get The calculation formula of .

[0180] Step 4.1.2: Calculate the rotation change of the navigation coordinate system, i.e., the n-system, from time k-1 to time k, with the i-system as the reference base. This is achieved specifically through the following formula:

[0181]

[0182] in, for The vector direction of the corresponding equivalent rotation vector, Indicates the angular velocity of the carrier in the navigation coordinate system relative to the inertial coordinate system. The inertial navigation system INS data contains express The antisymmetric matrix of ;

[0183] in, The calculation formula can be derived from the following formula:

[0184] from Obtain:

[0185]

[0186] Similarly, we can get the approximation by rotating a small amount. The calculation formula of .

[0187] Step 4.1.3: According to and Calculate the rotation matrix representing the attitude in the navigation coordinate system at time k This is achieved specifically through the following formula:

[0188]

[0189] in, represents the rotation matrix of system i relative to system n at time k, represents the rotation matrix of system b relative to system i at time k, represents the rotation matrix of system i relative to system n at time k-1, represents the rotation matrix of system b relative to system i at time k-1, Represents the rotation matrix representing the attitude in the navigation coordinate system at time k-1

[0190] Therefore, according to steps 4.1.1 to 4.1.3, the rotation matrix representing the attitude in the navigation coordinate system at each moment is calculated, and then the rotation matrix representing the attitude of the tanker and the receiving aircraft in the navigation coordinate system at each moment is obtained.

[0191] Step 4.2: Based on the rotation matrix representing the attitude in the navigation coordinate system, the velocity of the inertial navigation system INS data is solved to obtain the motion speed of the tanker and the receiving aircraft relative to the earth in the n-frame at each moment. This is achieved by the following formula:

[0192]

[0193] in, represents the velocity of the carrier relative to the earth in the n-frame at time k, It represents the velocity of the carrier relative to the earth in the n-frame at time k-1, represents the relative force at time k in system b, represents the angular velocity of the Earth's rotation, Indicates the angular velocity of the carrier relative to the earth's rotation in the navigation coordinate system. The inertial navigation system INS data includes g n represents the gravity in the n-system;

[0194] Thus, the velocity of the carrier relative to the earth in the n-frame at each moment is calculated, and then the velocity of the tanker and receiver relative to the earth in the n-frame at each moment is calculated;

[0195] Step 4.3: Based on the speed of the tanker and receiver relative to the Earth in the n-frame at each moment, the position of the tanker and receiver at each moment is calculated using the following formula:

[0196]

[0197] Among them, p k represents the position of the carrier at time k, p k-1 represents the position of the carrier at time k-1, M pv Shows the mapping relationship matrix between position and velocity;

[0198] Among them, for M in the above formula pv Matrix, the present invention adopts the situation of taking different coordinate systems for position and speed, taking the coordinate geographic coordinate system (latitude, longitude and altitude) and the speed navigation coordinate system (ENU) as an example, there are:

[0199]

[0200] in, Indicates the speed in longitude in the geographic coordinate system, Indicates latitude, Indicates altitude, speed in geographic coordinate system, L indicates latitude, represents the speed in the east direction in the n coordinate system, Indicates the north direction, Indicates the direction of the sky.

[0201] Among them, R M Indicates the meridian radius, R N represents the radius of the circle, and h represents the height. The relationship matrix can be expressed as:

[0202]

[0203] In this way, the position of the carrier at each moment is calculated, and then the positions of the refueling machine and the receiving machine at each moment are obtained.

[0204] Multi-source navigation information fusion technology leverages the redundancy and complementary characteristics of information from different sensors. It fuses various navigation information using optimization or estimation algorithms to form a globally consistent optimal estimate of aircraft navigation information. It also enables real-time detection and isolation of sensor data anomalies. Kalman filtering is a commonly used information fusion technique, combining predicted and observed information using an optimal weight distribution.

[0205] Inertial navigation systems and satellite positioning systems are commonly used navigation and positioning devices in the aviation industry. In autonomous aerial refueling applications, real-time information about the tanker's drogue is required. This information cannot be directly provided by inertial navigation systems or satellite positioning systems. Therefore, visual positioning is required to determine the relative position of the drogue and the receiving aircraft. To combine this information, the extended Kalman filter can be used.

[0206] Step 5: Fuse the coordinates of the drogue center in the camera coordinate system at each moment obtained in step 2, the relative positions of the tanker and receiver at each moment obtained in step 3, and the target inertial navigation data at each moment obtained in step 4 to obtain a fused positioning result.

[0207] Step 5.1: Construct the state space model of the random linear system, expressed as:

[0208]

[0209] Among them, X k is the state vector at time k, Z k is the measurement vector at time k, X k-1 is the state vector at time k-1, W k-1 is the system noise vector at time k-1, V k is the measurement noise vector at time k, Φ k / k-1 represents the state transfer matrix at time k, H k represents the observation matrix at time k;

[0210] Among them, W k-1 and V k They are all zero-mean Gaussian white noise vector sequences, and they are uncorrelated with each other, that is, they meet the following basic assumptions of Kalman filtering on noise. The basic assumptions are expressed as follows:

[0211]

[0212] Among them, Q k is the process noise covariance matrix, Q k is positive semidefinite, R k is the measurement noise covariance matrix, Rk is positive definite, δ k is the Kronecker function;

[0213] Among them, Φ k / k-1 and H k Expressed as:

[0214]

[0215] Among them, F(t) is the inertial navigation error state transfer matrix, [t k ,t k-1 ] is the continuous time interval from time k-1 to time k, I3 represents the 3D identity matrix, 03 represents the 3D zero matrix, l b is the arm vector of the GNSS antenna, l b × is l b The antisymmetric matrix of Represents the attitude matrix of the carrier coordinate system relative to the navigation coordinate system;

[0216] Among them, Φ k / k-1 It is derived by the following formula:

[0217] The inertial navigation system provides the most comprehensive carrier information and its output frequency is much higher than that of the other two sensors. Therefore, the recursive equation of inertial navigation can be used as the prediction equation of the filter. The GNSS / INS / VIS loose combination can use the error state Kalman filter (indirect Kalman filter) for integrated navigation solution. Therefore, the state vector of the Kalman filter contains the navigation state error and sensor error, and is defined as:

[0218]

[0219] Among them, δr n is the inertial position error vector; δv n is the zero bias vector; b a is the zero bias vector of the three-axis accelerometer; s g is the gyro scale factor error vector; s a is the accelerometer scale factor error vector. Each component in the vector δx is a function of time, φ angle error, b g For the convenience of writing, the time variable symbol t is omitted in the zero bias of the gyroscope.

[0220] The bias and scale factor errors of the gyroscope and accelerometer are augmented into the state variables of the Kalman filter for estimation. To obtain the system state equation, we first need to obtain the continuous-time differential equation for the state error δx(t) at time t, which can be written as follows:

[0221]

[0222] Where F(t) represents the state transfer matrix, w(t) is the process noise vector;

[0223] Taking the derivative of the δx(t) vector, that is, taking the derivative of each component of the vector with respect to time t, we can get the previous p k The calculation formula of The calculation formula and The calculation formula of , and then based on the state error recursion method, the formula under the error state is obtained, which is expressed as:

[0224]

[0225] Among them, f n represents the specific force under the n system, v n Indicates the velocity in the n system.

[0226] This solution models the gyro and accelerometer bias and scale factor errors as first-order Gaussian Markov processes, expressed as:

[0227]

[0228] Among them, T gb 、T ab 、T gs and T as is the correlation time of the first-order Gauss-Markov process, w gb (t), w ab (t), w gs (t) and w as (t) is the driving white noise of the first-order Gaussian Markov process.

[0229] Substituting the formula under the error state and the first-order Gauss-Markov process into the continuous time differential equation, we get F(t), according to The continuous-time system noise vector w(t) can be easily written as:

[0230]

[0231] Among them, w v and w φ are the measurement white noise of accelerometer and gyroscope respectively, w gb (t), w ab (t), w gs (t) and w as (t) is the driving white noise modeling the gyro and accelerometer bias and scale factor errors

[0232] In order to facilitate the use of the basic equations of discrete-time Kalman filtering, it is necessary to discretize them, including deriving the discrete-time state one-step transfer matrix Φ k / k-1and the equivalent discretization of the driving white noise (get w k ). The discretized system state equation is:

[0233] δx k =Φ k / k-1 δx k-1 +w k-1 ;

[0234] in,

[0235]

[0236] Among them, H k It can be derived by the following formula:

[0237] The GNSS (or visual) positioning solution gives the position coordinates of the antenna phase center (or camera center), and the INS mechanical arrangement gives the navigation results of the IMU measurement center. The two are physically not overlapping, so the lever arm effect correction needs to be performed during the data fusion solution.

[0238] The position conversion relationship between the GNSS antenna phase center (or camera center) and the IMU measurement center is:

[0239]

[0240] in, represents the actual position of the GNSS antenna phase center, Indicates the actual position of the IMU measurement center, which is expressed in geodetic coordinates of latitude L, longitude σ and height h. b is the arm vector of the GNSS antenna, that is, the projection of the vector from the IMU measurement center to the GNSS antenna phase center in the b system. b The measurement calibration can be done by precise measurement means, and it is generally believed that the error can be ignored. If the error state Kalman filter method is used, the error of each navigation state is considered. The formula can be written as:

[0241]

[0242] in, is the IMU center position vector calculated by inertial navigation, is the position vector of the GNSS antenna phase center calculated by inertial navigation, is the attitude matrix solved by inertial navigation. The position error matrix is ​​ignored in the above disturbance analysis. The influence of is very small. Reviewing the error perturbation analysis, the definition of attitude error is rewritten as follows

[0243]

[0244] Then sort out the available

[0245]

[0246] The position of the GNSS antenna phase center obtained by GNSS positioning solution is expressed as:

[0247]

[0248] in, is the GNSS position observation, n r is the position error of GNSS. Generally, in order to simplify the processing, the error of GNSS position measurement value is often modeled as a Gaussian white noise sequence, that is, n r,k ~N(0,R k ), The variance of the observation error R k It can generally be obtained from GNSS positioning solution program / software.

[0249] Therefore, the corresponding observation vector is expressed as the difference between the INS-calculated position and the GNSS position observation, which can be easily obtained

[0250]

[0251] Therefore, the GNSS position observation equation can be written as follows

[0252] δz r =H k δx+n r ;

[0253] in

[0254]

[0255] In actual calculation, H k in Use the latest inertial attitude Similarly, the arm error between the camera installation position and the IMU installation position can also be compensated according to this method, and the observation equation of the relative position relationship measured by the camera can also be obtained by this method.

[0256] In a loosely coupled multi-sensor solution, observations do not involve raw sensor data. Instead, they filter the position, velocity, attitude, and other information obtained after calculation with the predicted information. The operating principles of the sensors providing the observations are not involved, so the observation equations are relatively simple. Because the state includes position, velocity, and attitude, the observation equations only need to compensate for lever arm errors. If compensation for lever arm errors is not required, the observation matrix is ​​a combination of the identity matrix and the zero matrix.

[0257] Because the present invention employs a loosely coupled approach for the autonomous aerial refueling relative positioning and navigation mission, the positioning results from the satellite positioning system and visual ranging are directly integrated, rather than using raw data such as satellite pseudoranges or carrier phases and photo pixel positions. Therefore, the method for constructing the observation equation is relatively simple. Once the lever arm error is compensated, the observation value z has a one-to-one correspondence with the state x. Once the prediction and observation equations are established, filtering can be performed using the extended Kalman filter framework.

[0258] In terms of fusion strategy, the use of different sensors for information fusion under different conditions should also be considered in the autonomous aerial refueling mission. In actual application, reasonable threshold values ​​should be set according to the corresponding sensor working scenarios.

[0259] (1) When the camera is relatively far away from the tanker, it is difficult to capture the drogue, and the filter cannot obtain the observation value from the vision. In this case, the solution is to use the strategy of information fusion of IMU and GNSS.

[0260] (2) In the process of the relative position of the tanker and the receiver continuously decreasing, if the image processing algorithm can correctly capture the position of the drogue, and the tanker and the receiver are still a certain distance away and have not yet entered the docking preparation stage, the position information provided by the GNSS installed on the tanker is still of reference value, and a multi-sensor fusion positioning strategy using the three information sources of IMU / GNSS / vision is adopted.

[0261] (3) When the distance between the tanker and the receiver is relatively close, the absolute position information of the tanker provided by GNSS can no longer effectively assist the positioning and docking of the cone sleeve. Therefore, the strategy of information fusion between IMU and vision is adopted.

[0262] (4) When the refueling plug of the UAV is docked with the refueling drogue, the machine vision sensor’s field of view may be blocked and unable to provide relative position information. Since the docking is completed at this time, it is only necessary to ensure that the relative position of the UAV and the refueling machine remains unchanged, thereby reducing the pressure between the refueling plug and the refueling drogue. The solution at this time is to use the IMU and GNSS information fusion strategy.

[0263] However, the information output by the IMU, GNSS, and vision sensors varies in frequency. The IMU has the highest output frequency, with high-quality MEMS chips typically reaching 200 Hz, and military inertial navigation equipment even reaching kilohertz. GNSS output is typically 1 Hz, and typical vision sensor image output frequencies are often in the tens of Hz. For navigation and positioning, effective information fusion requires that the acquisition times of the information be aligned. While achieving perfect temporal alignment is difficult in practical engineering implementation, the IMU's very high output frequency allows for relatively suitable data to be found in the observation data—visual and GNSS measurements—to be filtered and updated with the IMU. Therefore, the multi-sensor fusion process of the IMU / GNSS / vision information sources does not always involve all three sensors.

[0264] In a multi-sensor autonomous aerial refueling system, the data provided by different sensors (such as GPS, machine vision, and radio sensors) can be considered categorical variables. The chi-square test can analyze whether there is a significant association between these categorical variables, thereby helping to determine which sensor combination can provide more accurate position information. During the aerial refueling process, the system needs to compare the observed position information with the theoretically expected position information in real time. The chi-square test measures the degree of deviation by calculating the difference between the observed frequency and the expected frequency (i.e., the chi-square value), thereby determining the accuracy of the current position information.

[0265] Step 5.2: Based on the soft chi-square Kalman filter, the state space model of the random linear system is improved to obtain the improved model, which is expressed as:

[0266]

[0267] in, represents the prior estimate at time k, represents the posterior estimate of the state at time k-1, Including the target inertial navigation data at time k-1, P k / k-1 represents the prior estimate of the covariance matrix at time k, P k-1 represents the posterior estimate of the covariance matrix at time k-1, Q k-1 represents the process noise covariance matrix at time k-1, r k represents the measurement prediction error, Z k represents the observation information at time k, Z k Including the coordinates of the drogue center in the camera coordinate system at time k and the relative positions of the tanker and receiver at time k, A k is the intermediate variable, R k represents the covariance matrix of observation noise, K krepresents the Kalman gain, represents the posterior estimate of the state at time k, P k represents the posterior estimate of the covariance matrix at time k, and I represents the identity matrix;

[0268] Step 5.3: According to A k and r k Calculate the statistic λ at time k k , which is specifically achieved through the following formula:

[0269]

[0270] Among them, λ k Obey the chi-square distribution with m degrees of freedom, that is, λ k ~χ 2 (m). Under normal measurement conditions, the statistic λ k The value of should be relatively small; if the measurement is abnormal, λ k Will become larger.

[0271] Step 5.4: Determine λ k Is it greater than the preset threshold T Dm , in λ k Greater than the preset threshold T Dm In this case, and P k As the fusion positioning result, in λ k Less than or equal to the preset threshold T Dm If yes, proceed to step 5.5;

[0272] When the chi-square test statistic is less than the theoretical threshold level, it can be considered that there is a significant difference between the observed data and the theoretical expectations, thereby triggering corresponding adjustment measures to ensure the smooth progress of the refueling process.

[0273] The premise for the effectiveness of the traditional chi-square detection method is that the filter system model is accurate. In practical applications such as integrated navigation, the system structure parameter modeling of the Kalman filter is generally relatively accurate and stable, while the noise parameters will change due to reasons such as motion state, imperfect modeling, system aging or operating environment, making it difficult to fully accurately model. This will make the chi-square detection threshold T DmIt is difficult to accurately determine this value strictly according to theoretical methods. Setting the threshold too high reduces the probability of fault detection and risks introducing a large number of outliers into the filtered measurement, thereby increasing filtering errors. Setting the threshold too low increases the probability of false alarms. Frequent false alarms reduce measurement utilization, and the reduced measurement correction effect also reduces filter estimation accuracy. The traditional chi-square detection method produces a binary result: either 0 or 1, with no intermediate states. This method primarily uses presence / absence as an indicator in fields such as radar target detection, and its application is very reasonable. However, in applications such as integrated navigation, there may be a large number of intermediate states (suspicious) between normal (trusted) and abnormal (discarded) measurement information. Simply using the binary chi-square detection result is not appropriate. Automatically adjusting the size of the measurement noise variance matrix based on the size of the measurement innovation effectively utilizes all measurement information. Compared to normal measurements, the measurement weight is reduced when the measurement innovation is moderate (suspicious), and the weight is very low when the innovation is significantly abnormal. If the weight approaches 0, the measurement is discarded. According to the characteristics of the new information utilization of adaptive filtering, the improved formula is used in step 5.5. and P k to update.

[0274] Step 5.5: and P k Update and get and P' k , which is specifically achieved through the following formula:

[0275]

[0276] Will and P' k As the fusion positioning result.

[0277] Based on the above technical solution, the present invention conducted experiments, and the experimental results are as follows Figure 2 ,have Figure 2 It can be seen that the algorithm proposed in this invention can achieve accurate collaborative positioning results between the tanker and the receiving aircraft, providing more accurate and comprehensive location information for the aerial refueling mission.

[0278] The present invention proposes a multi-source information fusion positioning method for aerial refueling, the key points of which are as follows:

[0279] 1) Multi-source information fusion technology: This technology integrates multiple navigation and positioning methods, including machine vision, differential satellite navigation, and an inertial navigation system (INS). Through an improved adaptive distributed Kalman filter algorithm, it achieves real-time synchronization and efficient integration of data, significantly improving navigation accuracy and reliability during aerial refueling docking.

[0280] 2) Adaptive weight adjustment mechanism based on innovation: An adaptive weight adjustment mechanism based on innovation is introduced to dynamically adjust the weight of each navigation source according to its real-time performance, ensuring high-precision position estimation in complex environments.

[0281] 3) Visual Data Processing Optimization: We use a YOLO v8-based object detection algorithm combined with geometric vision positioning technology to quickly and accurately estimate the position of the drogue. This approach not only improves the system's positioning efficiency but also enhances robustness and positioning accuracy in harsh environments.

[0282] 4) Application of differential satellite navigation algorithm: A differential satellite navigation algorithm based on a mobile base station is used to accurately calculate the relative position and velocity between the tanker and the receiving aircraft, overcoming the limitations of traditional single-point positioning methods, such as low update frequency and susceptibility to atmospheric interference.

[0283] 5) Complex sensor time synchronization strategy: Taking into account the differences in output frequencies of different sensors, an effective information acquisition time alignment scheme is designed, which enables the data of IMU, GNSS and vision sensors to be fused at the closest time point, ensuring the validity and timeliness of the information.

[0284] 6) Multi-Sensor Fusion Navigation Optimization Method Using Soft Chi-Square Test: We propose an optimization strategy based on a soft chi-square test to evaluate and optimize the results of multi-sensor data fusion. By automatically adjusting the size of the measurement noise variance matrix, we effectively utilize all observation information and take appropriate weighting measures for suspicious or abnormal data, improving the overall performance of the system.

[0285] 7) Flexible information fusion strategy: Based on the distance changes between the refueling and receiving aircraft at different stages, the most suitable information fusion strategy can be flexibly selected, including but not limited to using only IMU and GNSS, or a combination of IMU / GNSS / vision, to meet different mission requirements and environmental challenges.

[0286] The present invention proposes a multi-source information fusion positioning method for aerial refueling, specifically improving the limitations of existing algorithms in autonomous aerial refueling scenarios. Traditional methods mainly focus on information fusion from sensors on the receiving aircraft, which has the following shortcomings: the tanker's status and position are assumed to be known, the sensors on the tanker are not used for collaborative positioning, the tanker's status and position are not updated, and the relative position relationship is roughly processed. In contrast, the present invention integrates machine vision, differential satellite navigation, and inertial navigation systems, and adopts an improved adaptive distributed Kalman filter algorithm to achieve real-time synchronization and efficient integration of data, achieving significant technical effects and advantages, as follows:

[0287] 1) By combining the advantages of vision, DGNSS, and INS through multi-source information fusion technology, this method overcomes the limitations of single sensors and maintains high-precision position estimation in complex environments. Experimental results show that compared with traditional single-point positioning methods, this method improves positioning accuracy by at least 30%.

[0288] 2) This invention employs an adaptive weight adjustment mechanism based on innovation, dynamically adjusting the weights of each navigation source according to its real-time performance, ensuring high-precision position estimation in complex environments. Actual tests have shown that the system exhibits excellent stability under various adverse conditions, such as signal obstruction and electromagnetic interference.

[0289] 3) Taking into account the differences in output frequencies of different sensors, the present invention designs an effective time synchronization scheme, which enables the data of IMU, GNSS and vision sensors to be integrated at the closest time point, ensuring the validity and timeliness of the information, improving operational efficiency, and reducing errors caused by information delays.

[0290] 4) The present invention strengthens the motion state coupling relationship between the tanker and receiver, and uniformly predicts and updates the states of both, solving the problem of converting relative positions into absolute positions in traditional methods and improving the docking success rate.

[0291] 5) The present invention supports multi-sensor collaborative positioning when the tanker's position information and motion state are unknown, strengthens the constraints on the relative position relationship between the front and rear aircraft, and is more suitable for autonomous aerial refueling missions that require relative and absolute position information.

[0292] 6) Simplify the workflow of the dual-machine collaborative positioning algorithm: Through the optimized information fusion strategy, the pain point of having to perform the information fusion algorithm twice during the dual-machine collaborative positioning process is avoided, the workflow is simplified, and the overall performance of the system is improved.

[0293] The above description is merely a preferred embodiment of the present disclosure and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also encompass other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the above-mentioned inventive concept. For example, a technical solution formed by mutually replacing the above-mentioned features with (but not limited to) technical features having similar functions disclosed in the embodiments of the present disclosure.

Claims

1. A multi-source information fusion positioning method for aerial refueling, characterized in that: include: Step 1: Obtain visual raw data, global navigation satellite system GNSS data and inertial navigation system INS data; Step 2: Process the raw visual data at each moment to obtain the coordinates of the cone sleeve center in the camera coordinate system at each moment; Step 3: Using Kalman filtering, the GNSS data is calculated to obtain the relative positions of the tanker and receiver at each moment. The GNSS data includes carrier phase double-difference observations and pseudorange double-difference observations. Step 4: Using the tanker or receiver as the carrier, the inertial navigation system (INS) data is solved to obtain the target INS data at each moment. The target INS data at each moment includes the rotation matrix representing the attitude of the tanker and receiver in the navigation coordinate system at that moment, the speed of the tanker and receiver relative to the earth in the n-frame at that moment, and the position of the tanker and receiver at that moment. Step 5: Fuse the coordinates of the drogue center in the camera coordinate system at each moment obtained in step 2, the relative positions of the tanker and receiver at each moment obtained in step 3, and the target inertial navigation data at each moment obtained in step 4 to obtain a fused positioning result.

2. The multi-source information fusion positioning method for aerial refueling according to claim 1 is characterized in that: Step 1 specifically includes: Step 1.1: The camera on the receiving aircraft collects images of the drogue on the refueling aircraft and the environment surrounding the drogue at each moment. The images of the drogue and the environment surrounding the drogue constitute the raw visual data. Step 1.2: Receive satellite signals from multiple navigation satellites through the GNSS sensors configured on the tanker and the receiving aircraft. The satellite signals from all navigation satellites form the Global Navigation Satellite System (GNSS) data. Step 1.3: Use the inertial sensors on the tanker to monitor and record the accelerometer and gyroscope data output by the tanker's inertial navigation system. Calculate the tanker's position, velocity, and attitude based on the accelerometer and gyroscope data. Use the inertial sensors on the receiving aircraft to monitor and record the accelerometer and gyroscope data output by the receiving aircraft's inertial navigation system. Calculate the inertial navigation system (INS) data based on the accelerometer and gyroscope data.

3. The multi-source information fusion positioning method for aerial refueling according to claim 1 is characterized in that: Step 2 specifically includes: Step 2.1: Use the YOLO v8 algorithm to detect the image in the raw visual data at each moment and obtain the coordinates (u, v) of the tanker drogue center in the pixel coordinate system of the monocular camera model; Step 2.2: Convert the coordinates (u, v) of the cone sleeve center in the pixel coordinate system to the coordinates (x, y) of the cone sleeve center in the image coordinate system using the following formula: Among them, u0 and v0 represent the coordinates of the image center of the cone sleeve in the pixel coordinate system, d x with d y Indicates the actual physical size corresponding to each pixel unit in the image coordinate system; Step 2.3: Convert the coordinates (x, y) of the cone sleeve center in the image coordinate system to the coordinates (X C ,Y C ,Z C ), which is specifically achieved through the following formula: Where f is the focal length of the camera, that is, the difference between the camera coordinate system and the image coordinate system on the Z axis. f is calculated using the following formula: Where p is the pixel length or width of the cone sleeve, and w is the actual length or actual width of the cone sleeve; Thus, the coordinates of the cone sleeve center in the camera coordinate system at each moment are obtained.

4. The multi-source information fusion positioning method for aerial refueling according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: Obtain the GNSS carrier phase and pseudorange double difference observation model, expressed as: in, The double difference observation values ​​of the carrier phase of satellite p and satellite q for the receiver s configured for the tanker and the receiver r configured for the receiver, is the actual distance from the receiver r to the satellite p; is the actual distance from the receiver s to the satellite p; is the actual distance from the receiver r to the satellite q; is the actual distance from receiver s to satellite q; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite p; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite q; is the double difference noise of receiver r and receiver s with respect to satellite p and satellite q; is the double difference observation value of pseudorange of receiver r and receiver s about satellite p and satellite q; Step 3.2: Construct the state equation and measurement equation of the discretized carrier phase and pseudo-range differential positioning model, which can be expressed as: X' k =Φ k,k-1 X' k-1 +W' k-1 ,W' k-1 ~N(0,Q' k );- Z' k =H' k X' k +C' k ,V' k ~N(0,R' k ); Among them, X' k Represents the state vector of carrier phase and pseudorange differential positioning, Φ k,k-1 is the state transfer matrix of carrier phase and pseudorange differential positioning from time k-1 to k; W' k-1 is the system noise matrix of carrier phase and pseudorange differential positioning at time k-1, Q' k is the covariance matrix of the system noise of carrier phase and pseudorange differential positioning at time k; Z' k is the measurement vector of carrier phase and pseudo-range differential positioning at time k; H' k is the measurement matrix of carrier phase and pseudo-range differential positioning at time k; V' k represents the measurement noise matrix of carrier phase and pseudorange differential positioning at time k; R' k is the measurement noise covariance matrix of carrier phase and pseudorange differential positioning at time k; Step 3.3: Perform Kalman filtering to solve the state equation and measurement equation of the discretized carrier phase and pseudo-range differential positioning model to obtain the baseline vector at each moment, that is, the relative position of the tanker and receiver at each moment.

5. The multi-source information fusion positioning method for aerial refueling according to claim 4 is characterized in that: X' in step 3.2 k , Φ k,k-1 and Z' k Expressed as: F k,k-1 =I 3+m ; Among them, B k is the baseline vector, and B k =(δx,δy,δz), where δx is the distance between the receiving aircraft and the refueling aircraft in the x-direction, δy is the distance between the receiving aircraft and the refueling aircraft in the y-direction, and δz is the distance between the receiving aircraft and the refueling aircraft in the z-direction; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite 1; is the single-difference integer ambiguity of receiver r and receiver s with respect to satellite m, I 3+m is the identity matrix of 3+m dimensions; is the double difference observation value of pseudorange of receiver r and receiver s about satellite 1 and satellite 2; is the double difference observation value of pseudorange of receiver r and receiver s about satellite 1 and satellite m; is the double difference observation value of the carrier phase of satellite 1 and satellite 2 from receiver r and receiver s; are the double-difference observations of the carrier phase of satellite 1 and satellite 2 from receiver r and receiver s.

6. The multi-source information fusion positioning method for aerial refueling according to claim 4 is characterized in that: H' in step 3.2 k Obtained through: Step A1: Process the GNSS data using the pseudo-range single point positioning method to obtain the initial position (x0, y0, z0) of the receiver r; Step A2: The actual distance from the receiver r to the satellite p Perform linear expansion to obtain The linear representation of is: in, represents the distance from the initial position (x0, y0, z0) of the receiver r to the satellite p; Similarly, The linear representation of is: in, represents the distance from the initial position (x0, y0, z0) of the receiver r to the satellite q; Step A3: The actual distance from the receiver s to the satellite p Perform linear expansion at the initial position (x0, y0, z0) of the receiver r, and we get The linear representation of is: in, represents the unit line of sight vector from receiver r to satellite p; Similarly, The linear representation of is: in, represents the unit line of sight vector from receiver r to satellite q; Step A4: The linear representation of The linear representation of The linear representation of Substitute the linear representation of into the GNSS carrier phase and pseudorange double difference observation model to obtain H' k , expressed as: Where λ is the carrier wavelength, and D and E are expressed as: in, is the unit line of sight vector from receiver r to satellite 1, is the unit line of sight vector from receiver r to satellite 2, is the unit line of sight vector from receiver r to satellite m.

7. The multi-source information fusion positioning method for aerial refueling according to claim 1, characterized in that: Step 4 specifically includes: Step 4.1: Using the tanker or receiver as the carrier, perform attitude calculation on the INS data to obtain the rotation matrix representing the attitude of the tanker and receiver in the navigation coordinate system at each moment. Step 4.2: Based on the rotation matrix representing the attitude in the navigation coordinate system, the velocity of the inertial navigation system INS data is solved to obtain the motion speed of the tanker and the receiving aircraft relative to the earth in the n-frame at each moment. This is achieved by the following formula: in, represents the velocity of the carrier relative to the earth in the n-frame at time k, It represents the velocity of the carrier relative to the earth in the n-frame at time k-1, represents the relative force at time k in system b, represents the angular velocity of the Earth's rotation, Indicates the angular velocity of the carrier relative to the earth's rotation in the navigation coordinate system. The inertial navigation system INS data includes g n represents the gravity in the n-system; Thus, the velocity of the carrier relative to the earth in the n-frame at each moment is calculated, and then the velocity of the tanker and receiver relative to the earth in the n-frame at each moment is calculated; Step 4.3: Based on the speed of the tanker and receiver relative to the Earth in the n-frame at each moment, the position of the tanker and receiver at each moment is calculated using the following formula: Among them, p k represents the position of the carrier at time k, p k-1 represents the position of the carrier at time k-1, M pv Shows the mapping relationship matrix between position and velocity; In this way, the position of the carrier at each moment is calculated, and then the positions of the refueling machine and the receiving machine at each moment are obtained.

8. The multi-source information fusion positioning method for aerial refueling according to claim 7 is characterized in that: Step 4.1 specifically includes: Step 4.1.1: Calculate the rotation change of the carrier coordinate system (i.e., the b-system) from time k-1 to time k, with the inertial coordinate system (i.e., the i-system) as the reference base. This is achieved specifically through the following formula: Where I represents the identity matrix, for The vector direction of the corresponding equivalent rotation vector, τ represents the sampling time interval, is the angular velocity of the carrier in the carrier coordinate system relative to the inertial coordinate system. The inertial navigation system INS data contains express The antisymmetric matrix of ; Step 4.1.2: Calculate the rotation change of the navigation coordinate system, i.e., the n-system, from time k-1 to time k, with the i-system as the reference base. This is achieved specifically through the following formula: in, for The vector direction of the corresponding equivalent rotation vector, Indicates the angular velocity of the carrier in the navigation coordinate system relative to the inertial coordinate system. The inertial navigation system INS data contains express The antisymmetric matrix of ; Step 4.1.3: According to and Calculate the rotation matrix representing the attitude in the navigation coordinate system at time k This is achieved specifically through the following formula: in, represents the rotation matrix of system i relative to system n at time k, represents the rotation matrix of system b relative to system i at time k, represents the rotation matrix of system i relative to system n at time k-1, represents the rotation matrix of system b relative to system i at time k-1, Represents the rotation matrix representing the attitude in the navigation coordinate system at time k-1 Therefore, according to steps 4.1.1 to 4.1.3, the rotation matrix representing the attitude in the navigation coordinate system at each moment is calculated, and then the rotation matrix representing the attitude of the tanker and the receiving aircraft in the navigation coordinate system at each moment is obtained.

9. The multi-source information fusion positioning method for aerial refueling according to claim 1, characterized in that: Step 5 specifically includes: Step 5.1: Construct the state space model of the random linear system, expressed as: Among them, X k is the state vector at time k, Z k is the measurement vector at time k, X k-1 is the state vector at time k-1, W k-1 is the system noise vector at time k-1, V k is the measurement noise vector at time k, Φ k / k-1 represents the state transfer matrix at time k, H k represents the observation matrix at time k; Among them, Φ k / k-1 and H k Expressed as: Among them, F(t) is the inertial navigation error state transfer matrix, [t k ,t k-1 ] is the continuous time interval from time k-1 to time k, I3 represents the 3D identity matrix, 03 represents the 3D zero matrix, l b is the arm vector of the GNSS antenna, l b × is l b The antisymmetric matrix of Represents the attitude matrix of the carrier coordinate system relative to the navigation coordinate system; Step 5.2: Based on the soft chi-square Kalman filter, the state space model of the random linear system is improved to obtain the improved model, which is expressed as: in, represents the prior estimate at time k, represents the posterior estimate of the state at time k-1, Including the target inertial navigation data at time k-1, P k / k-1 represents the prior estimate of the covariance matrix at time k, P k-1 represents the posterior estimate of the covariance matrix at time k-1, Q k-1 represents the process noise covariance matrix at time k-1, r k represents the measurement prediction error, Z k represents the observation information at time k, Z k Including the coordinates of the drogue center in the camera coordinate system at time k and the relative positions of the tanker and receiver at time k, A k is the intermediate variable, R k represents the covariance matrix of observation noise, K k represents the Kalman gain, represents the posterior estimate of the state at time k, P k represents the posterior estimate of the covariance matrix at time k, and I represents the identity matrix; Step 5.3: According to A k and r k Calculate the statistic λ at time k k , which is specifically achieved through the following formula: Step 5.4: Determine λ k Is it greater than the preset threshold T Dm , in λ k Greater than the preset threshold T Dm In this case, and P k As the fusion positioning result, in λ k Less than or equal to the preset threshold T Dm If , proceed to step 5.5; Step 5.5: and P k Update and get and P' k , which is specifically achieved through the following formula: Will and P' k As the fusion positioning result.

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