Aircraft cluster cooperative positioning method based on multi-source sensor data fusion

Abstract

The invention belongs to the technical field of unmanned aerial vehicle cluster collaborative navigation, and discloses an aircraft cluster collaborative positioning method based on multi-source sensor data fusion. According to the invention, a dual-stage fusion structure is formed by self-adaptive Kalman filtering based on an observation noise adjustment mechanism and a residual error compensation network constructed based on an improved multi-layer full-connection structure neural network; firstly, an inertial measurement unit IMU mounted on an unmanned aerial vehicle and measurement information of radio equipment are fused through extracted adaptive Kalman filtering to obtain relatively accurate fusion positioning information, and then the IMU information, the measurement information of the radio equipment and the fusion positioning information are further taken as multi-source sensor data; and further inputting to a residual compensation network constructed based on an improved multi-layer full-connection structure neural network for precision compensation, thereby finally facilitating improvement of the cooperative positioning precision of the unmanned aerial vehicle in the rejection area of the global navigation satellite system.

Description

Technical Field

[0001] This invention belongs to the field of UAV swarm cooperative navigation technology, and specifically relates to a method for collaborative positioning of aircraft swarms based on multi-source sensor data fusion in the event of satellite denial. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are remotely controlled or autonomously operated aircraft widely used in military reconnaissance, environmental monitoring, and logistics transportation. With technological advancements, UAV swarms, as a form of collaborative mission execution involving multiple UAVs, possess enhanced mission adaptability, robustness, and spatial coverage capabilities. In satellite-denied environments where satellite signals are unavailable or interfered with, traditional navigation methods relying on global navigation satellite systems face severe challenges. To address this, UAV swarms integrate multi-source sensors (such as inertial navigation, radio systems, and ultra-wideband) with cooperative navigation algorithms, achieving information sharing and mutual positioning among members, thereby maintaining overall navigation accuracy and mission continuity. This cooperative navigation technology not only enhances the autonomy of unmanned systems in complex environments but also lays the foundation for the development of swarm intelligent navigation systems.

[0003] In UAV swarm cooperative navigation optimization algorithms, Kalman filtering is one of the most commonly used algorithms. Kalman filters combine system models with measurement data to achieve more accurate state estimation. However, traditional Kalman filters struggle to adapt to fluctuations in sensor errors under complex environments, potentially leading to decreased filtering performance or even estimation divergence. Therefore, researchers have begun to study adaptive Kalman filtering to automatically adjust filter parameters in unknown or dynamically changing noisy environments, maintaining stable estimation and high accuracy. This is particularly suitable for multi-source heterogeneous data fusion positioning tasks in complex systems such as UAVs.

[0004] Furthermore, in recent years, with the rapid development of artificial intelligence technology, machine learning has shown great potential in the field of UAV swarm cooperative navigation. Traditional cooperative navigation methods mostly rely on model-driven filtering algorithms, but when facing complex, nonlinear, and highly dynamic environments, model accuracy and parameter tuning face bottlenecks. Machine learning methods have the ability to automatically learn system dynamics and environmental characteristics from massive historical or real-time data, providing new ideas for solving problems such as modeling errors, sensor drift, and multi-source information fusion in UAV swarm cooperative navigation. When the Global Navigation Satellite System (GNSS) malfunctions or weakens, UAV swarm navigation based on multi-source cooperation can still provide reliable navigation services. Summary of the Invention

[0005] The purpose of this invention is to propose a collaborative localization method for aircraft swarms based on multi-source sensor data fusion. This method first fuses the measurement information of the inertial measurement unit (IMU) and radio equipment mounted on the UAV using the proposed adaptive Kalman filter to obtain a more accurate fused localization information. Then, the IMU information, radio equipment measurement information, and fused localization information are used as multi-source sensor data inputs and further input into an improved neural network model for accuracy compensation, which ultimately helps to improve the collaborative localization accuracy of UAVs in areas denied by the Global Navigation Satellite System (GNSS).

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A collaborative localization method for aircraft swarms based on multi-source sensor data fusion includes the following steps: Step 1. First, for the aircraft cluster consisting of an auxiliary aircraft and multiple reference aircraft, obtain the estimated three-dimensional coordinates of the auxiliary aircraft using radio ranging, which will be used as the measurement information for the radio equipment in Step 2; Step 2. Next, using the improved adaptive Kalman filtering method, the inertial measurement unit (IMU) information and the radio equipment measurement information mounted on the reference aircraft are adaptively fused to obtain fused positioning information; The improved adaptive Kalman filtering method introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of the observation residuals, building upon the traditional Kalman filter. The adjustment process of this adaptive observation noise adjustment mechanism is as follows: By calculating the Euclidean norm of the current observation residual at each time step and dynamically adjusting the observation covariance matrix based on the magnitude of the Euclidean norm, the Kalman filter gain is dynamically adjusted, thereby achieving adaptive updating of the state estimate. Step 3. Construct a residual compensation network based on an improved multi-layer fully connected neural network structure, and input the fused positioning information, IMU information and radio equipment measurement information as multi-source sensor data into the residual compensation network; The residual compensation network learns the mapping relationship between the input multi-source sensor data and the trajectory residual, and finally outputs the residual prediction value. Based on the residual prediction value, it performs accuracy compensation on the fused positioning information of the adaptive Kalman filter.

[0007] Furthermore, based on the aforementioned collaborative localization method for aircraft swarms based on multi-source sensor data fusion, this invention also proposes a corresponding collaborative localization system for aircraft swarms based on multi-source sensor data fusion, the scheme of which is as follows: A collaborative positioning system for aircraft swarms based on multi-source sensor data fusion includes the following modules: The preprocessing module is used to obtain the estimated three-dimensional coordinates of the auxiliary aircraft using radio ranging for a cluster of aircraft consisting of auxiliary aircraft and multiple reference aircraft, as measurement information for radio equipment. The Kalman filter module is used to adaptively fuse the inertial measurement unit (IMU) information and radio equipment measurement information mounted on the reference aircraft using an improved adaptive Kalman filter method to obtain fused positioning information. The improved adaptive Kalman filtering method introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of the observation residuals, building upon the traditional Kalman filter. The adjustment process of this adaptive observation noise adjustment mechanism is as follows: By calculating the Euclidean norm of the current observation residual at each time step and dynamically adjusting the observation covariance matrix based on the magnitude of the Euclidean norm, the Kalman filter gain is dynamically adjusted, thereby achieving adaptive updating of the state estimate. And a precision compensation module, used to build a residual compensation network based on an improved multi-layer fully connected neural network structure, which integrates positioning information, IMU information and wireless equipment measurement information as multi-source sensor data input to the residual compensation network; The residual compensation network learns the mapping relationship between the input multi-source sensor data and the trajectory residual, and finally outputs the residual prediction value. Based on the residual prediction value, it performs accuracy compensation on the fused positioning information of the adaptive Kalman filter.

[0008] Furthermore, based on the aforementioned collaborative localization method for aircraft swarms based on multi-source sensor data fusion, this invention also proposes a computer device, which includes a memory and one or more processors.

[0009] The executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the above-described aircraft swarm cooperative localization method based on multi-source sensor data fusion.

[0010] Furthermore, based on the aforementioned collaborative localization method for aircraft swarms based on multi-source sensor data fusion, this invention also proposes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of the aforementioned collaborative localization method for aircraft swarms based on multi-source sensor data fusion.

[0011] The present invention has the following advantages: As described above, this invention proposes a collaborative localization method for aircraft swarms based on multi-source sensor data fusion. This method employs a two-stage fusion structure, consisting of an adaptive Kalman filter based on an observation noise adjustment mechanism and a residual compensation network built upon an improved multi-layer fully connected neural network. First, the proposed adaptive Kalman filter fuses the measurement information from the inertial measurement unit (IMU) and radio equipment mounted on the UAV to obtain a relatively accurate fused localization information. Then, the IMU information, radio equipment measurement information, and the fused localization information are used as input to the improved neural network model for accuracy compensation, ultimately improving the collaborative localization accuracy of UAVs in areas denied by global navigation satellite systems (GNSS). This invention achieves a unified solution for ranging noise suppression, IMU drift suppression, and nonlinear error compensation. Compared to traditional methods relying solely on filters or machine learning, this invention simultaneously possesses high robustness, high real-time performance, and high accuracy. In complex environments with GNSS denial, severe obstruction, and significant multipath interference, this invention maintains stable trajectory estimation and significantly reduces 3D position errors, making it suitable for applications such as UAV swarming, collaborative intelligence, and high-reliability localization. The method of this invention significantly improves the positioning accuracy of auxiliary aircraft in an aircraft swarm. Furthermore, the algorithm of this invention is simple in principle and its process design is concise and clear, making it particularly suitable for application in environments where UAV cooperative navigation encounters satellite navigation rejection. Attached Figure Description

[0012] Figure 1 This is a flowchart of the collaborative localization method for aircraft swarms based on multi-source sensor data fusion in an embodiment of the present invention; Figure 2 This is a diagram showing the positional relationship of the aircraft in an embodiment of the present invention; Figure 3 This is a flowchart illustrating the overall processing flow of the improved adaptive Kalman filter combined with a neural network in this embodiment of the invention. Figure 4 This is a flight trajectory diagram of multiple drones in a specific embodiment of the present invention; Figure 5 This is an error diagram of the UAV in the X, Y, and Z directions in a specific embodiment of the present invention; wherein Figure 5 (a), (b), and (c) in the figure are the curves showing the change of the error of the UAV in the X, Y, and Z directions over time, respectively. Detailed Implementation

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment 1 describes a collaborative localization method for aircraft swarms based on multi-source sensor data fusion. This method proposes a collaborative navigation optimization algorithm combining an improved adaptive Kalman filter and an improved neural network. First, the improved adaptive Kalman filter fuses the inertial measurement unit (IMU) and radio equipment information mounted on the UAV to obtain a more accurate positioning information. Then, the IMU information, radio equipment measurement information, and the fused positioning information obtained through Kalman filtering are used as multi-source sensor data inputs and fed into the improved neural network model for further optimization, ultimately improving the collaborative localization accuracy of UAVs in areas denied by the Global Navigation Satellite System (GNSS).

[0014] like Figure 1 As shown, the collaborative localization method for aircraft swarms based on multi-source sensor data fusion includes the following steps: Step 1. First, for the aircraft cluster consisting of an auxiliary aircraft and multiple reference aircraft, obtain the estimated three-dimensional coordinates of the auxiliary aircraft using radio ranging, which will be used as the measurement information for the radio equipment in Step 2.

[0015] In this embodiment, the aircraft cluster may include, for example, one auxiliary aircraft with low positioning accuracy and multiple reference aircraft with high positioning accuracy, such as... Figure 2 As shown, the position of the auxiliary aircraft is... To improve the navigation accuracy of the auxiliary aircraft, a cooperative navigation model is established by acquiring sensor information between the auxiliary aircraft and the reference aircraft.

[0016] Define the distance between the i-th reference aircraft and the auxiliary aircraft as Radio ranging primarily estimates the distance between two points by utilizing the propagation characteristics of radio signals, and is widely used in UAV positioning and navigation systems.

[0017] Radio ranging typically uses the TOA (Time of Arrival) method. The TOA distance measurement formula is: .

[0018] in It is the measured distance. It's the speed of light. Signal transmission time, Signal reception time. The position of the auxiliary aircraft is... Reference drone The known coordinates are The distance between the assisted drone and the reference drone satisfies: .

[0019] Based on the first equation, subtract the other three equations to construct the linear form: .

[0020] Written in matrix form: ; in: ; ; ; in It is a coefficient matrix. It is a constant vector. Finally, using the least squares method, we obtain: ; This allows us to obtain the estimated three-dimensional coordinates of the auxiliary aircraft. This location information is the measurement information of the wireless equipment.

[0021] Next, a two-stage fusion structure is constructed using the proposed adaptive Kalman filter based on the observation noise adjustment mechanism and a residual compensation network built based on an improved multi-layer fully connected neural network. Figure 2 As shown.

[0022] The system first initializes the state and uses position and velocity information provided by the radio ranging device and inertial measurement unit to predict the state. Based on this, it calculates the observation residuals and dynamically adjusts the observation noise covariance, thereby achieving adaptive updates to the state estimate and obtaining fused position information, such as... Figure 2 Left side view.

[0023] Figure 2 The right-hand diagram shows the model structure of the residual compensation network of the improved multi-layer fully connected neural network. It extracts deep features from the fused input data through multiple hidden layers, further improving the trajectory estimation accuracy of the system.

[0024] This neural network can be used as a compensator for the filter output, improving the system's robustness to IMU drift or measurement errors.

[0025] Step 2. Using an improved adaptive Kalman filter method, the inertial measurement unit (IMU) information and radio equipment measurement information mounted on the reference aircraft are adaptively fused to obtain fused positioning information.

[0026] The improved adaptive Kalman filtering method introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of the observation residuals, building upon the traditional Kalman filter. The adjustment process of this adaptive observation noise adjustment mechanism is as follows: By calculating the Euclidean norm of the current observation residual at each time step and dynamically adjusting the observation covariance matrix based on the magnitude of the Euclidean norm, the Kalman filter gain is dynamically adjusted, thereby achieving adaptive updating of the state estimate.

[0027] This invention utilizes an improved adaptive Kalman filter to adaptively fuse IMU data and TOA calculation results to improve positioning accuracy. System Status The model defines a six-dimensional state vector, including position and velocity: .

[0028] in, It's about location. , It's speed. .

[0029] This invention introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of the observation residuals, building upon the traditional Kalman filter. At each time step, the Euclidean norm of the current observation residuals is calculated, and the observation covariance matrix is ​​dynamically adjusted based on its magnitude. This is achieved by introducing a nonlinear function to regulate the weights (parameters). This allows the filter to maintain a high level of confidence when the observation residuals are small, while automatically increasing the observation covariance matrix when the observation error changes abruptly or outliers occur, thereby reducing the impact of observations on state estimation and improving the system's robustness to noise changes and abnormal measurements.

[0030] The adaptive observation covariance adjustment mechanism based on the Euclidean norm of observation residuals can dynamically adjust the filter gain according to the real-time measurement reliability. The adjustment process of the adaptive observation noise adjustment mechanism is as follows: When the residual decreases, the observation covariance decreases accordingly, the Kalman filter gain increases, and the adaptive Kalman filter makes full use of stable and reliable radio ranging information to correct IMU drift, thereby improving positioning accuracy. As the residual increases, the observation covariance also increases, the Kalman filter gain decreases, and the adaptive Kalman filter reduces its dependence on anomalous measurements in order to suppress the impact of abrupt errors caused by multipath interference and signal occlusion on state estimation.

[0031] This adaptive observation noise adjustment mechanism significantly enhances the system's robustness in handling non-Gaussian noise and sudden anomalies, preventing oscillations or divergences in state estimation, thereby improving the stability and reliability of the cooperative positioning system in satellite navigation denial environments.

[0032] The processing flow of the improved adaptive Kalman filter method in this embodiment is as follows: Step 2.1. State initialization: Set the initial state and covariance.

[0033] initial state The formula is as follows: .

[0034] The initial covariance is The initial velocity is .

[0035] Step 2.2. Construct the state transition matrix : .

[0036] in It is a transformation matrix. Indicates time difference, This represents a 3×3 zero matrix.

[0037] Step 2.3. Perform state prediction, using the following formula: .

[0038] in This indicates an update to the current state. It indicates the state at the previous moment.

[0039] Step 2.4. The initial state velocity is corrected using IMU substitution, as shown in the following formula: .

[0040] in Indicates the current speed. This indicates the speed measured by the IMU.

[0041] Step 2.5. Predict the covariance update, the formula is as follows: ; .

[0042] in It is the process noise covariance matrix. It is the variance of process noise. It is the transformation matrix, i.e., the identity matrix. Let the covariance matrix at the current time be denoted as . This represents the covariance matrix before the transition at the previous time step.

[0043] Step 2.6. Dynamically adjust the Kalman filter gain based on an adaptive observation noise adjustment mechanism. The specific process is as follows: First, the observation matrix is ​​given. The expression, formula is as follows: .

[0044] in It is the transformation matrix, specifically the 3×3 identity matrix. This represents a 3×3 zero matrix.

[0045] Then calculate the observation residuals. The formula is as follows: .

[0046] in Indicates the location of the auxiliary aircraft. Represents the observation matrix. This indicates an update to the current state.

[0047] Then calculate the residual Euclidean norm. The formula is as follows: .

[0048] The adaptive observation noise covariance matrix is ​​then given. The expression, formula is as follows: .

[0049] in It is the fundamental variance of the observation noise. The adjustment coefficient is a fixed value, representing the weight, used for adjustment. , This represents the norm of the observed residuals using the hypertangent function. Perform nonlinear mapping.

[0050] Finally, dynamically adjust the Kalman filter gain. The formula is expressed as follows: ;in This represents the covariance matrix at the current time.

[0051] The adaptive observation noise adjustment mechanism proposed in this invention can dynamically adjust the noise matrix according to the real-time observation quality of the sensor, thereby automatically balancing the weights of observation information and prediction models, and avoiding the instability and error amplification problems caused by fixed noise assumptions.

[0052] This adaptive observation noise adjustment mechanism can effectively suppress abnormal measurements and outliers, significantly improve the robustness and accuracy of filtering in complex environments, and at the same time reduce the need for manual parameter tuning. This invention can intelligently adapt to the characteristics of noise changing with the environment, and is particularly suitable for UAV navigation scenarios where noise is unpredictable, such as satellite denial and multipath interference.

[0053] Step 2.7. Update Status: .

[0054] in Indicates the current state. This indicates an update to the current state; To observe the residuals.

[0055] Step 2.8. Update covariance: .

[0056] in This represents the updated covariance.

[0057] Step 2.9. Output estimated location : .

[0058] in , , They represent Coordinates in the X, Y, and Z directions.

[0059] The estimated location That is, by using an improved adaptive Kalman filter, the inertial measurement unit (IMU) information and radio equipment measurement information mounted on the reference aircraft are adaptively fused to obtain fused positioning information.

[0060] Next, in step 3, a feedforward neural network is used to learn the mapping relationship from multi-source sensor information to trajectory residuals, which is ultimately used to compensate for the accuracy of the fusion results of adaptive Kalman filtering.

[0061] Step 3. Construct a residual compensation network based on an improved multi-layer fully connected neural network structure, and input the fused positioning information, IMU information and radio equipment measurement information as multi-source sensor data into the residual compensation network.

[0062] The residual compensation network learns the mapping relationship between the input multi-source sensor data and the trajectory residual, and finally outputs the residual prediction value. Based on the residual prediction value, it performs accuracy compensation on the fused positioning information of the adaptive Kalman filter.

[0063] Input of residual compensation network The formula is expressed as follows: ; Indicates the location information of the IMU; in The coordinates obtained for the IMU in the X, Y, and Z directions; Indicates measurement information from wireless equipment; in These represent the coordinates measured by the wireless equipment in the X, Y, and Z directions, respectively. This indicates the fusion of location information; in , , Indicates fusion of location information Coordinates in the X, Y, and Z directions; This indicates the speed information of the IMU; in These represent the velocities in the X, Y, and Z directions acquired by the IMU, respectively.

[0064] For input Z-score standardization is performed using the following formula: ; in To standardize the processing results, It is the mean of each feature. It is the standard deviation of each feature.

[0065] The output target of the residual compensation network is the predicted residual value. The formula is as follows: ; in , , These represent the predicted residual values. Correction values ​​in the X, Y, and Z directions.

[0066] Multi-source sensor data fusion refers to the process of comprehensively processing data from multiple different sensors according to certain mathematical methods and strategies to obtain more accurate, stable, and reliable information than that from a single sensor.

[0067] The processing flow of the residual compensation network built based on the improved multi-layer fully connected neural network in this embodiment is as follows: Step 3.1. Input feature extraction to obtain multi-source sensor information.

[0068] Step 3.2. Linear transformation: Perform an affine transformation to generate the intermediate layer output, expressed by the following formula: ; in Indicates the fully connected layer number 1 Fully connected layer operations, It is a weight matrix. It is the output or input of the previous layer. It is the bias vector.

[0069] Step 3.3. Batch normalization: Standardize the features of each mini-batch. , ; in This represents the average value of all samples in the current mini-batch. This is the number of samples in the current mini-batch. It is the first The activation value of each sample. This represents the variance of the activation values ​​in the current mini-batch of the neural network.

[0070] This invention introduces batch normalization. Batch normalization is a method for standardizing the input features or intermediate activation values ​​of each layer in a neural network. Its goal is to address problems encountered during neural network training, such as vanishing / exploding gradients, slow training convergence, and activation distribution drift between different layers.

[0071] Step 3.4. Normalize the features, standardizing them to a mean of 0 and a variance of 1, and introduce a small regularization term. : .

[0072] in Indicates the first Normalized features of activation values ​​for each sample.

[0073] It is a very small positive number to prevent the denominator from being 0 and to improve numerical stability.

[0074] Step 3.5. Introduce Dropout to randomly disable some neurons to prevent overfitting. Dropout is a regularization method that randomly discards some neurons (i.e., sets their activation values ​​to 0) during training to prevent overfitting.

[0075] For the standardized output Generate a mask vector with the same dimensions as it. . It is a Bernoulli distribution, where: It is the Dropout mask. , is the retention probability.

[0076] Step 3.6. Perform scaling and translation to reconstruct a trainable distribution. .

[0077] in It is a trainable scaling factor that controls the amplitude after standardization. It is a trainable offset factor that controls the standardized bias, and the final output. Used to input the next level.

[0078] Step 3.7. Add the ReLU activation function: ; in This represents the activation function.

[0079] Adding or multiplying multiple fully connected layers can ultimately simplify to a linear function, resulting in a very weak model expressive power.

[0080] Step 3.7 introduces the ReLU activation function, which retains positive values ​​and discards negative values, introducing non-linearity so that the neural network can fit more complex relationships. Furthermore, the method is very simple, only performing a single maximum value comparison, making it very fast in both forward and backward propagation. The gradient of ReLU is 1 (for positive numbers), and it does not become extremely small as it moves away from 0.

[0081] Step 3.8. Repeat steps 3.2 to 3.7 to perform multi-layer deep feature learning.

[0082] Step 3.9. Output the predicted residual values ​​from the output layer. : ; in This represents the output layer of the neural network. This indicates the output of the third layer. This represents the output bias vector.

[0083] Step 3.10. Utilize residual prediction values Correct the predicted position and output the corrected trajectory estimation result. : ; in This represents the estimated position output using the improved adaptive Kalman filter method.

[0084] In practical cooperative navigation systems, the process noise and observation noise of traditional Kalman filters often exhibit uncertainties or dynamic changes. Traditional Kalman filters rely on statically preset covariance matrices, making it difficult to adapt to fluctuations in sensor errors in complex environments, potentially leading to decreased filtering performance or even estimation bias. Therefore, this invention proposes an improved Adaptive Kalman Filter (AKF). The AKF can automatically adjust its parameters, maintaining stable estimation and high accuracy in unknown or dynamically changing noise environments, making it particularly suitable for fusion positioning tasks using multi-source heterogeneous data in complex systems such as UAVs.

[0085] Furthermore, machine learning is becoming increasingly crucial in UAV cooperative navigation. Although it requires a large amount of training data and has relatively weak generalization ability, it can significantly improve positioning accuracy, robustness, and intelligence in dynamic environments, and optimize autonomous decision-making and multi-source data fusion. A neural network (NN) is essentially an information processing and learning system that mimics the operation of neurons in the human brain. This system employs a multi-layered structure containing a large number of "neurons," gradually extracting input features to ultimately complete tasks such as prediction, classification, and regression. Neural networks can not only learn the nonlinear relationships between complex multi-source data but also automatically extract important feature combinations, possessing powerful scalability. It can integrate temporal information or physical models to ultimately approximate a residual model that more closely resembles the actual trajectory. Therefore, neural networks are very suitable for solving cooperative navigation-related problems.

[0086] When the Global Navigation Satellite System (GNSS) fails or its signal weakens, this invention combines AKF (Automatic Acoustic Filter) with NN (Neural Network) to achieve cooperative positioning for UAVs. Specifically, in the state prediction stage, velocity information estimated by the inertial measurement unit (IMU) is introduced to replace the traditional model derivation of velocity-state components, significantly improving the real-time performance and physical consistency of state prediction. By dynamically adjusting the observation covariance matrix based on the observation residual norm, AKF can adaptively handle measurement anomalies and environmental uncertainties, effectively enhancing the robustness and estimation accuracy of the filter. The neural network uses multi-source heterogeneous information fusion as input, and its network architecture employs a multi-layer fully connected design, combined with batch normalization and random deactivation mechanisms, and introduces the ReLU activation function to support sparse responses. This results in a more stable convergence, faster training speed, and stronger generalization ability for the improved neural network, leading to high positioning accuracy. Furthermore, compared with existing methods, this invention also boasts lower computational complexity and resource consumption advantages.

[0087] This invention utilizes a residual compensation network based on an improved multilayer fully connected neural network to predict and correct errors, which not only improves the system's ability to model nonlinear errors but also enhances the robustness and accuracy of the final trajectory results.

[0088] In addition, to verify the effectiveness of the method proposed in this invention, the following experimental procedure is also given.

[0089] like Figure 4 The flight paths of four UAVs performing a collaborative mission are shown. Aircraft 1 has lower navigation accuracy, resulting in a larger positional error; therefore, it is designated as an auxiliary aircraft. The other aircraft (Aircraft 2, 3, and 4) have higher onboard navigation performance and are designated as reference aircraft.

[0090] To improve the positioning accuracy of the assisted aircraft, this invention uses a reference aircraft to measure and solve for the trajectory of the assisted aircraft. By utilizing the sensor information exchange between the reference aircraft and the assisted aircraft, a mathematical relationship is established, the flight trajectory of the assisted aircraft is calculated, and finally, the cooperative positioning method proposed in this invention is used to reduce positioning errors.

[0091] Table 1 Average Error

[0092] Comparison of the effects of the method of the present invention as follows Figure 5 As shown in Table 1, where Figure 5 (a), (b), and (c) in the figure are the curves showing the change of the error of the UAV in the X, Y, and Z directions over time, respectively.

[0093] As can be seen from Table 1, the X-axis error of the assisted UAV calculated by the method of the present invention is about 0.0873 meters, the Y-axis error is about 0.0628 meters, the Z-axis error is about 0.0758 meters, and the position error is about 0.1316 meters. It can be seen that the errors are all within a very low range, indicating that the method of the present invention has a great improvement on the positioning accuracy in satellite denial environment.

[0094] Example 2 This embodiment 2 describes a collaborative positioning system for aircraft swarms based on multi-source sensor data fusion. This system is based on the same inventive concept as the collaborative positioning method for aircraft swarms based on multi-source sensor data fusion in embodiment 1 above.

[0095] The system for collaborative localization of aircraft swarms based on multi-source sensor data fusion in this embodiment includes the following modules: The preprocessing module is used to obtain the estimated three-dimensional coordinates of the auxiliary aircraft using radio ranging for a cluster of aircraft consisting of auxiliary aircraft and multiple reference aircraft, as measurement information for radio equipment. The Kalman filter module is used to adaptively fuse the inertial measurement unit (IMU) information and radio equipment measurement information mounted on the reference aircraft using an improved adaptive Kalman filter method to obtain fused positioning information. The improved adaptive Kalman filtering method introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of the observation residuals, building upon the traditional Kalman filter. The adjustment process of this adaptive observation noise adjustment mechanism is as follows: By calculating the Euclidean norm of the current observation residual at each time step and dynamically adjusting the observation covariance matrix based on the magnitude of the Euclidean norm, the Kalman filter gain is dynamically adjusted, thereby achieving adaptive updating of the state estimate. And a precision compensation module, used to build a residual compensation network based on an improved multi-layer fully connected neural network structure, which integrates positioning information, IMU information and wireless equipment measurement information as multi-source sensor data input to the residual compensation network; The residual compensation network learns the mapping relationship between the input multi-source sensor data and the trajectory residual, and finally outputs the residual prediction value. Based on the residual prediction value, it performs accuracy compensation on the fused positioning information of the adaptive Kalman filter.

[0096] It should be noted that any content not mentioned in the above-described functional modules of the system described in this embodiment can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0097] Example 3 This embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the aircraft swarm cooperative localization method based on multi-source sensor data fusion described in embodiment 1 above.

[0098] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0099] Example 4 This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the aircraft swarm cooperative localization method based on multi-source sensor data fusion in embodiment 1 above.

[0100] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0101] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for cooperative positioning of an aircraft cluster based on multi-source sensor data fusion, characterized by comprising the following steps: Step 1. First, for an aircraft cluster composed of a reference aircraft and a plurality of reference aircrafts, a three-dimensional coordinate estimate of the reference aircraft is obtained by radio ranging, serving as radio device measurement information in Step 2. Step 2. Then, the improved adaptive Kalman filtering method is used to adaptively fuse the inertial measurement unit (IMU) information and the radio device measurement information mounted on the reference aircraft to obtain fusion positioning information. The improved adaptive Kalman filtering method introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of the observation residual on the basis of the traditional Kalman filter. The adjustment process of the adaptive observation noise adjustment mechanism is as follows: By calculating the Euclidean norm of the current observation residual at each time, the observation covariance matrix is dynamically adjusted based on the size of the Euclidean norm, and then the Kalman filter gain is dynamically adjusted to realize adaptive updating of the state estimate. Step 3. A residual compensation network based on an improved multi-layer fully connected structure neural network is built, and the fusion positioning information, the IMU information and the radio device measurement information are input into the residual compensation network as multi-source sensor data. The residual compensation network learns the mapping relationship from the input multi-source sensor data information to the trajectory residual, finally outputs the residual prediction value, and compensates the precision of the fusion positioning information of the adaptive Kalman filter based on the residual prediction value. In Step 2, the adjustment process of the adaptive observation noise adjustment mechanism is as follows:

2. The multi-source sensor data fusion based cooperative localization method for aircraft cluster according to claim 1, characterized in that, When the residual decreases, the observation covariance decreases, the Kalman filter gain increases, and the adaptive Kalman filter fully utilizes the stable and reliable radio ranging information to correct the IMU drift to improve the positioning accuracy. When the residual increases, the observation covariance increases, the Kalman filter gain decreases, and the adaptive Kalman filter reduces the dependence on abnormal measurements to suppress the influence of sudden errors caused by multipath interference and signal shielding on state estimation. In Step 2, the process of dynamically adjusting the Kalman filter gain by the adaptive observation noise adjustment mechanism is as follows:

3. The multi-source sensor data fusion based aircraft cluster cooperative localization method according to claim 1 or 2, characterized in that, The processing flow of the improved adaptive Kalman filtering method is as follows: First, the expression of the observation matrix is given as follows: ； wherein is a transformation matrix, i.e. a 3x3 identity matrix, denotes a 3x3 zero matrix; The observation residuals are then calculated as follows: ； wherein represents a position of an auxiliary aircraft, represents an observation matrix, represents a current state update; Recalculate the residual Euclidean norm The formula is as follows: ； The expression of the adaptive observation noise covariance matrix is given as follows: ； wherein is a base variance of the observation noise, is a tuning coefficient, which is a constant value, for tuning , denotes a non-linear mapping of the norm of the observation residual using a hyperbolic tangent function; denotes a non-linear mapping of the norm of the observation residual using a hyperbolic tangent function; Finally, the Kalman filter gain is adjusted dynamically and is expressed by the following formula: ; where represents the current time covariance matrix.

4. The multi-source sensor data fusion based cooperative localization method for aircraft cluster according to claim 3, characterized in that, Step 2.

1. State initialization, set the initial state and covariance; Step 2.

3. State prediction, formula as follows: Initial state The formula is as follows: ； The initial covariance is , and the initial velocity is ; Step 2.

2. Constructing the state transition matrix : ； wherein is a transformation matrix, i.e. a 3x3 identity matrix, denotes a time difference, denotes a 3x3 zero matrix; Step 2.

4. Replace the initial state velocity with the IMU correction, formula as follows: ； wherein represents the current state update, represents the previous time state; Step 2.

5. Predict covariance update, formula as follows: ； wherein denotes the current speed, denotes the speed measured with the IMU; Step 2.

7. Update state: ； ； wherein is a process noise covariance matrix, is a variance of the process noise, is a transformation matrix, i.e. a 6x6 identity matrix, denotes the covariance matrix at the current time instant, denotes the covariance matrix before the transition at the previous time instant; Step 2.

6. Dynamically adjust Kalman filter gain based on adaptive observation noise adjustment mechanism ; Step 2.

8. Update covariance: ； wherein represents the current time state, represents the current state update; is the observation residual; The processing flow of the residual compensation network is as follows: ； wherein denotes the updated covariance; Step 2.

9. Output estimated position The formula is expressed as follows: ； wherein , , respectively represent coordinates in the X, Y, Z directions.

5. The multi-source sensor data fusion based cooperative localization method for aircraft swarm according to claim 1, wherein, In step 3, the input of the residual compensation network The formula is expressed as follows: ； represents position information of the IMU; wherein X, Y, Z are the coordinates of the IMU in the three directions; represents radio device measurement information; wherein respectively represent the coordinates measured by the radio device in the X, Y, Z directions; represents fusion positioning information; wherein 、 、 representing fusion positioning information coordinates in X, Y, Z directions; represents velocity information of the IMU; wherein respectively represent the X, Y, Z directions of the speed obtained by the IMU.

6. The multi-source sensor data fusion based cooperative localization method for aircraft swarm according to claim 1, wherein, Step 3.

1. Input feature extraction, obtain multi-source sensor information; Step 3.

2. Linear transformation, perform affine transformation to generate intermediate layer output, formula expression as follows: Step 3.

3. Batch normalization, standardize the features of each mini-batch: ; wherein denotes the fully connected layer layer fully connected operation, is a weight matrix, is the output or input of the previous layer, is a bias vector; Step 3.

5. Introduce Dropout, randomly mask some neurons to prevent overfitting; ， ； where denotes the mean over all samples in the current mini-batch, is the number of samples in the current mini-batch, is the activation value of the -th sample, denotes the variance of the activation values of the neural network over the current mini-batch; Step 3.

4. Normalize features, standardize to mean 0, variance 1, and introduce a regularization term : ； wherein represents a normalized feature of an activation value of the th sample; Step 3.

7. Add activation function ReLU: Step 3.

6. Scaling and translation are performed, and the distribution with trainable-ability is restored, ; wherein is a trainable scaling factor that controls the amplitude of the normalized, is a trainable shift factor that controls the bias of the normalized, final output for input to the next layer; ​ ； wherein represents an activation function; Step 3.

8. Repeat steps 3.2 to 3.7 to learn multi-layer deep features; Step 3.

9. Output layer output residual prediction value : ； wherein denotes the output layer of the neural network, denotes the output of the third layer, denotes the bias vector of the output; Step 3.

10. Utilizing the residual prediction value correcting the predicted position, outputting a corrected trajectory estimation result : ； wherein represents the estimated position output using the improved adaptive Kalman filter method.

7. The multi-source sensor data fusion based cooperative localization method for aircraft swarm according to claim 1, wherein, The aircraft cluster cooperative positioning method is suitable for cooperative positioning in a global navigation satellite system denial area. The number of reference aircraft is at least three, and the positioning accuracy of the auxiliary aircraft is lower than that of the reference aircraft.

8. An aircraft cluster cooperative positioning system based on multi-source sensor data fusion, characterized in that, The system comprises the following modules: A preprocessing module is configured to obtain a three-dimensional coordinate estimation value of an auxiliary aircraft in a cluster of aircrafts composed of the auxiliary aircraft and multiple reference aircrafts by using a radio ranging method as radio device measurement information. A Kalman filtering module is configured to use an improved adaptive Kalman filtering method to adaptively fuse inertial measurement unit (IMU) information and radio device measurement information mounted on the reference aircrafts to obtain fusion positioning information. The improved adaptive Kalman filtering method introduces an adaptive observation noise adjustment mechanism based on the Euclidean norm of observation residuals on the basis of a traditional Kalman filter. The adjustment process of the adaptive observation noise adjustment mechanism is as follows: The Euclidean norm of the current observation residual is calculated at each time, and the observation covariance matrix is dynamically adjusted based on the size of the Euclidean norm, and then the Kalman filtering gain is dynamically adjusted to realize adaptive update of the state estimation. An accuracy compensation module is configured to build a residual compensation network based on an improved multi-layer fully connected structure neural network, and input the fusion positioning information, IMU information and radio device measurement information into the residual compensation network as multi-source sensor data. The residual compensation network learns the mapping relationship from the input multi-source sensor data information to the trajectory residual, finally outputs the residual prediction value, and compensates the fusion positioning information of the adaptive Kalman filter based on the residual prediction value.

9. A computer device comprising a memory and one or more processors; characterized in that, The executable code is stored in the memory, and when the processor executes the executable code, the steps of the aircraft cluster cooperative positioning method based on multi-source sensor data fusion in any one of claims 1-7 are implemented.

10. A computer readable storage medium having stored thereon a program; characterized in that, The program is executed by the processor, and the steps of the aircraft cluster cooperative positioning method based on multi-source sensor data fusion in any one of claims 1-7 are implemented.

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