Bit rate joint estimation method for non-full connected aircraft network

Abstract

The application belongs to the technical field of navigation and positioning, and particularly relates to a position and speed joint estimation method for a non-full-connection aircraft network, which can realize low-cost position and speed joint estimation by using a ranging sequence only, and avoid topological distortion caused by low network connectivity and incomplete observation information. Through an adaptive topology reconstruction algorithm, the application uses limited observation data to deduce missing information, so that the aircraft cluster system can still maintain high-precision continuous positioning by using the reconstructed global constraint in a poor environment with low network connectivity and incomplete observation data, effectively solving the problem that the traditional algorithm is prone to divergence in a low-connectivity network environment and breaking through the connectivity limitation.

Description

Technical Field

[0001] This invention belongs to the field of navigation and positioning technology, specifically relating to a joint estimation method for potential velocity in non-fully connected aircraft networks. Background Technology

[0002] In recent years, low-altitude aircraft such as drones have been widely deployed in military reconnaissance, formation flying, environmental monitoring, and logistics transportation due to their high flexibility, scalability, and low cost. In these complex application scenarios, high-precision position awareness is a prerequisite for achieving swarm formation control, collision avoidance, and task allocation. Currently, low-altitude aircraft mainly rely on Global Navigation Satellite Systems (GNSS) to obtain absolute position coordinates. However, in urban areas, canyons, or environments with strong electromagnetic interference, GNSS signals are susceptible to obstruction, multipath reflection, and malicious deception interference, leading to a significant decrease in positioning accuracy. Therefore, distributed relative positioning technology based on inter-aircraft radio ranging has become a core means to ensure the continuous operation of aircraft swarms in GNSS-constrained environments.

[0003] However, existing distributed positioning technologies still face the following challenges in practical deployment:

[0004] (1) Redundant observations missing in non-fully connected networks: Due to limitations in communication distance, power consumption control, and dynamic occlusion, aircraft networks often struggle to maintain a fully connected topology, resulting in insufficient redundancy in ranging observations. Traditional positioning algorithms, such as multidimensional scaling transformation and least squares methods, perform well in fully connected or highly connected networks with a large amount of redundant observation information. The core reason for this is that these algorithms can utilize the large amount of redundant observation information between node pairs to construct strong geometric constraints. However, when network connectivity is low, traditional algorithms are prone to getting trapped in local optima due to the incompleteness of observations, leading to severe topological distortions in the positioning results and making it difficult to guarantee global convergence.

[0005] (2) Single dimension of motion state perception: Most existing distributed positioning research focuses on static or quasi-static position coordinate acquisition, often ignoring the real-time perception of the aircraft's motion state. Current common speed control schemes usually rely on additional hardware such as Doppler radar and inertial measurement units, which not only significantly increases the cost of single-unit hardware and system power consumption, but also restricts the scalability of lightweight aircraft clusters.

[0006] In summary, how to recover redundant constraints using incomplete observation information from non-fully connected networks and simultaneously perform joint estimation of position and velocity parameters has become a pressing technical challenge in the field of navigation and positioning. Summary of the Invention

[0007] In view of this, the present invention provides a joint position and velocity estimation method for non-fully connected aircraft networks, which can achieve low-cost joint position and velocity estimation using only ranging sequences, avoiding topological distortion caused by low network connectivity and incomplete observation information.

[0008] To achieve the objectives of this invention, the following technical solutions are provided.

[0009] A joint potential-velocity estimation method for non-fully connected aircraft networks includes the following steps: Step 1: Using the existing incomplete observation subsets among the nodes in the non-fully connected network, obtain the preliminary relative coordinate framework of the node set through semidefinite programming techniques; Step 2: Using the aforementioned preliminary relative coordinate framework, adaptively extrapolate the node spacing of the missing ranging links, and reconstruct the sparse distance matrix into a full-rank matrix. Step 3: Perform the positioning solution again using the reconstructed full-element distance matrix, and use the completed topological constraints to eliminate topological distortion and obtain high-precision relative position coordinates; Step 4: Using the continuous time step ranging observation sequence, couple the radial relative rate with the reconstructed spatial direction vector to construct a set of velocity projection equations and solve the three-dimensional velocity vector of the aircraft.

[0010] Specifically, step 1 includes: Step 11: Obtain the incomplete distance measurement set between nodes at the current time, and establish a residual objective function that only includes known observations; Step 12: By introducing an auxiliary matrix, the positional distance is transformed into a linear expression of the matrix trace, and the rank constraint is ignored. The original non-convex problem is transformed into a convex semi-positive definite programming problem for solution, and the initial relative coordinate matrix is ​​obtained.

[0011] Specifically, step 2 includes: Step 21: Traverse all pairs of nodes that have not established physical connections, and use the initial relative coordinate matrix to calculate the estimated Euclidean distance between the nodes; Step 22: For node pairs with physical connections, retain the original distance values; for node pairs with missing connections, fill in the Euclidean distance estimates to reconstruct the full-element distance matrix.

[0012] Specifically, step 3 includes: Step 31: Reconstruct the cost function for secondary fine localization using the completed full topology constraints; Step 32: Perform semidefinite programming optimization again to obtain a high-precision local relative coordinate matrix.

[0013] Specifically, step 4 includes: Step 41: Perform first-order difference on two consecutive distance measurement observations between nodes to obtain the radial relative velocity; Step 42: Combining the relative direction vector obtained in Step 3, establish the projection equation that includes the nodal velocity vector; Step 43: Summarize the projection equations of all observation links and use the weighted least squares method to solve for the velocity vector of each aircraft.

[0014] The method uses only inter-machine radio ranging sequences to achieve joint estimation of position and velocity, without relying on global navigation satellite systems or additional velocity sensors.

[0015] Beneficial effects 1. This invention uses an adaptive topology reconstruction algorithm to extrapolate missing information from limited observation data. This enables the aircraft swarm system to maintain high-precision continuous positioning even in harsh environments with low network connectivity and incomplete observation data. It effectively solves the problem of traditional algorithms being prone to divergence in low-connectivity network environments and breaks through connectivity limitations.

[0016] 2. By exploring the evolution of ranging information over time, this invention achieves synchronous output of position coordinates and velocity vectors, providing higher-dimensional reference data for dynamic obstacle avoidance and formation coordination of aircraft swarms, and realizing full perception of motion status. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0019] This invention proposes a joint potential-velocity estimation method for non-fully connected aircraft networks, the process of which is as follows: Figure 1 As shown, it includes the following steps: Step 1: Initial Coarse Localization. Utilizing the existing incomplete observation subsets among the nodes in the not fully connected network (limited incomplete observation data in the not fully connected network), a preliminary relative coordinate framework of the node set is obtained through semi-positive definite programming techniques, thus constructing the preliminary relative coordinate framework of the target node group, as follows: Step 11: Construct the residual objective function. Obtain the incomplete distance measurement set between nodes at the current time step. Establish a residual objective function that contains only known observations: (1) in, Let be the coordinate matrix of the nodes to be solved; and Representing nodes respectively and 3D position vector; A set of indices for known observations; It is a weighting coefficient set based on the link signal-to-noise ratio, used to adjust the impact of different quality ranging values ​​on the positioning results.

[0020] Step 12: Relaxation solution of semidefinite programming. Since the original cost function is non-convex, direct solution easily falls into local optima. An auxiliary matrix is ​​introduced... (in (where T denotes transpose), transforming the positional distance into a linear expression of the matrix trace. By ignoring the rank constraint, the above non-convex problem can be transformed into the following convex semi-positive definite programming problem: (2) in, For indicator matrix; For the first Unit vectors; The trace of the matrix is ​​used to represent the origin of the matrix. By solving this problem, the globally optimal initial relative coordinate matrix can be obtained. .

[0021] Step 2: Adaptive Reconstruction of the Distance Matrix. Using the initial coarse localization results, the node spacing of missing ranging links (i.e., unobserved Euclidean distances) is adaptively extrapolated, reconstructing the sparse distance matrix into a full-rank, element-complete matrix, restoring the fully connected redundancy constraints between nodes. Specifically, using the initial topological constraints generated by the initial localization, the missing geometric ranging information is adaptively extrapolated, including: Step 21: Deducing the missing ranging term. Traverse all node pairs that have not established a physical connection (i.e., have no direct ranging signal). Using the initial relative coordinate matrix obtained in step 12 Calculate the estimated Euclidean distance between nodes. : (3) Step 22: Reconstruct the all-element distance matrix For node pairs with physical connections, the original ranging values ​​are retained to ensure accuracy; for node pairs with missing connections, the estimated values ​​from step 21 are used to fill in the missing values. This enables the transformation from a sparse matrix to a full-rank matrix, and reconstructs the global redundant observation constraints at the algorithm level.

[0022] Step 3: Secondary fine localization based on the reconstructed distance matrix. The localization solution is performed again using the reconstructed full-element distance matrix. The topological distortion in the coarse localization is eliminated using the completed complete topological constraints, i.e., the global redundant observation constraints are used to eliminate the topological distortion in the coarse localization, obtaining high-precision relative position coordinates, including: Step 31: Fine-tuning the cost function reconstruction. At this point, the completed full topology constraints are used. Reconstructing the cost function of quadratic fine localization : (4) in, The completed weighting coefficients. Indicates the completed first... The node and the first The Euclidean distance between nodes, where N is the total number of nodes after completion.

[0023] Step 32: High-precision quadratic solution. Perform semidefinite programming optimization again to obtain a high-precision local relative coordinate matrix. This serves as a spatial benchmark for subsequent joint estimation of potential velocity.

[0024] Step 4: Cluster velocity determination based on the rate of change of ranging. Using a continuous time-step ranging observation sequence, the radial relative rate is coupled with the reconstructed spatial direction vector to construct a set of velocity projection equations. The weighted least squares method is used to solve the three-dimensional velocity vector of the aircraft in real time, achieving velocity sensing without additional sensors.

[0025] This step is based on spatiotemporal coupling for joint position and velocity estimation, aiming to utilize the temporal evolution of ranging sequences to achieve single-source joint sensing of position and velocity, as detailed below: Step 41: Obtain the rate of change of distance measurement: For nodes and Two consecutive observations between and Perform a first-order difference to obtain the radial relative velocity. : (5) Step 42: Construct the potential velocity projection equation system: Let the nodes be... The velocity vector is ,node The velocity vector is Combined with the relative direction vector obtained in step 3 Establish the projection equation: (6) Step 43: Joint estimation and solution of velocity vectors: The projection equations of all observation links are summarized, and the velocity vectors of each spacecraft are solved using the weighted least squares method. This method requires no additional Doppler sensors; it can determine the dynamic evolution trend of the cluster simply by observing the temporal evolution of distance observations.

[0026] The projection equations of all observation links are summarized, and the velocity vectors of each aircraft are solved using the weighted least squares method. This method requires no additional Doppler sensors and can determine the dynamic evolution trend of the swarm simply by observing the time evolution of distance observations.

[0027] The method is applicable to harsh environments where aircraft network connectivity is low and observation data is incomplete.

[0028] This invention includes, but is not limited to, the above embodiments. Any equivalent substitutions or partial improvements made under the spirit and principles of this invention shall be considered within the scope of protection of this invention.

Claims

1. A joint potential-velocity estimation method for non-fully connected aircraft networks, characterized in that, Includes the following steps: Step 1: Using the existing incomplete observation subsets among the nodes in the non-fully connected network, obtain the preliminary relative coordinate framework of the node set through semidefinite programming techniques; Step 2: Using the aforementioned preliminary relative coordinate framework, adaptively extrapolate the node spacing of the missing ranging links, and reconstruct the sparse distance matrix into a full-rank matrix. Step 3: Perform the positioning solution again using the reconstructed full-element distance matrix, and use the completed topological constraints to eliminate topological distortion and obtain high-precision relative position coordinates; Step 4: Using the continuous time step ranging observation sequence, couple the radial relative rate with the reconstructed spatial direction vector to construct a set of velocity projection equations and solve the three-dimensional velocity vector of the aircraft.

2. The method according to claim 1, characterized in that, Step 1 specifically includes: Step 11: Obtain the incomplete distance measurement set between nodes at the current time, and establish a residual objective function that only includes known observations; Step 12: By introducing an auxiliary matrix, the positional distance is transformed into a linear expression of the matrix trace, and the rank constraint is ignored. The original non-convex problem is transformed into a convex semi-positive definite programming problem for solution, and the initial relative coordinate matrix is ​​obtained.

3. The method according to claim 2, characterized in that, Step 2 specifically includes: Step 21: Traverse all pairs of nodes that have not established physical connections, and use the initial relative coordinate matrix to calculate the estimated Euclidean distance between the nodes; Step 22: For node pairs with physical connections, retain the original distance values; for node pairs with missing connections, fill in the Euclidean distance estimates to reconstruct the full-element distance matrix.

4. The method according to claim 1, characterized in that, Step 3 specifically includes: Step 31: Reconstruct the cost function for secondary fine localization using the completed full topology constraints; Step 32: Perform semidefinite programming optimization again to obtain a high-precision local relative coordinate matrix.

5. The method according to claim 1, characterized in that, Step 4 specifically includes: Step 41: Perform first-order difference on two consecutive distance measurement observations between nodes to obtain the radial relative velocity; Step 42: Combining the relative direction vector obtained in Step 3, establish the projection equation that includes the nodal velocity vector; Step 43: Summarize the projection equations of all observation links and use the weighted least squares method to solve for the velocity vector of each aircraft.

6. The method according to any one of claims 1-5, characterized in that, The method achieves joint estimation of position and velocity using only inter-machine radio ranging sequences, without relying on global navigation satellite systems or additional velocity sensors.

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