A heterogeneous observability-driven air-ground cluster cooperative positioning and reference relay method

Abstract

The application discloses a heterogeneous observability driven air-ground cluster cooperative positioning and reference relay method. Specifically, the method comprises the following steps: acquiring multi-source measurements of air nodes and ground nodes and constructing a local collaborative candidate graph; the candidate collaborative edge quality, node health degree, heterogeneous observability index, resource state and reference continuity index are combined to form a joint scheduling state; under the same scheduling target, the topology weight, effective adjacency scale and reference relay decision are coupled to obtain the analytical initial value and the lightweight learning correction result, and the results are back-projected to a feasible region meeting the communication budget, local graph connectivity, reference reachability and air-ground key coupling constraints; according to the obtained enabled edge set and the current reference node, weighted factor graph optimization is performed, and the optimized posterior uncertainty and the updated resource state are fed back to the next scheduling period. The application can output the cluster position, velocity and uncertainty in the unified reference system under the conditions of link fluctuation and node degradation.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative navigation and positioning technology, and particularly relates to a heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method. Background Technology

[0002] With the rapid development of drone and unmanned vehicle technologies, heterogeneous air-ground clusters composed of air and ground nodes are showing broad application prospects in fields such as environmental monitoring, emergency rescue, and logistics distribution. In these applications, high-precision and high-reliability collaborative positioning capabilities are the foundation and key for cluster systems to complete complex tasks.

[0003] Existing cooperative localization methods can utilize information such as inertial, visual, wheel odometry, and inter-node ranging for state estimation, and can achieve multi-source fusion through factor graphs, filtering, or nonlinear optimization. These methods address the issue of how multiple types of measurements enter the localization backend. However, when node degradation, link fluctuations, and limited communication resources occur simultaneously, it is still necessary to dynamically determine which cooperative edges should be enabled, how many edges should be enabled, the weight of each edge, and which node should serve as the unified reference.

[0004] Existing solutions typically treat outlier edge selection, edge weight allocation, adjacency size selection, and reference node selection as independent steps: locally high-quality edges do not necessarily improve overall geometric observability, simply increasing adjacent edges increases communication and computational burden, and switching reference nodes alters reference reachability and topological constraints. Optimizing these variables separately can easily lead to conflicting results, such as the selected high-weight edge set failing to maintain reference connectivity, or the adjacency size selected to improve observability exceeding the available communication budget.

[0005] Therefore, the core technical problem addressed by this invention is not the calculation method of the residual of a single cooperative edge, but how to form a unified scheduling state that can characterize edge quality, node state, heterogeneous geometry, system resources and reference continuity, and make coupled decisions on multiple mutually influential scheduling variables accordingly.

[0006] First, it is necessary to jointly determine the topological weight of the cooperative edge, the effective adjacency size, and the reference relay decision under the same scheduling objective, so as to avoid local optima and decision conflicts caused by solving the three variables separately.

[0007] Second, it is necessary to ensure the feasibility of joint scheduling results under the constraints of communication budget, local graph connectivity, reference node reachability and air-ground critical coupling, and to avoid frequent switching or no reachable replacement nodes when reference nodes degrade.

[0008] Third, the joint scheduling results need to be able to directly affect the positioning backend, and the next scheduling cycle needs to be updated in reverse using posterior uncertainty, observability and resource status, so as to form a closed loop that can sustainably adapt to environmental changes.

[0009] Fourth, in a distributed implementation, it is also necessary to control the amount of information across nodes and suppress overconfidence caused by duplicate paths and old reference frame information. Summary of the Invention

[0010] The purpose of this invention is to provide a collaborative localization and reference relay method for heterogeneous air-ground clusters with a joint scheduler as the core. This method couples the topology weights, effective adjacency size, and reference relay decisions under the same objective function and the same set of constraints. Through constraint-consistent back projection, backend weight injection, and optimization state feedback, the scheduling results can still form an executable and continuous collaborative localization topology even under resource-constrained and reference node degradation conditions.

[0011] The technical solution to achieve the purpose of this invention is: a heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay method, comprising the following steps:

[0012] Step 1: Obtain multi-source measurements of air nodes and ground nodes, and establish an air-ground heterogeneous local cooperation candidate graph containing node status, motion edges and candidate cooperation edges according to node type.

[0013] Step 2: Based on the quality representation of candidate cooperative edges, the health of nodes at both ends of the edge, the heterogeneous observability index formed by candidate cooperative edges and local priors, the current communication and computing resource status, and the reference continuity index, a joint scheduling state is formed.

[0014] Step 3: Input the joint scheduling state into the joint scheduler, and coupled the topology weight, effective adjacency size and reference relay decision of each candidate cooperative edge under the same scheduling objective. The scheduling objective simultaneously considers graph observability gain, communication cost, topology switching cost and reference switching cost.

[0015] Step 4: Fuse the initial scheduling result obtained from parsing optimization with the correction amount obtained from lightweight learning inference, and backproject the fusion result to a feasible region that simultaneously satisfies the constraints of communication budget, topology size, local graph connectivity, reference node reachability, and air-ground key coupling; determine the set of enabled edges according to the topology weights and effective adjacency size after backprojection, and execute reference relay when the current reference node health is lower than the exit threshold and the candidate reference node satisfies the switching advantage margin;

[0016] Step 5: Inject the topological weights corresponding to the enabled edge set into the fixed-hysteresis sliding window factor graph through information matrix scaling, covariance adjustment or robust kernel parameter adjustment, and jointly optimize the state of the air node and the ground node using the current reference node or the reference node after the relay as a unified reference coordinate system.

[0017] Step 6: Based on the joint optimization results of Step 5, form the posterior state, feed back the posterior uncertainty, heterogeneous observability index and resource status to the next scheduling cycle, and output the cluster pose, velocity and uncertainty under a unified reference frame.

[0018] A heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay system is provided. This system is used to implement the aforementioned heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay method. The system specifically includes:

[0019] The system includes an air node, a visual camera, and an altitude sensor, and an air node and a ground node, respectively.

[0020] The candidate graph construction module is used to acquire multi-source measurements of air and ground nodes and to build a candidate graph of air-ground heterogeneous local cooperation based on node type.

[0021] The joint scheduling state construction module is used to form a joint scheduling state based on the quality representation of cooperative edges, node health, heterogeneity observability index, resource status, and reference continuity index.

[0022] The joint scheduling and backprojection module is used to coupled the calculation of topology weights, effective adjacency size and reference relay decision under the same scheduling objective, and backproject the scheduling results to the feasible region that satisfies the communication budget, local graph connectivity, reference node reachability and air-ground key coupling constraints;

[0023] The factor graph optimization and feedback module is used to inject topological weights into a fixed-hysteresis sliding window factor graph, output the cluster pose, velocity and uncertainty under a unified reference frame, and feed the optimization status back to the next scheduling cycle.

[0024] Furthermore, the system may also include a distributed consistency module for constructing cross-node factor summaries and performing conservative consistency scaling and injection based on duplicate path risk, information freshness, and reference switching source.

[0025] Compared with the prior art, the significant advantages of this invention are:

[0026] (1) The joint scheduler takes topology weight, effective adjacency size and reference relay decision as three mutually coupled outputs, and coordinates heterogeneous observability gain, communication cost and handover cost under the same goal, reducing topology conflicts caused by separate decisions;

[0027] (2) The analytical optimization provides interpretable initial scheduling results. The lightweight learning module only corrects the initial values. The corrected results are then uniformized back to the projection, thus taking into account both environmental adaptability and engineering constraints such as budget, connectivity and reference reachability.

[0028] (3) The reference relay decision is obtained simultaneously with the edge weight and adjacency size, and the relay is triggered by the exit threshold and the switching advantage margin, which can reduce the impact of reference node degradation and frequent switching on the continuity of the unified reference system.

[0029] (4) The joint scheduling results are applied to the positioning backend through the information matrix, covariance or robust kernel parameters, and the posterior uncertainty and observability state are fed back to the next cycle, so that topology selection and state estimation form a closed loop.

[0030] (5) Cross-node collaboration constraints are transmitted in the form of factor summaries and are conservatively scaled according to repeated paths, information freshness and reference switching sources, which can reduce communication burden and suppress overconfidence caused by repeated information. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay method of the present invention.

[0032] Figure 2 This is a schematic diagram of the air-ground heterogeneous local cooperative topology in this invention;

[0033] Figure 3 This is a schematic diagram showing the topology weights, effective adjacency size, and reference relay decisions output by the joint scheduler of this invention;

[0034] Figure 4 A schematic diagram of the three-channel weight injection backend optimization of this invention;

[0035] Figure 5 This is a diagram showing the fixed hysteresis sliding window factor and edge detection of the present invention.

[0036] Figure 6 This is a schematic diagram of the distributed factor digest exchange and consistency injection of the present invention. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The core technology chain of the present invention is "joint scheduling state construction—three-output coupled solution—constraint-consistent back projection—reference relay and weight injection—optimization feedback update". Residual statistics, non-line-of-sight identification, fixed lag solution, and factor summarization can all serve as specific implementations or subordinate protective layers of the above technology chain, and do not constitute the sole limitation on the source of the joint scheduling state, the solver form, and the summary encapsulation format.

[0038] This invention targets heterogeneous clusters composed of air and ground nodes, constructing a local cooperative candidate graph under a unified reference coordinate system. Unlike starting and stopping constraints based solely on the quality of a single edge, this invention encodes candidate edge quality, node health, heterogeneous geometric observability, communication and computing resources, and reference continuity into a joint scheduling state. A single joint scheduler simultaneously outputs topology weights, effective adjacency size, and reference relay decisions. Subsequently, constraint-consistent backprojection ensures that the output meets budget, connectivity, and reference reachability requirements, and a closed loop is formed through weighted factor graph optimization and feedback updates.

[0039] This invention discloses a heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay method, comprising the following steps:

[0040] Step 1: Obtain multi-source measurements of air nodes and ground nodes, and establish an air-ground heterogeneous local cooperation candidate graph containing node status, motion edges and candidate cooperation edges according to node type.

[0041] Step 2: Based on the quality representation of candidate cooperative edges, the health of nodes at both ends of the edge, the heterogeneous observability index formed by candidate cooperative edges and local priors, the current communication and computing resource status, and the reference continuity index, a joint scheduling state is formed.

[0042] Step 3: Input the joint scheduling state into the joint scheduler, and coupled the topology weight, effective adjacency size and reference relay decision of each candidate cooperative edge under the same scheduling objective. The scheduling objective simultaneously considers graph observability gain, communication cost, topology switching cost and reference switching cost.

[0043] Step 4: Fuse the initial scheduling result obtained from parsing optimization with the correction amount obtained from lightweight learning inference, and backproject the fusion result to a feasible region that simultaneously satisfies the constraints of communication budget, topology size, local graph connectivity, reference node reachability, and air-ground key coupling; determine the set of enabled edges according to the topology weights and effective adjacency size after backprojection, and execute reference relay when the current reference node health is lower than the exit threshold and the candidate reference node satisfies the switching advantage margin;

[0044] Step 5: Inject the topological weights corresponding to the enabled edge set into the fixed-hysteresis sliding window factor graph through information matrix scaling, covariance adjustment or robust kernel parameter adjustment, and jointly optimize the state of the air node and the ground node using the current reference node or the reference node after the relay as a unified reference coordinate system.

[0045] Step 6: Based on the joint optimization results of Step 5, form the posterior state, feed back the posterior uncertainty, heterogeneous observability index and resource status to the next scheduling cycle, and output the cluster pose, velocity and uncertainty under a unified reference frame.

[0046] Furthermore, the state vector of any node in step 1 is denoted as:

[0047]

[0048] in Represents a three-dimensional position vector. Represents a three-dimensional velocity vector. Represents attitude quaternions, and These represent the inertial biases of the accelerometer and gyroscope, respectively. Indicates the node type identifier;

[0049] This represents the additional calibration and degradation compensation parameter blocks related to the node type. The parameter blocks for air nodes include camera extrinsic parameters, radio ranging antenna installation offset, and altitude auxiliary parameters; the parameter blocks for ground nodes include camera extrinsic parameters, radio ranging antenna installation offset, wheel diameter dimensional parameters, and wheel slip degradation compensation parameters.

[0050] Local collaborative graph notation is ,in This is the set of state variables for each node within the window. For the candidate edge set;

[0051] For any measuring edge If at time Obtain Node With nodes Relative distance observation between Then the measurement equation and residual factor are written as follows:

[0052]

[0053]

[0054] in Represents the cost function, and Representing nodes respectively and nodes At any moment Location, This represents the distance correlation deviation coefficient. This represents the constant deviation term. This indicates the environmental additional deviation item. This indicates ranging noise.

[0055] Furthermore, the quality characterization of candidate cooperative edges can be obtained in various ways. As a subordinate implementation, a hybrid probability model is used for non-line-of-sight risk estimation of the residual sequence of candidate ranging edges, wherein the hybrid probability model satisfies:

[0056]

[0057] in For the first The mixed weighting coefficients of each component satisfy the following conditions: ; , The first The mean and covariance of each Gaussian component;

[0058] Edges are obtained based on Bayesian posterior. Non-line-of-sight risk indicators Furthermore, the residual mean, residual variance, median absolute deviation (MAD), and normalized innovation square (NIS) are calculated as input features of the joint scheduler.

[0059] Furthermore, the joint scheduler and constraint-consistent backprojection in steps 3 and 4 are detailed as follows:

[0060] (1) The joint scheduler takes the joint scheduling state as input and the topological weight set of each candidate cooperative edge, the effective adjacency size, and the reference relay decision as three mutually coupled outputs; the reference health of the reference node is defined as follows:

[0061]

[0062] In the formula This indicates the positioning accuracy score. Indicates the local observability score. Indicates the link quality score. Indicates short-term stability score. Indicates the score for collaborative support capabilities. In order to represent , , , , The weighting coefficients are referenced from the candidate gating. The following relation is given:

[0063]

[0064] in For nodes Link quality metrics, This indicates the minimum threshold for link quality. It is a local geometric observability index. This represents the minimum observability threshold. For nodes The covariance matrix of the position sub-states, This represents the location covariance trace, characterizing the magnitude of location uncertainty.

[0065] (2) The joint scheduler satisfies the following optimization objective:

[0066]

[0067] in For edge start / stop variables, Indicates the communication cost. Indicates the cost of topology switching. Indicates the reference decision variable. The observability index formed by the enabled edge and the local prior at time t is given by the following relationship:

[0068]

[0069] in This indicates the prevention of singular, tiny positive numbers. Let the information matrix at time t be denoted by:

[0070]

[0071] The constructed joint scheduler satisfies the following joint scheduling constraints:

[0072]

[0073] in Representing an edge The topological weights at time t and This indicates the upper and lower limits of the effective adjacent edge size. Representing an edge The communication load is B, where B is the total budget limit.

[0074] (3) The joint scheduler is implemented by combining analytical optimization, lightweight learning correction, and constraint-consistent backprojection as follows:

[0075] Step 3.1: Encode the cooperative edge quality, node state, geometric state, resource state, and reference continuity state into the joint scheduler input;

[0076] Step 3.2: Perform analytical optimization based on heterogeneous observability gain, communication load, topology switching cost and reference continuity cost to generate initial topology weights, initial adjacency size and reference candidate scores;

[0077] Step 3.3: Input the initial parsing value and the joint scheduling state into the lightweight learning inference module to obtain the topology weight correction amount and the adjacency size correction amount;

[0078] Step 3.4: Fuse the initial analytical values ​​and the learning correction results, and perform the constraint uniformity back projection described in Step 4 to obtain the enabled edge set and the current reference node.

[0079] Furthermore, the specific process of joint scheduling state construction and parsing optimization in steps 3.1 to 3.2 is as follows:

[0080] For each candidate cooperative edge at time t, extract edge-level quality characteristics and the health of the nodes at both ends of the edge; the edge-level quality characteristics include non-line-of-sight risk, link quality, communication load, and residual mean, residual variance, median absolute deviation, and normalized innovation squared obtained from the sliding window residual sequence.

[0081] Extracting global constraint states The global constraint state includes at least the communication budget. Processor load rate Bandwidth utilization and the number of currently enabled edges ;

[0082] Based on the input feature vector The analytical scoring for constructing candidate edges is as follows:

[0083]

[0084] The initial edge weights of the candidate edges are obtained based on the analytical scoring as follows:

[0085]

[0086] in, The function is the Sigmoid function; simultaneously, it is based on the average link quality of all candidate edges at the current time. Geometric mass mean Risk mean and bandwidth utilization The initial adjacency size is calculated as follows:

[0087]

[0088] in, This is the interval truncation operator.

[0089] Furthermore, in steps 3.3 to 3.4, lightweight learning correction and constraint-consistent back-projection are performed on the analytical initial values, as detailed below:

[0090] Analyze the initial edge weights Analyze the initial adjacency size Input feature vector and global constraint state Input the lightweight learning inference module to obtain the edge weight correction. and Adjacency Size Correction The forms are as follows:

[0091]

[0092] in, and These are edge weight correction networks and adjacency size correction networks, respectively. These are the parameters of the trained model;

[0093] Calculate the final edge weight and final adjacency size based on the initial edge weight, edge weight correction, initial adjacency size, and adjacency size correction.

[0094]

[0095]

[0096] in, The fusion coefficient is... For rounding operators;

[0097] The comprehensive score of candidate edges is recalculated based on the final edge weights as follows:

[0098]

[0099] Candidate edges are sorted from highest to lowest based on their comprehensive scores, and those that meet the requirements are... Candidate edges are selected sequentially under the given conditions to obtain the set of active edges;

[0100] When the sorting results do not meet the constraints of reference node reachability, local graph connectivity, or air-ground key coupling, candidate edges that contribute significantly to the improvement of reference connectivity, graph observability, and air-ground collaboration effectiveness are retained first, while edges with benefits lower than the set value or load higher than the set value are removed.

[0101] When the lightweight learning inference module fails to output corrected results due to insufficient computing power, inference timeout, or model unavailability, the joint scheduler degenerates into a pure analytical optimization mode, relying solely on... , and Complete edge weight allocation and topology scale setting; after the lightweight learning inference module returns to normal, switch to the working mode that combines parsing optimization and lightweight learning inference.

[0102] Furthermore, the cross-platform visual measurements obtained in step 1 are used as visual collaborative edges, preferably implemented using coded label edges; when coded labels are unavailable, shared environmental target edges or natural feature re-identification edges are used as equivalent implementation methods to construct visual collaborative edges.

[0103] When an airborne node recognizes a visual identifier carried by a ground node, it obtains a relative pose observation and constructs a relative pose factor residual. as follows:

[0104]

[0105] in The relative pose is obtained from visual observation. For the pose of the air node, For the pose of the ground node;

[0106] Visual identifier measurement further constructs corner reprojection factors, and the pixel observation model is as follows:

[0107]

[0108] The corresponding reprojection residual factor is:

[0109]

[0110] in, For the first The pixel coordinates of the corner points, where K is the camera intrinsic parameter matrix. For the extrinsic parameter transformation of the camera-to-air node system, For the external parameter transformation of the visual identifier to the ground node machine system, Provide the three-dimensional coordinates of the corner points for visual identification;

[0111] The covariance matrix of visual factors is determined by reprojection error, imaging area, viewing angle, and frame consistency, and satisfies the following:

[0112]

[0113] The corresponding information matrix is:

[0114]

[0115] When the reprojection error increases or the number of corner points decreases, increase or reduce This is to reduce the impact of visual factors on backend optimization.

[0116] Furthermore, in step 5, the optimal state estimate of the sliding window optimization satisfies:

[0117]

[0118] in, The set of state variables within the window. This represents the set of all factors within the window. For robust kernel functions, This is the information matrix after topological weight adjustment;

[0119] The factor set This includes inertial pre-integration factor, ground odometer factor, ranging factor, visual relative pose factor, altitude factor, and prior factors obtained from marginalization.

[0120] The overall objective function expands to:

[0121]

[0122] Expanding the objective function at the current linearization point yields the normal equation. ,in The total Jacobian matrix, This is a block diagonal weight matrix. For the total residual vector, For state increments;

[0123] As the sliding window moves forward, marginalization is performed on the oldest state, and the Hessian matrix and right-hand side terms are written in the following block form:

[0124]

[0125] in, This is a block of states to be edged out. To preserve the state block;

[0126] The new prior matrix and prior vector obtained through Schul complement are:

[0127]

[0128]

[0129] And further construct the a priori residuals:

[0130]

[0131] Furthermore, as an optional distributed implementation, the cross-node factor at the current linearization point is expanded as follows:

[0132]

[0133] in, For the linearized point residual constant term, , For each node and nodes The Jacobian matrix of the state, and This corresponds to the state increment;

[0134] The factor summary information constructed based on the linearization results is as follows:

[0135]

[0136] in, For timestamps, This is the cross-node factor information matrix after weight adjustment. It is in a start / stop state. For border rights;

[0137] The receiving node uses conservative, consistent scaling for factor summary information:

[0138]

[0139] Inject the scaled information matrix into the local sliding window to optimize the backend and suppress information redundancy caused by duplicate information;

[0140] The local cost term constructed at the receiver by the cross-node factor is:

[0141]

[0142] When multiple digests are injected simultaneously, the total digest cost at the receiver satisfies:

[0143]

[0144] in, For the summary edge set;

[0145] Scaling factor The algorithm is adaptively adjusted based on link quality, number of digest sources, number of potential duplicate paths, information freshness, and reference switching sources. This reduces the algorithm when the risk of duplicate information increases, the digest latency increases, or the digest comes from an old reference system, and increases the algorithm when the link is stable and the current reference continuous link is valid.

[0146] This invention also provides a heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay system, which is used to implement the aforementioned heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method. The system specifically includes:

[0147] The system includes an air node, a visual camera, and an altitude sensor, and an air node and a ground node, respectively.

[0148] The candidate graph construction module is used to acquire multi-source measurements of air and ground nodes and to build a candidate graph of air-ground heterogeneous local cooperation based on node type.

[0149] The joint scheduling state construction module is used to form a joint scheduling state based on the quality representation of cooperative edges, node health, heterogeneity observability index, resource status, and reference continuity index.

[0150] The joint scheduling and backprojection module is used to coupled the calculation of topology weights, effective adjacency size and reference relay decision under the same scheduling objective, and backproject the scheduling results to the feasible region that satisfies the communication budget, local graph connectivity, reference node reachability and air-ground key coupling constraints;

[0151] The factor graph optimization and feedback module is used to inject topological weights into a fixed-hysteresis sliding window factor graph, output the cluster pose, velocity and uncertainty under a unified reference frame, and feed the optimization status back to the next scheduling cycle.

[0152] Furthermore, the system may also include a distributed consistency module for constructing cross-node factor summaries and performing conservative consistency scaling and injection based on duplicate path risk, information freshness, and reference switching source.

[0153] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0154] Example

[0155] This embodiment presents a heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay method, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0156] Step 1: Obtain multi-source measurements of air nodes and ground nodes, and establish an air-ground heterogeneous local cooperation candidate graph containing node status, motion edges and candidate cooperation edges according to node type.

[0157] Step 2: Based on the quality representation of candidate cooperative edges, the health of nodes at both ends of the edge, the heterogeneous observability index formed by candidate cooperative edges and local priors, the current communication and computing resource status, and the reference continuity index, a joint scheduling state is formed.

[0158] Step 3: Input the joint scheduling state into the joint scheduler, and coupled the topology weight, effective adjacency size and reference relay decision of each candidate cooperative edge under the same scheduling objective. The scheduling objective simultaneously considers graph observability gain, communication cost, topology switching cost and reference switching cost.

[0159] Step 4: Fuse the initial scheduling result obtained from parsing optimization with the correction amount obtained from lightweight learning inference, and backproject the fusion result to a feasible region that simultaneously satisfies the constraints of communication budget, topology size, local graph connectivity, reference node reachability, and air-ground key coupling; determine the set of enabled edges according to the topology weights and effective adjacency size after backprojection, and execute reference relay when the current reference node health is lower than the exit threshold and the candidate reference node satisfies the switching advantage margin;

[0160] Step 5: Inject the topological weights corresponding to the enabled edge set into the fixed-hysteresis sliding window factor graph through information matrix scaling, covariance adjustment or robust kernel parameter adjustment, and jointly optimize the state of the air node and the ground node using the current reference node or the reference node after the relay as a unified reference coordinate system.

[0161] Step 6: Based on the joint optimization results of Step 5, form the posterior state, feed back the posterior uncertainty, heterogeneous observability index and resource status to the next scheduling cycle, and output the cluster pose, velocity and uncertainty under a unified reference frame.

[0162] As a specific example, step 1 specifically includes:

[0163] The system collects inertial measurements, visual identification measurements, and altitude measurements of air nodes, as well as inertial measurements, wheel odometer measurements, and radio ranging measurements between ground nodes and adjacent nodes.

[0164] Before entering the backend, all types of measurements undergo synchronization and registration under a unified time and space reference, as well as related preprocessing.

[0165] Inertial measurements are input continuously at high frequencies, while visual, ranging, odometer, and altitude measurements are input asynchronously at medium and low frequencies. The system uses critical moments as graph optimization moments and pre-integrates high-frequency inertial measurements between adjacent critical moments. For wheeled ground nodes, wheel slip or turning degradation segments are pre-marked by combining the consistency detection of wheel speed and inertial lateral acceleration.

[0166] Furthermore, the system selects a unified time base as... The reference coordinate system is For any sensor The original measurement can be denoted as ;

[0167] in, This is the local timestamp for the sensor;

[0168] Considering the time skew between different sensors Its time, mapped to a unified time base, can be written as:

[0169]

[0170] When the sensor measurement frequencies are different or the timestamps are not perfectly aligned, interpolation can be used to further align the measurements to the target time. For vector measurements, linear interpolation is used, written as:

[0171]

[0172] in, and For the target time The two most recent original timestamps.

[0173] Furthermore, set up sensors Fixed to the carrier coordinate system Above, the extrinsic transformation from the sensor coordinate system to the carrier coordinate system is as follows:

[0174]

[0175] in, Let be a rotation matrix. It is a translation vector.

[0176] If the pose of the carrier in the reference coordinate system is:

[0177]

[0178] The expression for mapping sensor measurements to a unified reference frame can then be written as:

[0179]

[0180] For any three-dimensional point expressed in the sensor coordinate system The result of its transformation to the reference coordinate system is:

[0181]

[0182] Furthermore, for a certain type of measurement that has a time delay to be calibrated between it and the system master clock, it is regarded as a fixed or slowly changing parameter and is entered into the measurement model as a compensation term in the preprocessing stage.

[0183] State Trajectory In other words, the corrected measurement prediction can be written as:

[0184]

[0185] like If the value is relatively small, it can be expanded as a first-order approximation:

[0186]

[0187] Furthermore, considering the different numerical ranges of inertial measurement, ranging, odometer, visual reprojection, and altitude measurement, the features are standardized with zero mean and normalized within intervals. If a feature is denoted as... Its standardized form can be written as:

[0188]

[0189] in, and These are the mean and standard deviation of the feature in the historical samples or the sliding window, respectively. To prevent the use of tiny positive numbers with a denominator of zero, we employ minimum-maximum normalization, which can then be written as:

[0190]

[0191] As a specific example, in step 1, the state of any node at time t is defined as:

[0192]

[0193] in Represents a three-dimensional position vector. Represents a three-dimensional velocity vector. Represents attitude quaternions, and These represent the inertial biases of the accelerometer and gyroscope, respectively. Indicates the node type identifier;

[0194] For additional parameter blocks related to node type, for air nodes, Used to characterize camera extrinsic parameters, radio ranging antenna installation offset, and altitude auxiliary parameters, for ground nodes, Used to characterize camera extrinsic parameters, UWB antenna offset, wheel diameter scale, and wheel slip degradation compensation parameters.

[0195] Therefore, this invention maintains a unified expression form in the main state space, while realizing heterogeneous modeling of air nodes and ground nodes through node type identifiers and additional parameter blocks.

[0196] If the window length is Then the overall state can be written as:

[0197]

[0198] For inertial propagation, a discrete-time state equation is used to describe the continuous kinematic process. Let the airborne or ground node be at time [time missing]. The sampling period is Then, position, velocity, attitude and bias satisfy the following update relationship, and subsequently, high-frequency inertial observations are compressed into inertial factors between adjacent key moments through pre-integration.

[0199] The position state update equation is derived from the following formula:

[0200]

[0201] This equation describes the position propagation process of a node between discrete moments, where The rotation matrix is ​​obtained from the attitude quaternions. The acceleration is measured by inertia. It is the gravity vector;

[0202] The velocity state update equation is derived from the following formula:

[0203]

[0204] This formula indicates that the velocity is updated by the current velocity, the debiased acceleration, and gravity.

[0205] The attitude state update equation is derived from the following formula:

[0206]

[0207] in, To measure angular velocity using a gyroscope, For Lie group index mapping, Represents quaternion multiplication;

[0208] The biased random walk model is derived from the following formula:

[0209]

[0210] This formula indicates that the IMU bias evolves according to a random walk pattern;

[0211] The IMU pre-integration factor between adjacent keyframes can be written as:

[0212]

[0213] The residual is obtained by comparing the pre-integral quantity with the current estimated state at the same linearization point. The inertia factor is used to maintain the continuity of the time series state at the same node and is the basic motion edge in the local graph.

[0214] Local collaborative candidate graphs such as Figure 2 As shown, it consists of air nodes, ground nodes, and candidate cooperative edges, specifically defined as follows:

[0215]

[0216] in This represents the set of all state nodes within the sliding window. This represents the set of moving edges of a node itself. Represents the set of candidate collaborative edges. This represents the set of cross-node summary edges. Candidate cooperative edges should include at least ranging edges and visual relative pose edges, and may also include auxiliary edges induced by shared landmarks or public reference nodes. In this embodiment, only ranging edges and visual relative pose edges are considered.

[0217] For any measuring edge If at time Obtain Node With nodes Relative distance observation between Then its measurement equation and residual factor can be written as follows:

[0218]

[0219]

[0220] in This represents the corresponding cost function. and Representing nodes respectively and nodes At any moment Location, This represents the distance correlation deviation coefficient. This represents the constant deviation term. This indicates the environmental additional deviation item. Indicates ranging noise;

[0221] node At any moment The received distance observation vectors of each neighboring node can be represented as:

[0222]

[0223] in This represents the distance observations between each adjacent node. Represents a node The number of adjacent rangings;

[0224] The corresponding theoretical distance function vector for multi-range observation is:

[0225]

[0226] For the wheel mileage constraints of ground nodes, the ground mileage factor can be used to describe the planar displacement and heading increment of ground nodes between adjacent time points.

[0227] As a specific example, suppose the relative pose observations of the ground odometry odom at adjacent time points are as follows: Then its residual factor can be expressed as:

[0228]

[0229] in These represent the ground nodes at... and Position at any given moment Represent the logarithmic mapping from Lie groups to Lie algebras;

[0230] For the altitude observation of the aerial node, let the equivalent vertical observation output be... Then the measurement equation for the height factor and the residual factor are:

[0231]

[0232]

[0233] in , Indicates the location of the air node. Indicates altitude observation noise;

[0234] Under a unified master state and a unified inertial propagation model, the system selects specific constraint factors based on node type. For airborne nodes, the altitude factor, visual relative pose factor, and inertial factor are prioritized; for ground nodes, the ground odometer factor, inertial factor, and cooperative ranging factor with neighboring nodes are prioritized.

[0235] When ground nodes are pre-marked as degraded segments of roller skating or turning, the ground odometer information matrix is ​​reduced; when airborne nodes are in segments with weak texture, short-term visual failure, or rapid attitude changes, the visual factor information matrix is ​​reduced and the relative weights of the inertial factor and altitude factor are increased.

[0236] For cross-platform visual identity measurement, as a specific example, an equivalent AprilTag coded identifier is set on the ground node. The air node uses a camera to acquire images and solves the relative pose of the ground node with respect to the air node. Its residual factor is defined as follows:

[0237]

[0238] This represents the relative pose residual factor between air nodes and ground nodes obtained from visual identifiers, where and Represent the poses of the airborne and ground nodes, respectively;

[0239] To describe the projection process of AprilTag corner points from 3D space to the image plane, the corner point pixel imaging model is constructed as follows:

[0240]

[0241] The corresponding reprojection residual factor is:

[0242]

[0243] in, For the first The pixel coordinates of the corner points, where K is the camera intrinsic parameter matrix. For the extrinsic parameter transformation of the camera-to-air node system, For the external parameter transformation of the visual identifier to the ground node machine system, Provide the three-dimensional coordinates of the corner points for visual identification;

[0244] To ensure that measurements from different sensors are uniformly fed into the backend, the entire pose estimation problem is written as a unified probabilistic graphical model. Let the observation set be Z and the state set be X. Then, the posterior distribution is composed of prior terms, motion transition terms, and multi-source observation terms.

[0245] Under the assumption of Gaussian noise or approximately Gaussian noise, the weighted nonlinear least squares objective can be obtained by taking the negative logarithm of the posterior. The cost term for each class of observation factors f can be written as:

[0246]

[0247] in For residuals, For information matrix, For robust kernel functions;

[0248] The posterior probability model for the entire optimization problem is then:

[0249]

[0250] In the formula Let X be the posterior distribution of state X given observation Z. As the initial prior, Let be the state transition probability, where To control the input, Let f be the observation probability corresponding to the f-th factor;

[0251] The overall weighted cost function can be expanded as follows:

[0252]

[0253] The state update from the s-th iteration to the (s+1)-th iteration is given by the following formula:

[0254]

[0255] in Represents a unified state update operator on Euclidean space and attitude manifold;

[0256] Using the above expression, different types of constraints can be solved in a unified form in the same backend.

[0257] As an optional generation method for edge-level quality representation in the joint scheduling state, the system can perform consistency statistics and probability modeling on the residual sequence formed by candidate cooperative edges within the current sliding window; this edge-level quality representation is only one of the inputs of the joint scheduler and does not independently determine the start and stop of cooperative edges.

[0258] For the ranging edge, a Gaussian mixture model is used to describe three statistical states: normal line-of-sight, slight offset, and severe non-line-of-sight. The ranging residual factor... The probability density is written as:

[0259]

[0260] in For the first The mixed weighting coefficients of each component, The mean is Covariance is Gaussian distribution;

[0261] Furthermore, in order to distinguish between normal view distance edges, slightly offset edges, and severely offset edges online without relying on a fixed hard threshold, the following EM iteration is adopted:

[0262]

[0263] in This indicates that the nth residual sample belongs to the nth residual sample. The posterior responsibility of each mixture component is given by the following formula, where the mixture weight coefficients, mean, and covariance are updated as follows:

[0264]

[0265] Edges can be computed using Bayesian posterior. Non-line-of-sight risk indicators belonging to anomalous components :

[0266]

[0267] In the formula Defined as the set of components of NLOS. Representing an edge For components Degree of responsibility;

[0268] For ranging edges that are determined to have a slight bias, they are not directly removed, but are retained and included in the bias compensation model, and the distance-related bias coefficient, constant bias term, and environmental additional bias term are updated online; for ranging edges that are determined to have a severe non-line-of-sight bias, their information matrix is ​​reduced or they are temporarily disabled.

[0269] Furthermore, statistics such as residual mean, residual variance, median absolute deviation (MAD), normalized innovation square (NIS), continuous packet loss rate, message latency, and visual reprojection consistency can be compressed into edge-level quality representations, which, together with node health, heterogeneous observability, resource status, and reference continuity, form a joint scheduling state.

[0270] As the core implementation of this invention, the joint scheduler and constraint-consistent back-projection in steps 3 to 4 are specifically as follows:

[0271] (1) such as Figure 3 As shown, the joint scheduler adopts a coupled structure with multiple inputs and three outputs. The inputs are categorized by their technical function into cooperative edge quality state, heterogeneous observability and node health state, and resource and reference continuity state. The three coupled outputs are the topology weight vector, effective adjacency size, and reference relay decision, respectively. These three outputs jointly determine the set of activated edges and the current reference node, rather than determining them independently in sequence.

[0272] The reference health of the reference node is defined as follows:

[0273]

[0274]

[0275] In the formula Indicates the reference candidate gating, This indicates the positioning accuracy score. Indicates the local observability score. Indicates the link quality score. Indicates short-term stability score. Indicates the score for collaborative support capabilities. In order to represent , , , , The weighting coefficients, This represents the set of reference candidates that pass through the gating system and remain connected to the current subgraph.

[0276] Reference candidate gating The following relation is given:

[0277]

[0278] in For nodes Link quality metrics, This indicates the minimum threshold for link quality. It is a local geometric observability index. This represents the minimum observability threshold. For nodes The covariance matrix of the position sub-states, This represents the location covariance trace, characterizing the magnitude of location uncertainty.

[0279] When the current reference node's global reference positioning accuracy decreases due to environmental constraints and is insufficient to serve as a global reference, reference relay is triggered. The triggering rules satisfy the following constraints:

[0280]

[0281] in Indicates the reference node exit threshold. This indicates the reference switching advantage margin;

[0282] Edge weights, adjacency size, and reference relay are directly coupled: edge weights and adjacency size jointly change the local graph information matrix and communication load, while the reference relay requires the selected edge set to remain reachable from candidate reference nodes. Therefore, this invention solves for the three decision variables in the same objective function and projects them back under a unified set of constraints, avoiding the unexecutable combinations that result from separate processing.

[0283] Observability index By enabling the approximate Fisher information matrix corresponding to the edge set To measure. If it represents a prior information matrix, Representing an edge Jacobian matrix, If we represent the original information matrix, then the observability can be taken as... The minimum eigenvalue, Functions of value or condition number, with relevant evaluation metrics as follows:

[0284]

[0285]

[0286]

[0287]

[0288]

[0289] in This is an approximate geometric information matrix formed by the geometric relationships of the current candidate edges. Used to characterize the lower bound of a theory Used to characterize the quality of geometric configuration, where G is a local geometric matrix composed of the observation direction vectors corresponding to the current candidate cooperative edge, used to evaluate the spatial constraint capability of the current topology on the target state;

[0290] Furthermore, for the candidate cooperative edge set The measurement function corresponding to each edge The Jacobian for evaluating the substate p is denoted as The geometric matrix of the current local collaboration graph is then defined as:

[0291]

[0292] The joint scheduler is not limited to using a single observability metric, but integrates Fisher information, and The normalized results together constitute the geometric quality term, and the geometric quality index is given by the following formula:

[0293]

[0294] (2) The optimization objective of the joint scheduler is as follows:

[0295]

[0296] in For edge start / stop variables, Indicates the communication cost. Indicates the cost of topology switching. Indicates the reference decision variable. The observability index formed by the enabled edge and the local prior at time t is given by the following relationship:

[0297]

[0298] in This indicates the prevention of singular, tiny positive numbers. Let the information matrix at time t be denoted by:

[0299]

[0300] The constructed joint scheduler satisfies the following joint scheduling constraints:

[0301]

[0302] in Representing an edge The topological weights at time t and This indicates the upper and lower limits of the effective adjacent edge size. Representing an edge The communication load is B, where B is the total budget limit.

[0303] When the joint scheduler runs in a distributed manner, it can be used on each node. Define local cost function And perform distributed consensus optimization with projection on the adjacency communication graph to obtain globally approximately consistent edge weights and adjacency sizes;

[0304] Nodes in distributed scheduling scenarios The local cost function is:

[0305]

[0306] Furthermore, the edge weights and adjacency scales are updated as follows:

[0307]

[0308] in Represents the projection operator. Represents a node The set of scheduling communication neighbors, Indicates the iteration step size;

[0309] This distributed implementation allows nodes to achieve near-cooperative scheduling by jointly obtaining edge weights and adjacency sizes, relying solely on local information exchange.

[0310] like Figure 4 As shown, the topology weights after constraint-consistent backprojection are injected into the backend optimization through one of three channels: information matrix scaling, covariance adjustment, and robust kernel parameter adjustment. The weight injection is the execution interface for joint scheduling decision-making and reduces edge weight oscillation and topology jitter through smoothing and hysteresis.

[0311] As a specific example, in step 5, the overall objective function of the fixed-hysteresis sliding window is written as:

[0312]

[0313] F includes inertial pre-integration factor, ranging factor, visual relative pose factor, ground mileage factor, altitude factor, and prior factor.

[0314] In a fixed-hysteresis sliding window, the most recent state is retained and the oldest state is marginalized, such as... Figure 5 As shown, for the oldest state of the sliding window, Schur complement marginalization is used to obtain a new prior factor, thereby maintaining a fixed lag solution size. The prior residual can be expressed as:

[0315]

[0316] The Schul complement marginalization refers to compressing the constraint influence of the state variable on the retained state variable into a new prior factor without explicitly retaining the state variable to be marginalized, thereby retaining historical information while controlling the optimization dimension.

[0317] The Hessian matrix and right-hand side terms can be written in the following block form:

[0318]

[0319] in, This is a block of states to be edged out. To preserve the state block;

[0320] The new prior matrix and prior vector obtained through Schul complement are:

[0321]

[0322]

[0323] Subscript Indicates the oldest state block that will be marginalized and removed, index This indicates a block that retains the state.

[0324] The uncertainty is obtained by approximation of the posterior covariance corresponding to the current retained state block, which can be given by the Hessian matrix of the normal equation or the inverse matrix of the retained block after marginalization.

[0325] like Figure 6 As shown, cross-node constraints are linearized locally to form a factor summary, which is then transmitted between nodes and conservatively scaled before being injected into the backend optimization at the receiving end.

[0326] As an optional distributed implementation, considering that directly transmitting the complete local graph across multiple nodes would increase bandwidth consumption, a first-order expansion of the cross-node factors is performed at the current linearization point to form a transportable factor summary. For any cross-node factor, we have:

[0327]

[0328] in, For the linearized point residual constant term, and For each node and nodes The Jacobian matrix of the state, and This corresponds to the state increment;

[0329] Based on the linearization results, the following factor summary information is constructed:

[0330]

[0331] Where t is the timestamp. This is the cross-node factor information matrix after weight adjustment. It is in a start / stop state. For border rights;

[0332] Furthermore, the receiving node applies conservative and consistent scaling to the factor summary information:

[0333]

[0334] The scaling factor is given by the following expression:

[0335]

[0336] In the formula Indicates the base scaling factor. The time constant is the delay decay time. This represents the correction function that determines link quality. This represents the number of abstract sources. The number of potential duplicate paths. For reference, here are the source switching correction items;

[0337] The scaled information matrix is ​​then injected into the local sliding window to optimize the backend, thereby suppressing information redundancy caused by duplicate information.

[0338] The local cost term constructed at the receiving end by the cross-node factor is:

[0339]

[0340] Furthermore, when multiple digests are injected simultaneously, the total digest cost at the receiver satisfies:

[0341]

[0342] in, For the summary edge set;

[0343] Scaling factor The algorithm is adaptively adjusted based on link quality, number of digest sources, number of potential duplicate paths, information freshness, and reference switching sources. This reduces the algorithm when the risk of duplicate information increases, the digest latency increases, or the digest comes from an old reference system, and appropriately increases it when the link is stable and the current reference continuous link is valid.

[0344] In summary, this invention does not simply chain together edge evaluation, topology selection, and reference switching, but constructs a closed loop centered on a joint scheduler: First, it unifies the scheduling state by considering cooperative edge quality, node health, heterogeneous observability, resource status, and reference continuity; then, under the same objective, it couples and calculates topology weights, effective adjacency size, and reference relay decisions, and obtains the executable set of enabled edges and the current reference node through constraint-consistent backprojection; the scheduling results are applied to the fixed-hysteresis factor graph via weight injection, and the uncertainty and observability status obtained from the backend are fed back to the next cycle. Residual probability modeling, visual quality evaluation, and factor summary scaling are respectively used as input construction or distributed implementation methods, belonging to the aforementioned joint decision-making main line.

[0345] The above are merely preferred embodiments of the present invention. It should be noted that the above embodiments are only used to explain the technical concept of the present invention, and are not intended to limit the scope of protection of the present invention. Equivalent substitutions, improvements, or modifications made to node size, sensor combinations, scheduling methods, solver types, and summary encapsulation formats without departing from the core idea of ​​the present invention should all be considered within the scope of protection of the present invention.

Claims

1. A heterogeneous observability-driven air-to-ground cluster cooperative localization and reference relay method, characterized in that, Includes the following steps: Step 1: Obtain multi-source measurements of air nodes and ground nodes, and establish an air-ground heterogeneous local cooperation candidate graph containing node status, motion edges and candidate cooperation edges according to node type. Step 2: Based on the quality representation of candidate cooperative edges, the health of nodes at both ends of the edge, the heterogeneous observability index formed by candidate cooperative edges and local priors, the current communication and computing resource status, and the reference continuity index, a joint scheduling state is formed. Step 3: Input the joint scheduling state into the joint scheduler, and coupled the topology weight, effective adjacency size and reference relay decision of each candidate cooperative edge under the same scheduling objective. The scheduling objective simultaneously considers graph observability gain, communication cost, topology switching cost and reference switching cost. Step 4: Fuse the initial scheduling result obtained from parsing optimization with the correction amount obtained from lightweight learning inference, and backproject the fusion result to a feasible region that simultaneously satisfies the constraints of communication budget, topology size, local graph connectivity, reference node reachability, and air-ground key coupling; determine the set of enabled edges according to the topology weights and effective adjacency size after backprojection, and execute reference relay when the current reference node health is lower than the exit threshold and the candidate reference node satisfies the switching advantage margin; Step 5: Inject the topological weights corresponding to the enabled edge set into the fixed-hysteresis sliding window factor graph through information matrix scaling, covariance adjustment or robust kernel parameter adjustment, and jointly optimize the state of the air node and the ground node using the current reference node or the reference node after the relay as a unified reference coordinate system. Step 6: Based on the joint optimization results of Step 5, form the posterior state, feed back the posterior uncertainty, heterogeneous observability index and resource status to the next scheduling cycle, and output the cluster pose, velocity and uncertainty under a unified reference frame.

2. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 1, characterized in that, The state vector of any node in step 1 is denoted as: in Represents a three-dimensional position vector. Represents a three-dimensional velocity vector. Represents attitude quaternions, and These represent the inertial biases of the accelerometer and gyroscope, respectively. Indicates the node type identifier; This represents the additional calibration and degradation compensation parameter blocks related to the node type. The parameter blocks for air nodes include camera extrinsic parameters, radio ranging antenna installation offset, and altitude auxiliary parameters; the parameter blocks for ground nodes include camera extrinsic parameters, radio ranging antenna installation offset, wheel diameter dimensional parameters, and wheel slip degradation compensation parameters. Local collaborative graph notation is ,in This is the set of state variables for each node within the window. For the candidate edge set; For any measuring edge If at time Obtain Node With nodes Relative distance observation between Then the measurement equation and residual factor are written as follows: in Represents the cost function, and Representing nodes respectively and nodes At any moment Location, This represents the distance correlation deviation coefficient. This represents the constant deviation term. This indicates the environmental additional deviation item. This indicates ranging noise.

3. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 1, characterized in that, In step 2, a hybrid probability model is used to generate the quality characterization of the candidate cooperative edges based on the residual sequences of the candidate ranging edges. The hybrid probability model satisfies: in For the first The mixed weighting coefficients of each component satisfy the following conditions: ; , The first The mean and covariance of each Gaussian component; Edges are obtained based on Bayesian posterior. Non-line-of-sight risk indicators Furthermore, the residual mean, residual variance, median absolute deviation (MAD), and normalized innovation square (NIS) are calculated as input features of the joint scheduler.

4. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 1, characterized in that, The joint scheduler and constraint-consistent backprojection in steps 3 and 4 are detailed below: (1) The joint scheduler takes the joint scheduling state as input and the topological weight set of each candidate cooperative edge, the effective adjacency size, and the reference relay decision as three mutually coupled outputs; the reference health of the reference node is defined as follows: In the formula This indicates the positioning accuracy score. Indicates the local observability score. Indicates the link quality score. Indicates short-term stability score. Indicates the score for collaborative support capabilities. In order to represent , , , , The weighting coefficients are referenced from the candidate gating. The following relation is given: in For nodes Link quality metrics, This indicates the minimum threshold for link quality. It is a local geometric observability index. This represents the minimum observability threshold. For nodes The covariance matrix of the position sub-states, This represents the location covariance trace, characterizing the magnitude of location uncertainty. (2) The joint scheduler satisfies the following optimization objective: in For edge start / stop variables, Indicates the communication cost. Indicates the cost of topology switching. Indicates the reference decision variable. The observability index formed by the enabled edge and the local prior at time t is given by the following relationship: in This indicates the prevention of singular, tiny positive numbers. Let the information matrix at time t be denoted by: The constructed joint scheduler satisfies the following joint scheduling constraints: in Representing an edge The topological weights at time t and This indicates the upper and lower limits of the effective adjacent edge size. Representing an edge The communication load is B, where B is the total budget limit. (3) The joint scheduler is implemented by combining analytical optimization, lightweight learning correction, and constraint-consistent backprojection as follows: Step 3.1: Encode the cooperative edge quality, node state, geometric state, resource state, and reference continuity state into the joint scheduler input; Step 3.2: Perform analytical optimization based on heterogeneous observability gain, communication load, topology switching cost and reference continuity cost to generate initial topology weights, initial adjacency size and reference candidate scores; Step 3.3: Input the initial parsing value and the joint scheduling state into the lightweight learning inference module to obtain the topology weight correction amount and the adjacency size correction amount; Step 3.4: Fuse the initial analytical values ​​and the learning correction results, and perform the constraint uniformity back projection described in Step 4 to obtain the enabled edge set and the current reference node.

5. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 4, characterized in that, The specific process of joint scheduling state construction and parsing optimization in steps 3.1 and 3.2 is as follows: For each candidate cooperative edge at time t, extract edge-level quality characteristics and the health of the nodes at both ends of the edge; the edge-level quality characteristics include non-line-of-sight risk, link quality, communication load, and residual mean, residual variance, median absolute deviation, and normalized innovation squared obtained from the sliding window residual sequence. Extracting global constraint states The global constraint state includes at least the communication budget. Processor load rate Bandwidth utilization and the number of currently enabled edges ; Based on the input feature vector The analytical scoring for constructing candidate edges is as follows: The initial edge weights of the candidate edges are obtained based on the analytical scoring as follows: in, The function is the Sigmoid function; simultaneously, it is based on the average link quality of all candidate edges at the current time. Geometric mass mean Risk mean and bandwidth utilization The initial adjacency size is calculated as follows: in, This is the interval truncation operator.

6. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 5, characterized in that, In steps 3.3 and 3.4, lightweight learning correction and constraint-consistent back-projection are performed on the analytical initial values, as detailed below: Analyze the initial edge weights Analyze the initial adjacency size Input feature vector and global constraint state Input the lightweight learning inference module to obtain the edge weight correction. and Adjacency Size Correction The forms are as follows: in, and These are edge weight correction networks and adjacency size correction networks, respectively. These are the parameters of the trained model; Calculate the final edge weight and final adjacency size based on the initial edge weight, edge weight correction, initial adjacency size, and adjacency size correction. in, The fusion coefficient is... For rounding operators; The comprehensive score of candidate edges is recalculated based on the final edge weights as follows: Candidate edges are sorted from highest to lowest based on their comprehensive scores, and those that meet the requirements are... Candidate edges are selected sequentially under the given conditions to obtain the set of active edges; When the sorting results do not meet the constraints of reference node reachability, local graph connectivity, or air-ground key coupling, candidate edges that contribute significantly to the improvement of reference connectivity, graph observability, and air-ground collaboration effectiveness are retained first, while edges with benefits lower than the set value or load higher than the set value are removed. When the lightweight learning inference module fails to output correction results, the joint scheduler degenerates into a pure analytical optimization mode, relying solely on... , and Complete edge weight allocation and topology scale setting; after the lightweight learning inference module returns to normal, switch to the working mode that combines parsing optimization and lightweight learning inference.

7. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 1, characterized in that, The cross-platform visual measurements obtained in step 1 are used as visual collaborative edges, preferably implemented using coded label edges; when coded labels are unavailable, shared environmental target edges or natural feature re-identification edges are used as equivalent implementation methods to construct visual collaborative edges. When an airborne node recognizes a visual identifier carried by a ground node, it obtains a relative pose observation and constructs a relative pose factor residual. as follows: in The relative pose is obtained from visual observation. For the pose of the air node, For the pose of the ground node; Visual identifier measurement further constructs corner reprojection factors, and the pixel observation model is as follows: The corresponding reprojection residual factor is: in, For the first The pixel coordinates of the corner points, where K is the camera intrinsic parameter matrix. For the extrinsic parameter transformation of the camera-to-air node system, For the external parameter transformation of the visual identifier to the ground node machine system, Provide the three-dimensional coordinates of the corner points for visual identification; The covariance matrix of visual factors is determined by reprojection error, imaging area, viewing angle, and frame consistency, and satisfies the following: The corresponding information matrix is: When the reprojection error increases or the number of corner points decreases, increase or reduce This is to reduce the impact of visual factors on backend optimization.

8. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 4, characterized in that, In step 5, the optimal state estimate of the sliding window optimization satisfies: in, The set of state variables within the window. This represents the set of all factors within the window. For robust kernel functions, This is the information matrix after topological weight adjustment; The factor set This includes inertial pre-integration factor, ground odometer factor, ranging factor, visual relative pose factor, altitude factor, and prior factors obtained from marginalization. The overall objective function expands to: Expanding the objective function at the current linearization point yields the normal equation. ,in The total Jacobian matrix, This is a block diagonal weight matrix. For the total residual vector, For state increments; As the sliding window moves forward, marginalization is performed on the oldest state, and the Hessian matrix and right-hand side terms are written in the following block form: in, This is a block of states to be edged out. To preserve the state block; The new prior matrix and prior vector obtained through Schul complement are: And further construct the a priori residuals: 。 9. The heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay method according to claim 1, characterized in that, In the distributed implementation, the cross-node factor is expanded at the current linearization point as follows: in, For the linearized point residual constant term, , For each node and nodes The Jacobian matrix of the state, and This corresponds to the state increment; The factor summary information constructed based on the linearization results is as follows: in, For timestamps, This is the cross-node factor information matrix after weight adjustment. It is in a start / stop state. For border rights; The receiving node uses conservative, consistent scaling for factor summary information: Inject the scaled information matrix into the local sliding window to optimize the backend and suppress information redundancy caused by duplicate information; The local cost term constructed at the receiver by the cross-node factor is: When multiple digests are injected simultaneously, the total digest cost at the receiver satisfies: in, For the summary edge set; Scaling factor The algorithm is adaptively adjusted based on link quality, number of digest sources, number of potential duplicate paths, information freshness, and reference switching sources. This reduces the algorithm when the risk of duplicate information increases, the digest latency increases, or the digest comes from an old reference system, and increases the algorithm when the link is stable and the current reference continuous link is valid.

10. A heterogeneous observability-driven air-to-ground cluster cooperative positioning and reference relay system, characterized in that, The system is used to implement the method according to any one of claims 1 to 9, wherein the system specifically includes: The system includes an air node, a visual camera, and an altitude sensor, and an air node and a ground node, respectively. The candidate graph construction module is used to acquire multi-source measurements of air and ground nodes and to build a candidate graph of air-ground heterogeneous local cooperation based on node type. The joint scheduling state construction module is used to form a joint scheduling state based on the quality representation of cooperative edges, node health, heterogeneity observability index, resource status, and reference continuity index. The joint scheduling and backprojection module is used to coupled the calculation of topology weights, effective adjacency size and reference relay decision under the same scheduling objective, and backproject the scheduling results to the feasible region that satisfies the communication budget, local graph connectivity, reference node reachability and air-ground key coupling constraints; The factor graph optimization and feedback module is used to inject topological weights into a fixed-hysteresis sliding window factor graph, output the cluster pose, velocity and uncertainty under a unified reference frame, and feed the optimized state back to the next scheduling cycle.

Images