Variational factor graph optimization co-location method based on generative conditional normalized flow

Abstract

This invention provides a variational factor graph optimization collaborative positioning method based on generative conditional normalized flow, which breaks through the dependence of traditional spatiotemporal network positioning and navigation technologies on prior physical models. It can automatically learn the radio propagation characteristics in complex environments, effectively solving the positioning performance degradation problems caused by model mismatch and non-Gaussian noise. It can simultaneously output high-precision positioning results and quantified uncertainty information, significantly improving the credibility and reliability of positioning results. It adopts a globally shared lightweight architecture and a non-iterative inference mechanism, reducing computational complexity and hardware consumption. It has good engineering feasibility and scalability, and can flexibly adapt to various aerospace collaborative positioning scenarios, providing solid technical support for the integrated air-space-ground navigation, positioning, and timing system.

Description

Technical Field

[0001] This invention relates to a model-free, prior-defined environment spatiotemporal network (NLN) positioning and navigation method, based on generative conditional normalized flow (CNF) and hierarchical variational Bayesian inference as its core principles. It constructs a unified positioning framework that deeply fuses generative deep models with multi-epoch factor graph optimization, achieving spatiotemporal collaborative positioning. It is applicable to complex environments lacking prior physical models, such as aerospace telemetry and control, deep space exploration, satellite formation, aircraft swarms, and UAV swarms. It belongs to the fields of aerospace, aviation, and navigation and positioning technology. Background Technology

[0002] NLN (Launching Network) technology achieves reliable positioning of mobile intelligent agents through spatiotemporal cooperation among nodes such as satellite constellations, spacecraft formations, and aircraft clusters. It is a key space information infrastructure in the aerospace field and has been widely deployed in scenarios such as spacecraft formation control, aircraft coordination, and aerospace emergency telemetry and control. Although traditional satellite navigation systems can achieve meter-level positioning accuracy in open aerospace environments, they encounter problems such as weak signals, signal interruptions, and severe multipath effects in scenarios such as deep space exploration, spacecraft body blockage, dynamic formation blockage, aerospace telemetry and control multipath interference, and complex electromagnetic countermeasures. These problems lead to a significant decrease in positioning performance or even complete failure.

[0003] NLN technology relies on spatial cooperation between nodes to achieve network-wide location coupling at the current moment. It uses temporal measurements within nodes to transmit spatial correlation features across time slots, effectively overcoming the scenario limitations of traditional GNSS and demonstrating significant potential for improved positioning accuracy and system reliability in complex environments. Current NLN technologies are primarily based on model-driven methods, establishing positioning theory performance analysis and algorithmic frameworks. In the July 2018 paper "A Theoretical Foundation of Network Localization and Navigation" published in *Proceedings of the IEEE*, Volume 106, Issue 7, pp. 1136-1165, model-driven NLN uses the physical mechanism and mathematical statistical model of radio signal propagation as its core to construct a mapping relationship between observations and node spatial positions, achieving positioning state estimation through probabilistic reasoning and optimization solutions. However, this paradigm relies heavily on explicit physical propagation models and noise distribution assumptions. In the complex aerospace environment, the uncertainty of signal propagation paths, the time-varying nature of multipath effects, and the randomness of electromagnetic interference can lead to a serious mismatch between the physical model and the actual scenario. Furthermore, the measurement noise exhibits significant heavy tails and multimodal non-Gaussian characteristics. Traditional positioning methods based on Gaussian assumptions will experience problems such as sharp performance degradation and solution divergence.

[0004] Data-driven methods, centered on machine learning and deep learning technologies, can directly learn the nonlinear mapping relationship between signal features and node positions from massive amounts of observation data, eliminating the need for manually constructing precise physical propagation models. However, combining data-driven methods with the NLN algorithm still suffers from three major drawbacks, failing to meet the high-reliability positioning requirements of the aerospace field. 1) Lack of probabilistic representation capability. Discriminative data-driven methods can only output point estimates of positioning status, failing to represent the posterior probability distribution and uncertainty of the positioning results. This is inherently incompatible with the core logic of probabilistic inference in factor graph optimization, making it difficult to achieve global fusion and credibility assessment of multi-epoch observations, and thus unable to meet the reliability requirements of positioning results in high-safety aerospace scenarios. 2) Insufficient spatiotemporal fusion capability. Existing generative data-driven methods mostly remain at the level of single-epoch distribution fitting, failing to achieve deep integration with the factor graph optimization framework of multi-epoch joint solution in NLN. This prevents the utilization of the redundancy advantages of spatiotemporal collaborative observations to improve positioning stability, and makes it difficult to adapt to dynamic collaborative scenarios such as spacecraft formations and aircraft clusters. 3) Explosive computational complexity. When CNF is directly used to model high-dimensional joint posterior, the dimensional invariance constraint of reversible bijection can easily lead to computational explosion, making it difficult to adapt to high-dimensional spatiotemporal collaborative positioning scenarios with multiple nodes and multiple epochs.

[0005] Currently, for robust NLN positioning in complex, model-free prior environments in the aerospace field, there is no complete technical solution that can simultaneously take into account positioning accuracy, posterior probability representation capability, multi-epoch time series fusion capability, and low-complexity solution efficiency. This cannot meet the urgent need for highly reliable autonomous navigation in the integrated air-space-ground navigation, positioning, and timing (PNT) system. Summary of the Invention

[0006] To address the problems of existing technologies in complex, model-less aerospace environments, such as reliance on physical models, lack of probabilistic representation, insufficient temporal fusion, and high computational complexity, this invention provides a data-driven variational factor graph optimization localization method that integrates generative conditional normalized flows. The proposed framework is as follows: Figure 1 As shown, by constructing a model-prior-free nonlinear state-space model and a hierarchical variational Bayesian inference framework, a deep fusion of generative deep models and multi-epoch factor graph optimization is achieved; a multi-module globally shared conditional normalization flow architecture is designed to solve the computational explosion problem of high-dimensional posterior modeling; end-to-end training and non-iterative forward inference are realized, simultaneously outputting high-precision positioning results and uncertain quantitative information without any physical model priors, significantly improving the robustness, reliability, and real-time performance of spatiotemporal network positioning in complex aerospace environments.

[0007] A variational factor graph optimization co-localization method based on generative conditional normalized flow includes the following steps:

[0008] Step S1: Construct a nonlinear state-space model for a model-free prior scenario, including state transition equations and observation equations. The state transition equations are used to characterize the evolution of node states over time, and the observation equations are used to characterize the mapping relationship between observations between nodes and node states. Step S2: Based on the observation independence assumption and the first-order Markov assumption, the joint posterior probability density function of the spatiotemporal cooperative network localization is decomposed into a factor graph form to obtain the factor graph decomposition results, which include the initial state prior factors describing the probability distribution of the initial state of the nodes, the state transition factors describing the temporal evolution of the node states, and the observation likelihood factors describing the constraints of the observations on the node states. Step S3: Introduce low-dimensional global latent features and construct a hierarchical variational Bayesian inference framework that includes generative CNF and variational inference CNF modules to maximize the lower bound of evidence. As an optimization objective, the generative model constructs a directed graph structure from latent variables to states and from states to observations according to physical causal logic, and the variational inference model uses block mean field decomposition to construct a structured variational posterior. Step S4: Using Conditional Normalized Flow (CNF) as the probabilistic modeling module, design a Generative Conditional Normalized Flow CNF module and a Variational Inference Conditional Normalized Flow CNF module. All modules adopt a globally shared backbone network architecture. The Generative Conditional Normalized Flow CNF module includes an initial joint state prior submodule, a globally shared spatiotemporal transition prior submodule, and a globally shared multi-source observation likelihood submodule. The Variational Inference Conditional Normalized Flow CNF module includes an initial epoch joint condition submodule and a globally shared spatiotemporal transition submodule. Step S5: Supervised training is performed on the Generative Conditional Normalization Flow (CNF) module, the Variational Inference Conditional Normalization Flow (CNF) module, and the Spatiotemporal Feature Encoding Network. During the training process, batch training data is input into the Spatiotemporal Feature Encoding Network to extract the distribution parameters of low-dimensional global latent features. Latent feature samples are obtained through reparameterization sampling. The sampled latent features and the true joint state sequence are respectively input into the Variational Inference Conditional Normalization Flow (CNF) module and the Generative Conditional Normalization Flow (CNF) module. The log density terms corresponding to the lower bound of evidence are calculated, and the negative lower bound of evidence is used as the loss function. All network parameters are updated through backpropagation and the optimizer. After training, the observation sequence to be inferred is input into the spatiotemporal feature encoding network to obtain the latent feature distribution parameters. Multiple latent feature samples are independently sampled from the latent feature distribution. Each latent feature sample is input into the variational inference conditional normalization flow (CNF) module to generate the conditional posterior distribution of the corresponding multi-epoch multi-node joint state. The Monte Carlo approximation of the mean of all posterior distributions is used as the point estimate of the multi-node joint state to output the localization result. At the same time, the uncertainty quantification information of the localization result is output by calculating the covariance matrix of the posterior distribution.

[0009] Preferably, in step S1, the state transition equation and the observation equation are as follows: (1.1) in, For nodes k In the n The state vector of an epoch, where It is a three-dimensional position vector. It is a three-dimensional velocity vector; For nodes k In the n-1 The state vector of an epoch; The nonlinear state transition function is unknown. For nodes k In the n epoch process noise; For nodes k and j In the n The observation vector of an epoch includes both non-cooperative and cooperative observations; For unknown nonlinear observation functions; For nodes j In the n The state vector of an epoch; For nodes k and j In the n Epochal observation noise; For non-cooperative localization scenarios, the observation equation degenerates into: (1.2) in, This is the set of navigation reference nodes.

[0010] Preferably, the factor graph decomposition result in step S2 is expressed as follows: (1.3) In the formula, For the full observation dataset, For the set of all nodes, For spacecraft / aircraft node set, For the number of spacecraft / aircraft nodes, This refers to the number of navigation reference nodes; Represents time points from 1 to N A concatenated vector of the states of each spacecraft / aircraft node; Let N be the true probability density function, and N be the total number of epochs. Let be the probability density function corresponding to the state transition equation; Let be the probability density function corresponding to the observation equation; , which is the prior factor of the initial state.

[0011] Preferably, the joint distribution of the generative model in step S3 is represented as follows: (1.4) The structured decomposition of the generative model is implicitly aligned with the probabilistic modeling logic of the factor graph, where global latent features... prior distribution Let the initial state be a standard Gaussian distribution; the prior distribution of the initial state is... Corresponding factor diagram: initial state factor; state transition distribution Corresponding factor plot state transition factor; observed likelihood distribution The likelihood factor was observed in the corresponding factor plot.

[0012] Preferably, the block mean field decomposition of the variational inference model described in step S3 is expressed as: (1.5) In the formula, It is a variational approximation of the probability density function; The set of learnable parameters for the CNF module of variational inference; The set of learnable parameters for a spatiotemporal feature coding network; variational distribution of the feature layer. Parameterization by spatiotemporal feature encoding network; variational distribution of state layer and CNF module parameterization is inferred from variational inference.

[0013] Preferably, the maximization of the lower bound of evidence described in step S3 is:

[0014] The lower bound of negative evidence is used as the loss function for model training.

[0015] Preferably, in step S4, the conditional normalized flow CNF models the complex probability distribution through stacked invertible affine transformations: for the conditional input c, the invertible transformation... Map the observation z to standard Gaussian hidden variables The conditional probability density can be calculated without approximation using the Jacobian determinant. (1.8) In the formula, It follows a standard Gaussian distribution. To transform the Jacobian matrix of T, Let be the determinant of the Jacobian matrix; These are the parameters for the conditionally normalized flow model.

[0016] Preferably, in step S4, the CNF generation module includes the following three sub-modules: The initial joint state prior CNF submodule takes the initial epoch state as its input. Along with the global latent feature H, we fit the prior distribution of the initial joint state of all nodes. ; The globally shared spacetime transition prior CNF submodule takes the state of the previous epoch n-1 as input. Current epoch n state The global latent feature H is used to fit the temporal evolution of the joint state of multiple nodes. All epochs share the same set of parameters; A globally shared multi-source observation likelihood CNF submodule is used to fit the physical mapping from state to observation. The backbone network is globally shared, and it adapts to non-cooperative and cooperative observations through different input conditions. The input condition for non-cooperative observation is the state of a single spacecraft / aircraft node k in the nth epoch. The global latent feature H and the cooperative observation condition input are the splicing state of the two spacecraft / aircraft nodes k and j in the nth epoch. With global latent feature H; The variational inference CNF module includes the following three sub-modules: The initial epoch joint condition CNF submodule takes the initial epoch state as its input. Using the global latent feature H, model the posterior distribution of the initial joint state of all nodes. ; The globally shared spacetime transition CNF submodule takes the state of the previous epoch (n-1) as input. Current epoch n state Along with global latent features H, used to model the conditional posterior distribution of temporal states. All epochs share the same parameters.

[0017] The present invention has the following beneficial effects: This invention breaks through the reliance of traditional spatiotemporal network positioning and navigation technologies on prior physical models. It can automatically learn the radio propagation characteristics in complex environments, effectively solving the positioning performance degradation problems caused by model mismatch and non-Gaussian noise. It can simultaneously output high-precision positioning results and quantified uncertainty information, significantly improving the credibility and reliability of positioning results. It adopts a globally shared lightweight architecture and a non-iterative inference mechanism, reducing computational complexity and hardware consumption. It has good engineering feasibility and scalability, and can flexibly adapt to various aerospace collaborative positioning scenarios, providing solid technical support for the integrated air-space-ground navigation, positioning, and timing system. Attached Figure Description

[0018] Figure 1This is a flowchart of the variational factor graph optimization cooperative localization method based on generative conditional normalized flow of the present invention. Figure 2 This is a schematic diagram of the training process of the present invention. Detailed Implementation

[0019] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] like Figure 1 As shown, a data-driven variational factor graph optimization localization method incorporating generative conditional normalization flow includes the following steps: Step 1: Construct a nonlinear state-space model for the model-free prior scenario To address the core issue of the lack of prior knowledge in physical models for complex aerospace environments, a general nonlinear state-space model is established that does not rely on any explicit physical propagation functions or noise distribution assumptions.

[0021] (1.1) in, For nodes k In the n The state vector of an epoch, where It is a three-dimensional position vector. It is a three-dimensional velocity vector; For nodes k In the n-1 The state vector of an epoch; The nonlinear state transition function is unknown. For nodes k In the n epoch process noise; For nodes k and j In the n The observation vector of an epoch includes both non-cooperative and cooperative observations; For unknown nonlinear observation functions; For nodes j In the n The state vector of an epoch; For nodes k and j In the n Epochal observation noise.

[0022] In equation (1.1), the state transition equation describes the evolution of the spacecraft / aircraft state over time, while the observation equation describes the physical mapping relationship between observations and node states, as well as between navigation reference nodes. For non-cooperative positioning scenarios, the observation equation degenerates into: (1.2) in, For the set of navigation reference nodes, This refers to the number of navigation reference nodes; The number of spacecraft / aircraft nodes; A set of spacecraft / aircraft nodes; Step 2: Factor graph structured decomposition of joint posterior probabilities Based on the observation independence assumption and the first-order Markov assumption, the joint posterior probability density function of spatiotemporal cooperative network localization is decomposed into a factor graph form, realizing a modular representation of high-dimensional joint probability: (1.3) In the formula, For the full observation dataset, For the set of all nodes; Let be the true probability density function. N This represents the total epoch number; Let be the probability density function corresponding to the state transition equation; Let be the probability density function corresponding to the observation equation; In formula (1.3), each factor after decomposition corresponds to one of the three types of core factors in the factor diagram, and the initial state prior factors. Describes the probability distribution of the initial state of a node (spacecraft / aircraft); state transition factor Describes the evolution of spacecraft / aircraft node states in adjacent time series; observes likelihood factors. Describes the constraints of observations on the nodal states of a spacecraft / aircraft.

[0023] Step 3: Construct a hierarchical variational Bayesian inference framework Introducing low-dimensional global latent features To achieve dimensionality reduction and decoupling of high-dimensional parameters, a hierarchical variational Bayesian framework comprising a generative model and a variational inference model is constructed to address the computational complexity problem of high-dimensional posterior modeling. 1) Generative model construction: Constructing latent variables according to physical causal logic to state Then from state To observe The directed graph structure, with joint distribution, is represented as: (1.4) The structured decomposition of the generative model is implicitly aligned with the probabilistic modeling logic of the factor graph, where global latent features... prior distribution Set as a standard Gaussian distribution Initial state prior distribution The initial state factors correspond to the factor diagram; the state transition distribution. Corresponding factor plot state transition factor; observed likelihood distribution The likelihood factor was observed in the corresponding factor plot.

[0024] 2) Construction of variational inference model: A structured variational posterior is constructed using block mean field decomposition, which can preserve the complete spatiotemporal dependencies within the block while reducing computational complexity. (1.5) In the formula, It is a variational approximation of the probability density function; The set of learnable parameters for the CNF module in variational inference. Feature layer variational distribution. Parameterization by spatiotemporal feature encoding network; variational distribution of state layer and CNF module parameterization is inferred from variational inference.

[0025] 3) Derivation of ELBO optimization objective: Minimizing the KL divergence between the variational posterior and the true posterior is equivalent to maximizing the lower bound of evidence ( ): (1.6) in, For variational distribution q The mathematical expectation; Expanding this, we get the detailed expression that can be directly used for training: (1.7) Using negative ELBO as the loss function for model training .

[0026] Step 4: Multi-module globally shared conditional normalized flow parameterization design CNF is used as the core probabilistic modeling module. Two main types of modules are designed: the CNF generation module and the variational inference CNF module. All modules adopt a globally shared backbone network architecture to alleviate the parameter explosion problem.

[0027] CNF models complex probability distributions by stacking invertible affine transformations. For a conditional input c, the invertible transformation... Map the observation z to standard Gaussian hidden variables The conditional probability density can be calculated without approximation using the Jacobian determinant: (1.8) In the formula, It follows a standard Gaussian distribution. Let T be the Jacobian matrix of the transformation T.

[0028] 1) Generate CNF module (used only during the training phase), including the following three sub-modules: The initial joint state prior CNF submodule takes the initial epoch state as its input. Along with the global latent feature H, we fit the prior distribution of the initial joint state of all nodes. ; The globally shared spacetime transition prior CNF submodule takes the state of the previous epoch n-1 as input. Current epoch n state The global latent feature H is used to fit the temporal evolution of the joint state of multiple nodes. All epochs share the same set of parameters; A globally shared multi-source observation likelihood CNF submodule is used to fit the physical mapping from state to observation. The backbone network is globally shared, and it adapts to non-cooperative and cooperative observations through different input conditions. The input condition for non-cooperative observation is a single spacecraft / aircraft node. k The state in the nth epoch With global latent features H The collaborative observation conditions input is a dual spacecraft / aircraft node. k , j In the n The splicing state of each epoch With the global latent feature H.

[0029] 2) Variational Inference CNF Module (Core of the Inference Phase), which includes the following three sub-modules: The initial epoch joint condition CNF submodule takes the initial epoch state as its input. Using the global latent feature H, model the posterior distribution of the initial joint state of all nodes. .

[0030] The globally shared spacetime transition CNF submodule takes the state of the previous epoch (n-1) as input. Current epoch n state Along with global latent features H, used to model the conditional posterior distribution of temporal states. All epochs share the same parameters.

[0031] The global parameter sharing design ensures that the number of model parameters does not increase with the sequence length and the number of nodes, thus avoiding parameter explosion and overfitting problems in large-scale collaborative networks.

[0032] Step 5: Supervised training and non-iterative forward inference, such as Figure 2 As shown, it specifically includes: 1) Supervised training process: First, feedforward feature extraction involves inputting batch training data Z into a spatiotemporal feature encoding network (using a bidirectional GRU or Transformer architecture) to obtain the Gaussian distribution parameters of the low-dimensional global latent features. and ; Then, reparameterization sampling is performed to obtain latent feature samples using reparameterization techniques. This ensures that the gradient of the random sampling process can be backpropagated; Next, the logarithmic density values ​​of each term in the ELBO loss function are calculated. First, the sampled H and the real joint state sequence of multiple nodes are input into the variational inference CNF module and the generation CNF module, respectively, and then the logarithmic density values ​​of the corresponding terms in ELBO are calculated. Next, the loss and backpropagation are calculated. A loss function is constructed based on negative ELBO, and the learnable parameters of the CNF module in the generative model are calculated using an automatic differentiation tool. Learnable parameters of spatiotemporal feature coding networks Learnable parameters of the variational inference CNF module Finally, the parameters are updated using the Adam optimizer to update all network parameters. The above steps are repeated until the validation set ELBO converges.

[0033] 2) Non-iterative forward inference process: After training, the inference process only requires forward propagation of the network, without any iterative numerical optimization or external solvers. The specific process is as follows: First, feature extraction is performed by inputting the observed sequence Z to be inferred into a trained spatiotemporal feature encoding network to obtain the latent feature distribution parameters. and ; Re-Monte Carlo sampling, independently sampling M latent feature samples from the latent feature distribution. ; Then, the posterior distribution is generated jointly for each latent feature sample. The input variational inference CNF module generates the conditional posterior distribution of the corresponding multi-epoch multi-node joint state; Next, the localization results can be output. The final point estimate of the joint state of the multi-nodes is the Monte Carlo approximation of the mean of all posterior distributions as follows: (1.9) The above formula represents the state variables. In distribution The expected operation is performed below.

[0034] Finally, the uncertainty can be quantified by calculating the covariance matrix of the posterior distribution and outputting the 95% confidence interval of the positioning result.

[0035] All symbols used in this invention are uniformly defined as follows: For spacecraft / aircraft node set, The number of nodes to be located; For the set of navigation reference nodes, The number of baseline nodes; For the set of all nodes; For discrete time epochs, This is a time index, where N is the total number of epochs; , For node indexing. Let be the state vector of node k in the nth epoch, where It is a three-dimensional position vector. It is a three-dimensional velocity vector; Let be the observation vectors of nodes k and j at the nth epoch, including non-cooperative observations and cooperative observations; This is the full observation dataset. The nonlinear state transition function is unknown. For unknown nonlinear observation functions; For the process noise of node k in the nth epoch, H represents the observation noise of nodes k and j at the nth epoch; H is the low-dimensional global latent feature vector with dimension . ; To generate the set of learnable parameters for the CNF module of the model, This is the set of learnable parameters for a spatiotemporal feature encoding network. This is the set of learnable parameters for the CNF module of variational inference. Let be the true probability density function. It is a variational approximation of the probability density function; Let be the mathematical expectation of the variational distribution q. The Kohlbek-Leibler divergence is the distance between the variational distribution q and the true distribution p. For Kronecker product, This is a matrix transpose operation. This refers to the 2-norm operation for vectors. For parameters Conditional normalized flow model, Let f be the Jacobian matrix of the invertible transformation f. Let be the determinant of the Jacobian matrix.

[0036] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A variational factor graph optimization cooperative localization method based on generative conditional normalized flow, characterized in that, Includes the following steps: Step S1: Construct a nonlinear state-space model for a model-free prior scenario, including state transition equations and observation equations. The state transition equations are used to characterize the evolution of node states over time, and the observation equations are used to characterize the mapping relationship between observations between nodes and node states. Step S2: Based on the observation independence assumption and the first-order Markov assumption, the joint posterior probability density function of the spatiotemporal cooperative network localization is decomposed into a factor graph form to obtain the factor graph decomposition results, which include the initial state prior factors describing the probability distribution of the initial state of the nodes, the state transition factors describing the temporal evolution of the node states, and the observation likelihood factors describing the constraints of the observations on the node states. Step S3: Introduce low-dimensional global latent features and construct a hierarchical variational Bayesian inference framework that includes generative CNF and variational inference CNF modules to maximize the lower bound of evidence. As an optimization objective, the generative model constructs a directed graph structure from latent variables to states and from states to observations according to physical causal logic, and the variational inference model uses block mean field decomposition to construct a structured variational posterior. Step S4: Using Conditional Normalized Flow CNF as the probabilistic modeling module, design and generate the Conditional Normalized Flow CNF module and the Variational Inference Conditional Normalized Flow CNF module. All modules adopt a globally shared backbone network architecture. The Generative Conditional Normalization Flow CNF module includes an initial joint state prior submodule, a globally shared spatiotemporal transition prior submodule, and a globally shared multi-source observation likelihood submodule; the Variational Inference Conditional Normalization Flow CNF module includes an initial epoch joint condition submodule and a globally shared spatiotemporal transition submodule. Step S5: Supervised training is performed on the Generative Conditional Normalization Flow (CNF) module, the Variational Inference Conditional Normalization Flow (CNF) module, and the Spatiotemporal Feature Encoding Network. During the training process, batch training data is input into the Spatiotemporal Feature Encoding Network to extract the distribution parameters of low-dimensional global latent features. Latent feature samples are obtained through reparameterization sampling. The sampled latent features and the true joint state sequence are respectively input into the Variational Inference Conditional Normalization Flow (CNF) module and the Generative Conditional Normalization Flow (CNF) module. The log density terms corresponding to the lower bound of evidence are calculated, and the negative lower bound of evidence is used as the loss function. All network parameters are updated through backpropagation and the optimizer. After training, the observation sequence to be inferred is input into the spatiotemporal feature encoding network to obtain the latent feature distribution parameters. Multiple latent feature samples are independently sampled from the latent feature distribution. Each latent feature sample is input into the variational inference conditional normalization flow (CNF) module to generate the conditional posterior distribution of the corresponding multi-epoch multi-node joint state. The Monte Carlo approximation of the mean of all posterior distributions is used as the point estimate of the multi-node joint state to output the localization result. At the same time, the uncertainty quantification information of the localization result is output by calculating the covariance matrix of the posterior distribution.

2. The method according to claim 1, characterized in that, In step S1, the state transition equation and the observation equation are as follows: (1.1) in, For nodes k In the n The state vector of an epoch, where It is a three-dimensional position vector. It is a three-dimensional velocity vector; For nodes k In the n-1 The state vector of an epoch; The nonlinear state transition function is unknown. For nodes k In the n epoch process noise; For nodes k and j In the n The observation vector of an epoch includes both non-cooperative and cooperative observations; For unknown nonlinear observation functions; For nodes j In the n The state vector of an epoch; For nodes k and j In the n Epochal observation noise; For non-cooperative localization scenarios, the observation equation degenerates into: （1.2） in, This is the set of navigation reference nodes.

3. The method according to claim 2, characterized in that, The factor graph decomposition result described in step S2 is expressed as follows: （1.3） In the formula, For the full observation dataset, For the set of all nodes, For spacecraft / aircraft node set, For the number of spacecraft / aircraft nodes, This refers to the number of navigation reference nodes; Representing time points from 1 to N A concatenated vector of the states of each spacecraft / aircraft node; Let N be the true probability density function, and N be the total number of epochs. Let be the probability density function corresponding to the state transition equation; Let be the probability density function corresponding to the observation equation; , which is the prior factor of the initial state.

4. The method according to claim 3, characterized in that, The joint distribution of the generated model in step S3 is represented as follows: （1.4） The structured decomposition of the generative model is implicitly aligned with the probabilistic modeling logic of the factor graph, where global latent features... prior distribution Let the initial state be a standard Gaussian distribution; the prior distribution of the initial state is... Corresponding factor diagram: initial state factor; state transition distribution Corresponding factor plot state transition factor; observed likelihood distribution The likelihood factor was observed in the corresponding factor plot.

5. The method according to claim 4, characterized in that, The block mean field decomposition of the variational inference model described in step S3 is expressed as: （1.5） In the formula, It is a variational approximation of the probability density function; The set of learnable parameters for the CNF module of variational inference; This is the set of learnable parameters for a spatiotemporal feature coding network. Feature layer variational distribution Parameterized by spatiotemporal feature encoding network; State layer variational distribution and Parameterization of CNF modules is inferred from variational inference.

6. The method according to claim 5, characterized in that, The maximization of the lower bound of evidence mentioned in step S3 is as follows: The lower bound of negative evidence is used as the loss function for model training.

7. The method according to claim 1, characterized in that, In step S4, the conditionally normalized flow CNF models the complex probability distribution through stacked invertible affine transformations: for the conditional input c, the invertible transformation... Map the observation z to standard Gaussian hidden variables ; The conditional probability density can be calculated without approximation using the Jacobian determinant: （1.8） In the formula, It follows a standard Gaussian distribution. To transform the Jacobian matrix of T, Let be the determinant of the Jacobian matrix; These are the parameters for the conditionally normalized flow model.

8. The method according to claim 1, characterized in that, In step S4, the CNF generation module includes the following three sub-modules: The initial joint state prior CNF submodule takes the initial epoch state as its input. Along with the global latent feature H, we fit the prior distribution of the initial joint state of all nodes. ; The globally shared spacetime transition prior CNF submodule takes the state of the previous epoch n-1 as input. Current epoch n state The global latent feature H is used to fit the temporal evolution of the joint state of multiple nodes. All epochs share the same set of parameters; A globally shared multi-source observation likelihood CNF submodule is used to fit the physical mapping from state to observation. The backbone network is globally shared, and it adapts to non-cooperative and cooperative observations through different input conditions. The input condition for non-cooperative observation is the state of a single spacecraft / aircraft node k in the nth epoch. The global latent feature H and the cooperative observation condition input are the splicing state of the two spacecraft / aircraft nodes k and j in the nth epoch. With global latent feature H; The variational inference CNF module includes the following three sub-modules: The initial epoch joint condition CNF submodule takes the initial epoch state as its input. Using the global latent feature H, model the posterior distribution of the initial joint state of all nodes. ; The globally shared spacetime transition CNF submodule takes the state of the previous epoch (n-1) as input. Current epoch n state Along with global latent features H, used to model the conditional posterior distribution of temporal states. All epochs share the same parameters.

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