Hardware delay dynamic tracking method based on augmented state extended kalman filter

Abstract

This invention provides a method for dynamic hardware delay tracking based on an augmented state extended Kalman filter, comprising: constructing a satellite constellation topology map based on historical inter-satellite link observation data, inputting the satellite constellation topology map into a pre-trained graph neural network for processing, and outputting the initial hardware delay of each satellite in the constellation; constructing an augmented state vector for the satellites, and initializing the augmented state vector using the initial hardware delay of each satellite in the constellation, and initializing the covariance matrix of the augmented state vector; the augmented state vector includes the satellite's orbital state, clock bias state, and hardware delay value; acquiring real-time inter-satellite link observation data, and iteratively predicting and updating the initialized augmented state vector and its covariance matrix based on the extended Kalman filter algorithm, and outputting the real-time updated hardware delay value of each satellite in the constellation.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and communication technology, specifically relating to a hardware delay dynamic tracking method based on augmented state extended Kalman filter. Background Technology

[0002] In high-precision positioning applications of Global Navigation Satellite Systems (GNSS), such as in the automated monitoring and early warning of geological disasters like landslides and subsidence, achieving high-precision deformation monitoring is crucial for successful early warning. Inter-satellite link technology, through direct communication and ranging between satellites, significantly enhances the autonomous operation capability and overall navigation accuracy of the constellation. During the ranging process in inter-satellite links, the signal travels through its respective hardware channels from the transmitting satellite to the receiving satellite; the resulting signal delay is known as hardware delay. This delay is one of the key error sources affecting the accuracy of inter-satellite ranging and the final navigation and positioning performance.

[0003] Traditional methods typically treat hardware delay as a fixed constant or a function strictly following the orbital period, estimating and subtracting it through ground calibration or parametric models used in data post-processing. However, practice shows that the hardware delay of inter-satellite links is not static. It is dynamically affected by various factors, such as: frequent adjustments to satellite attitude causing changes in antenna phase center; periodic fluctuations in the operating temperature of onboard electronics depending on illumination conditions; and the aging effects of electronic components over time. These factors cause small but critical dynamic drifts in hardware delay, and these drifts may be asymmetrical in the signal transmission and reception channels.

[0004] The fixed-period model used in existing technologies is based on the fundamental assumption that changes in hardware latency strictly follow the satellite's orbital period. This model cannot effectively capture non-periodic, random, or slowly drifting dynamic characteristics. This presents a technical challenge: to achieve higher-precision navigation services, these dynamically changing asymmetric delays must be accurately compensated for. However, constructing a high-frequency dynamic model capable of adapting to these changes in real time, such as a complex time-series network, would significantly increase the onboard computational burden and place high demands on the continuity and density of observation data. This contradicts the non-uniform, intermittent link establishment characteristics of inter-satellite link data in satellite systems like BeiDou, potentially leading to insufficient data for effective convergence and updates, or even introducing larger errors than static models. Summary of the Invention

[0005] To overcome the problems of high computational burden for hardware delay compensation in existing technologies, and the existence of significant errors despite high requirements for observation data quality, this invention provides a dynamic hardware delay tracking method based on augmented state extended Kalman filters. By constructing the satellite constellation as a topological graph and utilizing graph neural networks to achieve high-precision, batch decoupling of constellation-level hardware delay, the method continuously corrects the augmented state vector, which incorporates hardware delay state, using observational information in the iterative update process. This creatively transforms the hardware delay estimation problem into a dynamic state optimal estimation problem. Under conditions of limited computational resources and sparse observation data, this method can accurately and robustly track and compensate for time-varying hardware delay dynamically.

[0006] According to one aspect of the present invention, a hardware delay dynamic tracking method based on an augmented state extended Kalman filter is provided, comprising:

[0007] A satellite constellation topology map is constructed based on historical inter-satellite link observation data, and the satellite constellation topology map is input into a pre-trained graph neural network for processing, outputting the initial hardware latency of each satellite in the satellite constellation.

[0008] An augmented state vector for the satellite is constructed, and the augmented state vector is initialized using the initial hardware delay of each satellite in the satellite constellation, and the covariance matrix of the augmented state vector is initialized; the augmented state vector includes the satellite's orbital state, clock error state, and hardware delay value.

[0009] Real-time inter-satellite link observation data is acquired, and based on the extended Kalman filter algorithm, the initialized augmented state vector and its covariance matrix are iteratively predicted and updated, outputting the hardware delay value of each satellite in the satellite constellation in real time.

[0010] As a further technical solution, in the satellite constellation topology diagram, nodes represent satellites in the constellation, and edges are dynamic edges that change over time, representing effective inter-satellite link observations between satellites.

[0011] As a further technical solution, the graph neural network adopts a spatiotemporal graph convolutional network. It captures the spatial correlation between satellites in the satellite constellation topology graph through graph convolutional layers and captures the temporal autocorrelation of the hardware delay of a single satellite through temporal convolutional layers. The graph neural network performs forward propagation calculation on the input satellite constellation topology graph and outputs the estimated transmission hardware delay and the estimated reception hardware delay of each satellite in the satellite constellation, respectively, as the initial hardware delay of each satellite in the satellite constellation.

[0012] As a further technical solution, the graph neural network pre-training process is based on the physical constraint loss function defined by the inter-satellite link observation equation.

[0013] As a further technical solution, in the satellite's augmented state vector,

[0014] The orbital state of a satellite refers to its position and velocity parameters in space;

[0015] The clock bias status of a satellite refers to the clock bias and clock speed parameters of the satellite's onboard clock;

[0016] The satellite's hardware delay status specifically includes the satellite's launch hardware delay and reception hardware delay. During the initialization process, the launch hardware delay estimate from the initial hardware delay of each satellite in the satellite constellation output by the graph neural network is assigned to the satellite launch hardware delay, and the reception hardware delay estimate is assigned to the reception hardware delay.

[0017] As a further technical solution, the augmented state vector and its covariance matrix after initialization are iteratively predicted and updated. For any time step after initialization, whenever a valid inter-satellite link observation value is detected in the received real-time inter-satellite link observation data, the augmented state vector and its covariance matrix of the previous time step of the current time step are iteratively predicted and updated. Otherwise, the augmented state vector and its covariance matrix of the previous time step of the current time step are maintained as the augmented state vector and its covariance matrix of the current time step.

[0018] As a further technical solution, the steps of iteratively predicting and updating the augmented state vector and its covariance matrix of the previous time step at the current time step include:

[0019] Based on the augmented state vectors of each satellite in the current time step, the predicted pseudorange observations of each inter-satellite link at the current time step are calculated using nonlinear observation equations, and the observation equations for the current time step are also calculated.

[0020] Subtract the predicted pseudorange observation value of each inter-satellite link from the real-time inter-satellite link observation data of the current time step to generate the observation information sequence of the current time step.

[0021] Based on the augmented state vector and its covariance matrix of the previous time step, the orbit and clock bias states in the augmented state vector of the current time step are predicted according to the satellite dynamics model and clock bias model. The hardware delay state in the augmented state vector of the current time step is predicted according to the stochastic process model, and the covariance matrix of the augmented state vector is updated accordingly to obtain the predicted augmented state vector and the predicted covariance matrix of the current time step.

[0022] The Kalman gain for the current time step is calculated using the observed innovation sequence, the predicted covariance matrix, and the observed matrix. Based on the Kalman gain and the observed innovation sequence, the predicted augmented state vector and the predicted covariance matrix for the current time step are optimally corrected, and the updated augmented state vector and covariance matrix for the current time step are output.

[0023] As a further technical solution, the mathematical expression of the nonlinear observation equation is as follows:

[0024]

[0025] In the formula, For identifying the launched satellite in the inter-satellite link, This serves as the identifier for the receiving satellite in the inter-satellite link. express The time step receives the inter-satellite link pseudorange observations of satellite B to the launching satellite A; express The geometric distance between the transmitting satellite A and the receiving satellite B at the time step. express The three-dimensional position vector of satellite A launched at the time step. express The three-dimensional position vector of satellite B is received at the time step; express The satellite clock bias of satellite A launched at the time step; express The time step receives the satellite clock bias of satellite B; c represents the speed of light; express The time step satellite A, as the launcher, experiences hardware delays in its launch channel. express The hardware delay of the receiving channel of time-step satellite B as the receiver; This represents the observation noise and unmodeled error of the inter-satellite link.

[0026] According to another aspect of this specification, a hardware delay dynamic tracking system based on an augmented state extended Kalman filter is provided, which is applied to a hardware delay dynamic tracking method based on an augmented state extended Kalman filter, including: a data collection module, an initialization module, and a dynamic tracking module;

[0027] The data collection module is used to construct a satellite constellation topology map based on historical inter-satellite link observation data, and input the satellite constellation topology map into a pre-trained graph neural network for processing, outputting the initial hardware latency of each satellite in the satellite constellation;

[0028] The initialization module is used to construct the augmented state vector of the satellite, and initializes the augmented state vector with the initial hardware delay of each satellite in the satellite constellation, and initializes the covariance matrix of the augmented state vector; the augmented state vector includes the satellite's orbital state, clock error state and hardware delay value.

[0029] The dynamic tracking module is used to acquire real-time inter-satellite link observation data. Based on the extended Kalman filter algorithm, it iteratively predicts and updates the initialized augmented state vector and its covariance matrix, and outputs the hardware delay value of each satellite in the satellite constellation in real time.

[0030] According to another aspect of this specification, a computer device is provided, including a memory and a processor, the memory storing program instructions executable by the processor, the processor invoking the program instructions to perform a hardware delay dynamic tracking method based on an augmented state extended Kalman filter.

[0031] Compared with existing technologies, the advantages of this invention are as follows: By constructing the satellite constellation as a topological graph and utilizing graph neural networks to simultaneously capture the spatial correlation between satellites and the temporal autocorrelation of individual satellite hardware delays, this invention achieves high-precision, batch decoupling of constellation-level hardware delays. By incorporating prior observation equation knowledge into network training through a loss function with physical constraints, the deep learning model is no longer a black box, and the output results have clear physical meaning. Filtered tracking provides a reliable initial state of the entire network's hardware delays with accuracy far exceeding traditional calibration methods.

[0032] This invention creatively transforms the problem of hardware delay estimation into a dynamic state optimal estimation problem by tailoring a stochastic process model for the hardware delay state during iterative updates of the augmented state vector and continuously refining it using observational information. This approach allows the system to adaptively track its true time-varying characteristics without relying on any pre-defined, fixed hardware delay variation model, thus completely overcoming the inherent shortcomings of traditional fixed-period models in dealing with non-periodic and asymmetric delay variations caused by satellite attitude adjustments, temperature fluctuations, etc.

[0033] This invention solves the problem of dynamic hardware delay compensation through a two-stage strategy of offline initialization and online tracking. In the offline stage, a graph neural network is used to process historical inter-satellite link data in batches. Leveraging nonlinear fitting and spatiotemporal feature extraction capabilities, the initial hardware delay value for each satellite is decoupled with high precision from the mixed observation signals. In the online stage, by incorporating hardware delay as a state variable into an extended Kalman filter, combined with prediction and update mechanisms, continuous dynamic tracking of hardware delay is achieved. This adapts to the intermittent nature of inter-satellite link data, maintaining robust tracking performance even under sparse observation conditions. Furthermore, an innovation-based adaptive mechanism is introduced, which dynamically adjusts filter parameters according to the system state, maintaining smooth estimation in stable phases and rapid response in abrupt changes, thus improving tracking accuracy and system robustness against non-periodic and time-varying delays. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 A flowchart illustrating the hardware delay dynamic tracking method based on augmented state extended Kalman filter provided in an embodiment of the present invention;

[0036] Figure 2 A schematic diagram of the hardware delay dynamic tracking system based on augmented state extended Kalman filter provided in an embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of the structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0038] It should be noted that:

[0039] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0040] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices. The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be decomposed, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0042] like Figure 1 As shown, this invention provides a hardware delay dynamic tracking method based on an augmented state extended Kalman filter, applicable to geological disaster monitoring, including:

[0043] Step 1: Construct a satellite constellation topology map based on historical inter-satellite link observation data, and input the satellite constellation topology map into a pre-trained graph neural network for processing, outputting the initial hardware latency of each satellite in the satellite constellation;

[0044] Step 2: Construct the augmented state vector of the satellite, and initialize the augmented state vector using the initial hardware delay of each satellite in the satellite constellation, and initialize the covariance matrix of the augmented state vector; the augmented state vector includes the satellite's orbital state, clock error state and hardware delay value;

[0045] Step 3: Acquire real-time inter-satellite link observation data. Based on the extended Kalman filter algorithm, iteratively predict and update the initialized augmented state vector and its covariance matrix, and output the hardware delay value of each satellite in the satellite constellation in real time.

[0046] Optionally, in step 1, the step of acquiring historical inter-satellite link observation data includes: collecting historical observation data of the satellite constellation over a relatively long period (e.g., several days or weeks), including but not limited to inter-satellite two-way pseudorange observations, carrier phase observations, signal-to-noise ratio, as well as satellite broadcast ephemeris, preliminary drafts of precise ephemeris, and telemetry data (such as equipment temperature, attitude angular velocity, etc.).

[0047] In step 1, in the satellite constellation topology diagram, nodes represent satellites in the constellation, and edges are dynamic edges that change over time, representing effective inter-satellite link observations between satellites.

[0048] Specifically, the satellite constellation topology is a dynamic spatiotemporal diagram. Among them, the node set Represents all the satellites in the constellation. v represents a satellite, the subscript indicates the satellite number, and N is the number of satellites in the satellite constellation; edge set It changes over time, at any time step If satellite and If there are valid inter-satellite link observations, then there exists an edge in the graph. .

[0049] Among them, satellites and Valid pseudorange observations of inter-satellite links were successfully obtained.

[0050] Furthermore, in step 1, the graph neural network adopts a spatiotemporal graph convolutional network (ST-GCN), which captures the spatial correlation between satellites in the satellite constellation topology graph through graph convolutional layers and captures the temporal autocorrelation of the hardware delay of a single satellite through temporal convolutional layers. The graph neural network performs forward propagation calculation on the input satellite constellation topology graph and outputs the estimated transmit hardware delay and the estimated receive hardware delay of each satellite in the satellite constellation, respectively, as the initial hardware delay of each satellite in the satellite constellation.

[0051] Specifically, the Spatiotemporal Graph Convolutional Network (ST-GCN) of the present invention is composed of multiple spatiotemporal convolutional modules stacked together. Each spatiotemporal convolutional module contains a graph convolutional layer and a temporal convolutional layer.

[0052] Graph convolutional layers: At each time slice, mechanisms such as graph attention networks (GAT) or gated graph convolutions are used to aggregate information from neighboring nodes (i.e., other satellites with linked connections), aiming to capture spatial correlations of hardware latency, such as common-mode errors caused by components produced in the same batch or by a common space environment (e.g., radiation).

[0053] Temporal Convolutional Layer: Following the graph convolutional layer, the temporal series features formed by each node (satellite) are processed using a temporal convolutional network (TCN) or a gated recurrent unit (GRU). The aim is to capture the autocorrelation of hardware delays in a single satellite over time, such as periodic oscillations caused by temperature changes and long-term drift trends caused by device aging.

[0054] As an optional implementation, the forward propagation computation outputs not only the hardware latency estimate, but also the uncertainty of the hardware latency estimate:

[0055] The output layer of the graph neural network is specially designed to output the mean and variance of each hardware delay estimate. The variance represents the uncertainty of the graph neural network regarding the estimate based on the current input data. This uncertainty is filled into the corresponding position of the covariance matrix of the augmented state vector during the subsequent initialization of the augmented state vector, providing the filter with an accurate initial uncertainty measure, thereby accelerating filter convergence and improving the stability of the tracking process.

[0056] In addition, the pre-training process of the graph neural network is based on the physical constraint loss function defined by the inter-satellite link observation equation.

[0057] As a specific implementation method, the mathematical representation of the physical constraint loss function includes:

[0058] For any observation link (from satellite) To satellite ), calculate pseudorange observations The observation equation is expressed as:

[0059]

[0060] in, It is a time step satellite To satellite Pseudo-distance observations; It is a time step satellite To satellite geometric distance, and They are satellites and The clock difference, It's the speed of light; and They are satellites Launch hardware delays and satellites The receiving hardware delay; It is a time step satellite To satellite Observation noise.

[0061] Physical constraint loss function Defined as the sum of squared observation residuals across all observation links and at all time steps:

[0062]

[0063] in, It is calculated based on prior orbital information. Time step satellite To satellite The theoretical value of geometric distance; , The satellite is calculated based on prior clock bias information. Theoretical values ​​of clock bias and satellite The theoretical value of clock error, while and It is the satellite at time step t output by ST-GCN. Launch hardware delay value and satellite The received hardware delay value. By minimizing this loss function, ST-GCN learns the hardware delay that can account for the observation residuals.

[0064] In an optional embodiment, the physical constraint loss function L adopts a mean squared error loss function with signal-to-noise ratio weighting, mathematically expressed as:

[0065]

[0066] In the formula, It is with satellite To satellite The weighting coefficients that are positively correlated with the signal-to-noise ratio of pseudorange observations. For actual pseudorange observations of inter-satellite links, The pseudorange prediction value of the inter-satellite link is obtained based on the satellite status;

[0067] in, From satellite To satellite Obtain the signal-to-noise ratio from the observation data Then, through a monotonically increasing function, The mapping to weights is expressed mathematically as follows:

[0068]

[0069] In the formula, It is a reference signal-to-noise ratio value used for normalization; exponent It is a real number greater than 0, used to control the sensitivity of the weight to the signal-to-noise ratio, and its typical value range is [0.5, 2].

[0070]

[0071] In the formula, Indicates the three-dimensional position of the satellite. For satellite clock bias, At the speed of light, and These are satellites output by the graph neural network. Launch hardware delay estimation and satellite Estimated hardware delay for receiving data.

[0072] In this embodiment, high signal-to-noise ratio observation data has a greater weight in the loss function, guiding the graph neural network to prioritize fitting high-quality data. This effectively suppresses the interference of noise in low-quality observation data on hardware delay estimation, further improving the accuracy and robustness of the decoupling results.

[0073] In another alternative embodiment, the physical constraint loss function is a composite loss function that incorporates a temporal smoothing regularization term. Mathematically, it is expressed as:

[0074]

[0075] in, This is the fitting error based on the observation equation; represent Hardware latency estimates for each time step. It is the regularization coefficient. It penalizes drastic changes in hardware latency between adjacent time steps and incorporates prior knowledge of the smooth evolution of hardware latency over time as a constraint into the training process.

[0076] This physical constraint loss function ensures that the initial hardware delay sequence output by the graph neural network not only conforms to the observation equation but also has good temporal smoothness, making it more consistent with the actual physical changes.

[0077] In step 1, ST-GCN is pre-trained using historical inter-satellite link observation data based on the physical constraint loss function. After training, ST-GCN can process the input historical inter-satellite link observation data in batches and output high-precision estimates of the transmission and reception hardware delays for each satellite in the constellation. These values ​​will be used as the initial hardware delays in subsequent steps during the online dynamic tracking phase.

[0078] As an alternative implementation, forward propagation computation is the residual of hardware latency relative to a nominal value.

[0079] The pre-training objective of a graph neural network is to learn the deviation between hardware latency and a prior nominal value (such as a ground-level calibration or long-term average). Its loss function is accordingly modified to minimize the residuals. In this embodiment, the network output is... , This represents the hardware latency residual. Indicates actual hardware latency. This represents the nominal hardware latency. This design focuses the network's learning task on capturing dynamically changing components, reducing the learning difficulty. It is particularly suitable for scenarios with small variations in hardware latency and can effectively improve the estimation accuracy of small signal changes.

[0080] In this invention, step 1 utilizes the powerful nonlinear mapping and feature extraction capabilities of graph neural networks to separate the independent transmission and reception hardware delays of each satellite from historical observation data mixed with orbital errors, clock errors, and other noise, thereby achieving comprehensive and refined calibration of constellation-level hardware delays.

[0081] By using a loss function constrained by the physical observation equation as a guide for network training, it is ensured that the decoupled hardware delay initial value not only satisfies the goodness of fit of the data, but also has clear physical interpretability. This provides a reliable and high-precision initial benchmark for the subsequent filter initialization, fundamentally avoiding the problem of slow filter convergence or divergence caused by excessive deviation of the initial value.

[0082] By adopting a batch processing mode for historical inter-satellite link observation data, the computationally intensive and complex decoupling process is completed offline, which greatly reduces the occupation of on-board real-time computing resources and perfectly meets the actual constraints of the limited computing power of the on-board platform.

[0083] In step 2, constructing the augmented state vector elevates hardware latency from a fixed parameter to be subtracted in the traditional model to a state variable that requires real-time dynamic estimation, on par with satellite orbital state and clock bias state. In terms of structural design, the augmented state vector defined for each satellite not only includes basic dynamic and time synchronization states but also explicitly incorporates hardware state variables characterizing the inherent latency of signal transceiver equipment. In some preferred embodiments, the augmented state vector can be further extended to include environmental or health states directly related to the physical causes of latency.

[0084] Specifically, in the satellite's augmented state vector,

[0085] The orbital state of a satellite refers to its position and velocity parameters in space;

[0086] The clock bias status of a satellite refers to the clock bias and clock speed parameters of the satellite's onboard clock;

[0087] The satellite's hardware delay status specifically includes the satellite's launch hardware delay and reception hardware delay. During the initialization process, the hardware delay estimate in the initial hardware delay of each satellite in the satellite constellation output by the graph neural network is assigned to the satellite launch hardware delay, and the reception hardware delay estimate is assigned to the reception hardware delay.

[0088] As a specific implementation method, the augmented state vector incorporates the satellite's dynamic state (orbital state), time synchronization state (clock difference state), and the inherent delay state of the signal transceiver equipment (hardware delay state) as its constituent elements. For each satellite... Construct an augmented state vector Mathematically, this is expressed as:

[0089]

[0090] Among them, the dynamic state includes and , respectively representing satellites Position three-dimensional vector and velocity three-dimensional vector; time synchronization status includes and , respectively representing satellites The clock bias (the deviation between the satellite's onboard atomic clock and the system time) and clock velocity (the rate of change of the satellite clock bias over time); ellipses represent other dynamic state parameters that need to be estimated (such as solar radiation pressure coefficient); the inherent delay state of the transceiver equipment includes... and These are satellites The transmission hardware delay (the internal delay from signal generation to transmission through the antenna) and the reception hardware delay (the internal delay from signal reception by the satellite antenna to entry into the processing module).

[0091] Preferably, in the process of constructing augmented state vectors, differentiated schemes can be adopted according to the application scenario requirements, including establishing independent delayed states for multi-frequency signals, designing hierarchical joint state vectors for large-scale constellations, or realizing intelligent state vectors whose dimensions can be dynamically adjusted according to system anomaly diagnosis.

[0092] In an optional preferred embodiment, a simplified implementation for constructing augmented state vectors for computationally limited scenarios includes:

[0093] The transmit and receive hardware delays of the same satellite are merged into a unified integrated hardware delay. The augmented state vector includes the satellite's orbital state, clock bias state, and the integrated hardware delay state. During initialization, the weighted average of the initial hardware delays of the graph neural network is assigned to the integrated hardware delay state.

[0094] In another optional preferred embodiment, for scenarios requiring high-precision positioning at multiple frequencies, constructing an augmented state vector is an enhanced implementation method that includes:

[0095] In addition to the basic orbital and clock bias states, the state vector also defines independent hardware delays for multiple operating frequencies for each transmit and receive channel.

[0096] The graph neural network processes historical inter-satellite link observation data in batches to obtain initial values ​​of the sub-channel hardware delay corresponding to different frequency points. During initialization, the initial values ​​of the sub-channel hardware delay corresponding to different frequency points obtained by the graph neural network are assigned to the corresponding frequency-related hardware delay states in the state vector.

[0097] Step 2 fundamentally changes the processing paradigm of hardware delay by elevating it from a fixed parameter to be subtracted in the traditional model to a state variable to be estimated alongside orbit and clock error, transforming it from a static error source into a dynamically trackable system state.

[0098] Further, the augmented state vector initialization in step 2 includes: using the initial hardware delay obtained in step 1 based on historical inter-satellite link observation data to initialize the augmented state vector and its covariance matrix, resulting in... and , To initialize the time step, and They are respectively the corresponding The augmented state vector and covariance matrix at each time step. This provides a good starting point for the filter, avoiding the long convergence time problem caused by cold start.

[0099] Preferably, historical calibration data and uncertainty measures can be integrated to set reasonable initial uncertainties for each state variable, avoiding the problem of slow convergence or divergence of the filter due to excessive initial value deviation, improving the stability and convergence speed of the dynamic tracking process, and laying the optimal starting point for subsequent filtering and tracking.

[0100] In step 3, the augmented state vector and its covariance matrix after initialization are iteratively predicted and updated. For any time step after the initialization time step, whenever a valid inter-satellite link observation value is detected in the received real-time inter-satellite link observation data, the augmented state vector and its covariance matrix of the previous time step of the current time step are iteratively predicted and updated. Otherwise, the augmented state vector and its covariance matrix of the previous time step of the current time step are maintained as the augmented state vector and its covariance matrix of the current time step.

[0101] The steps for iteratively predicting and updating the augmented state vector and its covariance matrix of the previous time step at the current time step include:

[0102] Step 3-1: Based on the augmented state vectors of each satellite in the current time step satellite constellation, use nonlinear observation equations to calculate the predicted pseudorange observations of each inter-satellite link at the current time step, and calculate the observation equations for the current time step.

[0103] In step 3-1, after receiving real-time inter-satellite two-way ranging observation data from the satellite constellation, when When the time step receives the inter-satellite link observation, it triggers the subsequent filtering update process.

[0104] Furthermore, the nonlinear observation equations in this invention relate the augmented state vector to the pseudorange observations (which incorporate the hardware delay to be estimated). and (Included), based on which the Jacobian matrix of the nonlinear observation equation about the predicted value of the current augmented state vector is calculated (the partial derivative matrix of the observation equation with respect to the augmented state vector is calculated as the Jacobian matrix), as the observation matrix.

[0105] Specifically, the partial derivative matrix of the nonlinear observation equations of the global satellite constellation at time step t with respect to the augmented state vector, which is also the complete Jacobian matrix used in the Extended Kalman Filter (EKF) update step, is mathematically expressed as:

[0106]

[0107] In the formula, Indicates time step The global partial derivative matrix, which is also the global Jacobian matrix used in the update step of the Extended Kalman Filter (EKF); Let m represent the row vector of the Jacobian matrix corresponding to any inter-satellite link, where m is the total number of inter-satellite links that change with time t.

[0108] Among them, the Jacobian matrix row vector of the inter-satellite link The calculation process includes:

[0109] To make this clear, As an identifier for launched satellites in inter-satellite links. As an identifier for the launching satellite in an inter-satellite link, for satellites... Transmit signals to satellite The inter-satellite link has the following nonlinear observation equation:

[0110]

[0111] In the formula, For identifying the launched satellite in the inter-satellite link, This serves as the identifier for the receiving satellite in the inter-satellite link. express The time step receives the inter-satellite link pseudorange observations of satellite B to the launching satellite A; express The geometric distance between the transmitting satellite A and the receiving satellite B at the time step. express The three-dimensional position vector of satellite A launched at the time step. express The three-dimensional position vector of satellite B is received at the time step; express The satellite clock bias of satellite A launched at the time step; express The time step receives the satellite clock bias of satellite B; c represents the speed of light; express The time step satellite A, as the launcher, experiences hardware delays in its launch channel. express The hardware delay of the receiving channel of time-step satellite B as the receiver; This represents the observation noise and unmodeled error of the inter-satellite link.

[0112] Further calculation of the Jacobian matrix row vector corresponding to the inter-satellite link BA. (Right now The structure of ) is as follows:

[0113]

[0114] In the formula, Represents the row vector of the Jacobian matrix corresponding to the inter-satellite link BA; The observation equations represent the position of the launched satellite. The partial derivatives (i.e.) ); Indicates a correspondence; The observation equations represent the positions of the receiving satellites. The partial derivatives (i.e.) ); This indicates that the channel is inactive and is currently in use. This indicates that zero elements are omitted.

[0115] Step 3-2: Subtract the predicted values ​​of the pseudorange observations of each inter-satellite link from the predicted values ​​of the real-time inter-satellite link observation data to generate a sequence of observation information.

[0116] In step 3-2, the difference between the observed value and the predicted value is used as the innovation. The received actual pseudorange observation value is subtracted from the calculated theoretical pseudorange observation (predicted value) to generate an observation innovation sequence. This innovation sequence quantifies the difference between the prediction and the actual observation.

[0117] Step 3-3: Based on the augmented state vector and its covariance matrix of the previous time step, predict the orbit and clock bias states in the augmented state vector of the current time step according to the satellite dynamics model and clock bias model, and predict the hardware delay state in the augmented state vector of the current time step according to the stochastic process model, and update the covariance matrix of the augmented state vector accordingly to obtain the predicted augmented state vector and the predicted covariance matrix of the current time step.

[0118] Specifically, step 3-3 essentially involves, based on the state transition model, starting from the time step... augmented state vector Predict the current time step augmented state vector ,include:

[0119] For orbital and clock bias states, predictions are made using known satellite dynamics models and random clock models.

[0120] For newly added hardware delay states, since their precise physical evolution model is unknown, they can be modeled as a first-order Gaussian-Markov process or a simpler random walk process. Taking the random walk model as an example, its state transition equation is:

[0121]

[0122]

[0123] in, and It has a mean of zero and a specific spectral density. Gaussian white noise, also known as process noise, represents the tiny random drift of hardware delay over time.

[0124] Steps 3-4: Calculate the Kalman gain of the current time step using the observed innovation sequence, predicted covariance matrix, and observed matrix. Then, based on the Kalman gain and observed innovation sequence of the current time step, perform optimal correction on the predicted augmented state vector and predicted covariance matrix of the current time step, and output the updated augmented state vector and covariance matrix of the current time step.

[0125] 3-4-1. Calculate the Kalman gain based on the observed information sequence and the predicted pseudorange observations of each inter-satellite link at the current time step. The Kalman gain at time step t is... The standard calculation formula is as follows:

[0126]

[0127] In the formula, This represents the prior covariance matrix at time step t, which is also the predicted covariance matrix at time step t. Let represent the observation noise covariance matrix at time step t.

[0128] 3-4-2. Update the augmented state vector and its covariance matrix based on the calculated Kalman gain and the observed information sequence.

[0129] The Kalman gain determines the weight of the observation innovation on the state correction. The Kalman gain is calculated. Then, the augmented state vector is updated according to the following formula:

[0130]

[0131] in, Let each be an augmented state vector estimate of satellite k at the current time step. This represents the augmented state vector estimate of satellite k at the current time step; For the observation sequence at time step t.

[0132] Specifically, the augmented state vector and its covariance matrix are updated simultaneously using the observed information sequence, mathematically represented as:

[0133]

[0134]

[0135] in, , These are the augmented state vector and covariance matrix after the optimal correction at the current time step, respectively. Indicates the observed predicted value; Represents the identity matrix; , indicating the observed new information sequence.

[0136] The current time step state estimate and covariance are used as the initial conditions for the next time step (k+1 time step). By continuously iterating the prediction and update steps (steps 3-1 to 3-4), the recursive and optimal estimation of the hardware delay state variables is achieved, thus completing dynamic tracking.

[0137] In this application, the process of predicting the augmented state vector in step 3 involves using a satellite dynamics model to handle the orbital state, a random clock model to handle the clock error state, and a random walk model to predict the hardware delay state. The spectral density of the process noise is initialized based on the slow drift characteristics of the hardware delay.

[0138] In the process of updating the augmented state vector, theoretical observations (pseudorange observations) are calculated by constructing a nonlinear observation equation that includes hardware delay state variables, and the local linearization of the system is achieved by calculating the Jacobian matrix of this equation. By comparing the actual observation data with the theoretical predictions, the system generates an observation innovation sequence, and calculates the Kalman gain based on this sequence, thereby performing optimal correction on the predicted augmented state vector.

[0139] In an alternative embodiment, step 3, iteratively predicting and updating the augmented state vector, is implemented using a federated filtering architecture.

[0140] Each satellite subnet within the satellite constellation (e.g., satellites within the same orbital plane) is configured with a sub-filter for local state estimation. Simultaneously, a master filter is set up to fuse the local estimates from all sub-filters and generate the globally optimal estimate. In this architecture, each sub-filter can run a simplified version of augmented state filtering independently and in parallel, significantly distributing the computational load. This distributed approach is particularly suitable for navigation constellations with a large number of satellites, significantly improving the computational efficiency and scalability of the entire ground processing system while maintaining tracking accuracy.

[0141] In another alternative embodiment, step 3, iteratively predicting and updating the augmented state vector, refers to a data-driven method that uses a long short-term memory network instead of a traditional filtering framework.

[0142] One or more dedicated LSTM models need to be trained offline. A high-precision ground truth sequence with hardware latency can be obtained using a large amount of historical data processed by GNN. Training samples are constructed, and their input feature sequences can include past data. The pseudorange observation information and related satellite telemetry data (such as equipment temperature, attitude angular velocity, etc.) at each time step are output as the change in hardware delay at the next time step. .

[0143] Initialization: Initial values ​​for hardware latency It is also provided by the graph neural network in Implementation Example 1.

[0144] Cyclic Prediction and Update: At each real-time processing time step, the latest observation data is collected and the information is calculated. Simultaneously, the latest telemetry data is acquired. The latest feature vector, constructed from this data, is then fed into the input sequence of the LSTM model. The LSTM model then outputs the predicted hardware latency variation. Finally, update the hardware latency status: .

[0145] This updated hardware latency value This will be used to calculate the pseudorange prediction for the next time step, thereby generating new information and forming a data-driven closed-loop tracking system. The core advantage of this approach is that LSTM, as a data-driven method, does not require a pre-set physical model. Instead, it learns complex patterns in historical data to implicitly construct a nonlinear mapping relationship from input to output, thus better handling the nonlinear dynamics of unknown models.

[0146] The present invention also provides an embodiment that optimizes the EKF in the online dynamic tracking stage based on the aforementioned implementation method, and proposes an adaptive extended Kalman filter to further improve its robustness and tracking accuracy.

[0147] Adaptive adjustment of process noise covariance:

[0148] In standard EKF, the process noise covariance matrix (This includes the spectral density of the hardware-delayed random walk model) This is typically set to a fixed empirical value. However, the actual rate of change of hardware latency is not constant. For example, its drift rate increases significantly when the satellite undergoes drastic attitude adjustments or experiences sudden temperature changes. If the value cannot adapt to this dynamic, the filter may "not keep up" when the delay changes rapidly, resulting in hysteresis error; or it may introduce too much noise when the delay is stable, resulting in unsmooth estimation results.

[0149] To address this issue, this embodiment introduces an adaptive adjustment mechanism. After each update step of the EKF, a module is added to adjust the observed information sequence. Dynamically adjust the components of the process noise covariance matrix corresponding to the hardware delay state. .

[0150] Specifically, an adaptive algorithm based on innovation covariance (such as Sage-HusaEKF) can be used. The core idea of ​​this algorithm is that, ideally, the observed innovation sequence should be zero-mean white noise. When the model mismatches (e.g., the actual hardware latency changes much faster than the model prediction), the statistical properties of the observed innovation sequence change. By comparing the difference between the sample covariance of the actual innovation and the theoretical innovation covariance, this can be corrected in reverse. matrix.

[0151] Variable window length event triggering mechanism: The above adaptive algorithm usually relies on a sliding window of fixed length. Calculating the sample covariance of the innovation introduces a new contradiction: long window estimation is smooth but slow, while short window estimation is fast but noisy. Therefore, this embodiment further introduces an event-triggered variable window length mechanism.

[0152] After each EKF update step, calculate the Normalized Innovation Squared (NIS) value. : ,in It is the theoretical information covariance. The NIS value is an indicator of the "unexpectedness" of the model, and ideally it follows a chi-square distribution.

[0153] To improve the robustness of detection, a cumulative sum (CUSUM) control chart algorithm is used to monitor the NIS sequences. This algorithm can sensitively detect systematic model mismatch by accumulating small deviations, while being insensitive to isolated noise spikes. CUSUM statistics are calculated to detect positive and negative mean shifts. and :

[0154]

[0155] in, It is the standardized NIS value. These are reference values. When any statistic exceeds the decision threshold, a model mismatch event is determined to have occurred.

[0156] Steady state: When the CUSUM statistic does not exceed the limit, the system is in a steady state, using a relatively long sliding window. (e.g., N=50) to ensure process noise Smoothness of the estimate.

[0157] Model mismatch event: When the CUSUM event is triggered, immediately switch the sliding window length to a shorter window. (e.g., N=5), or even use instantaneous information updates. The modification is made to enable a rapid response to state changes.

[0158] To further improve adaptability, the decision threshold and reference value of the CUSUM algorithm can also be dynamically self-tuned. Its core idea is to correlate the sensitivity of the decision with the uncertainty of the filter itself in relation to hardware delay.

[0159] Specifically, after each EKF update, the covariance matrix of the augmented state vector is... In, for example, the first Given an augmented state vector, extract the diagonal elements corresponding to the hardware latency. This value is the estimated variance of hardware latency. .

[0160] Then, based on this variance value, the decision threshold and reference value are dynamically adjusted using a preset mapping function (such as a piecewise function or a tanh function). For example, when When the values ​​are large (indicating high uncertainty in the filter's estimation of hardware delay), the decision threshold and reference value should be appropriately relaxed (increased) to reduce the false alarm rate; conversely, when... When the values ​​are small, the decision threshold and reference value are tightened (reduced) to improve detection sensitivity.

[0161] Through the aforementioned progressive adaptive mechanism, the EKF in this embodiment can intelligently adjust its internal parameters under different operating conditions, achieving a balance between robustness and accuracy.

[0162] The implementation of the various embodiments of the present invention is based on programmed processing through a system with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a hardware delay dynamic tracking system based on an augmented state extended Kalman filter, which is used to execute the hardware delay dynamic tracking method based on an augmented state extended Kalman filter in the above method embodiments.

[0163] See Figure 2 The system includes: a data collection module, an initialization module, and a dynamic tracking module;

[0164] The data collection module is used to construct a satellite constellation topology map based on historical inter-satellite link observation data, and input the satellite constellation topology map into a pre-trained graph neural network for processing, outputting the initial hardware delay of each satellite in the satellite constellation.

[0165] The initialization module is used to construct the augmented state vector of the satellite, and initializes the augmented state vector with the initial hardware delay of each satellite in the satellite constellation, and initializes the covariance matrix of the augmented state vector; the augmented state vector includes the satellite's orbital state, clock error state and hardware delay value.

[0166] The dynamic tracking module is used to acquire real-time inter-satellite link observation data. Based on the extended Kalman filter algorithm, it iteratively predicts and updates the initialized augmented state vector and its covariance matrix, and outputs the hardware delay value of each satellite in the satellite constellation in real time.

[0167] It should be noted that the system embodiments provided by the present invention are used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is that corresponding functional modules are set. The principle is basically the same as that of the above system embodiments provided by the present invention. As long as those skilled in the art can improve the modules in the above system embodiments by referring to the specific technical solutions in other method embodiments and combining technical features to obtain corresponding technical means and technical solutions composed of these technical means, on the basis of the above system embodiments, and on the premise of ensuring the practicality of the technical solutions, they can obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

[0168] The method in this embodiment of the invention is implemented using a computer device; therefore, it is necessary to describe the relevant computer device. For this purpose, embodiments of the invention provide a computer device, such as... Figure 3 As shown, the computer device includes at least one processor, a communications interface, at least one memory, and a communications bus, wherein the at least one processor, the communications interface, and the at least one memory communicate with each other via the communications bus. The at least one processor invokes logical instructions stored in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0169] Furthermore, when the logical instructions in at least one of the aforementioned memories are implemented as software functional units and sold or used as independent products, they are stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, is embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (a personal computer, server, or network device) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks—various media for storing program code.

[0170] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, located in one place, or distributed across multiple network units. The purpose of this embodiment is achieved by selecting some or all of the modules according to actual needs. Those skilled in the art will understand and implement this without any inventive effort.

[0171] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0172] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0173] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0174] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0175] Based on the same technical concept as the foregoing embodiments, the present invention provides a non-transitory computer-readable storage medium that stores computer instructions that cause the computer to execute a hardware delay dynamic tracking method based on an augmented state extended Kalman filter.

[0176] In summary, this invention discloses a dynamic hardware delay tracking method based on an augmented state extended Kalman filter, belonging to the field of satellite navigation and communication technology. The method includes: acquiring historical inter-satellite link observation data of a satellite constellation, and batch processing the historical inter-satellite link observation data using a graph neural network model to obtain the initial hardware delay value for each satellite in the constellation; constructing an augmented state vector, using the satellite's orbital state, clock bias state, and hardware delay as the state variables to be estimated, and initializing the augmented state vector using the initial hardware delay value; and iteratively predicting and updating the augmented state vector using real-time acquired inter-satellite link observation data. This invention solves the problem of dynamic hardware delay compensation through a two-stage strategy of offline initialization and online tracking.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A hardware delay dynamic tracking method based on an augmented state extended Kalman filter, characterized in that: include, A satellite constellation topology map is constructed based on historical inter-satellite link observation data, and the satellite constellation topology map is input into a pre-trained graph neural network for processing, outputting the initial hardware latency of each satellite in the satellite constellation. An augmented state vector for the satellite is constructed, and the augmented state vector is initialized using the initial hardware delay of each satellite in the satellite constellation, and the covariance matrix of the augmented state vector is initialized; the augmented state vector includes the satellite's orbital state, clock error state, and hardware delay value. Real-time inter-satellite link observation data is acquired, and based on the extended Kalman filter algorithm, the initialized augmented state vector and its covariance matrix are iteratively predicted and updated, outputting the hardware delay value of each satellite in the satellite constellation in real time.

2. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 1, characterized in that, In the satellite constellation topology diagram, nodes represent satellites in the constellation, and edges are dynamic edges that change over time, representing effective inter-satellite link observations between satellites.

3. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 1, characterized in that, The graph neural network employs a spatiotemporal graph convolutional network. It captures the spatial correlation between satellites in the satellite constellation topology graph through graph convolutional layers and captures the temporal autocorrelation of the hardware delay of a single satellite through temporal convolutional layers. The graph neural network performs forward propagation calculations on the input satellite constellation topology graph and outputs the estimated transmit hardware delay and the estimated receive hardware delay of each satellite in the satellite constellation, which serve as the initial hardware delay of each satellite in the satellite constellation.

4. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 1, characterized in that, The graph neural network pre-training process is based on the physical constraint loss function defined by the inter-satellite link observation equation.

5. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 3, characterized in that, In the augmented state vector of the satellite, The orbital state of a satellite refers to its position and velocity parameters in space; The clock bias status of a satellite refers to the clock bias and clock speed parameters of the satellite's onboard clock; The satellite's hardware delay status specifically includes the satellite's launch hardware delay and reception hardware delay. During the initialization process, the launch hardware delay estimate from the initial hardware delay of each satellite in the satellite constellation output by the graph neural network is assigned to the satellite launch hardware delay, and the reception hardware delay estimate is assigned to the reception hardware delay.

6. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 5, characterized in that, The process involves iteratively predicting and updating the initialized augmented state vector and its covariance matrix. For any time step after the initialization time step, whenever a valid inter-satellite link observation value is detected in the received real-time inter-satellite link observation data, the augmented state vector and its covariance matrix of the previous time step of the current time step are iteratively predicted and updated. Otherwise, the augmented state vector and its covariance matrix of the previous time step of the current time step are maintained as the augmented state vector and its covariance matrix of the current time step.

7. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 6, characterized in that, The steps for iteratively predicting and updating the augmented state vector and its covariance matrix from the previous time step at the current time step include: Based on the augmented state vectors of each satellite in the current time step, the predicted pseudorange observations of each inter-satellite link at the current time step are calculated using nonlinear observation equations, and the observation equations for the current time step are also calculated. Subtract the predicted pseudorange observation value of each inter-satellite link from the real-time inter-satellite link observation data of the current time step to generate the observation information sequence of the current time step. Based on the augmented state vector and its covariance matrix of the previous time step, the orbit and clock bias states in the augmented state vector of the current time step are predicted according to the satellite dynamics model and clock bias model. The hardware delay state in the augmented state vector of the current time step is predicted according to the stochastic process model, and the covariance matrix of the augmented state vector is updated accordingly to obtain the predicted augmented state vector and the predicted covariance matrix of the current time step. The Kalman gain for the current time step is calculated using the observed innovation sequence, the predicted covariance matrix, and the observed matrix. Based on the Kalman gain and the observed innovation sequence, the predicted augmented state vector and the predicted covariance matrix for the current time step are optimally corrected, and the updated augmented state vector and covariance matrix for the current time step are output.

8. The hardware delay dynamic tracking method based on augmented state extended Kalman filter as described in claim 7, characterized in that, The mathematical expression of the nonlinear observation equation is as follows: ; In the formula, For identifying the launched satellite in the inter-satellite link, This serves as the identifier for the receiving satellite in the inter-satellite link. express The time step receives the inter-satellite link pseudorange observations of satellite B to the launching satellite A; express The geometric distance between the transmitting satellite A and the receiving satellite B at the time step. express The three-dimensional position vector of satellite A launched at the time step. express The three-dimensional position vector of satellite B is received at the time step; express The satellite clock bias of satellite A launched at the time step; express The time step receives the satellite clock bias of satellite B; c represents the speed of light; express The time step satellite A, as the launcher, experiences hardware delays in its launch channel. express The hardware delay of the receiving channel of time-step satellite B as the receiver; This represents the observation noise and unmodeled error of the inter-satellite link.

9. A hardware delay dynamic tracking system based on an augmented state extended Kalman filter, employing the hardware delay dynamic tracking method based on an augmented state extended Kalman filter as described in any one of claims 1 to 8, characterized in that, include: Data collection module, initialization module, and dynamic tracking module; The data collection module is used to construct a satellite constellation topology map based on historical inter-satellite link observation data, and input the satellite constellation topology map into a pre-trained graph neural network for processing, outputting the initial hardware delay of each satellite in the satellite constellation. The initialization module is used to construct the augmented state vector of the satellite, and initializes the augmented state vector with the initial hardware delay of each satellite in the satellite constellation, and initializes the covariance matrix of the augmented state vector; the augmented state vector includes the satellite's orbital state, clock error state and hardware delay value. The dynamic tracking module is used to acquire real-time inter-satellite link observation data. Based on the extended Kalman filter algorithm, it iteratively predicts and updates the initialized augmented state vector and its covariance matrix, and outputs the hardware delay value of each satellite in the satellite constellation in real time.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the hardware delay dynamic tracking method based on an augmented state extended Kalman filter according to any one of claims 1 to 8.

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