Pseudo-range prediction correction-based factor graph optimization Beidou inertial navigation positioning method and system

Abstract

The invention discloses a Beidou inertial navigation positioning method and system based on pseudo-range prediction correction factor graph optimization, and the method comprises the steps: obtaining observation feature data and inertial navigation data, and constructing a current navigation state vector of a vehicle; according to the signal state of the Beidou satellite navigation system, training a reinforcement learning model through observation characteristic data and inertial navigation data, and determining a pseudo-range value; according to a factor graph optimization method, introducing a pseudo-range value as an observation factor, and converting a navigation state vector of the vehicle at the current moment into a multi-factor constrained optimal problem; and carrying out global optimal state sequence solution on the multi-factor constrained optimal problem through a Levenberg-Marquardt algorithm by adopting nonlinear least square optimization, so as to obtain a positioning estimation result of the vehicle. According to the invention, dynamic complementation and intelligent cooperation of Beidou and inertial navigation information can be realized, and the precision of positioning estimation is improved. The Beidou inertial navigation positioning method and system based on pseudo-range prediction correction factor graph optimization can be widely applied to the technical field of satellite positioning.

Description

Technical Field

[0001] The present invention relates to the field of satellite positioning technology, and in particular to a Beidou inertial navigation positioning method and system based on factor graph optimization of pseudorange prediction and correction. Background Art

[0002] In current navigation and positioning systems, the fusion of the BeiDou Navigation Satellite System (BDS) and the Inertial Navigation System (INS) can effectively complement each other and maintain system continuity and robustness in complex environments. In the BDS / INS fusion system, the BDS serves as the primary external measurement source, and its observation accuracy directly determines the overall accuracy and stability of the fused positioning. In BDS observations, pseudorange is the most basic and important observation quantity, directly used to calculate absolute position. Its measurement quality is crucial to overall navigation accuracy and continuity and is a key factor in determining the system's positioning accuracy. However, in typical BDS signal-denial environments such as urban canyons, tunnels, and underground spaces, the signal is extremely susceptible to obstruction and interference, resulting in the failure of pseudorange observations or a significant increase in errors, which in turn leads to reduced positioning accuracy and even navigation interruption.

[0003] In related technologies, research has explored the use of deep learning to predict and correct pseudorange errors and interruptions. Typical work, such as PrNet, uses convolutional neural networks to learn the mapping relationship between pseudorange errors and raw observation data, achieving prediction and correction of pseudoranges and achieving good results on Android raw measurement data. However, methods such as PrNet rely on static feature extraction and lack modeling of the system's dynamic state. This leads to weak generalization and stability in complex dynamic environments, and makes it difficult to ensure real-time performance. This makes it difficult to meet the requirements for high-precision and continuous positioning in satellite signal denial scenarios. Summary of the Invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a Beidou inertial navigation positioning method and system based on pseudorange prediction and correction factor graph optimization, which can realize dynamic complementarity and intelligent collaboration of Beidou and inertial navigation information and improve the accuracy of positioning estimation.

[0005] The first technical solution adopted by the present invention is: a BeiDou inertial navigation positioning method optimized based on a factor graph of pseudorange prediction correction, comprising the following steps:

[0006] Obtain observation feature data and inertial navigation data, and construct the vehicle's current navigation state vector;

[0007] According to the signal status of the BeiDou satellite navigation system, the reinforcement learning model is trained by observing feature data and inertial navigation data to determine the pseudorange value;

[0008] According to the factor graph optimization method, the pseudo-range value is introduced as the observation factor, and the vehicle's current navigation state vector is transformed into an optimal problem with multiple factor constraints.

[0009] Nonlinear least squares optimization is adopted to solve the optimal problem with multiple factor constraints through the Levenberg-Marquardt algorithm to obtain the global optimal state sequence and obtain the vehicle positioning estimation result.

[0010] Furthermore, the step of obtaining the observation feature data and the inertial navigation data and constructing the vehicle's current navigation state vector specifically includes:

[0011] Collecting observation characteristic data of the BeiDou satellite navigation system through a BDS receiver, the observation characteristic data including pseudorange, signal-to-noise ratio and altitude angle of visible satellites;

[0012] Acquiring inertial navigation data of an inertial navigation system through an inertial measurement unit, wherein the inertial navigation data includes a current speed of the vehicle, a current posture of the vehicle, and a current acceleration of the vehicle;

[0013] Obtain the historical state sequence of the vehicle, combine the current position, speed and posture of the vehicle, and construct the navigation state vector of the vehicle at the current moment.

[0014] Furthermore, the step of determining the pseudorange value by training a reinforcement learning model based on the signal state of the Beidou satellite navigation system by observing the feature data and the inertial navigation data specifically includes:

[0015] The reinforcement learning model is trained by observing feature data and inertial navigation data to obtain a trained reinforcement learning model;

[0016] If the signal status of the BeiDou satellite navigation system is interrupted, the pseudorange prediction is performed using the trained reinforcement learning model, and the pseudorange prediction result is used as the pseudorange value;

[0017] If the signal status of the BeiDou satellite navigation system is normal, the true pseudorange observation value is corrected through the trained reinforcement learning model, and the corrected true pseudorange observation value is used as the pseudorange value.

[0018] Furthermore, the step of training the reinforcement learning model by observing the feature data and the inertial navigation data to obtain the trained reinforcement learning model specifically includes:

[0019] Define the interaction framework between the agent and the navigation system, with the preset pseudorange prediction accuracy as the optimization goal;

[0020] Constructing a multidimensional observation space, the observation space including observation feature data, inertial navigation data, and vehicle historical position features;

[0021] Constructing an action space, wherein the action space represents a vector of predicted pseudoranges for each satellite, and minimizing the difference between the predicted pseudorange and the true pseudorange is used as a reward function;

[0022] Based on the pseudoranges of visible satellites of the Beidou satellite navigation system collected as supervision signals, combined with the multi-dimensional observation space, action space and reward function as the experience pool, the strategy optimization direction is calculated through generalized advantage estimation, and the policy network and evaluation network parameters are iteratively updated until the preset pseudorange prediction accuracy is met, and the trained reinforcement learning model is output.

[0023] Furthermore, the expression of the reward function is specifically as follows:

[0024]

[0025] In the above formula, r t represents the reward function, represents the prediction result of the agent for the pseudorange of the i-th satellite at time t, It represents the true pseudo-range observation of the satellite, and S represents the number of visible satellites at the current moment.

[0026] Furthermore, the step of introducing the pseudorange value as an observation factor and converting the vehicle's current navigation state vector into an optimal problem with multiple factor constraints according to the factor graph optimization method specifically includes:

[0027] Define system state variables as state nodes in the factor graph, where the system state variables include navigation information of the vehicle's position, velocity, and posture at time k;

[0028] Constructing a multi-source observation factor, wherein the multi-source observation factor includes a motion factor, an inertial measurement unit (INS) factor, and a Beidou pseudorange observation factor. The motion factor represents a state variable connecting consecutive moments. The inertial measurement unit (INS) factor includes the vehicle's current speed and acceleration provided by the inertial measurement unit (IMU). The Beidou pseudorange observation factor represents a pseudorange value.

[0029] Combining system state variables with multi-source observation factors, a factor graph model is constructed;

[0030] According to the factor graph model, the vehicle's current navigation state vector is transformed into an optimal problem with multiple factor constraints.

[0031] Furthermore, the expression of the optimal problem of multi-factor constraints is specifically as follows:

[0032]

[0033] In the above formula, X * represents the objective function, represents the pseudorange observation error term of the i-th satellite at the k-th time, represents the motion model factor error, represents the INS factor error, They represent the covariance matrices of the corresponding factors.

[0034] The second technical solution adopted by the present invention is: optimizing the BeiDou inertial navigation positioning system based on a factor graph of pseudorange prediction correction, including:

[0035] The first module is used to obtain observation feature data and inertial navigation data, and construct the vehicle's current navigation state vector;

[0036] The second module is used to determine the pseudorange value by training the reinforcement learning model through observing feature data and inertial navigation data according to the signal status of the Beidou satellite navigation system;

[0037] The third module is used to introduce pseudo-range values ​​as observation factors based on the factor graph optimization method to transform the vehicle's current navigation state vector into an optimal problem with multiple factor constraints;

[0038] The fourth module is used to use nonlinear least squares optimization to solve the optimal problem with multiple factor constraints through the Levenberg-Marquardt algorithm to obtain the global optimal state sequence and obtain the vehicle positioning estimation result.

[0039] The beneficial effects of the method and system of the present invention are as follows: the present invention obtains observation feature data and inertial navigation data, and constructs the navigation state vector of the vehicle at the current moment, further trains a reinforcement learning model based on the signal state of the Beidou satellite navigation system through the observation feature data and inertial navigation data, determines the pseudorange value, takes the current state information of the navigation system as input, trains a strategy network model through the reinforcement learning method, and predicts the pseudorange observation value of the currently visible Beidou satellite in real time, which is used as the "pseudo-observation input" in the case of Beidou signal interruption, forming an intelligent compensation mechanism for Beidou observation loss, and further introduces the pseudorange value as the observation factor according to the factor graph optimization method. The vehicle's current navigation state vector is converted into an optimal problem with multiple factor constraints. The Beidou pseudorange value predicted by reinforcement learning is introduced into the factor graph optimization framework to construct the Beidou pseudorange factor. It acts together with the INS factor on the navigation state node to form a sparse graph structure, realizing the cross-time fusion of Beidou / INS multi-source observations. Finally, nonlinear least squares optimization is adopted to solve the optimal problem with multiple factor constraints through the Levenberg-Marquardt algorithm to obtain the global optimal state sequence and obtain the vehicle's positioning estimation result, realizing the dynamic complementarity and intelligent collaboration of Beidou and inertial navigation information, and improving the accuracy of positioning estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flowchart of the steps of the Beidou inertial navigation positioning method based on the factor graph of pseudorange prediction correction of the present invention;

[0041] Figure 2 It is a structural block diagram of the BeiDou inertial navigation positioning system optimized based on the factor graph of pseudorange prediction correction of the present invention;

[0042] Figure 3 It is a structural diagram of a factor graph model provided by a specific embodiment of the present invention;

[0043] Figure 4 It is a schematic diagram of a BeiDou inertial navigation positioning method provided by a specific embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0045] First, it's important to note that the fusion of the BeiDou Navigation Satellite System (BDS) and the Inertial Navigation System (INS) is currently widely used in intelligent vehicles, unmanned systems, and robotic navigation. The BDS provides high-precision global spatiotemporal information, while the INS, through its inertial measurement unit, independently provides continuous navigation solutions in a short period of time. The two complement each other to achieve stable, high-precision integrated navigation. However, this fusion approach faces significant challenges in practical applications, particularly in environments where the BDS signal is unavailable or degraded, such as in urban areas with tall buildings (urban canyons), tunnels, and underground garages. The BDS signal is highly susceptible to obstruction, interference, and reflections, leading to signal loss, interruption, or even complete denial. During BDS outages, the fused system degenerates to relying solely on INS navigation. Due to the integral drift characteristic of the INS, errors accumulate rapidly over time, ultimately causing the navigation solution to deviate significantly from the true position, compromising system stability and accuracy.

[0046] In addition, in recent years, Factor Graph Optimization (FGO) has gradually become an important method in fusion positioning. It achieves the optimal estimation of the global trajectory by modeling the graph structure constraint relationship between state quantities and observation quantities. Compared with traditional filters, FGO can effectively utilize historical information and perform global optimization, thereby enhancing the accuracy and robustness of the positioning system.

[0047] However, existing technologies often suffer from the following problems when GNSS (including BeiDou Satellite Navigation System) signals are unavailable or interrupted:

[0048] 1) Although pseudorange prediction or position increment prediction methods based on deep neural networks (such as PrNet or LSTM incremental prediction) have achieved certain results in static or simple scenarios through end-to-end learning, they generally rely on large-scale, scenario-specific training data, resulting in poor generalization and weak adaptability to dynamic environments. Furthermore, such methods often ignore the dynamic evolution of system states and only fit static features, making them difficult to handle in complex dynamic environments such as urban canyons and sharp turns. Furthermore, some methods output position increments or residuals, which lack the physical rationality of observation constraints when directly involved in state estimation, resulting in limited global accuracy.

[0049] 2) Error modeling methods based on filtering frameworks, such as the improved extended Kalman filter or adaptive filtering methods, usually jointly estimate GNSS measurement residuals through weight adjustment or state update. However, such methods are highly dependent on the prior knowledge of the system noise characteristics, and the filtering structure is a recursive estimation method that can only use information from the current and previous moments. It cannot fully explore the deep connection between the historical state of long time series and multi-source information, resulting in unstable estimation results and significant errors when GNSS is completely interrupted.

[0050] Based on this, an embodiment of the present invention proposes a Beidou inertial navigation positioning method based on factor graph optimization of pseudorange intelligent prediction and correction. In the normal stage of the BDS signal, the nonlinear mapping relationship between the navigation state (position, speed, INS data) and the BDS pseudorange is dynamically learned through the reinforcement learning model, which is used to correct the original pseudorange online and improve the observation accuracy; at the same time, the strategy is continuously updated to adapt to environmental changes. When the BDS signal is interrupted, the system calls the trained model to predict the pseudorange observation value at the current moment, and introduces the prediction result as the BDS pseudorange factor into the factor graph optimization framework, and jointly models it with factors such as INS observations to complete the global optimization of the system state. This solution combines the dynamic modeling capability of reinforcement learning and the multi-constraint optimization capability of factor graphs to achieve high-precision, high-continuity and high-robustness navigation and positioning in complex BDS-denied environments.

[0051] Reference Figure 1 and Figure 4 The present invention provides a BeiDou inertial navigation positioning method based on factor graph optimization of pseudorange prediction correction, which includes the following steps:

[0052] S100, obtaining observation feature data and inertial navigation data, and constructing the vehicle's current navigation state vector;

[0053] Specifically, the observation feature data of the Beidou satellite navigation system is collected through the BDS receiver, and the observation feature data includes the pseudorange, signal-to-noise ratio and altitude angle of the visible satellites; the inertial navigation data of the inertial navigation system is obtained through the inertial measurement unit, and the inertial navigation data includes the current speed, current posture and current acceleration of the vehicle; the historical state sequence of the vehicle is obtained, and the navigation state vector of the vehicle at the current moment is constructed by combining the current position, current speed and current posture of the vehicle.

[0054] In this embodiment, raw data is acquired through a BDS receiver and inertial measurement unit (IMU). This data includes satellite characteristics such as pseudorange, signal-to-noise ratio, and altitude angle for each visible satellite, as well as INS characteristics such as the vehicle's current velocity, attitude, and acceleration. The current navigation state vector, consisting of position, velocity, attitude, and a historical state sequence, is used for RL state input and factor graph state node modeling.

[0055] S200, according to the signal status of the Beidou satellite navigation system, training a reinforcement learning model by observing feature data and inertial navigation data to determine a pseudorange value;

[0056] Specifically, a reinforcement learning model is trained by observing feature data and inertial navigation data to obtain a trained reinforcement learning model; if the signal state of the Beidou satellite navigation system is an interrupted state, the pseudorange prediction is performed through the trained reinforcement learning model, and the pseudorange prediction result is used as the pseudorange value; if the signal state of the Beidou satellite navigation system is normal, the true pseudorange observation value is corrected through the trained reinforcement learning model, and the corrected true pseudorange observation value is used as the pseudorange value.

[0057] Among them, it should be noted that for the training of the reinforcement learning model, the interaction framework between the intelligent agent and the navigation system is first defined, with the preset pseudorange prediction accuracy as the optimization target; a multidimensional observation space is constructed, which includes observation feature data, inertial navigation data and vehicle historical position characteristics; an action space is constructed, which represents a vector composed of pseudorange prediction quantities of each satellite, and minimizing the gap between the predicted pseudorange and the actual pseudorange is used as the reward function; based on the collected pseudoranges of the visible satellites of the Beidou satellite navigation system as supervision signals, the multidimensional observation space, action space and reward function are combined as the experience pool, the strategy optimization direction is calculated through generalized advantage estimation, the policy network and evaluation network parameters are iteratively updated until the preset pseudorange prediction accuracy is met, and the trained reinforcement learning model is output.

[0058] In this embodiment, the system determines in real time whether the current BDS signal is interrupted. If it is, the system directly uses the real pseudorange observations and uses the data from this phase to continuously train and update the RL model policy network. The RL output also assists in correcting the pseudorange observations. If it is interrupted, the system uses the trained RL model to perform pseudorange predictions instead of real observations.

[0059] To achieve pseudorange compensation prediction for the BeiDou satellite navigation system in signal-interrupted or restricted environments, the present invention designed and trained a pseudorange prediction model based on reinforcement learning (RL). This model takes the current state of the navigation system as input and outputs pseudorange estimates of currently visible satellites, which are introduced into a factor graph optimization framework as pseudo-observation factors.

[0060] The training of reinforcement learning models specifically includes:

[0061] 1) Construction of learning environment:

[0062] The agent interacts with the environment, aiming to learn a pseudorange prediction strategy that maximizes cumulative reward. The environment state consists of the vehicle's navigation state and visible satellite information. The agent outputs a pseudorange estimate for the currently visible satellites, receiving the difference between the estimated pseudorange and the true pseudorange as a reward. This sequence of state, action, and reward constitutes a reinforcement learning triplet, ultimately achieving more accurate pseudorange estimation through policy optimization.

[0063] 2) Construction of observation space:

[0064] The construction of the observation space aims to reflect the navigation status of the vehicle in a complex environment. It mainly integrates multi-dimensional information from satellite observations, historical trajectories, and inertial navigation systems, specifically including the following three types of observation features.

[0065] First, satellite observation features provide key information about the quality and spatial geometry of current BDS observations. These features, including pseudorange, satellite carrier-to-noise ratio (C / N0), and elevation angle, reveal the stability and availability of satellite signals. These features are crucial for analyzing the sources of BDS pseudorange errors and also support policy adjustments in reinforcement learning.

[0066] Secondly, historical position features are used to characterize the evolution of navigation status. By introducing the position difference between the predicted position and the historical trajectory points, the vehicle's inertia and path continuity can be captured, thereby improving the ability to identify dynamic changes in the current state and facilitating the generation of more stable pseudorange estimates.

[0067] Finally, inertial navigation observation features are derived from the output data of the vehicle's inertial navigation system and reflect the vehicle's own dynamic characteristics. These features include triaxial velocity, angular velocity, acceleration, and attitude angles (such as pitch, roll, and heading). They can effectively supplement the state representation when BDS observations are insufficient, providing redundant information support in the event of signal interruption or obstruction.

[0068] 3) Action space construction:

[0069] The action space A represents the predicted output of the agent. In this invention, the action is a vector of estimated values ​​of pseudoranges of all currently visible satellites. Assume that at time step t, the agent is based on the current state o t Output action a t , which represents the predicted pseudorange values ​​of all visible satellites.

[0070] Assume that at the current time t, S satellites can be observed, then the action It is represented as a vector of pseudorange predictions for each satellite, namely:

[0071]

[0072] in, represents the agent's prediction of the pseudorange of the i-th satellite at time t. This prediction will be introduced as a pseudorange observation factor in the subsequent factor graph optimization to fill the observation gap caused by the lack of real BDS observation signals.

[0073] 4) Reward function design:

[0074] In order to accurately evaluate the effectiveness of the pseudorange prediction action, the prediction error is used as the reward function. Its goal is to minimize the gap between the predicted pseudorange and the actual pseudorange, encouraging the agent to learn to output more accurate pseudorange values. This reward function describes the degree of fit between the model pseudorange output and the actual observation, and is defined as follows:

[0075]

[0076] in, represents the prediction result of the agent for the pseudorange of the i-th satellite at time t, represents the true pseudorange observation of the satellite, and S is the number of visible satellites at the current moment. The negative sign indicates that the smaller the pseudorange error, the greater the reward, thereby guiding the agent to learn a more accurate prediction strategy.

[0077] 5) Model training and deployment:

[0078] During the training phase, the model is pre-trained on trajectory data. First, the receiver collects pseudorange data sequences from multiple visible satellites during the BDS's normal operating hours, along with navigation state information such as velocity, acceleration, and angular velocity provided by the inertial navigation system. This data is used to construct the observed state characteristics at each moment. Based on this, the true pseudoranges are used as supervisory signals to construct a reward function to guide the reinforcement learning agent in updating its strategy.

[0079] This paper employs an agent-based architecture to evaluate and output actions separately, and employs a policy gradient method to train the agent. During training, an experience pool is constructed to store trajectory segments, including information such as state, action, reward, and next state. The advantage function is then calculated based on generalized advantage estimation to guide the agent in optimizing the policy network and evaluation network.

[0080] Ultimately, the model converges the reinforcement learning network parameters by minimizing the error between the predicted and true pseudoranges. After training, the model is deployed to the pseudorange prediction module. When the BDS signal fails, the system invokes the trained policy network to predict the pseudorange estimates for each visible satellite, which serve as the pseudo-observation input to the factor graph optimization system, maintaining navigation continuity.

[0081] S300, according to the factor graph optimization method, introducing the pseudo-range value as the observation factor, and converting the vehicle's current navigation state vector into an optimal problem with multiple factor constraints;

[0082] Specifically, system state variables are defined and used as state nodes in a factor graph. The system state variables include navigation information of the vehicle's position, speed and posture at time k. A multi-source observation factor is constructed. The multi-source observation factor includes a motion factor, an inertial measurement unit (INS) factor and a Beidou pseudo-range observation factor. The motion factor represents the state variables connecting consecutive moments. The inertial measurement unit (INS) factor includes the vehicle's current speed and acceleration provided by an inertial measurement unit (IMU). The Beidou pseudo-range observation factor represents the pseudo-range value. A factor graph model is constructed by combining the system state variables and the multi-source observation factors. According to the factor graph model, the vehicle's navigation state vector at the current moment is converted into an optimal problem with multi-factor constraints.

[0083] In this embodiment, the system constructs an FGO framework and models the navigation state estimation as an optimization problem in a sparse graph structure, where the state node represents the navigation state.

[0084] This paper uses Factor Graph Optimization (FGO) to achieve tightly coupled navigation state estimation between inertial navigation and reinforcement learning-based predicted pseudorange observations. FGO models the navigation state and various observations using a graph structure. Using nonlinear least-squares optimization, it achieves continuous, stable, and highly accurate global positioning estimation even in incomplete observation scenarios, such as BDS signal interruptions.

[0085] To describe the continuous motion of the vehicle during navigation, the system defines a state vector, which includes navigation information such as the vehicle's position, velocity, and attitude at time k. This state vector serves as a state node in the factor graph and is used for subsequent constraints and state estimation of various observation factors.

[0086] Construct a factor graph model, the factor graph structure is as follows Figure 3 As shown in Figure 1, it consists of multiple state nodes and observation factors. Each node represents the state variable of the navigation system at a specific moment, and different types of factors are used to describe the dynamic constraints between state nodes or the observational relationships between them and the observed variables. By constructing a sparse graph structure and performing nonlinear least-squares optimization on the entire graph, the system can simultaneously integrate inertial measurement information with BeiDou satellite system observation information (including predicted pseudoranges), achieving high-precision state estimation on a global scale.

[0087] 1) Motion factor: This factor is used to connect state variables at consecutive moments and establish a priori dynamic model of the system state evolution over time. A constant velocity model is usually used to improve the continuity and smoothness of trajectory estimation and reduce state jumps.

[0088] 2) Inertial Navigation (INS) Factor: This factor, based on the acceleration and angular velocity data provided by the inertial measurement unit (IMU), provides short-term, high-frequency navigation compensation during brief BDS outages. By introducing an error function between INS observations and states, it constrains the velocity and attitude changes of the navigation state in the inertial coordinate system, compensating for trajectory drift caused by BDS outages.

[0089] 3) BeiDou Pseudorange Observation Factor: This factor constrains the residual between the current position and the pseudorange observed or predicted by the BeiDou receiver. When the BeiDou signal is available, the factor is constructed directly using the corrected pseudorange. When the BeiDou signal is unavailable, a reinforcement learning model is used to predict pseudorange observations in real time and construct the pseudorange factor. This provides continuous external observation constraints on the navigation state, improving global positioning accuracy and continuity.

[0090] S400 uses nonlinear least squares optimization and Levenberg-Marquardt algorithm to solve the optimal problem with multiple factor constraints in the global optimal state sequence and obtain the vehicle positioning estimation result.

[0091] In this embodiment, after constructing the factor graph optimization structure, the navigation state estimation problem is transformed into a nonlinear least squares optimization problem under multi-factor constraints. In the tightly coupled FGO modeling framework, the system state sequence X = {x1, x2, ..., x k It consists of multiple state nodes. Various observations are introduced into the graph in the form of factors, which ultimately form the objective function, which is expressed as:

[0092]

[0093] in, represents the pseudorange observation error term of the i-th satellite at the k-th time, which is derived from the corrected BDS observation when the BDS signal is available and is replaced by the pseudorange value predicted by the reinforcement learning model when the signal is interrupted; Represents the motion model factor error, which is used to describe the prior constraints between adjacent states; Represents the INS factor error, reflecting the constraint relationship between acceleration measurement and state transformation; are the covariance matrices of the corresponding factors, which are used to regulate the weights of the factors on the optimization results.

[0094] Using the Levenberg-Marquardt algorithm for nonlinear least squares optimization, the system outputs a positioning estimate. Ultimately, the system outputs an optimal state estimate, including position, velocity, and attitude. The system outputs an optimized state sequence, including position, velocity, and attitude, maintaining high accuracy, continuity, and robustness in complex environments.

[0095] In summary, the embodiment of the present invention proposes a factor graph optimization Beidou inertial navigation positioning method based on pseudorange intelligent prediction and correction, which is intended to solve the problem of navigation accuracy decline and positioning failure caused by Beidou system signal obstruction and interruption in complex environment. The method combines the advantages of Beidou system high frequency multi-star, observation redundancy, etc., and in the normal signal stage, dynamically learns the nonlinear mapping relationship between navigation state (such as position, speed, INS observation, etc.) and Beidou pseudorange observation through reinforcement learning model, realizes modeling and real-time correction of pseudorange error, and improves original pseudorange quality and system stability. When Beidou signal is unavailable due to typical rejection environments such as urban obstruction and tunnel obstruction, the system calls the reinforcement learning model trained, predicts the pseudorange observation value of each satellite online according to the current navigation state, and introduces it into the factor graph optimization framework as Beidou pseudorange factor. By jointly modeling with multi-source information such as inertial navigation data (INS factor) and motion model factor, global optimization solution is performed, and continuous and high-precision state estimation result is output.

[0096] Therefore, the embodiments of the present invention have the following differences compared to the prior art:

[0097] 1) Construct a reinforcement learning pseudorange prediction model for Beidou navigation. This embodiment of the present invention takes the current state information of the navigation system as input, trains a policy network model through reinforcement learning, and predicts the pseudorange observation values ​​of the currently visible Beidou satellites in real time. This is used as the "pseudo-observation input" when the Beidou signal is interrupted, forming an intelligent compensation mechanism for Beidou observation loss.

[0098] 2) Based on factor graph optimization of joint modeling of Beidou pseudorange factor and INS factor, the embodiment of the present invention uses the Beidou pseudorange value predicted by reinforcement learning and introduces it into the factor graph optimization framework to construct the Beidou pseudorange factor. It acts together with the INS factor on the navigation state node to form a sparse graph structure, realizes the cross-time fusion of Beidou / INS multi-source observations, and improves the continuity and robustness of state estimation.

[0099] 3) Collaborative fusion mechanism of reinforcement learning and factor graph optimization. The embodiment of the present invention proposes a collaborative fusion mechanism that combines a reinforcement learning model with a factor graph optimization system. The basic idea is: when the BDS signal is normal, the system uses historical navigation data to train the reinforcement learning model to learn the relationship between the system state and the pseudorange; when the BDS signal is unavailable, the system will call the trained reinforcement learning model to predict the pseudorange at the current moment based on the current position, speed and INS information; the predicted pseudorange is introduced into the factor graph optimization as a pseudorange factor, and participates in state estimation together with factors such as INS and motion model. This fusion mechanism enables the reinforcement learning module to supplement the observation information, and the factor graph module to fuse the optimized state results. The two work together to complete highly robust navigation and positioning in complex environments.

[0100] 4) Supporting Beidou's robust continuous positioning in complex BDS-denied environments. By constructing a "Beidou pseudorange learnable observation + factor graph modeling + multi-source information fusion" solution, the embodiments of the present invention solve the problem of traditional methods' reduced or ineffective positioning capabilities in scenarios such as weak BDS signals, jumps, and interruptions. In particular, it has high stability and positioning accuracy in typical BDS-denied environments such as urban canyons, underground spaces, tunnels, and forests.

[0101] Compared with the prior art, the embodiments of the present invention have the following advantages:

[0102] 1) Reinforcement learning predicts BeiDou pseudoranges, providing a more generalizable solution to missing observations. Compared to deep neural network-based approaches that directly predict position deviations or state increments, the reinforcement learning model designed in this paper directly outputs pseudorange observations through policy learning. This model can more flexibly respond to different trajectory states and environmental disturbances, possessing a certain degree of generalization capability. It is particularly suitable for predicting observation information with strong physical interpretability, such as pseudoranges, effectively improving the system's robust compensation for missing BDS observations.

[0103] 2) A factor graph optimization method is used to improve global consistency and accuracy. Traditional filtering methods are mainly based on recursive estimation, which makes it difficult to fully utilize historical information and is prone to error accumulation after a brief interruption of the Beidou signal. In contrast, based on the factor graph optimization framework, this paper jointly models the Beidou pseudorange factors predicted by reinforcement learning and the INS factors. It globally optimizes the multi-time state within a sliding window, fully utilizing the geometric constraints of the Beidou pseudorange and the continuity of the INS, effectively improving trajectory accuracy and temporal consistency.

[0104] 3) A BeiDou Inertial Navigation (INS) collaborative architecture ensures stability in complex scenarios. This embodiment of the present invention builds a collaborative fusion architecture combining reinforcement learning for BeiDou pseudorange prediction, BeiDou pseudorange factoring, and INS inertial navigation modeling. This architecture enables dynamic complementarity and intelligent collaboration between BeiDou and INS information. High-precision, continuous positioning performance is maintained in typical BeiDou signal-denied environments, such as urban canyons, tunnels, and underground spaces, significantly outperforming traditional solutions.

[0105] Reference Figure 2 , based on pseudorange prediction and correction factor graph optimization BeiDou inertial navigation positioning system, including:

[0106] The first module 201 is used to obtain observation feature data and inertial navigation data, and construct the vehicle's current navigation state vector;

[0107] The second module 202 is used to determine the pseudorange value by training the reinforcement learning model through observing the feature data and the inertial navigation data according to the signal status of the Beidou satellite navigation system;

[0108] The third module 203 is used to introduce the pseudo-range value as an observation factor according to the factor graph optimization method to transform the vehicle's current navigation state vector into an optimal problem with multiple factor constraints;

[0109] The fourth module 204 is used to use nonlinear least squares optimization to solve the optimal problem with multiple factor constraints by using the Levenberg-Marquardt algorithm to obtain a global optimal state sequence and obtain a vehicle positioning estimation result.

[0110] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0111] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A BeiDou inertial navigation positioning method optimized based on pseudorange prediction and correction factor graph is characterized in that: The following steps are involved: Obtain observation feature data and inertial navigation data, and construct the vehicle's current navigation state vector; According to the signal status of the BeiDou satellite navigation system, the reinforcement learning model is trained by observing feature data and inertial navigation data to determine the pseudorange value; According to the factor graph optimization method, the pseudo-range value is introduced as the observation factor, and the vehicle's current navigation state vector is transformed into an optimal problem with multiple factor constraints. Nonlinear least squares optimization is adopted to solve the optimal problem with multiple factor constraints through the Levenberg-Marquardt algorithm to obtain the global optimal state sequence and obtain the vehicle positioning estimation result.

2. The BeiDou inertial navigation positioning method based on pseudorange prediction and correction factor graph optimization according to claim 1 is characterized in that: The step of obtaining the observation feature data and the inertial navigation data and constructing the vehicle's current navigation state vector specifically includes: Collecting observation characteristic data of the BeiDou satellite navigation system through a BDS receiver, the observation characteristic data including pseudorange, signal-to-noise ratio and altitude angle of visible satellites; Acquiring inertial navigation data of an inertial navigation system through an inertial measurement unit, wherein the inertial navigation data includes a current speed of the vehicle, a current posture of the vehicle, and a current acceleration of the vehicle; Obtain the historical state sequence of the vehicle, combine the current position, speed and posture of the vehicle, and construct the navigation state vector of the vehicle at the current moment.

3. The BeiDou inertial navigation positioning method based on pseudorange prediction and correction factor graph optimization according to claim 2 is characterized in that: The step of determining the pseudorange value by training a reinforcement learning model based on the signal state of the Beidou satellite navigation system by observing feature data and inertial navigation data specifically includes: The reinforcement learning model is trained by observing feature data and inertial navigation data to obtain a trained reinforcement learning model; If the signal status of the BeiDou satellite navigation system is interrupted, the pseudorange prediction is performed using the trained reinforcement learning model, and the pseudorange prediction result is used as the pseudorange value; If the signal status of the BeiDou satellite navigation system is normal, the true pseudorange observation value is corrected through the trained reinforcement learning model, and the corrected true pseudorange observation value is used as the pseudorange value.

4. The BeiDou inertial navigation positioning method based on pseudorange prediction and correction factor graph optimization according to claim 3 is characterized in that: The step of training the reinforcement learning model by observing the feature data and the inertial navigation data to obtain the trained reinforcement learning model specifically includes: Define the interaction framework between the agent and the navigation system, with the preset pseudorange prediction accuracy as the optimization goal; Constructing a multidimensional observation space, the observation space including observation feature data, inertial navigation data, and vehicle historical position features; Constructing an action space, wherein the action space represents a vector of predicted pseudoranges for each satellite, and minimizing the difference between the predicted pseudorange and the true pseudorange is used as a reward function; Based on the pseudoranges of visible satellites of the Beidou satellite navigation system collected as supervision signals, combined with the multi-dimensional observation space, action space and reward function as the experience pool, the strategy optimization direction is calculated through generalized advantage estimation, and the policy network and evaluation network parameters are iteratively updated until the preset pseudorange prediction accuracy is met, and the trained reinforcement learning model is output.

5. The BeiDou inertial navigation positioning method based on pseudorange prediction and correction factor graph optimization according to claim 4 is characterized in that: The expression of the reward function is as follows: In the above formula, r t represents the reward function, represents the prediction result of the agent for the pseudorange of the i-th satellite at time t, It represents the true pseudo-range observation of the satellite, and S represents the number of visible satellites at the current moment.

6. The BeiDou inertial navigation positioning method based on pseudorange prediction and correction factor graph optimization according to claim 5 is characterized in that: The step of introducing the pseudorange value as an observation factor and converting the vehicle's current navigation state vector into an optimal problem with multiple factor constraints according to the factor graph optimization method specifically includes: Define system state variables as state nodes in the factor graph, where the system state variables include navigation information of the vehicle's position, velocity, and posture at time k; Constructing a multi-source observation factor, wherein the multi-source observation factor includes a motion factor, an inertial measurement unit (INS) factor, and a Beidou pseudorange observation factor. The motion factor represents a state variable connecting consecutive moments. The inertial measurement unit (INS) factor includes the vehicle's current speed and acceleration provided by the inertial measurement unit (IMU). The Beidou pseudorange observation factor represents a pseudorange value. Combining system state variables with multi-source observation factors, a factor graph model is constructed; According to the factor graph model, the vehicle's current navigation state vector is transformed into an optimal problem with multiple factor constraints.

7. The BeiDou inertial navigation positioning method based on pseudorange prediction and correction factor graph optimization according to claim 6 is characterized in that: The expression of the optimal problem with multiple factor constraints is specifically as follows: In the above formula, X * represents the objective function, represents the pseudorange observation error term of the i-th satellite at the k-th time, represents the motion model factor error, represents the INS factor error, They represent the covariance matrices of the corresponding factors.

8. The BeiDou inertial navigation positioning system is optimized based on the factor graph of pseudorange prediction correction, characterized in that: Includes the following modules: The first module is used to obtain observation feature data and inertial navigation data, and construct the vehicle's current navigation state vector; The second module is used to determine the pseudorange value by training the reinforcement learning model through observing feature data and inertial navigation data according to the signal status of the Beidou satellite navigation system; The third module is used to introduce pseudo-range values ​​as observation factors based on the factor graph optimization method to transform the vehicle's current navigation state vector into an optimal problem with multiple factor constraints; The fourth module is used to use nonlinear least squares optimization to solve the optimal problem with multiple factor constraints through the Levenberg-Marquardt algorithm to obtain the global optimal state sequence and obtain the vehicle positioning estimation result.

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