A graph-optimized GNSS and IMU integrated navigation method and system

Abstract

This invention discloses a graph-optimized GNSS and IMU integrated navigation method and system, comprising: acquiring first target data and performing a first preprocessing on the first target data, the first preprocessing including at least calculating a first substitution constraint; establishing a first graph optimization model based on the first preprocessed first target data; solving the first graph optimization model; and determining the navigation state based on the solution result. Through graph optimization technology, this invention can effectively fuse IMU and GNSS data, maintaining the stability and accuracy of the navigation system even in the event of GNSS signal interruption or insufficient satellite numbers.

Description

Technical Field

[0001] This invention relates to the field of guide line condition monitoring technology, and in particular to a graph-optimized GNSS and IMU integrated navigation method and system. Background Technology

[0002] Traditional GNSS / IMU integrated navigation methods primarily rely on Kalman filtering (KF) technology. Kalman filtering fuses high-frequency, short-term accurate motion sensor data from the IMU with low-frequency, long-term accurate positioning data from the GNSS through recursive prediction and update steps. However, Kalman filtering is prone to accumulation of estimation errors and degraded system performance when faced with GNSS signal interruptions or insufficient satellite numbers. Furthermore, Kalman filtering is sensitive to outliers (such as pseudorange errors caused by multipath effects), further limiting its effectiveness in complex environments.

[0003] In recent years, graph optimization (GO) methods have gradually become a powerful tool for solving the aforementioned problems. GO represents the navigation system's state and observation data as nodes and edges in a graph, and utilizes batch optimization techniques to simultaneously consider observation information from multiple times and multiple satellites, thereby improving the system's global consistency and robustness. However, traditional graph optimization methods still face challenges such as decreased positioning accuracy and insufficient system stability when encountering GNSS signal loss or satellite obstruction.

[0004] In the field of conductor galloping monitoring, accurate positioning and attitude estimation are crucial for real-time monitoring of conductor status, disaster prevention, and maintaining the stable operation of power systems. Conductors may exhibit complex galloping patterns under the influence of external factors such as wind and temperature changes, placing higher demands on the real-time performance and accuracy of navigation systems. Traditional GNSS / IMU integrated navigation systems, especially in electromagnetic interference-rich galloping monitoring scenarios, suffer from significant noise interference over long periods, exhibiting weak noise immunity and difficulty maintaining high-precision and stable positioning performance, thus affecting the reliability and effectiveness of conductor galloping monitoring. Summary of the Invention

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, the present invention provides a graph-optimized GNSS and IMU integrated navigation method and system that can solve the problems mentioned in the background art.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] In a first aspect, the present invention provides a graph-optimized GNSS and IMU integrated navigation method, comprising: acquiring first target data and performing a first preprocessing on the first target data, the first preprocessing including at least calculating a first substitution constraint; establishing a first graph optimization model based on the first preprocessed first target data; solving the first graph optimization model; and determining the navigation state based on the solution result.

[0009] As a preferred embodiment of the graph-optimized GNSS and IMU integrated navigation method of the present invention, the first graph optimization model includes:

[0010] The first graph optimization model includes a first objective function and a first constraint condition;

[0011] The first objective function is any function that calculates the total cost;

[0012] The first constraint is the first alternative constraint.

[0013] As a preferred embodiment of the graph-optimized GNSS and IMU integrated navigation method described in this invention, the first graph optimization model consists of several nodes and several factors;

[0014] The aforementioned factors constitute the first objective function;

[0015] The nodes include at least the receiver's state vector at different times and the satellite's position vector.

[0016] As a preferred embodiment of the graph-optimized GNSS and IMU integrated navigation method of the present invention, the step of solving the first graph optimization model includes:

[0017] Solving the optimization model of the first figure yields the first increment;

[0018] A first threshold is preset, and the relationship between the first increment and the first threshold is determined.

[0019] Complete the solution based on the judgment result.

[0020] As a preferred embodiment of the graph-optimized GNSS and IMU integrated navigation method of the present invention, wherein: the first objective function includes at least an IMU factor, a GNSS pseudorange factor, and a virtual pseudorange factor;

[0021] The IMU factor connects the receiver states at adjacent time points;

[0022] The GNSS pseudorange factor connects the receiver status with the satellite position at the corresponding time.

[0023] The virtual pseudorange factor connects the receiver status with the predicted satellite position.

[0024] As a preferred embodiment of the graph-optimized GNSS and IMU integrated navigation method of the present invention, the step of acquiring first target data and performing a first preprocessing on the first target data includes:

[0025] The first target data includes at least several pseudorange measurements of the target guideline by satellites at each time point and their rate of change.

[0026] The first preprocessing includes predicting the virtual pseudorange at the next time step based on the pseudorange and pseudorange change rate at the previous time step;

[0027] Virtual pseudorange provides a first alternative constraint when real pseudorange is unavailable.

[0028] As a preferred embodiment of the graph-optimized GNSS and IMU integrated navigation method of the present invention, the first objective function further includes:

[0029] The IMU factor is the IMU error function at a certain moment;

[0030] The GNSS pseudorange factor is a GNSS pseudorange error function of several satellites at a certain moment.

[0031] The virtual pseudorange factor is a virtual pseudorange error function of several satellites at a certain moment.

[0032] Secondly, the present invention provides a graph-optimized GNSS and IMU integrated navigation system, comprising:

[0033] A preprocessing module is used to acquire first target data and perform a first preprocessing on the first target data, wherein the first preprocessing includes at least calculating a first substitution constraint;

[0034] The model building module is used to build a first graph optimization model based on the first preprocessed first target data;

[0035] The solution module is used to solve the optimization model of the first graph and determine the navigation state based on the solution results.

[0036] Thirdly, the present invention provides an electronic device, comprising:

[0037] Memory and processor;

[0038] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the method.

[0039] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0040] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention proposes a graph-optimized GNSS and IMU integrated navigation method and system, which acquires first target data and performs a first preprocessing on the first target data, the first preprocessing including at least calculating a first substitution constraint; establishing a first graph optimization model based on the first preprocessed first target data; solving the first graph optimization model; and determining the navigation state based on the solution results. Through graph optimization technology, this invention can effectively integrate IMU and GNSS data, maintaining the stability and accuracy of the navigation system even when GNSS signals are interrupted or the number of satellites is insufficient. The system of this invention has stronger robustness when facing outliers, such as pseudorange errors caused by multipath effects, reducing sensitivity to outliers. In the field of conductor galloping monitoring, the method and system provided by this invention can provide accurate positioning and attitude estimation, which helps to monitor conductor status in real time, prevent disasters, and maintain the stable operation of the power system. The graph-optimized GNSS and IMU integrated navigation method and system of this invention, through improvements in optimization algorithms, improves the application effect in complex environments, especially in the scenario of conductor galloping monitoring with strong electromagnetic interference, and has better noise resistance. The system design of this invention is flexible and can adapt to navigation needs under different environments and conditions, providing new ideas and solutions for the development of navigation technology. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A flowchart illustrating a graph-optimized GNSS and IMU integrated navigation method and system according to an embodiment of the present invention;

[0043] Figure 2 A detailed and feasible flowchart of a graph-optimized GNSS and IMU integrated navigation method and system provided in one embodiment of the present invention. Detailed Implementation

[0044] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0045] Example 1

[0046] Reference Figures 1-2 This is the first embodiment of the present invention, which provides a graph-optimized GNSS and IMU integrated navigation method and system, including:

[0047] Existing technologies have several drawbacks. For example, GNSS signals are easily blocked in environments such as urban canyons, tunnels, or indoors, leading to decreased positioning accuracy. While IMUs (Inertial Measurement Units) can provide continuous motion information, their errors accumulate over time, affecting long-term navigation accuracy. Furthermore, traditional methods often fail to adequately account for the dynamic changes of various error sources when fusing GNSS and IMU data, thus limiting navigation performance.

[0048] This application provides a method that can effectively solve the problems mentioned above. The following will describe in detail how to implement the map-optimized GNSS and IMU integrated navigation method with multiple embodiments.

[0049] Figure 1 A flowchart illustrating a graph-optimized GNSS and IMU integrated navigation method and system is shown, including:

[0050] S101, Obtain first target data and perform first preprocessing on the first target data, the first preprocessing including at least calculating first substitution constraints;

[0051] In this embodiment of the application, obtaining the first target data and performing a first preprocessing on the first target data includes:

[0052] The first target data includes at least several satellite pseudorange measurements of the target guideline and their rate of change at each time point;

[0053] The first preprocessing step includes predicting the virtual pseudorange at the next time step based on the pseudorange and pseudorange change rate at the previous time step.

[0054] Virtual pseudorange provides a first alternative constraint when real pseudorange is unavailable.

[0055] In an optional embodiment, the first target data may further include measurements from the IMU's accelerometer and gyroscope. These measurements are used to estimate the target's motion state, including velocity and attitude information. The IMU data allows for modeling of the target's dynamic changes, thus maintaining navigation continuity and accuracy even when GNSS signals are lost or inaccurate.

[0056] In an optional embodiment, the first preprocessing may further include filtering the IMU data to reduce the impact of noise and errors. The filtering algorithm may be Kalman filtering, extended Kalman filtering, or particle filtering, to suit different application scenarios and accuracy requirements. Filtering can improve the reliability of the IMU data, thereby enhancing the performance of the entire navigation system.

[0057] In an optional embodiment, the first preprocessing may further include correcting for multipath effects on the satellite signal to ensure the accuracy of pseudorange measurements.

[0058] It should be noted that multipath effect correction typically involves complex signal processing techniques, such as spatial correlation analysis or time series analysis. These preprocessing steps work together to provide high-quality data input for subsequent graph optimization processing, ensuring the stability and accuracy of the navigation system.

[0059] In an optional embodiment, predicting the virtual pseudorange for the next moment, based on the pseudorange and pseudorange rate of change of the previous moment, can be achieved by establishing a dynamic model. The dynamic model can predict the future position of the target based on its motion characteristics, such as velocity and acceleration. This prediction method reduces reliance on real-time GNSS signals, thus providing continuous navigation information even in the event of temporary signal loss.

[0060] It should be noted that the prediction model can incorporate historical data and statistical information to improve prediction accuracy. In practical applications, a Kalman filter can be used to integrate the prediction model and observation data to optimize the navigation solution process. In this way, even in the event of unstable or interrupted GNSS signals, the integrated navigation system can maintain high positioning accuracy and reliability.

[0061] In this embodiment of the application, pseudorange measurements of the i-th satellite are collected at each time k. and its rate of change Based on the pseudorange and pseudorange change rate of the previous time step, predict the virtual pseudorange of the next time step. Virtual pseudorange when real pseudorange is unavailable Provide a first alternative constraint;

[0062] It should be noted that acquiring the first target data and performing a first preprocessing on it, including at least calculating a first alternative constraint, can significantly improve the robustness of the system. This first preprocessing effectively reduces pseudorange measurement errors caused by signal obstruction or interference, thereby improving the overall performance of the navigation system. Furthermore, the first preprocessing also includes filtering and noise suppression of the data, ensuring that more accurate and reliable data can be used in subsequent graph optimization processes. This processing not only enhances the system's anti-interference capability but also provides high-quality input data for the graph optimization algorithm, thus maintaining navigation continuity and accuracy even when GNSS signals are unstable or interrupted.

[0063] S102, Establish a first graph optimization model based on the first target data after the first preprocessing;

[0064] In an optional embodiment, the first graph optimization model can be represented using a factor graph, where nodes represent state variables and edges represent observation constraints. In the factor graph, each factor node can be represented as a factor function that maps the connected variable nodes to a non-negative value representing the compatibility between the observed data and the model predictions. The optimal state estimate can be solved by minimizing the product of the factor functions.

[0065] In an optional embodiment, the first graph optimization model may include multiple constraints, such as kinematic constraints, observation constraints, and prior knowledge constraints, to ensure the accuracy and reliability of the navigation solution. In practical applications, the construction of the first graph optimization model needs to consider the balance between computational efficiency and accuracy to adapt to different application scenarios and real-time requirements.

[0066] In this embodiment of the application, the first graph optimization model includes:

[0067] The first graph optimization model includes a first objective function and a first constraint condition;

[0068] The first objective function is any function that calculates the total cost;

[0069] The first constraint is the first alternative constraint.

[0070] In an optional embodiment, the first objective function can employ the least squares method to minimize the difference between the observed data and the model predictions. This approach ensures the accuracy of the navigation solution while reducing computational complexity.

[0071] In an optional embodiment, the first objective function may also include one or more regularization terms to prevent overfitting and enhance the model's generalization ability.

[0072] It should be noted that these regularization terms can be constraints based on prior knowledge, such as limits on velocity or acceleration, to ensure the physical plausibility of the solution. By adjusting the weights of these regularization terms, an optimal balance can be found between the accuracy and stability of the navigation solution.

[0073] In an optional embodiment, the first objective function may further include one or more dynamic noise terms that reflect the dynamic characteristics of the system during actual operation. By introducing dynamic noise terms, the model can better adapt to environmental changes and improve navigation solution performance under complex dynamic conditions.

[0074] In an alternative embodiment, the introduction of dynamic noise terms can also help the model identify and correct anomalous data caused by sensor errors or external interference, thereby improving the robustness of the overall navigation system.

[0075] In this embodiment of the application, the first graph optimization model consists of several nodes and several factors;

[0076] Several factors constitute the first objective function;

[0077] Several nodes include at least the receiver's state vector at different times and the satellite's position vector.

[0078] In the embodiments of this application, the first objective function includes at least an IMU factor, a GNSS pseudorange factor, and a virtual pseudorange factor;

[0079] IMU factors connect the receiver states at adjacent time points;

[0080] The GNSS pseudorange factor connects the receiver status with the satellite position at the corresponding time.

[0081] The virtual pseudorange factor connects the receiver status with the predicted satellite position.

[0082] In this embodiment of the application, the first objective function further includes:

[0083] The IMU factor is the IMU error function at a certain moment;

[0084] The GNSS pseudorange factor is a function of the GNSS pseudorange error of several satellites at a certain moment.

[0085] The virtual pseudorange factor is a function of the virtual pseudorange error of several satellites at a certain moment.

[0086] For example, the nodes and factors of a graph optimization model are constructed, where the nodes include the receiver's state vector x at different times. k and the satellite's position vector P k satThe factors include IMU factor, GNSS pseudorange factor and virtual pseudorange factor. The IMU factor connects the receiver state at adjacent times, the GNSS pseudorange factor connects the receiver state with the satellite position at the corresponding time, and the virtual pseudorange factor connects the receiver state with the predicted satellite position.

[0087] Furthermore, the IMU factor is calculated, which is the IMU error function e at time k. IMU,k ;

[0088] Furthermore, the GNSS pseudorange factor is calculated, which is the GNSS pseudorange error function e of the i-th satellite at time k. GNSS,k,i ;

[0089] Furthermore, the virtual pseudorange factor is calculated, which is the virtual pseudorange error function e of the i-th satellite at time k. VC,k,i ;

[0090] Furthermore, a total cost function is constructed using IMU factor, GNSS pseudorange factor, and virtual pseudorange factor;

[0091] e IMU,k =x k -h(x k-1 ,c k-1 ,z IMU,k-1 )

[0092] Where, x k This represents the state vector of the IMU at time k.

[0093] Where h(·) represents the IMU state transition function; x k-1 c represents the state vector at time k-1; k-1 The z represents the IMU bias at time k-1; IMU,k-1 p represents the IMU measurement at time k-1; k v represents the position vector at time k; k R represents the velocity vector at time k; k b represents the IMU attitude rotation matrix at time k; a,k Indicates the accelerometer deviation at time k; b ω,k This indicates the gyroscope deviation at time k;

[0094] Furthermore, h(·) has the following specific forms:

[0095]

[0096] v k =v k-1 +R k-1 (a k-1 -ba,k-1 )Δt

[0097] R k =R k-1 exp((ω k-1 -b ω,k-1 )Δt)

[0098]

[0099] Where Δt represents the time interval between consecutive moments; exp(·) represents the exponential mapping from the rotation vector to the rotation matrix; and Process noise from accelerometer and gyroscope deviations, respectively, a k-1 ω represents the acceleration measured by the IMU at time k-1; k-1 This represents the angular velocity measured by the IMU at time k-1.

[0100]

[0101] in, b represents the Euclidean distance between the receiver location and the location of the i-th satellite. k This represents the receiver clock offset at time k.

[0102]

[0103] in, The predicted position vector of the i-th satellite at time k.

[0104] Furthermore, the total cost function is constructed using the following method:

[0105]

[0106] Where E represents the total cost function, Σ IMU,k The covariance matrix Σ represents the error function of the IMU. GNSS,k,i The covariance matrix Σ represents the GNSS pseudorange error function. VC,k,i The covariance matrix represents the virtual pseudorange error function.

[0107] It should be noted that establishing a first graph optimization model based on the first target data after the first preprocessing improves the accuracy of data processing. The graph optimization model allows for a more accurate estimation of the sensor's error state. It also optimizes computational efficiency, enabling the first graph optimization model to quickly converge to the optimal solution, reducing computation time. Furthermore, it enhances the system's robustness, maintaining stable navigation performance even in complex environments. Through the iterative process of the graph optimization model, data from different sensors can be effectively fused, improving the overall performance of the navigation system.

[0108] S103, Solve the optimization model of the first diagram, and determine the navigation state based on the solution results.

[0109] In an optional embodiment, the first graph optimization model can be solved using a graph-based optimization algorithm, such as least squares or gradient descent. Through iterative calculation, the optimal solution is gradually approximated, thereby obtaining an estimate of the sensor error state. During the solution process, appropriate convergence conditions, such as an error threshold or an upper limit on the number of iterations, can be set to ensure computational efficiency and accuracy. After the solution is completed, the navigation state can be accurately determined based on the obtained error state estimate, thereby achieving high-precision positioning and navigation.

[0110] In an optional embodiment, the Kalman filter algorithm can also be used to solve the first graph optimization model. This algorithm estimates the system state by establishing a state-space model and combining sensor data with a prediction model. At each time step, the Kalman filter first makes a prediction and then updates it based on new observation data, thus obtaining a more accurate state estimate. This method is particularly suitable for dynamic systems, effectively handling noise and uncertainty, and improving the stability and accuracy of the navigation system. Furthermore, the Kalman filter has high computational efficiency, making it suitable for real-time or near-real-time navigation applications. In this way, the performance of the navigation system can be further improved, ensuring navigation accuracy in various complex environments.

[0111] In an optional embodiment, the first graph optimization model can also be solved using a particle filtering algorithm. This algorithm represents the probability distribution using a series of random samples (particles), each particle representing a possible state of the system. During the filtering process, the particles are resampled based on the observed data and the system model to reflect the latest state information. Particle filters are particularly suitable for nonlinear, non-Gaussian noise systems, providing more flexible and robust navigation solutions. Through particle filtering, complex dynamic environments can be effectively handled, improving the adaptability and accuracy of the navigation system. Furthermore, the parallel processing capability of particle filters gives them good scalability on multi-core processors, further enhancing real-time processing capabilities.

[0112] In this embodiment of the application, solving the optimization model of the first graph includes:

[0113] Solving the optimization model of the first graph yields the first increment;

[0114] A first threshold is preset, and the relationship between the first increment and the first threshold is determined.

[0115] Complete the solution based on the judgment result.

[0116] For example, a Taylor expansion of the total cost function is performed to linearize the total cost function, resulting in the Jacobian matrix J and the residual vector e;

[0117] The weighted Jacobian matrix J is calculated based on the Jacobian matrix J and the residual vector e. w and weighted residual vector e w ;

[0118] Constructing weighted incremental equations

[0119] The conjugate gradient method is used to solve for the state variable increment Δx.

[0120] Check if the norm of the state variable increment Δx is less than a preset threshold. If the norm of the state variable increment Δx is less than the preset value, update the state vector x←x+Δx; otherwise, re-collect data and repeat the overall steps.

[0121] Weighted Jacobian matrix J w The calculation method is as follows:

[0122] J w =Σ -1 / 2 J

[0123] Weighted residual vector e w The calculation method is as follows:

[0124] -1 / 2

[0125] e w =Σe

[0126] in, Σ -1 / 2 It is the inverse square root of the covariance matrix Σ.

[0127] In summary, this invention proposes a graph-optimized GNSS and IMU integrated navigation method. The method acquires first target data and performs a first preprocessing step, which includes at least calculating a first substitution constraint. A first graph optimization model is then established based on the preprocessed first target data. The first graph optimization model is solved, and the navigation state is determined based on the solution results. Through graph optimization technology, this invention effectively integrates IMU and GNSS data, maintaining the stability and accuracy of the navigation system even when GNSS signals are interrupted or the number of satellites is insufficient. The system of this invention exhibits stronger robustness to outliers, such as pseudorange errors caused by multipath effects, reducing sensitivity to outliers. In the field of conductor galloping monitoring, the method and system provided by this invention can provide accurate positioning and attitude estimation, facilitating real-time monitoring of conductor status, disaster prevention, and maintenance of stable power system operation. The graph-optimized GNSS and IMU integrated navigation method and system of this invention, through improvements in optimization algorithms, enhances application performance in complex environments, especially in conductor galloping monitoring scenarios with strong electromagnetic interference, exhibiting better noise resistance. The system design of this invention is flexible and can adapt to navigation needs under different environments and conditions, providing new ideas and solutions for the development of navigation technology.

[0128] Example 2

[0129] In a preferred embodiment, the following specific method steps can be designed based on the above embodiments, such as... Figure 2 As shown:

[0130] Step 1: At each time k, collect the pseudorange measurement value of the i-th satellite. and its rate of change Based on the pseudorange and pseudorange change rate of the previous time step, predict the virtual pseudorange of the next time step. Virtual pseudorange when real pseudorange is unavailable Provide alternative constraints;

[0131] Step 2: Construct the nodes and factors of the graph optimization model. The nodes include the receiver's state vector x at different times. k and the satellite's position vector The factors include IMU factor, GNSS pseudorange factor and virtual pseudorange factor. The IMU factor connects the receiver state at adjacent times, the GNSS pseudorange factor connects the receiver state with the satellite position at the corresponding time, and the virtual pseudorange factor connects the receiver state with the predicted satellite position.

[0132] Step 3: Calculate the IMU factor, which is the IMU error function e at time k. IMU,k ;

[0133] Step 4: Calculate the GNSS pseudorange factor, which is the GNSS pseudorange error function e of the i-th satellite at time k. GNSS,k,i ;

[0134] Step 5: Calculate the virtual pseudorange factor, which is the virtual pseudorange error function e of the i-th satellite at time k. VC,k,i ;

[0135] Step 6: Construct the total cost function using the IMU factor, GNSS pseudorange factor, and virtual pseudorange factor;

[0136] Step 7: Perform a Taylor expansion on the total cost function from Step 6 to linearize the total cost function, and obtain the Jacobian matrix J and the residual vector e;

[0137] Step 8: Calculate the weighted Jacobian matrix J based on the Jacobian matrix J and the residual vector e. w and weighted residual vector e w ;

[0138] Step 9: Construct the weighted incremental equation

[0139] Step 10: Use the conjugate gradient method to solve for the state variable increment Δx;

[0140] Step 11: Check if the norm of the state variable increment Δx is less than a preset threshold. If the norm of the state variable increment Δx is less than the preset value, proceed to step 12; otherwise, proceed to step 1.

[0141] Step 12: Update the state vector x←x+Δx.

[0142] Specifically,

[0143]

[0144] in, This represents the predicted virtual pseudorange. This represents the pseudorange measurement value of the i-th satellite at time k. Let Δt represent the pseudorange change rate of the i-th satellite at time k, and let Δt represent the time interval between consecutive moments. This represents the position vector of the i-th satellite at time k+1. Let v represent the position vector of the receiver at time k, and v represent the velocity vector of the receiver.

[0145] Specifically,

[0146] e IMU,k =x k -h(x k-1 ,c k-1 ,z IMU,k-1 )

[0147] Where, x k This represents the state vector of the IMU at time k.

[0148] h(·) represents the IMU state transition function; x k-1 c represents the state vector at time k-1; k-1 The z represents the IMU bias at time k-1; IMU,k-1 p represents the IMU measurement at time k-1; k v represents the position vector at time k; k R represents the velocity vector at time k; k b represents the IMU attitude rotation matrix at time k; a,k Indicates the accelerometer deviation at time k; b ω,k This indicates the gyroscope deviation at time k;

[0149] In an optional embodiment, h(·) has the following specific form:

[0150]

[0151] v k =v k-1 +R k-1 (a k-1 -b a,k-1 )Δt

[0152] R k =R k-1 exp((ω k-1 -b ω,k-1 )Δt)

[0153]

[0154] Δt represents the time interval between consecutive moments; exp(·) represents the exponential mapping from the rotation vector to the rotation matrix; and Process noise from accelerometer and gyroscope deviations respectively; a k-1 ω represents the acceleration measured by the IMU at time k-1; k-1 This represents the angular velocity measured by the IMU at time k-1.

[0155] Specifically,

[0156]

[0157] in, b represents the Euclidean distance between the receiver location and the location of the i-th satellite. k This represents the receiver clock offset at time k.

[0158] Specifically,

[0159]

[0160] in, The predicted position vector of the i-th satellite at time k.

[0161] Specifically, the total cost function is constructed using the following method:

[0162]

[0163] Where E represents the total cost function, Σ IMU,k The covariance matrix Σ represents the error function of the IMU. GNSS,k,i The covariance matrix Σ represents the GNSS pseudorange error function. VC,k,i The covariance matrix represents the virtual pseudorange error function.

[0164] Specifically, the weighted Jacobian matrix J w The calculation method is as follows:

[0165] J w =Σ -1 / 2 J

[0166] Weighted residual vector e w The calculation method is as follows:

[0167] -1 / 2

[0168] e w =Σe

[0169] in, Σ -1 / 2 It is the inverse square root of the covariance matrix Σ.

[0170] It should be noted that in the scenario of line galloping monitoring, due to the high electromagnetic noise, GNSS often struggles to provide stable, high-precision position information. Although IMU can provide continuous position and attitude updates in a short time, the cumulative error of the IMU, especially the drift phenomenon, becomes increasingly apparent over time. Therefore, it is necessary to combine IMU and GNSS to achieve high-precision, continuous position information updates. However, existing integrated navigation methods do not differentiate the weighting of measurement signals in scenarios with high and low electromagnetic noise, resulting in poor system robustness.

[0171] To address these issues, this invention proposes a graph optimization method based on weighted least squares and introduces virtual pseudorange as a novel constraint mechanism. Specifically, when GNSS pseudorange cannot be acquired normally, the system predicts the virtual pseudorange for the next moment based on the pseudorange and its rate of change from the previous moment, serving as a substitute constraint for the GNSS pseudorange. This mechanism effectively solves the problem of position information interruption caused by limited GNSS signals, thereby improving the robustness and continuity of the system.

[0172] In an optional embodiment, virtual pseudorange predicts pseudorange at future times using known motion information. When GNSS signals are unavailable, virtual pseudorange can serve as a constraint to prevent system position drift. In addition to virtual pseudorange, this invention combines IMU and GNSS pseudorange through a graph optimization framework. Graph optimization methods construct nodes and edges in a graph and utilize the constraint relationships between adjacent nodes to progressively optimize the system state. The graph optimization model of this invention includes the receiver's state vector at different times and the satellite's position vector. The IMU factor, GNSS pseudorange factor, and virtual pseudorange factor describe the IMU error, GNSS pseudorange error, and virtual pseudorange error, respectively, and these factors together constitute the key constraints in the graph optimization model.

[0173] In an optional embodiment, the IMU factor links the receiver state at adjacent time points, describing the state changes of the inertial measurement unit. The GNSS pseudorange factor links the receiver and satellite position states, reflecting the deviation of pseudorange measurements. The virtual pseudorange factor provides compensation through predicted pseudorange when GNSS signals are unavailable, ensuring the continuity of the graph optimization process.

[0174] In an optional embodiment, to improve the system's robustness against errors, a total cost function is constructed, incorporating error terms from IMU, GNSS pseudorange, and virtual pseudorange. A weight matrix controls the impact of different error terms on the system's solution. To optimize the state variables, the conjugate gradient method is employed to solve the weighted incremental equations, significantly accelerating the solution speed for large-scale optimization problems. The application of the conjugate gradient method not only effectively reduces computational complexity but also ensures that the method can achieve efficient solutions with fewer computational resources in practical applications.

[0175] In an optional embodiment, the system updates the state variables iteratively multiple times during the solution process. At the end of each iteration, the norm of the state variable increment is checked to see if it is less than a preset threshold. If the norm of the increment is less than the preset value, the system solution process stops, indicating that the navigation system has reached a stable state. If the increment exceeds the threshold, the system continues iterative optimization until the expected accuracy is achieved. This iterative process ensures that the system maintains stability as it gradually approaches the optimal solution and improves the system's anti-interference capability through weighted error constraints.

[0176] Example 3

[0177] This embodiment also provides a graph-optimized GNSS and IMU integrated navigation system, including:

[0178] A preprocessing module is used to acquire first target data and perform first preprocessing on the first target data, the first preprocessing including at least calculating a first substitution constraint;

[0179] The model building module is used to build a first graph optimization model based on the first preprocessed first target data.

[0180] The solution module is used to solve the optimization model of the first diagram and determine the navigation state based on the solution results.

[0181] The above-mentioned unit modules can be embedded in the processor of the computer device in hardware form or independent of it, or they can be stored in the memory of the computer device in software form, so that the processor can call and execute the corresponding operations of the above modules.

[0182] This embodiment also provides an electronic device, which includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. The processor of this computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface of the computer device is used for wired or wireless communication with external terminals. Wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements a method for analyzing bus undervoltage load transfer. The display screen of the computer device can be a liquid crystal display (LCD) or an e-ink display. The input device of the computer device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse, etc.

[0183] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method proposed in the above embodiments.

[0184] The storage medium proposed in this embodiment belongs to the same inventive concept as the method proposed in the above embodiments. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0185] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0186] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

[0187] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented 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. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0188] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. 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... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0189] 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.

[0190] 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.

[0191] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0192] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A graph-optimized GNSS and IMU integrated navigation method, characterized in that, include: Obtain first target data and perform a first preprocessing on the first target data, wherein the first preprocessing includes at least calculating a first substitution constraint; A first graph optimization model is established based on the first preprocessed first target data; The optimization model of the first image is solved, and the navigation state is determined based on the solution results; The first graph optimization model includes: The first graph optimization model includes a first objective function and a first constraint condition; The first objective function is any function that calculates the total cost; The first constraint is the first alternative constraint; The first graph optimization model consists of several nodes and several factors; The aforementioned factors constitute the first objective function; The nodes include at least the receiver's state vector at different times and the satellite's position vector; Solving the optimization model of the first graph includes: Solving the optimization model of the first figure yields the first increment; A first threshold is preset, and the relationship between the first increment and the first threshold is determined. Complete the solution based on the judgment result; The first objective function includes at least the IMU factor, the GNSS pseudorange factor, and the virtual pseudorange factor; The IMU factor connects the receiver states at adjacent time points; The GNSS pseudorange factor connects the receiver status with the satellite position at the corresponding time. The virtual pseudorange factor connects the receiver status with the predicted satellite position; The first objective function also includes: The IMU factor is the IMU error function at a certain moment; The GNSS pseudorange factor is a GNSS pseudorange error function of several satellites at a certain moment. The virtual pseudorange factor is a virtual pseudorange error function of several satellites at a certain moment. The step of acquiring the first target data and performing a first preprocessing on the first target data includes: The first target data includes at least several pseudorange measurements of the target guideline by satellites at each time point and their rate of change. The first preprocessing includes predicting the virtual pseudorange at the next time step based on the pseudorange and pseudorange change rate at the previous time step; Virtual pseudorange provides a first alternative constraint when real pseudorange is unavailable.

2. A graph-optimized GNSS and IMU integrated navigation system, employing the graph-optimized GNSS and IMU integrated navigation method as described in claim 1, characterized in that, include: A preprocessing module is used to acquire first target data and perform a first preprocessing on the first target data, wherein the first preprocessing includes at least calculating a first substitution constraint; The model building module is used to build a first graph optimization model based on the first preprocessed first target data; The solution module is used to solve the optimization model of the first graph and determine the navigation state based on the solution results.

3. An electronic device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the method of claim 1.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method of claim 1.

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