A GPS / INS integrated navigation system error compensation method and system

Abstract

The present invention relates to an error compensation method and system for a GPS / INS integrated navigation system, wherein the method comprises: obtaining navigation data of GPS and INS, calculating and tracking the difference between the navigation data of GPS and INS to generate error data; constructing an error prediction model, inputting the error data into the error prediction model for training, and performing error prediction; when the GPS signal is in a lost-lock stage, obtaining real-time navigation data in the signal lost-lock stage according to the navigation data of INS in the signal lost-lock stage and the navigation data of GPS at the start time; performing error compensation on the real-time navigation data in the GPS signal lost-lock stage according to the error prediction data output by the error prediction model. The present invention significantly improves the accuracy, stability and adaptability of the navigation system by accurately tracking and quantifying errors, performing error prediction using a KAN network, and performing error compensation on real-time navigation data when the GPS signal is lost-lock.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation technology, and in particular to an error compensation method and system for a GPS / INS integrated navigation system. Background Art

[0002] GPS (Global Positioning System) and INS (Inertial Navigation System) are two widely used navigation technologies. The GPS system is well-known for its high-precision positioning capabilities, however, it also has some inherent limitations. Especially in certain specific environments, such as tunnels and urban areas with dense high-rise buildings, GPS is prone to losing communication with satellites, resulting in a significant reduction in navigation accuracy. This problem of signal loss or weakening makes navigation systems that rely solely on GPS unreliable in these scenarios.

[0003] In order to make up for this shortcoming of GPS, the INS system was introduced into the navigation solution. The INS system continuously measures and calculates acceleration and angular velocity through an inertial measurement unit (IMU), and then estimates the position, velocity and attitude of the carrier. However, the INS system also has its own shortcomings: because the inertial sensor has tiny measurement errors, and these errors will accumulate over time, long-term use of INS for navigation will lead to a gradual decrease in positioning accuracy.

[0004] In order to comprehensively utilize the advantages of GPS and INS and make up for their respective shortcomings, the GPS / INS combined navigation system came into being. This combined system aims to improve the overall accuracy and reliability of navigation by integrating navigation information based on two different principles. When the GPS signal is stable, it can be used to correct the accumulated error of INS; when the GPS signal is lost or unstable, INS can provide continuous navigation information to ensure the continuity of navigation.

[0005] However, the GPS / INS integrated navigation system also faces a series of challenges. First, the need to integrate two navigation systems and design corresponding error compensation algorithms increases the complexity and implementation cost of the system. Second, in order to achieve higher navigation accuracy, more expensive high-precision inertial sensors and GPS receivers may be required, which further increases the system cost. In addition, although the GPS signal can correct the INS error under normal circumstances, the INS error will still accumulate rapidly when the GPS signal is interrupted for a long time or the quality is poor, affecting the navigation accuracy.

[0006] In the GPS / INS integrated navigation system, Kalman filter or its derivative algorithms are often used to fuse the positioning and navigation information of GPS and INS and perform error compensation. Kalman filter fuses the data of different sensors through optimal estimation theory to improve navigation accuracy. However, the performance of Kalman filter is affected by many factors, including but not limited to model error, sensor noise and uncertainty of initial state. These factors may lead to inaccurate filtering results, thus affecting the performance of the entire navigation system. Summary of the invention

[0007] 1. Technical issues to be resolved

[0008] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides an error compensation method and system for a GPS / INS integrated navigation system, which solves the technical problems faced by the existing GPS / INS integrated navigation system, such as system complexity, cost and Kalman filter performance influencing factors.

[0009] (II) Technical solution

[0010] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0011] In a first aspect, an embodiment of the present invention provides an error compensation method for a GPS / INS integrated navigation system, comprising:

[0012] Obtain navigation data of GPS and INS of the GPS / INS integrated navigation system, calculate and track the difference of various attributes between the navigation data of GPS and INS to generate error data;

[0013] An error prediction model is constructed based on the Kolmogorov-Arnold network, error data is input into the error prediction model for training, and the trained error prediction model is used for error prediction;

[0014] When the GPS signal is in the unlocking stage, the real-time navigation data of the signal unlocking stage is obtained according to the navigation data of the INS in the signal unlocking stage and the navigation data of the GPS at the start time of the signal unlocking stage;

[0015] According to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss stage is error compensated, and the error-compensated navigation data is output.

[0016] Optionally, obtaining navigation data of GPS and INS of a GPS / INS integrated navigation system, and calculating and tracking the difference of each attribute between the navigation data of GPS and INS to generate error data includes:

[0017] Receive the raw data from the GPS component of the GPS / INS integrated navigation system and resolve it into GPS navigation data including speed, coordinates and attitude angles in three directions;

[0018] Receive the raw data from the INS component of the GPS / INS integrated navigation system, combine it with the GPS navigation data, and solve it into INS navigation data including the speed, coordinates, attitude angle, zero deflection angle of the accelerometer and the zero deflection angle of the gyroscope in three directions through integration processing, and use the solved GPS navigation data to correct the INS navigation data;

[0019] Calculate the difference in velocity error, coordinate error, attitude angle error, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope between the navigation data of the GPS and the navigation data of the INS in three directions at set intervals or in response to a received difference obtaining instruction, track and record the difference, and generate error data;

[0020] in,

[0021] The navigation data of GPS is: ;

[0022] In the formula, They are the speed information in three directions respectively. Three-dimensional coordinate information in the inertial coordinate system, Respectively represent the attitude angle information in three directions;

[0023] The navigation data of INS is: ;

[0024] In the formula, is the zero deflection angle of the accelerometer in three directions, is the zero deflection angle of the gyroscope in three directions;

[0025] The error data is: ;

[0026] In the formula, They are the velocity error, coordinate error, attitude angle error, accelerometer zero deflection angle and gyroscope zero deflection angle differences in three directions.

[0027] Optionally, when the GPS signal is in a lock-lost stage, obtaining the real-time navigation data of the signal lock-lost stage according to the acquired navigation data of the INS in the signal lock-lost stage and the navigation data of the GPS at the start time of the signal lock-lost stage includes:

[0028] Obtain GPS navigation data including speed, coordinates and attitude angle information at the start time of the GPS signal loss phase;

[0029] Acquire the real-time data of the INS component of the GPS / INS integrated navigation system during the GPS signal loss phase, perform time integration on the real-time data of the INS component, and calculate the speed and displacement data at each moment during the GPS signal loss phase;

[0030] For each moment during the GPS signal loss phase t The calculated speed and displacement data are fused with the GPS navigation data at the last moment of the signal lock phase to obtain the signal loss phase t Real-time navigation information at all times;

[0031] in,

[0032] The GPS navigation data at the start of the GPS signal loss phase is: ;

[0033] The INS component in the GPS signal loss phase t The velocity and displacement data at the moment are: ;

[0034] GPS signal lost lock stage t The real-time navigation information at this moment is: ;

[0035] ;

[0036] In the formula, for t The speed in three directions at the moment, for t The coordinates in three directions at the moment, for t The attitude angles in three directions at the moment.

[0037] Optionally, error compensation is performed on real-time navigation data in the GPS signal loss phase according to the error prediction data output by the error prediction model, and outputting the error-compensated navigation data includes:

[0038] Using the error prediction model, according to the start time of the GPS signal loss phase and t The difference of real-time navigation information at the moment, output t Error prediction data at the moment;

[0039] according to t Error prediction data at time, construct t The error state equation at time t;

[0040] Using the error state equation at time t, t The real-time navigation data at the moment is error compensated to obtain navigation data after error compensation;

[0041] in,

[0042] t The error state equation at time is: ;

[0043] The navigation information after the error compensation stage is: .

[0044] Optionally, according to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss lock stage is error compensated, and after the error-compensated navigation data is output, the method further includes:

[0045] The first Kalman filter is introduced, and the prediction part of the first Kalman filter is used to calculate the prior state estimate of the INS and the error covariance of the INS based on the state estimate of the previous time step and the navigation data of the INS;

[0046] Based on the update part of the first Kalman filter, the posterior state estimate of the INS and the updated INS error covariance are calculated according to the prior estimate of the INS and the error covariance of the INS;

[0047] The gain of the first Kalman filter is adjusted to minimize the error covariance of the updated INS, thereby obtaining the navigation data of the INS after noise is filtered out;

[0048] Introducing a second Kalman filter, using a prediction part of the second Kalman filter, and calculating a priori state estimate of the error-compensated navigation data and an error covariance of the error-compensated navigation data based on a state estimate of a previous time step and the error-compensated navigation data;

[0049] Based on the updating part of the second Kalman filter, calculating the a posteriori state estimate of the error-compensated navigation data and the updated error covariance of the error-compensated navigation data according to the a priori estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data;

[0050] The gain of the second Kalman filter is adjusted to minimize the error covariance of the updated error-compensated navigation data, thereby obtaining the error-compensated navigation data after noise is filtered out.

[0051] In a second aspect, an embodiment of the present invention provides an error compensation system for a GPS / INS integrated navigation system, comprising:

[0052] An integrated navigation module, including a GPS component and an INS component coupled to the GPS component, configured to automatically switch the GPS component or the INS component for navigation according to the state of the GPS signal acquired by the GPS component;

[0053] A data acquisition module is configured to obtain navigation data of GPS and INS of a GPS / INS integrated navigation system, calculate and track the difference of various attributes between the navigation data of GPS and INS to generate error data;

[0054] The KAN network module is configured to build an error prediction model based on the Kolmogorov-Arnold network, perform model training according to input error data, and perform error prediction using the trained error prediction model;

[0055] The error compensation module is configured to obtain real-time navigation data of the signal loss stage according to the navigation data of the INS in the signal loss stage and the navigation data of the GPS at the start time of the signal loss stage when the GPS signal is in the loss stage, perform error compensation on the real-time navigation data of the GPS signal loss stage according to the error prediction data output by the error prediction model, and output the navigation data after error compensation;

[0056] The central control module is configured to receive at least one item of data from the integrated navigation module, the data acquisition module, the KAN network module and the error compensation module, and perform at least one operation of solving, compensating, adjusting and outputting the received data.

[0057] Optionally, the combined navigation module includes:

[0058] A GPS component is configured to collect GPS raw data and send the GPS raw data to a central control module to calculate CPS navigation data including speed information, position information, and attitude angle information;

[0059] An INS component, operating in parallel with the GPS component and coupled to each other, includes an accelerometer and a gyroscope, and is configured to collect INS raw data and send the INS raw data to the central control module to be resolved into INS navigation data including speed, coordinates, attitude angle, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope in three directions through integration processing;

[0060] The processing unit is connected to the GPS component and the INS component respectively, and is configured to automatically switch to the INS component for navigation when the GPS signal is in a lost lock stage.

[0061] Optionally, the data acquisition module includes:

[0062] A GPS data acquisition unit is configured to receive raw data from a GPS component of a GPS / INS integrated navigation system and resolve it into GPS navigation data including speed, coordinates and attitude angles in three directions;

[0063] An INS data acquisition unit is configured to receive raw data from an INS component of a GPS / INS integrated navigation system, combine the raw data with the GPS navigation data, and calculate the raw data into INS navigation data including speed, coordinates, attitude angle, zero deflection angle of an accelerometer and zero deflection angle of a gyroscope in three directions through integration processing;

[0064] An INS data correction unit configured to correct the navigation data of the INS using the resolved GPS navigation data;

[0065] an error data generating unit, configured to calculate the difference in velocity error, coordinate error, attitude angle error, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope between the navigation data of the GPS and the navigation data of the INS in three directions at every set period or in response to a received difference obtaining instruction, track and record the difference, and generate error data;

[0066] in,

[0067] The navigation data of GPS is: ;

[0068] In the formula, They are the speed information in three directions respectively. Three-dimensional coordinate information in the inertial coordinate system, Respectively represent the attitude angle information in three directions;

[0069] The navigation data of INS is: ;

[0070] In the formula, is the zero deflection angle of the accelerometer in three directions, The zero deflection angle of the gyroscope in three directions;

[0071] The error data is: ;

[0072] In the formula, They are the velocity error, coordinate error, attitude angle error, accelerometer zero deflection angle and gyroscope zero deflection angle differences in three directions.

[0073] Optionally, the error compensation module includes:

[0074] The error data acquisition unit is configured to acquire GPS navigation data including speed, coordinates and attitude angle information at the start time of the GPS signal loss phase; acquire real-time data of the INS component of the GPS / INS combined navigation system during the GPS signal loss phase, perform time integration operation on the real-time data of the INS component, and calculate the speed and displacement data at each time during the GPS signal loss phase;

[0075] The data fusion processing unit is configured to process the GPS signal at each moment of the loss of lock. t The calculated speed and displacement data are fused with the GPS navigation data at the last moment of the signal lock phase to obtain the signal loss phase t Real-time navigation information at all times;

[0076] The error state output unit is configured to use the error prediction model to output the difference between the start time of the GPS signal loss lock phase and the real-time navigation information at time t. t The error prediction data at the moment is based on t Error prediction data at time, construct t The error state equation at time t;

[0077] The error compensation unit is configured to utilize t The error state equation at time t The real-time navigation data at the moment is error compensated to obtain navigation data after error compensation;

[0078] in,

[0079] The GPS navigation data at the start of the GPS signal loss phase is: ;

[0080] The INS component in the GPS signal loss phase t The velocity and displacement data at the moment are: ;

[0081] GPS signal lost lock stage t The real-time navigation information at this moment is: ;

[0082] In the formula, for t The speed in three directions at the moment, for t The coordinates in three directions at the moment, for t The attitude angles in three directions at the moment;

[0083] t The error state equation at time is: ;

[0084] The navigation information after the error compensation stage is: .

[0085] Optionally include:

[0086] The first Kalman filter is arranged at the output end of the INS component, and includes a prediction part and an update part, and is configured to calculate the prior state estimate of the INS and the error covariance of the INS based on the prediction part according to the state estimate of the previous time step and the navigation data of the INS; based on the update part, calculate the posterior state estimate of the INS and the updated error covariance of the INS according to the prior estimate of the INS and the error covariance of the INS; and then, adaptively adjust the gain to minimize the error covariance of the updated INS, so as to obtain the navigation data of the INS after filtering out the noise;

[0087] The first Kalman filter is arranged at the output end of the error compensation module, and includes a prediction part and an update part, and is configured to calculate, based on the prediction part, a priori state estimate of the error-compensated navigation data and an error covariance of the error-compensated navigation data according to the state estimate of the previous time step and the error-compensated navigation data; based on the update part of the second Kalman filter, calculate, based on the a priori estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data, a posteriori state estimate of the error-compensated navigation data and an updated error covariance of the error-compensated navigation data; and then, adaptively adjust the gain to minimize the error covariance of the updated error-compensated navigation data, so as to obtain the error-compensated navigation data after noise is filtered out.

[0088] (III) Beneficial effects

[0089] The beneficial effects of the present invention are:

[0090] First, the present invention generates error data by acquiring the navigation data of GPS and INS of the GPS / INS integrated navigation system and calculating the difference between the two, which provides accurate basic data for subsequent error compensation. This method can comprehensively and accurately track and quantify the errors of navigation data, providing a scientific basis for error compensation.

[0091] Secondly, the present invention builds an error prediction model based on the Kolmogorov-Arnold network (KAN network), and uses the powerful learning ability of the network to accurately learn and approximate the error distribution law of the vehicle-mounted GPS / INS combined navigation system. This not only improves the accuracy of error compensation, but also enhances the system's adaptability to different environmental conditions, allowing the navigation system to maintain high accuracy and stability in various complex environments.

[0092] Furthermore, when the GPS signal is in the unlocking stage, the present invention can obtain the real-time navigation data of the signal unlocking stage according to the real-time INS navigation data and the GPS navigation data at the start time of the signal unlocking stage. This ensures that the navigation system can still provide continuous navigation information in the case of GPS signal loss, thus ensuring the continuity of navigation.

[0093] Finally, according to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss phase is error compensated, thereby outputting error-compensated navigation data. This not only further improves the accuracy of the navigation data, but also enables the navigation system to maintain high-precision navigation services when the GPS signal is unstable or lost.

[0094] Therefore, the present invention significantly improves the accuracy, stability and adaptability of the navigation system by accurately tracking and quantifying errors, using the KAN network to predict errors, and performing error compensation for real-time navigation data when the GPS signal is lost, and effectively solves the technical problems faced by the existing GPS / INS integrated navigation system, such as system complexity, cost and Kalman filter performance influencing factors. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 A flowchart of an error compensation method for a GPS / INS integrated navigation system provided by an embodiment of the present invention;

[0096] Figure 2 A specific flow chart of step S1 of an error compensation method for a GPS / INS integrated navigation system provided by an embodiment of the present invention;

[0097] Figure 3 A schematic diagram of the structure of a KAN network of an error compensation method for a GPS / INS integrated navigation system provided by an embodiment of the present invention;

[0098] Figure 4 A specific flow chart of step S3 of an error compensation method for a GPS / INS integrated navigation system provided by an embodiment of the present invention;

[0099] Figure 5 A specific flow chart of step S4 of an error compensation method for a GPS / INS integrated navigation system provided by an embodiment of the present invention;

[0100] Figure 6 A schematic diagram of the composition of an error compensation system of a GPS / INS integrated navigation system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0101] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0102] Prior to this, in order to facilitate understanding of the technical solution provided by the present invention, some concepts are first introduced below.

[0103] GPS signal lock: refers to the ability of the GPS component to stably receive satellite signals of sufficient quantity and quality to ensure the accuracy and reliability of navigation solutions. Specifically, it needs to meet the following conditions: (1) The GPS component successfully captures and tracks at least four visible satellite signals, which is the minimum number of satellites required to achieve three-dimensional positioning and time synchronization. (2) The received satellite signal strength is sufficient and higher than a preset signal strength threshold to ensure the stability and accuracy of signal transmission. (3) The signal-to-noise ratio (SNR) of the satellite signal is higher than a preset threshold, indicating that the received signal quality is good and the interference is low. (4) The positioning result obtained by GPS solution is continuous and stable, and the positioning error is within the predetermined acceptable range.

[0104] GPS signal lockout: refers to the GPS component failing to meet any one or more of the above "GPS signal lock" conditions. This may include failure to capture a sufficient number of satellite signals, insufficient received signal strength, signal-to-noise ratio below a preset threshold, or discontinuous, unstable or unacceptable positioning results obtained through GPS solution. In the case of GPS signal lockout, the accuracy and reliability of the navigation system will be affected, and other navigation methods or systems may be needed to assist in positioning.

[0105] like Figure 1 As shown, an error compensation method for a GPS / INS integrated navigation system proposed in an embodiment of the present invention includes: obtaining navigation data of GPS and INS of the GPS / INS integrated navigation system, calculating and tracking the difference of each attribute between the navigation data of GPS and INS to generate error data; constructing an error prediction model based on a Kolmogorov-Arnold network, inputting the error data into the error prediction model for training, and performing error prediction using the trained error prediction model; when the GPS signal is in a lock-lost stage, obtaining real-time navigation data of the signal lock-lost stage according to the navigation data of INS acquired in the signal lock-lost stage and the navigation data of GPS at the starting moment of the signal lock-lost stage; performing error compensation on the real-time navigation data of the GPS signal lock-lost stage according to the error prediction data output by the error prediction model, and outputting the navigation data after error compensation.

[0106] First, the present invention generates error data by acquiring the navigation data of GPS and INS of the GPS / INS integrated navigation system and calculating the difference between the two, which provides accurate basic data for subsequent error compensation. This method can comprehensively and accurately track and quantify the errors of navigation data, providing a scientific basis for error compensation.

[0107] Secondly, the present invention builds an error prediction model based on the Kolmogorov-Arnold network (KAN network), and uses the powerful learning ability of the network to accurately learn and approximate the error distribution law of the vehicle-mounted GPS / INS combined navigation system. This not only improves the accuracy of error compensation, but also enhances the system's adaptability to different environmental conditions, allowing the navigation system to maintain high accuracy and stability in various complex environments.

[0108] Furthermore, when the GPS signal is in the unlocking stage, the present invention can obtain the real-time navigation data of the signal unlocking stage according to the real-time INS navigation data and the GPS navigation data at the start time of the signal unlocking stage. This ensures that the navigation system can still provide continuous navigation information in the case of GPS signal loss, thus ensuring the continuity of navigation.

[0109] Finally, according to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss phase is error compensated, thereby outputting error-compensated navigation data. This not only further improves the accuracy of the navigation data, but also enables the navigation system to maintain high-precision navigation services when the GPS signal is unstable or lost.

[0110] Therefore, the present invention significantly improves the accuracy, stability and adaptability of the navigation system by accurately tracking and quantifying errors, using the KAN network to predict errors, and performing error compensation for real-time navigation data when the GPS signal is lost, and effectively solves the technical problems faced by the existing GPS / INS integrated navigation system, such as system complexity, cost and Kalman filter performance influencing factors.

[0111] In order to better understand the above technical solution, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer and more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0112] Specifically, an embodiment of the present invention provides an error compensation method for a GPS / INS integrated navigation system, which includes:

[0113] S1. Obtain navigation data of GPS and INS of a GPS / INS integrated navigation system, calculate and track the difference of various attributes between the navigation data of GPS and INS to generate error data.

[0114] Furthermore, if Figure 2 As shown, step S1 includes:

[0115] S11, receiving raw data from the GPS component of the GPS / INS integrated navigation system, and solving it into GPS navigation data including speed, coordinates and attitude angles in three directions.

[0116] In this step, the raw data of the GPS component is solved and converted into GPS navigation data in the geodetic coordinate system, including speed, coordinates and attitude angles in three directions. Since GPS navigation data is usually more accurate and stable, during the GPS signal locking stage, the GPS navigation data is used to correct the previously solved INS navigation data to improve the overall navigation accuracy.

[0117] S12, receiving the raw data from the INS component of the GPS / INS integrated navigation system, combining it with the GPS navigation data, and solving it through integration processing into the INS navigation data including the speed, coordinates, attitude angle, zero deflection angle of the accelerometer and the zero deflection angle of the gyroscope in three directions, and using the solved GPS navigation data to correct the INS navigation data.

[0118] Next, the raw data from the INS component in the GPS / INS integrated navigation system is received. These raw data mainly include the readings of the accelerometer and the gyroscope. Through integration processing, the readings of the accelerometer are converted into velocity information in three directions (usually X, Y, and Z axes), and further integration of the velocity obtains displacement or coordinate information in three directions. At the same time, the readings of the gyroscope are processed to obtain the attitude angle information of the INS system. In addition, the zero deflection information of the accelerometer and the gyroscope can also be extracted from the raw data of the accelerometer and the gyroscope. Based on the navigation information calculated by the above GPS, after this series of processing, we obtain the navigation data of the INS including the velocity, coordinates, attitude angle, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope in three directions.

[0119] Afterwards, the output data of the GPS component and the INS component are preprocessed, including data alignment, data format conversion, data smoothing, etc., to ensure the accuracy and consistency of the data.

[0120] S13. Calculate the difference in speed error, coordinate error, attitude angle error, accelerometer zero deflection angle, and gyroscope zero deflection angle between the GPS navigation data and the INS navigation data in three directions at set intervals or in response to a received difference obtaining instruction, track and record the difference, and generate error data.

[0121] The velocity error, coordinate error, and attitude angle error of the GPS navigation data and the INS navigation data in three directions are calculated at set time intervals or in response to received difference-finding instructions. In addition, the difference between the zero deflection angle of the accelerometer and the zero deflection angle of the gyroscope is also taken into account. These differences are tracked and recorded, and a comprehensive set of error data is finally generated. This data can then be used for error model training of the KAN module to optimize and improve the performance of the entire navigation system.

[0122] In one embodiment, navigation data of GPS and INS are acquired from a GPS / INS integrated navigation system, and the error is calculated by comparing these data.

[0123] The navigation data of GPS is specifically expressed as: ;

[0124] In the formula, They are the speed information in three directions respectively. is the three-dimensional coordinate information in the inertial coordinate system, Respectively represent the attitude angle information in three directions.

[0125] At the same time, the navigation data of INS is: ;

[0126] In the formula, is the zero deflection angle of the accelerometer in three directions, is the zero deflection angle of the gyroscope in three directions;

[0127] The error data is specifically expressed as: ;

[0128] Where: They are the velocity error, coordinate error, attitude angle error, accelerometer zero deflection angle and gyroscope zero deflection angle differences in three directions.

[0129] S2. Build an error prediction model based on the Kolmogorov-Arnold network, input the error data into the error prediction model for training, and use the trained error prediction model to perform error prediction.

[0130] Specifically, the design of the KAN network based on the Kolmogorov-Arnold Representation Theorem (KART) aims to use this theorem to represent any multivariable continuous function as a combination of a finite number of univariable continuous functions. According to KART, any multivariable continuous function f defined on a bounded domain can be represented as a combination of a finite number of univariable continuous functions and addition operations. This means that the learning of any high-dimensional multivariable function can ultimately be reduced to the learning of a set of univariate functions. Multivariable continuous functions can be written as: ;

[0131] in, is a single variable continuous function.

[0132] The KAN network learns each single variable continuous function, namely the activation function, during the training process. In order to achieve the learnability (differentiability) of the activation function, the B-spline function is used. The B-spline function is determined by a series of points Pi, and is differentiable with respect to all points Pi. Therefore, Pi can be trained by gradient descent to train different activation functions.

[0133] The KAN network is designed according to the computational graph of KART and has a three-layer or more structure to fit any function. Since each univariate function may be very complex, the KAN network can improve the fitting ability by deepening the depth. In the implementation, residual connections and weights w are introduced. Although the weights w are computationally redundant, they can more directly control the magnitude of each activation function. The weights w are initialized using the Xavier initialization method, and the parameters ci in the B-spline are sampled from a normal distribution with a mean of 0 and a very small variance. During the training process, first train on the B-spline function with a large interval, and then gradually refine it.

[0134] With the increase of parameters and the increase of Grid (that is, the number of points Pi in the B-spline function increases and the spacing becomes smaller), the KAN network can fit more complex functions, thereby improving the model capability. The prediction accuracy of INS errors that change over time can also be higher than other traditional network models based on multi-layer perceptron (MLP).

[0135] In traditional MLP, the activation function is fixed and usually located at the nodes (i.e., "neurons") of the neural network. The characteristic of KAN is that it places the activation function on the edges (i.e., "weights") of the network instead of on the nodes. This makes the activation function learnable instead of fixed. MLP uses a traditional linear weight matrix. Instead of using a linear weight matrix, KAN replaces each weight parameter with a learnable univariate function, which is usually parameterized in the form of a spline curve. The number of parameters of MLP is usually large and often not interpretable. Due to the design of KAN, it can be relatively small in number of parameters, and due to the learnability of its activation function and intuitive visualization ability, KAN often has better interpretability. From both theoretical and empirical perspectives, KAN has a faster growth law of neural network scale (i.e., neural scaling law) than MLP. In data fitting and partial differential equation solving tasks, even smaller KANs can achieve comparable or better accuracy than larger MLPs. Among them, the model formula of MLP can be approximated as: ;

[0136] In the formula, in the formula, w i is the weight parameter, b i is the bias parameter, is a nonlinear activation function, a i is the coefficient.

[0137] The KAN model formula can be expressed as: ;

[0138] In the formula, , is a single variable continuous function.

[0139] like Figure 3 As shown in the figure, the construction method of KAN network is mainly based on Kolmogorov-Arnold representation theorem (KAT), which provides a new perspective for the approximation of multivariate continuous functions. Any multivariate continuous function can be expressed as a two-layer nested addition of a finite number of single variable, continuous functions. KAN network mainly consists of two classes: Hidden_layer and Output_layer. Hidden_layer is responsible for processing the conversion from input layer to hidden layer, while Output_layer is responsible for processing the conversion from hidden layer to output layer.

[0140] In the KAN network, each layer contains learnable parameters such as k, A, w1, phi1, B, w2, phi2, etc. These parameters are updated through forward propagation and back propagation to minimize the loss function.

[0141] The KAN network applies a learnable activation function to the weights instead of using a fixed activation function on the nodes (neurons). This approach enables the KAN network to process and learn complex relationships of input data in a more flexible and closer way to the Kolmogorov-Arnold representation theorem. In KAN, nodes perform simple addition operations and do not contain nonlinear activation functions.

[0142] When defining the model, you need to set the width of the model, and you can also set other parameters such as the grid size and the number of kernel functions (k). grid is set to 3 and k is set to 3.

[0143] The obtained error data is used for the training dataset, which usually includes the input features as time and the corresponding label error state equation. The dataset is divided into training set, validation set and test set according to 8:2 to facilitate model evaluation and selection during the training process. The optimizer LBFGS is used to update the weights of the model. In each training step, the training data is input into the model, the loss between the predicted result and the true label is calculated, and the optimizer is used to minimize the loss. Use the validation set to monitor the training process and stop training or use early stopping when the validation loss no longer decreases. The performance of the model is evaluated on the test set, usually using indicators such as accuracy, recall, and F1 score.

[0144] It is worth noting that the training of the KAN model may be slower than the traditional MLP model because it needs to learn the activation function on each edge. Therefore, it may take more computing resources and time to train the KAN model.

[0145] S3. When the GPS signal is in the unlocking stage, the real-time navigation data of the signal unlocking stage is obtained according to the navigation data of the INS in the signal unlocking stage and the navigation data of the GPS at the start time of the signal unlocking stage.

[0146] Furthermore, if Figure 4 As shown, S2 includes:

[0147] S31, obtaining GPS navigation data including speed, coordinates and attitude angle information at the start time of the GPS signal loss phase.

[0148] S32, acquiring real-time data of the INS component of the GPS / INS integrated navigation system in the GPS signal loss stage, performing time integration operation on the real-time data of the INS component, and calculating the speed and displacement data at each moment in the GPS signal loss stage.

[0149] S33, for each moment of the GPS signal loss phase t The calculated speed and displacement data are fused with the GPS navigation data at the last moment of the signal lock phase to obtain the signal loss phase t Real-time navigation information at all times.

[0150] In one embodiment, during the signal lock-out phase: the INS component transmits the heading and attitude angle data of the gyroscope and the acceleration data of the accelerometer to the central control module for time integration to obtain velocity and displacement data. The GPS data at the last moment of the signal phase should be added to the output data of the INS system. Specifically:

[0151] The GPS navigation data at the start of the GPS signal loss phase, i.e. the last moment of the signal lock phase, is: ;

[0152] In the formula, They are the speed information in three directions at the start time of the GPS signal loss phase, It is the three-dimensional coordinate information in the inertial coordinate system at the beginning of the GPS signal loss phase. They respectively represent the attitude angle information in three directions at the starting moment of the GPS signal loss phase.

[0153] The INS components in the signal loss phase are t The velocity and displacement data at the moment are: ;

[0154] In the formula, is the speed of the INS component at time t when the GPS signal is lost, It is the displacement data of the INS component at time t when the GPS signal is lost.

[0155] Signal loss phase t The real-time navigation information at this moment is: ; ;

[0156] In the formula, for t The speed in three directions at the moment, for t The coordinates in three directions at the moment, for tThe attitude angles in three directions at the moment.

[0157] S4. According to the error prediction data output by the error prediction model, error compensation is performed on the real-time navigation data in the GPS signal loss lock stage, and the error-compensated navigation data is output.

[0158] Furthermore, if Figure 5 As shown, step S4 includes:

[0159] S41, using the error prediction model, according to the start time of the GPS signal loss phase and t The difference of real-time navigation information at the moment, output t Error prediction data at time.

[0160] S42, according to t Error prediction data at time, construct t The error state equation at time .

[0161] S43. Utilization t The error state equation at time t The real-time navigation data at the moment is error compensated to obtain error-compensated navigation data.

[0162] in,

[0163] t The error state equation at time is: ;

[0164] The navigation information after the error compensation stage is: .

[0165] Furthermore, after step S4, the method further includes:

[0166] A41. Introduce the first Kalman filter and use the prediction part of the first Kalman filter to calculate the prior state estimate of INS and the error covariance of INS based on the state estimate of the previous time step and the navigation data of INS.

[0167] A42. Based on the update part of the first Kalman filter, the a priori estimate of the INS and the error covariance of the INS are used to calculate the a posteriori state estimate of the INS and the updated error covariance of the INS.

[0168] A43. Adjust the gain of the first Kalman filter to minimize the error covariance of the updated INS, thereby obtaining the navigation data of the INS after noise is filtered out.

[0169] A44. Introduce a second Kalman filter, use the prediction part of the second Kalman filter, and calculate the prior state estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data based on the state estimate of the previous time step and the error-compensated navigation data.

[0170] A45. Based on the updating part of the second Kalman filter, according to the a priori estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data, calculate the a posteriori state estimate of the error-compensated navigation data and the updated error covariance of the error-compensated navigation data.

[0171] A46. Adjust the gain of the second Kalman filter to minimize the error covariance of the updated error-compensated navigation data, thereby obtaining the error-compensated navigation data after noise is filtered out.

[0172] The Kalman filter is used to filter out noise during the signal unlocking stage. The Kalman filter performs well in filtering out noise. It is based on the linear system state equation and uses the system input and output observation data to optimally estimate the system state. The following is a detailed assumption of the Kalman filter filtering out noise. The system state is linear, and both the process noise and the observation noise are Gaussian distributed. The Kalman filter achieves state estimation through two steps: prediction and update. In the prediction stage, the current state is predicted based on the previous state and control input of the system; in the update stage, the prediction is updated using new measurement data, and a Kalman gain is calculated, which determines which part of the prediction and measurement is more reliable. The Kalman filter performs state estimation in a recursive manner. The state estimation at each moment takes into account the estimation result of the previous moment and the current observation value.

[0173] During the update phase, the Kalman filter calculates a Kalman gain, which determines which part of the prediction or measurement is more reliable. If the observation noise is small, it relies more on the observation value; if the prediction uncertainty is small, it relies more on the prediction value.

[0174] In this way, the Kalman filter is able to filter out noise in the observed data, providing a more accurate and reliable estimate of the system state.

[0175] In one embodiment, the Kalman filter: its implementation process is shown in the following formula.

[0176] ;

[0177] In the formula, and represents the probability density function, where To estimate the state based on the previous time step and the prediction of the current state based on the current input, it is expressed as , which is called the prior estimate, which is calculated before using the current measurement value. The above equation can be rewritten as: ;

[0178] In the formula, Use the current measurement to update the estimate, and the final result is called the posterior estimate.

[0179] Therefore, it can be seen that the Kalman filter is divided into two parts: prediction and update. In the prediction part, the prior state estimate and its error covariance are calculated, and it is known that the covariance has the following properties: if Y = FX, the covariance of X is P, then the covariance of Y is .

[0180] ;

[0181] In the update phase, the prior estimate is used to calculate the posterior state estimate and its error covariance: ;

[0182] Adjusting Kalman filter gains , so that the error covariance of the updated state value Minimum.

[0183] It is worth noting that two extreme cases need to be considered. When the measurement noise variance R is 0, , , that is, the a posteriori estimate of the state quantity depends entirely on the measured value. When it is 0, , , that is, the posterior estimate of the state quantity depends entirely on the prior estimate.

[0184] In addition, if Figure 6 As shown, an embodiment of the present invention further provides an error compensation system for a GPS / INS integrated navigation system, comprising:

[0185] The combined navigation module includes a GPS component and an INS component coupled with the GPS component, and is configured to automatically switch the GPS component or the INS component for navigation according to the state of the GPS signal acquired by the GPS component.

[0186] The data acquisition module is configured to obtain navigation data of GPS and INS of the GPS / INS integrated navigation system, calculate and track the difference of each attribute between the navigation data of GPS and INS to generate error data.

[0187] The KAN network module is configured to build an error prediction model based on the Kolmogorov-Arnold network, perform model training according to input error data, and perform error prediction using the trained error prediction model.

[0188] The error compensation module is configured to obtain real-time navigation data of the signal loss stage according to the navigation data of the INS in the signal loss stage and the navigation data of the GPS at the starting time of the signal loss stage when the GPS signal is in the loss stage, perform error compensation on the real-time navigation data of the GPS signal loss stage according to the error prediction data output by the error prediction model, and output the navigation data after error compensation.

[0189] The central control module is configured to receive at least one item of data from the integrated navigation module, the data acquisition module, the KAN network module and the error compensation module, and perform at least one operation of solving, compensating, adjusting and outputting the received data.

[0190] The combined navigation module includes: a GPS component, configured to collect GPS raw data, and send the GPS raw data to a central control module, so as to solve CPS navigation data including speed information, position information and attitude angle information; an INS component, which operates in parallel with the GPS component and is mutually coupled, includes an accelerometer and a gyroscope, and is configured to collect INS raw data, and send the INS raw data to the central control module, so as to solve the INS navigation data including speed, coordinates, attitude angle, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope in three directions through integration processing; a processing unit, which is respectively connected to the GPS component and the INS component, and is configured to automatically switch to the INS component for navigation when the GPS signal is in a lost lock stage.

[0191] Specifically, the GPS component includes a GPS receiver for receiving GPS signals. The GPS signals passing through the receiver are transmitted to the central control module and resolved into real-time navigation information. The INS component is a navigation system that is highly autonomous, does not rely on external information, and does not radiate energy to the outside. The inertial navigation system is a navigation parameter solution system with gyroscopes and accelerometers as sensitive devices. By measuring the acceleration of the carrier in the inertial reference system, integrating it over time, and transforming it into the navigation coordinate system, the speed, yaw angle, and position of the carrier in the navigation coordinate system are obtained. Among them, the inertial measurement device includes an accelerometer and a gyroscope, which are used to measure the acceleration and angular velocity of the carrier. The gyroscope is used to form a navigation coordinate system, stabilize the measuring axis of the accelerometer in the coordinate system, and give the heading and attitude angle. The accelerometer is used to measure the acceleration of the carrier, and the velocity is obtained by integrating it once over time, and the displacement can be obtained by integrating the velocity once over time.

[0192] When the signal from the satellite can be received normally, it is in the signal stage. The processing unit uses the satellite information received by GPS as the correct navigation information for navigation, and corrects the navigation information such as speed, position and attitude angle independently solved by INS. When the satellite signal cannot be fully received, such as in areas with poor satellite signal quality such as underground parking lots, the GPS component is in the signal loss stage. When the signal is lost, the processing unit uses the INS component to solve the navigation information in the inertial navigation coordinate system for navigation.

[0193] Next, the data acquisition module includes:

[0194] The GPS data acquisition unit is configured to receive raw data from the GPS component of the GPS / INS integrated navigation system and resolve it into GPS navigation data including speed, coordinates and attitude angles in three directions.

[0195] The INS data acquisition unit is configured to receive raw data from the INS component of the GPS / INS combined navigation system, combine it with the GPS navigation data, and solve it into INS navigation data including speed, coordinates, attitude angle, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope in three directions through integration processing.

[0196] The INS data correction unit is configured to correct the navigation data of the INS using the solved GPS navigation data.

[0197] an error data generating unit, configured to calculate the difference in velocity error, coordinate error, attitude angle error, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope between the navigation data of the GPS and the navigation data of the INS in three directions at every set period or in response to a received difference obtaining instruction, track and record the difference, and generate error data;

[0198] in,

[0199] The navigation data of GPS is: ;

[0200] In the formula, They are the speed information in three directions respectively. is the three-dimensional coordinate information in the inertial coordinate system, Respectively represent the attitude angle information in three directions

[0201] The navigation data of INS is: ;

[0202] In the formula, is the zero deflection angle of the accelerometer in three directions, is the zero deflection angle of the gyroscope in three directions;

[0203] The error data is: ;

[0204] In the formula, They are the velocity error, coordinate error, attitude angle error, accelerometer zero deflection angle and gyroscope zero deflection angle differences in three directions.

[0205] Then, the KAN network module mainly includes a Kolmogorov-Arnold network to learn the error law and predict the time accumulated error of INS.

[0206] Then, the error compensation module includes:

[0207] The error data acquisition unit is configured to acquire GPS navigation data including speed, coordinates and attitude angle information at the start time of the GPS signal loss phase; acquire real-time data of the INS component of the GPS / INS combined navigation system during the GPS signal loss phase, perform time integration operation on the real-time data of the INS component, and calculate the speed and displacement data at each time during the GPS signal loss phase.

[0208] The data fusion processing unit is configured to process the GPS signal at each moment of the loss of lock. t The calculated speed and displacement data are fused with the GPS navigation data at the last moment of the signal lock phase to obtain the signal loss phase t Real-time navigation information at all times.

[0209] The error state output unit is configured to use the error prediction model to output the difference between the start time of the GPS signal loss lock phase and the real-time navigation information at time t. t The error prediction data at the moment is based on t Error prediction data at time, construct t The error state equation at time .

[0210] The error compensation unit is configured to utilize t The error state equation at time t The real-time navigation data at the moment is error compensated to obtain error-compensated navigation data.

[0211] in,

[0212] The GPS navigation data at the start of the GPS signal loss phase is: ;

[0213] In the formula, They are the speed information in three directions at the start time of the GPS signal loss phase, It is the three-dimensional coordinate information in the inertial coordinate system at the beginning of the GPS signal loss phase. They respectively represent the attitude angle information in three directions at the starting moment of the GPS signal loss phase.

[0214] The INS components in the signal loss phase are t The velocity and displacement data at the moment are: ;

[0215] In the formula, is the speed of the INS component at time t when the GPS signal is lost, It is the displacement data of the INS component at time t when the GPS signal is lost.

[0216] Signal loss phase t The real-time navigation information at this moment is: ; ;

[0217] In the formula, for t The speed in three directions at the moment, for t The coordinates in three directions at the moment, for t The attitude angles in three directions at the moment;

[0218] t The error state equation at time is: ;

[0219] The navigation information after the error compensation stage is: .

[0220] And, central control module: The central control module is responsible for coordinating the work of each module, conveying commands to execute the functions of each module, and adjusting the error compensation parameters according to actual needs to achieve the best error compensation effect.

[0221] The central control module is responsible for coordinating and managing the operation of the entire system. Here are some details and functions of the central control module in the GPS / INS system:

[0222] The central control module is the core part of the GPS / INS system. It is responsible for receiving, processing, fusing and outputting data from GPS and INS sensors. Through efficient algorithms and powerful computing capabilities, the central control module can provide accurate and reliable navigation and positioning information in real time.

[0223] In order to improve positioning accuracy, the central control module will use a variety of error correction technologies, such as satellite clock error correction, ionospheric delay correction, tropospheric delay correction, etc. In addition, it will also use the data provided by the INS sensor to assist in correcting the GPS positioning results.

[0224] The central control module will output the solution results to external devices or systems in a standard format. Through advanced algorithms and error correction technology, the central control module can provide high-precision navigation and positioning information. The central control module has the ability to quickly process large amounts of data and can achieve real-time navigation and positioning functions. With redundant design and fault-tolerant technology, the central control module can maintain stable operation in harsh environments. The central control module supports a variety of interfaces and protocols, and can be easily integrated and expanded with other systems or devices.

[0225] Furthermore, the system also includes: a first Kalman filter, which is arranged at the output end of the INS component, including a prediction part and an update part, and is configured to calculate the prior state estimate of the INS and the error covariance of the INS based on the prediction part according to the state estimation of the previous time step and the navigation data of the INS; based on the update part, calculate the posterior state estimate of the INS and the updated INS error covariance according to the prior estimate of the INS and the error covariance of the INS; then, adaptively adjust the gain to minimize the error covariance of the updated INS, so as to obtain the navigation data of the INS after filtering out the noise.

[0226] The first Kalman filter is arranged at the output end of the error compensation module, and includes a prediction part and an update part, and is configured to calculate, based on the prediction part, a priori state estimate of the error-compensated navigation data and an error covariance of the error-compensated navigation data according to the state estimate of the previous time step and the error-compensated navigation data; based on the update part of the second Kalman filter, calculate, based on the a priori estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data, a posteriori state estimate of the error-compensated navigation data and an updated error covariance of the error-compensated navigation data; and then, adaptively adjust the gain to minimize the error covariance of the updated error-compensated navigation data, so as to obtain the error-compensated navigation data after noise is filtered out.

[0227] The Kalman filter is used to filter out noise during the signal unlocking phase. The Kalman filter performs well in filtering out noise. It is based on the linear system state equation and uses the system input and output observation data to optimally estimate the system state. The following is a detailed assumption of the Kalman filter filtering out noise. The system state is linear, and both the process noise and the observation noise are Gaussian distributed. The Kalman filter implements state estimation through two steps: prediction and update. In the prediction phase, the current state is predicted based on the previous state and control input of the system; in the update phase, the prediction is updated using new measurement data, and a Kalman gain is calculated, which determines which part of the prediction and measurement is more reliable. The Kalman filter performs state estimation in a recursive manner. The state estimation at each moment takes into account the estimation result of the previous moment and the current observation value.

[0228] During the update phase, the Kalman filter calculates a Kalman gain, which determines which part of the prediction or measurement is more reliable. If the observation noise is small, it relies more on the observation value; if the prediction uncertainty is small, it relies more on the prediction value.

[0229] In this way, the Kalman filter is able to filter out noise in the observed data, providing a more accurate and reliable estimate of the system state.

[0230] In one embodiment, the Kalman filter: its implementation process is shown in the following formula.

[0231] ;

[0232] In the formula, and represents the probability density function, where To estimate the state based on the previous time step and the prediction of the current state based on the current input, it is expressed as , which is called the prior estimate, which is calculated before using the current measurement value. The above equation can be rewritten as: ;

[0233] In the formula, Use the current measurement to update the estimate, and the final result is called the posterior estimate.

[0234] As we can see, the Kalman filter is divided into two parts: prediction and update. In the prediction part, the prior state estimate and its error covariance are calculated, and it is known that the covariance has the following properties: If Y = FX, the covariance of X is P, then the covariance of Y is .

[0235] ;

[0236] In the update phase, the prior estimate is used to calculate the posterior state estimate and its error covariance: ;

[0237] Adjusting Kalman filter gains , so that the error covariance of the updated state value Minimum.

[0238] It is worth noting that two extreme cases need to be considered. When the measurement noise variance R is 0, , that is, the a posteriori estimate of the state quantity depends entirely on the measured value. When it is 0, , that is, the posterior estimate of the state quantity depends entirely on the prior estimate.

[0239] In summary, the embodiment of the present invention provides an error compensation method and system for a GPS / INS integrated navigation system. The present invention first obtains navigation data of GPS and INS, and generates error data by calculating and tracking the data difference between the two. Subsequently, an error prediction model is constructed, and the previously obtained error data is input into the model for training to perform future error prediction. In particular, in the case of GPS signal loss of lock, the method uses the INS navigation data during the loss of lock and the GPS data at the start to estimate the real-time navigation data of the period. Finally, the real-time navigation data during the loss of GPS signal is error compensated using the predicted data output by the error prediction model. Accordingly, the present invention also designs a GPS / INS integrated navigation error compensation system, whose main architecture includes four modules: data acquisition, KAN network, error compensation, and central control. This system realizes the fusion and error compensation of GPS and INS data through the KAN network, which not only combines the advantages of both, but also significantly improves the accuracy and reliability of the entire navigation system. It is worth mentioning that the KAN network, with its excellent data processing capabilities and fast response speed, can efficiently analyze GPS and INS data, and then provide accurate error compensation to ensure that the system can maintain the real-time and accuracy of navigation in a changing dynamic environment.

[0240] Therefore, the present invention cleverly utilizes the powerful learning ability of the KAN network to accurately learn and simulate the error distribution law of the vehicle-mounted GPS / INS combined navigation system. Through this innovative application, the present invention achieves more accurate compensation for navigation system errors. Compared with traditional error compensation technology, the solution of the present invention has significantly improved accuracy and exhibits stronger environmental adaptability, and can effectively cope with and handle error problems under a variety of different environmental conditions. In addition, the present invention also adheres to the concept of modular design, which not only greatly simplifies the implementation and maintenance process of the system, but also enables the system to have excellent scalability. This design facilitates flexible functional expansion and performance optimization according to actual application requirements, thereby providing users with more convenient and efficient navigation services.

[0241] It should be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention may 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.

[0242] It should be noted that in the scheme of the invention, the word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention may be implemented by means of hardware comprising a number of different components and by means of a suitably programmed computer. Where a number of means are listed, several of these means may be embodied by the same hardware. The use of the words first, second, third, etc., is for convenience only and does not indicate any order.

[0243] In addition, it should be noted that, in the description of this specification, the description of the terms "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0244] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments after being aware of the basic creative concepts. Therefore, the present invention should be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalents, the present invention should also include these modifications and variations.

Claims

1. A method for error compensation of a GPS / INS integrated navigation system, characterized in that: include: Obtain navigation data of GPS and INS of the GPS / INS integrated navigation system, calculate and track the difference of various attributes between the navigation data of GPS and INS to generate error data; An error prediction model is constructed based on the Kolmogorov-Arnold network, error data is input into the error prediction model for training, and the trained error prediction model is used for error prediction; When the GPS signal is in the unlocking stage, the real-time navigation data of the signal unlocking stage is obtained according to the navigation data of the INS in the signal unlocking stage and the navigation data of the GPS at the start time of the signal unlocking stage; According to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss stage is error compensated, and the error-compensated navigation data is output; The steps of obtaining the navigation data of GPS and INS of the GPS / INS integrated navigation system, calculating and tracking the difference of each attribute between the navigation data of GPS and INS to generate error data include: Receive the raw data from the GPS component of the GPS / INS integrated navigation system and resolve it into GPS navigation data including speed, coordinates and attitude angles in three directions; Receive the raw data from the INS component of the GPS / INS integrated navigation system, combine it with the GPS navigation data, and solve it into INS navigation data including the speed, coordinates, attitude angle, zero deflection angle of the accelerometer and the zero deflection angle of the gyroscope in three directions through integration processing, and use the solved GPS navigation data to correct the INS navigation data; Calculate the difference in velocity error, coordinate error, attitude angle error, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope between the navigation data of the GPS and the navigation data of the INS in three directions at set intervals or in response to a received difference obtaining instruction, track and record the difference, and generate error data; in, The navigation data of GPS is: ； In the formula, They are the speed information in three directions respectively. is the three-dimensional coordinate information in the inertial coordinate system, Respectively represent the attitude angle information in three directions; The navigation data of INS is: ； In the formula, is the zero deflection angle of the accelerometer in three directions, is the zero deflection angle of the gyroscope in three directions; The error data is: ； In the formula, They are the velocity error, coordinate error, attitude angle error, accelerometer zero deflection angle and gyroscope zero deflection angle differences in three directions respectively; And, when the GPS signal is in the unlocking stage, the real-time navigation data of the signal unlocking stage is obtained according to the navigation data of the INS in the signal unlocking stage and the navigation data of the GPS at the start time of the signal unlocking stage, including: Obtain GPS navigation data including speed, coordinates and attitude angle information at the start time of the GPS signal loss phase; Acquire the real-time data of the INS component of the GPS / INS integrated navigation system during the GPS signal loss phase, perform time integration on the real-time data of the INS component, and calculate the speed and displacement data at each moment during the GPS signal loss phase; For each moment during the GPS signal loss phase t The calculated speed and displacement data are fused with the GPS navigation data at the last moment of the signal lock phase to obtain the signal loss phase t Real-time navigation information at all times; in, The GPS navigation data at the start of the GPS signal loss phase is: ； The INS component in the GPS signal loss phase t The acceleration and attitude angle data at the moment are: ； GPS signal lost lock stage t The real-time navigation information at this moment is: ； In the formula, for t The speed in three directions at the moment, for t The coordinates in three directions at the moment, for t The attitude angles in three directions at the moment; Then, according to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss stage is error compensated, and the output navigation data after error compensation includes: Using the error prediction model, according to the start time of the GPS signal loss phase and t The difference of real-time navigation information at the moment, output t Error prediction data at the moment; according to t Error prediction data at time, construct t The error state equation at time t; Using the error state equation at time t, t The real-time navigation data at the moment is error compensated to obtain navigation data after error compensation; in, t The error state equation at time is: ； The navigation information after the error compensation stage is: 。 2. The error compensation method of the GPS / INS integrated navigation system as claimed in claim 1, characterized in that: According to the error prediction data output by the error prediction model, the real-time navigation data in the GPS signal loss lock stage is error compensated, and after the error compensated navigation data is output, the following is also included: The first Kalman filter is introduced, and the prediction part of the first Kalman filter is used to calculate the prior state estimate of the INS and the error covariance of the INS based on the state estimate of the previous time step and the navigation data of the INS; Based on the update part of the first Kalman filter, the posterior state estimate of the INS and the updated INS error covariance are calculated according to the prior estimate of the INS and the error covariance of the INS; The gain of the first Kalman filter is adjusted to minimize the error covariance of the updated INS, thereby obtaining the navigation data of the INS after noise is filtered out; Introducing a second Kalman filter, using a prediction part of the second Kalman filter, calculating a priori state estimate of the error-compensated navigation data and an error covariance of the error-compensated navigation data based on a state estimate of a previous time step and the error-compensated navigation data; Based on the updating part of the second Kalman filter, calculating the a posteriori state estimate of the error-compensated navigation data and the updated error covariance of the error-compensated navigation data according to the a priori estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data; The gain of the second Kalman filter is adjusted to minimize the error covariance of the updated error-compensated navigation data, thereby obtaining the error-compensated navigation data after noise is filtered out.

3. An error compensation system for a GPS / INS integrated navigation system, characterized in that: include: The integrated navigation module includes a GPS component and an INS component coupled with the GPS component, and is configured to automatically switch between the GPS component and the INS component for navigation according to the state of the GPS signal acquired by the GPS component; A data acquisition module is configured to obtain navigation data of GPS and INS of a GPS / INS integrated navigation system, calculate and track the difference of various attributes between the navigation data of GPS and INS to generate error data; The KAN network module is configured to build an error prediction model based on the Kolmogorov-Arnold network, perform model training according to input error data, and perform error prediction using the trained error prediction model; The error compensation module is configured to obtain real-time navigation data of the signal loss stage according to the navigation data of the INS in the signal loss stage and the navigation data of the GPS at the start time of the signal loss stage when the GPS signal is in the loss stage, perform error compensation on the real-time navigation data of the GPS signal loss stage according to the error prediction data output by the error prediction model, and output the navigation data after error compensation; The central control module is configured to receive at least one item of data from the integrated navigation module, the data acquisition module, the KAN network module and the error compensation module, and perform at least one operation of solving, compensating, adjusting and outputting the received data; The data acquisition module includes: A GPS data acquisition unit is configured to receive raw data from a GPS component of a GPS / INS integrated navigation system and resolve it into GPS navigation data including speed, coordinates and attitude angles in three directions; An INS data acquisition unit is configured to receive raw data from an INS component of a GPS / INS integrated navigation system, combine the raw data with the GPS navigation data, and calculate the raw data into INS navigation data including speed, coordinates, attitude angle, zero deflection angle of an accelerometer and zero deflection angle of a gyroscope in three directions through integration processing; An INS data correction unit configured to correct the navigation data of the INS using the resolved GPS navigation data; an error data generating unit, configured to calculate the difference in velocity error, coordinate error, attitude angle error, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope between the navigation data of the GPS and the navigation data of the INS in three directions at every set period or in response to a received difference obtaining instruction, track and record the difference, and generate error data; in, The navigation data of GPS is: ； In the formula, They are the speed information in three directions respectively. is the three-dimensional coordinate information in the inertial coordinate system, Respectively represent the attitude angle information in three directions; The navigation data of INS is: ； In the formula, is the zero deflection angle of the accelerometer in three directions, is the zero deflection angle of the gyroscope in three directions; The error data is: ； In the formula, They are the velocity error, coordinate error, attitude angle error, accelerometer zero deflection angle and gyroscope zero deflection angle differences in three directions respectively; And, the error compensation module includes: The error data acquisition unit is configured to acquire GPS navigation data including speed, coordinates and attitude angle information at the start time of the GPS signal loss phase; acquire real-time data of the INS component of the GPS / INS combined navigation system during the GPS signal loss phase, perform time integration operation on the real-time data of the INS component, and calculate the speed and displacement data at each time during the GPS signal loss phase; The data fusion processing unit is configured to process the GPS signal at each moment of the loss of lock. t The calculated speed and displacement data are fused with the GPS navigation data at the last moment of the signal lock phase to obtain the signal loss phase t Real-time navigation information at all times; The error state output unit is configured to use the error prediction model to calculate the error state according to the starting time of the GPS signal loss lock phase and the t The difference of real-time navigation information at the moment, output t The error prediction data at the moment is based on t Error prediction data at time, construct t The error state equation at time t; The error compensation unit is configured to utilize t The error state equation at time t The real-time navigation data at the moment is error compensated to obtain navigation data after error compensation; in, The GPS navigation data at the start of the GPS signal loss phase is: ； The INS component in the GPS signal loss phase t The acceleration and attitude angle data at the moment are: ； GPS signal lost lock stage t The real-time navigation information at this moment is: ； ； In the formula, for t The speed in three directions at the moment, for t The coordinates in three directions at the moment, for t The attitude angles in three directions at the moment; t The error state equation at time is: ； The navigation information after the error compensation stage is: 。 4. The error compensation system of the GPS / INS integrated navigation system as claimed in claim 3, characterized in that: The integrated navigation module includes: A GPS component is configured to collect GPS raw data and send the GPS raw data to a central control module to calculate GPS navigation data including speed information, position information and attitude angle information; An INS component, operating in parallel with the GPS component and coupled to each other, includes an accelerometer and a gyroscope, and is configured to collect INS raw data and send the INS raw data to the central control module to be resolved into INS navigation data including speed, coordinates, attitude angle, zero deflection angle of the accelerometer and zero deflection angle of the gyroscope in three directions through integration processing; The processing unit is connected to the GPS component and the INS component respectively, and is configured to automatically switch to the INS component for navigation when the GPS signal is in a lost lock stage.

5. The error compensation system of the GPS / INS integrated navigation system as claimed in claim 3, characterized in that: include: a first Kalman filter, disposed at an output of the INS component, comprising a prediction portion and an update portion, configured to calculate, based on the prediction portion, a priori state estimate of the INS and an error covariance of the INS according to a state estimate of a previous time step and navigation data of the INS; Based on the update part, the posterior state estimate of INS and the updated error covariance of INS are calculated according to the prior estimate of INS and the error covariance of INS; Afterwards, the gain is adaptively adjusted to minimize the error covariance of the updated INS, thereby obtaining the navigation data of the INS after noise is filtered out; a second Kalman filter, disposed at an output end of the error compensation module, comprising a prediction part and an update part, configured to calculate, based on the prediction part, a priori state estimate of the error-compensated navigation data and an error covariance of the error-compensated navigation data according to a state estimate of a previous time step and the error-compensated navigation data; Based on the updating part of the second Kalman filter, calculating the a posteriori state estimate of the error-compensated navigation data and the updated error covariance of the error-compensated navigation data according to the a priori estimate of the error-compensated navigation data and the error covariance of the error-compensated navigation data; Afterwards, the gain is adaptively adjusted to minimize the error covariance of the updated error-compensated navigation data, thereby obtaining the error-compensated navigation data after noise is filtered out.

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