A super-high-precision fiber inertial measurement unit temperature modeling method based on a Transformer algorithm
By using an intelligent modeling method based on the Transformer algorithm, which combines physical modeling with intelligent algorithm prediction of residuals, the problems of unmodelable errors and structural deformation errors in ultra-high precision fiber optic inertial navigation systems are solved, achieving high-precision temperature modeling and improving the accuracy of inertial instruments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING AEROSPACE TIMES OPTICAL ELECTRONICS TECH
- Filing Date
- 2026-04-29
- Publication Date
- 2026-07-24
AI Technical Summary
Existing temperature modeling methods cannot effectively compensate for unmodelable errors and structural deformation errors in ultra-high precision fiber optic inertial navigation systems, leading to a decrease in the accuracy of inertial instruments. Furthermore, commonly used least-squares fitting methods involve large computational loads and are difficult to fit nonlinear relationships.
An intelligent modeling method based on the Transformer algorithm is adopted, which combines physical modeling with intelligent algorithm prediction of residuals. By generating training data, identifying the optimal calibration parameters, and fitting with a BP neural network, an optimal temperature model is established to compensate for unmodelable errors and reduce structural deformation errors.
It improves the modeling accuracy of fiber optic inertial navigation systems, reduces the amount of computation, and effectively compensates for unmodelable errors and structural deformation errors, thereby enhancing the accuracy of inertial instruments.
Smart Images
Figure CN122452134A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for temperature modeling of ultra-high precision fiber optic inertial measurement units (FIMs), and more particularly to a method for temperature modeling of ultra-high precision fiber optic inertial measurement units based on the Transformer algorithm, which belongs to the field of inertial measurement unit combination modeling and calibration. Background Technology
[0002] With advancements in technology and manufacturing processes, and driven by applications in underwater and long-duration ship navigation, the accuracy of fiber optic inertial navigation systems (INS) is developing towards ultra-high precision. For example, the zero-bias stability of fiber optic gyroscopes is better than 0.0005° / h, and that of accelerometers is better than 5µg. As inertial devices achieve ultra-high precision, conventional temperature modeling methods are no longer suitable for modeling ultra-high precision fiber optic INS. Inaccurate modeling methods can lead to a decrease in the accuracy of inertial instruments, resulting in a mismatch between modeling methods and ultra-high precision instruments.
[0003] For three-self fiber optic inertial navigation systems (INS), a common temperature modeling method involves performing full-parameter self-calibration at various temperature points to obtain the zero-point, scaling factor, and installation error angle parameters at each temperature. Then, least-squares fitting is used to fit the relationships between the zero-point, scaling factor, and installation error angle with respect to temperature, temperature variability, and temperature gradient. However, for ultra-high-precision three-self fiber optic INS, the commonly used temperature modeling methods have the following problems: 1. The full-parameter self-calibration algorithm has errors, which can be even higher than the accuracy of ultra-high precision inertial devices. Moreover, these errors are not easy to model and compensate for, and they have strong nonlinearity. 2. The three-self fiber optic inertial navigation system (IINS) has structural deformation during the modeling process. This deformation will increase the error of the inertial instrument, which is not negligible in ultra-high precision fiber optic IINS. However, the commonly used temperature modeling methods cannot accurately calculate this part through modeling. 3. The zero point, scale factor and installation error curves of ultra-high precision inertial instruments have strong nonlinearity, which cannot be fitted by ordinary least squares fitting. Piecewise fitting will increase the amount of calculation and the segments must be fine enough to achieve accurate fitting. Summary of the Invention
[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide an ultra-high precision fiber optic inertial navigation system (FIS) temperature modeling method based on the Transformer algorithm. This method achieves ultra-high precision FIS temperature modeling by combining physical modeling with intelligent algorithm prediction of residuals.
[0005] The technical solution of this invention is: A method for ultra-high precision fiber optic inertial navigation system temperature modeling based on the Transformer algorithm includes the following steps: (1) Generate training data; (2) Identify the optimal calibration parameters based on the generated training data; (3) Iteratively solve the optimal calibration parameters at each temperature point, establish the functional relationship between the optimal calibration parameters and the influencing factors, and obtain the optimal temperature model of the fiber optic inertial navigation system by fitting it with a BP neural network.
[0006] Furthermore, the process of generating training data includes: (1.1) In Perform a full parameter self-calibration of the fiber optic inertial navigation system at the temperature point to obtain... The calibration parameters at the temperature point, among which ; Calibration parameters include , They represent The zero point of the triaxial gyroscope and the zero point of the triaxial accelerometer at the specified temperature; They represent The scaling factor of the triaxial gyroscope and the scaling factor of the triaxial accelerometer at the temperature point; They represent Installation errors of the gyroscope and accelerometer at the temperature point; (1.2) The calibration parameters in step (1.1) are traversed and set. The traversal setting of each calibration parameter includes the traversal range, traversal step size and number of loops; (1.3) Substitute each set of calibration parameters from (1.2) into the inertial error compensation model to obtain the compensated IMU data; (1.4) Perform strapdown navigation simulation on the compensated IMU data to obtain the velocity error under each set of calibration parameters. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. (1.5) Take each set of calibration parameters in step (1.2) as input and the velocity error in step (1.4) as output to obtain training data.
[0007] Furthermore, the calibration parameters are iterated and set, and the settings for each calibration parameter are shown in the table below:
[0008] Furthermore, the inertial error compensation model is an inertial instrument output error model based on the orthogonal coordinate system of the accelerometer, as shown in the following equation:
[0009]
[0010] In the above formula, These represent the measurement errors of the gyroscope instruments on the X, Y, and Z axes, respectively. These represent the measurement errors of the accelerometers on the X, Y, and Z axes, respectively. and These represent the outputs of the gyroscope and accelerometer, respectively. , , It is the zero position of the X, Y, and Z axis gyroscope instrument. , , It is the zero bias of the X, Y, and Z axis accelerometers.
[0011] Furthermore, the identification of optimal calibration parameters based on the generated training data specifically involves: (2.1) Train the Transformer network with the training data, where the input data is the calibration parameters of the traversal: The output data is the speed error. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. (2.2) Based on the traversal range of the calibration parameters, the calibration parameters are encoded using floating-point encoding, and a fitness function for the speed error is established; (2.3) Set the number of iterations and the population size for the GA algorithm; (2.4) Perform the selection, crossover, and mutation operations of the GA algorithm to update the individuals; (2.5) Substitute the individual into the trained Transformer network and calculate the fitness value according to the fitness function; (2.6) Record the minimum fitness value and solve for it. The optimal calibration parameters at the specified temperature point.
[0012] Furthermore, the fitness function for the velocity error is established as follows:
[0013] In the formula, Indicates the three-axis velocity. ; This represents the weighting coefficient for each speed error; The root mean square error representing the velocity; This indicates the number of velocity data points; Indicates each velocity point; This represents the true value of velocity, whose theoretical value is 0. It is the fitness function value.
[0014] Furthermore, the optimal calibration parameters at each temperature point are solved iteratively to establish a functional relationship between the optimal calibration parameters and the influencing factors. The optimal temperature model of the fiber optic inertial navigation system is then obtained by fitting a BP neural network. Specifically: (3.1) Repeat steps (1) and (2) to obtain Optimal calibration parameters at the specified temperature point; (3.2) Establish the functional relationship between the optimal calibration parameters and the influencing factors, including temperature, temperature variability, temperature gradient, and higher-order nonlinear error. The specific functional relationship is as follows:
[0015]
[0016]
[0017] In the above formula, These represent the zero point, scale factor, and installation error of the inertial instrument, respectively. These represent temperature, rate of temperature change, and temperature gradient, respectively. The i-th term represents the temperature; These represent the zero-partial constant, the zero-partial linear coefficient with respect to temperature, the zero-partial quadratic coefficient with respect to temperature, the zero-partial cubic coefficient with respect to temperature, the zero-partial linear coefficient with respect to the rate of temperature change, and the zero-partial linear coefficient with respect to the temperature gradient, respectively. These represent the constant value of the scaling factor, the coefficient of the first term of the scaling factor with respect to temperature, the coefficient of the second term of the scaling factor with respect to temperature, the coefficient of the third term of the scaling factor with respect to temperature, the coefficient of the first term of the scaling factor with respect to temperature change, and the coefficient of the first term of the scaling factor with respect to temperature gradient, respectively. These represent the constant value of installation error, the first-order coefficient of installation error with respect to temperature, the second-order coefficient of installation error with respect to temperature, the third-order coefficient of installation error with respect to temperature, the first-order coefficient of installation error with respect to temperature change rate, and the first-order coefficient of installation error with respect to temperature gradient, respectively. These represent stochastic processes for zero position, scaling factor, and installation error, respectively. The stochastic process represents unmodelable errors other than random walks. (3.3) The relationship between the optimal calibration parameters and the influencing factors was fitted by a BP neural network to obtain the full-temperature model of the ultra-high precision fiber optic inertial navigation system.
[0018] Furthermore, the unmodelable error is equivalent to a first-order Gaussian-Markov process:
[0019] In the above formula, Represents the inverse correlation time function, and Obtained by solving the Allan variance curve. The clustering time corresponding to the minimum point when the slope of the Allan variance curve is in the -0.5 region. , ; , This represents the variance value in the flat region where the slope of the Allan variance curve is 0. For Dirac function; Expressing expectations; For equivalent unmodelable error curves, Represents a zero-mean white noise process. To indicate different times.
[0020] Secondly, this invention also proposes an ultra-high precision fiber optic inertial navigation system temperature modeling system, comprising: Data generation module: Generates training data according to the following process; exist Perform a full parameter self-calibration of the fiber optic inertial navigation system at the temperature point to obtain... The calibration parameters at the temperature point, among which Calibration parameters include: , They represent The zero point of the triaxial gyroscope and the zero point of the triaxial accelerometer at the specified temperature; They represent The scaling factor of the triaxial gyroscope and the scaling factor of the triaxial accelerometer at the temperature point; They represent Installation errors of the gyroscope and accelerometer at the temperature point; The calibration parameters are iterated and set, including the iteration range, iteration step size and number of iterations for each calibration parameter; Substitute each set of calibration parameters after iteration into the inertial error compensation model to obtain the compensated IMU data; Strapdown navigation simulation was performed on the compensated IMU data to obtain the velocity error under each set of calibration parameters. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. The training data is obtained by taking each set of calibration parameters after traversal as input and the speed error as output. Parameter identification module: Identifies the optimal calibration parameters based on the generated training data; The optimal model determination module iteratively solves for the optimal calibration parameters at each temperature point, establishes the functional relationship between the optimal calibration parameters and the influencing factors, and obtains the optimal temperature model of the fiber optic inertial navigation system by fitting it with a BP neural network.
[0021] The advantages of this invention compared to the prior art are: (1) The method of the present invention can compensate for the unmodelable error in the full parameter self-calibration algorithm, making the calibration parameters at each temperature point more accurate; (2) The method of the present invention does not require calculation of inertial instrument errors caused by structural deformation during the modeling process. Instead, it uses intelligent algorithms to incorporate these errors into the error model, thereby further improving the modeling accuracy. (3) The method of the present invention uses a BP neural network that is easy to implement in DSP to replace the least squares algorithm for data fitting, which can reduce the amount of computation while improving the modeling accuracy. Attached Figure Description
[0022] Figure 1 This illustrates the steps involved in generating training data; Figure 2 The steps for identifying the optimal calibration parameters are shown. Figure 3 This shows the steps for constructing the optimal temperature model. Detailed Implementation
[0023] This invention addresses the unmodelable errors present in the modeling process of ultra-high precision fiber optic inertial navigation systems (ISS), such as algorithmic errors and structural deformation errors. It integrates a Transformer+GA+BP neural network intelligent algorithm into the ordinary full-parameter self-calibration modeling process, using the intelligent algorithm to allocate these errors to the error model. Temperature modeling of ultra-high precision fiber optic ISS is achieved through a combination of physical modeling and intelligent algorithm prediction of residuals.
[0024] The present invention proposes an ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm, which includes three implementation steps.
[0025] The first step is the generation of training data; The second step is to identify the optimal calibration parameters based on the generated training data; The third step is to construct the optimal temperature model: iteratively solve for the optimal calibration parameters at each temperature point, establish the functional relationship between the optimal calibration parameters and the influencing factors, and obtain the optimal temperature model of the fiber optic inertial navigation system by fitting it with a BP neural network.
[0026] The above three steps enable the intelligent acquisition of the optimal calibration parameters at each temperature point. A BP neural network is used to fit the relationship between the optimal calibration parameters and the influencing factors. The influencing factors include temperature, temperature change rate, temperature gradient, etc., which have strict physical meaning, as well as high-order nonlinear errors that cannot be modeled. These errors are mainly caused by non-negligible errors in the modeling process of ultra-high precision fiber optic inertial navigation systems, such as errors generated by self-calibration algorithms and errors caused by structural deformation in temperature modeling.
[0027] like Figure 1 As shown, the specific process for generating training data includes: (1.1) In Perform a full parameter self-calibration of the fiber optic inertial navigation system at the temperature point to obtain... The calibration parameters at the temperature point, among which ; Calibration parameters include , They represent The zero point of the triaxial gyroscope and the zero point of the triaxial accelerometer at the specified temperature; They represent The scaling factor of the triaxial gyroscope and the scaling factor of the triaxial accelerometer at the temperature point; They represent Installation errors of the gyroscope and accelerometer at the temperature point; (1.2) The calibration parameters in step (1.1) are traversed and set. The traversal setting of each calibration parameter includes the traversal range, traversal step size and number of loops; (1.3) Substitute each set of calibration parameters from (1.2) into the inertial error compensation model to obtain the compensated IMU data; (1.4) Perform strapdown navigation simulation on the compensated IMU data to obtain the velocity error under each set of calibration parameters. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. (1.5) Take each set of calibration parameters in step (1.2) as input and the velocity error in step (1.4) as output to obtain training data.
[0028] In this invention, the inertial error compensation model is an inertial instrument output error model based on the orthogonal coordinate system of the accelerometer, as shown in the following equation:
[0029]
[0030] In the above formula, These represent the measurement errors of the gyroscope instruments on the X, Y, and Z axes, respectively. These represent the measurement errors of the accelerometers on the X, Y, and Z axes, respectively. and These represent the outputs of the gyroscope and accelerometer, respectively. , , It is the zero position of the X, Y, and Z axis gyroscope instrument. , , It is the zero bias of the X, Y, and Z axis accelerometers.
[0031] like Figure 2 As shown, based on the generated training data, the optimal calibration parameters are identified, specifically as follows: (2.1) Train the Transformer network with the training data, where the input data is the calibration parameters of the traversal: The output data is the speed error. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. (2.2) Based on the traversal range of the calibration parameters, the calibration parameters are encoded using floating-point encoding, and a fitness function for the speed error is established; (2.3) Set the number of iterations and the population size for the GA algorithm; (2.4) Perform the selection, crossover, and mutation operations of the GA algorithm to update the individuals; (2.5) Substitute the individual into the trained Transformer network and calculate the fitness value according to the fitness function; (2.6) Record the minimum fitness value and solve for it. The optimal calibration parameters at the specified temperature point.
[0032] In this invention, the fitness function for velocity error is established as follows:
[0033] In the formula, Indicates the three-axis velocity. ; This represents the weighting coefficient for each speed error; The root mean square error representing the velocity; This indicates the number of velocity data points; Indicates each velocity point; This represents the true value of velocity, whose theoretical value is 0. It is the fitness function value.
[0034] like Figure 3As shown, the optimal calibration parameters at each temperature point are solved iteratively to establish a functional relationship between the optimal calibration parameters and the influencing factors. The optimal temperature model of the fiber optic inertial navigation system is then obtained by fitting a BP neural network. Specifically: (3.1) Repeat steps (1) and (2) to obtain Optimal calibration parameters at the specified temperature point; (3.2) Establish the functional relationship between the optimal calibration parameters and the influencing factors, including temperature, temperature variability, temperature gradient, and higher-order nonlinear error. The specific functional relationship is as follows:
[0035]
[0036]
[0037] In the above formula, These represent the zero point, scale factor, and installation error of the inertial instrument, respectively. These represent temperature, rate of temperature change, and temperature gradient, respectively. The i-th term represents the temperature; These represent the zero-partial constant, the zero-partial linear coefficient with respect to temperature, the zero-partial quadratic coefficient with respect to temperature, the zero-partial cubic coefficient with respect to temperature, the zero-partial linear coefficient with respect to the rate of temperature change, and the zero-partial linear coefficient with respect to the temperature gradient, respectively. These represent the constant value of the scaling factor, the coefficient of the first term of the scaling factor with respect to temperature, the coefficient of the second term of the scaling factor with respect to temperature, the coefficient of the third term of the scaling factor with respect to temperature, the coefficient of the first term of the scaling factor with respect to temperature change, and the coefficient of the first term of the scaling factor with respect to temperature gradient, respectively. These represent the constant value of installation error, the first-order coefficient of installation error with respect to temperature, the second-order coefficient of installation error with respect to temperature, the third-order coefficient of installation error with respect to temperature, the first-order coefficient of installation error with respect to temperature change rate, and the first-order coefficient of installation error with respect to temperature gradient, respectively. These represent stochastic processes for zero position, scaling factor, and installation error, respectively. The stochastic process represents unmodelable errors other than random walks. (3.3) The relationship between the optimal calibration parameters and the influencing factors was fitted by a BP neural network to obtain the full-temperature model of the ultra-high precision fiber optic inertial navigation system.
[0038] Furthermore, the unmodelable error is equivalent to a first-order Gaussian-Markov process:
[0039] In the above formula, Represents the inverse correlation time function, and Obtained by solving the Allan variance curve. The clustering time corresponding to the minimum point when the slope of the Allan variance curve is in the -0.5 region. , ; , This represents the variance value in the flat region where the slope of the Allan variance curve is 0. For Dirac function; Expressing expectations; For equivalent unmodelable error curves, Represents a zero-mean white noise process. To indicate different times.
[0040] Example: This method mainly consists of three implementation steps, each of which is further divided into several implementation steps, as detailed below: Step 1: Generating Training Data. Calibration parameters play a decisive role in navigation results, and there is an inherently complex relationship between the two. Therefore, this method utilizes the Transformer algorithm to fit the relationship between them. Calibration parameters include... The navigation result selected is velocity error because the true value of attitude error is difficult to obtain accurately, while the true value of velocity error is 0. Velocity error can also reflect position error. Velocity error includes... .
[0041] The generation of training data can be broken down into the following steps: ① In Temperature points were calibrated once using 19 positions with full parameters. The calibration parameters at the temperature point, among which The calibration parameters include .
[0042] ② For the calibration parameters in step ① The calibration parameters were iterated and configured. To improve the accuracy of the Transformer model, the training data sample was increased to a certain range. Combined with the performance indicators of the ultra-high precision inertial instrument, the calibration parameters were iterated and configured. The settings for each calibration parameter are shown in the table below:
[0043] The number of calibration parameter sets formed by combining the calibration parameters in the table above is the sum of the number of cycles n plus 1 to the power of 6, which is 11. 11 11 11 11 11=11 6That is, the training data samples are 11 6 Group.
[0044] ③ Adjust the calibration parameters (11) in ② 6 Substituting the group into the 19-position compensation model, we obtain the compensated IMU data (11). 6 (Group). The position output error model of inertial instrument 19 based on the orthogonalized coordinate system of the accelerometer is shown in the following equation:
[0045]
[0046] In the above formula, These represent the measurement errors of the gyroscope instruments on the X, Y, and Z axes, respectively. These represent the measurement errors of the accelerometers on the X, Y, and Z axes, respectively. and These represent the outputs of the gyroscope and accelerometer, respectively. , , It is the zero position of the X, Y, and Z axis gyroscope instrument. , , It is the zero bias of the X, Y, and Z axis accelerometers.
[0047] ④ Substitute the compensated IMU data into the pure inertial simulation program sequentially. Since the calibration data at position 19 is performed under purely static conditions, the true value of the velocity is 0. The velocity error under each set of calibration parameters can then be calculated. .
[0048] ⑤ Using each set of calibration data as input and the speed error as output, we obtain 11. 6 Group training data.
[0049] Step Two: Identification of Optimal Calibration Parameters. This step involves continuously updating individual data points using the GA algorithm after training the Transformer model. These updated data points are then fed back into the Transformer model to obtain the fitness value for each individual. The GA algorithm uses this fitness value as the evaluation criterion to continuously optimize and ultimately identify the optimal parameters. The detailed steps are as follows: ① Train the Transformer using training data. This is an acyclic, synchronous, highly efficient algorithm with self-attention. The input data for the algorithm consists of the calibration parameters of the traversal: The output data is the speed error. That is, the eastward velocity error, the northward velocity error, and the celestial velocity error; ② Encode the calibration parameters and establish a fitness function. Based on the traversal range of the calibration parameters, adopt an intuitive, high-precision, and continuously optimizable floating-point encoding method.
[0050] The fitness function for velocity error is established as follows:
[0051] In the formula, Indicates the three-axis velocity. ; This represents the weighting coefficient for each speed error; The root mean square error representing the velocity; This indicates the number of velocity data points; Indicates each velocity point; This represents the true value of velocity, whose theoretical value is 0. It is the fitness function value.
[0052] ③ Set the number of iterations and population size for the GA algorithm. Based on the range of calibration parameters, the population size is set to 200, the number of iterations is 200, the crossover probability is set to 0.9, the mutation probability is 0.8, and the selection strategy is roulette wheel selection.
[0053] ④ Perform selection, crossover, and mutation operations using the GA algorithm to update the individuals; ⑤ Input the updated individuals into the trained Transformer network and calculate the fitness value of each individual based on the fitness function; ⑥ Record the minimum fitness value and solve for it. The optimal calibration parameters at a given temperature point. The optimal calibration parameters are those corresponding to the individual with the minimum fitness value, and these values are recorded and saved in each iteration.
[0054] Step 3: Construction of the Optimal Temperature Model. This step involves modeling the temperature based on the optimal calibration parameters obtained in Step 2. This step establishes the functional relationship between the optimal calibration parameters and influencing factors, including temperature, temperature variability, temperature gradient, and higher-order nonlinear errors. The specific error formula is as follows:
[0055]
[0056]
[0057] These represent the zero point, scale factor, and installation error of the inertial instrument, respectively. These represent temperature, rate of temperature change, and temperature gradient, respectively. The i-th term represents the temperature; These represent the zero-partial constant, the zero-partial linear coefficient with respect to temperature, the zero-partial quadratic coefficient with respect to temperature, the zero-partial cubic coefficient with respect to temperature, the zero-partial linear coefficient with respect to the rate of temperature change, and the zero-partial linear coefficient with respect to the temperature gradient, respectively. These represent the constant value of the scaling factor, the coefficient of the first term of the scaling factor with respect to temperature, the coefficient of the second term of the scaling factor with respect to temperature, the coefficient of the third term of the scaling factor with respect to temperature, the coefficient of the first term of the scaling factor with respect to temperature change, and the coefficient of the first term of the scaling factor with respect to temperature gradient, respectively. These represent the constant value of installation error, the first-order coefficient of installation error with respect to temperature, the second-order coefficient of installation error with respect to temperature, the third-order coefficient of installation error with respect to temperature, the first-order coefficient of installation error with respect to temperature change rate, and the first-order coefficient of installation error with respect to temperature gradient, respectively. Let represent the stochastic processes for zero position, scaling factor, and installation error, respectively. The stochastic process represents the unmodelable error other than the random walk, and this part of the error is equivalent to a first-order Gaussian-Markov process:
[0058] In the above formula, Represents the inverse correlation time function, and Obtained by solving the Allan variance curve. The clustering time corresponding to the minimum point when the slope of the Allan variance curve is in the -0.5 region. , ; , This represents the variance value in the flat region where the slope of the Allan variance curve is 0. For Dirac function; Expressing expectations; For equivalent unmodelable error curves, Represents a zero-mean white noise process. To indicate different times.
[0059] ③ A BP neural network is used to fit the relationship between the optimal calibration parameters and the influencing factors to obtain the full-temperature model of the ultra-high precision fiber optic inertial navigation system. The BP neural network has a relatively simple function expression formula, is easy to implement in DSP, has less computational cost than multiple piecewise modeling, and has better fitting accuracy than piecewise least squares modeling.
[0060] The parts of this invention not described in detail are common knowledge to those skilled in the art.
Claims
1. A method for ultra-high precision fiber optic inertial navigation system temperature modeling based on the Transformer algorithm, characterized in that, include: Generate training data; Based on the generated training data, the optimal calibration parameters are identified; The optimal calibration parameters at each temperature point are solved iteratively to establish the functional relationship between the optimal calibration parameters and the influencing factors. The optimal temperature model of the fiber optic inertial navigation system is obtained by fitting the model using a BP neural network.
2. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 1, characterized in that: The process of generating training data includes: (1.1) In Perform a full parameter self-calibration of the fiber optic inertial navigation system at the temperature point to obtain... The calibration parameters at the temperature point, among which ; Calibration parameters include , They represent The zero point of the triaxial gyroscope and the zero point of the triaxial accelerometer at the specified temperature; They represent The scaling factor of the triaxial gyroscope and the scaling factor of the triaxial accelerometer at the specified temperature point; They represent Installation errors of the gyroscope and accelerometer at the temperature point; (1.2) The calibration parameters in step (1.1) are traversed and set. The traversal setting of each calibration parameter includes the traversal range, traversal step size and number of loops; (1.3) Substitute each set of calibration parameters from (1.2) into the inertial error compensation model to obtain the compensated IMU data; (1.4) Perform strapdown navigation simulation on the compensated IMU data to obtain the velocity error under each set of calibration parameters. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. (1.5) Take each set of calibration parameters in step (1.2) as input and the velocity error in step (1.4) as output to obtain training data.
3. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 2, characterized in that: The calibration parameters are set iteratively, and the settings for each calibration parameter are shown in the table below: 。 4. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 2, characterized in that: The inertial error compensation model is the inertial instrument output error model based on the orthogonal coordinate system of the accelerometer, as shown in the following equation: In the above formula, These represent the measurement errors of the gyroscope instruments on the X, Y, and Z axes, respectively. These represent the measurement errors of the accelerometers on the X, Y, and Z axes, respectively. and These represent the outputs of the gyroscope and accelerometer, respectively. , , It is the zero position of the X, Y, and Z axis gyroscope instrument. , , It is the zero bias of the X, Y, and Z axis accelerometers.
5. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 2, characterized in that: The identification of optimal calibration parameters based on the generated training data specifically involves: (2.1) Train the Transformer network with the training data, where the input data is the calibration parameters of the traversal: The output data is the speed error. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. (2.2) Based on the traversal range of the calibration parameters, the calibration parameters are encoded using floating-point encoding, and a fitness function for the speed error is established; (2.3) Set the number of iterations and the population size for the GA algorithm; (2.4) Perform the selection, crossover, and mutation operations of the GA algorithm to update the individuals; (2.5) Substitute the individual into the trained Transformer network and calculate the fitness value according to the fitness function; (2.6) Record the minimum fitness value and solve for it. The optimal calibration parameters at the specified temperature point.
6. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 5, characterized in that: The fitness function for velocity error is established as follows: In the formula, Indicates the three-axis velocity. ; This represents the weighting coefficient for each speed error; The root mean square error representing the velocity; This indicates the number of velocity data points; Indicates each velocity point; This represents the true value of velocity, whose theoretical value is 0. It is the fitness function value.
7. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 5, characterized in that: The process involves iteratively solving for the optimal calibration parameters at each temperature point, establishing a functional relationship between the optimal calibration parameters and influencing factors, and then fitting the optimal temperature model of the fiber optic inertial navigation system using a BP neural network. Specifically: (3.1) Repeat steps (1) and (2) to obtain Optimal calibration parameters at the specified temperature point; (3.2) Establish the functional relationship between the optimal calibration parameters and the influencing factors, including temperature, temperature variability, temperature gradient, and higher-order nonlinear error. The specific functional relationship is as follows: In the above formula, These represent the zero point, scale factor, and installation error of the inertial instrument, respectively. These represent temperature, rate of temperature change, and temperature gradient, respectively. The i-th term represents the temperature; These represent the zero-partial constant, the zero-partial linear coefficient with respect to temperature, the zero-partial quadratic coefficient with respect to temperature, the zero-partial cubic coefficient with respect to temperature, the zero-partial linear coefficient with respect to the rate of temperature change, and the zero-partial linear coefficient with respect to the temperature gradient, respectively. These represent the constant value of the scaling factor, the coefficient of the first term of the scaling factor with respect to temperature, the coefficient of the second term of the scaling factor with respect to temperature, the coefficient of the third term of the scaling factor with respect to temperature, the coefficient of the first term of the scaling factor with respect to temperature change, and the coefficient of the first term of the scaling factor with respect to temperature gradient, respectively. These represent the constant value of installation error, the first-order coefficient of installation error with respect to temperature, the second-order coefficient of installation error with respect to temperature, the third-order coefficient of installation error with respect to temperature, the first-order coefficient of installation error with respect to temperature change rate, and the first-order coefficient of installation error with respect to temperature gradient, respectively. These represent stochastic processes for zero position, scaling factor, and installation error, respectively. The stochastic process represents unmodelable errors other than random walks. (3.3) The relationship between the optimal calibration parameters and the influencing factors was fitted by a BP neural network to obtain the full-temperature model of the ultra-high precision fiber optic inertial navigation system.
8. The ultra-high precision fiber optic inertial navigation system temperature modeling method based on the Transformer algorithm according to claim 7, characterized in that: The unmodelable error is equivalent to a first-order Gaussian-Markov process: In the above formula, Represents the inverse correlation time function, and Obtained by solving the Allan variance curve. The clustering time corresponding to the minimum point when the slope of the Allan variance curve is in the -0.5 region. , ; , This represents the variance value in the flat region where the slope of the Allan variance curve is 0. For Dirac function; Expressing expectations; For equivalent unmodelable error curves, Represents a zero-mean white noise process. To indicate different times.
9. An ultra-high precision fiber optic inertial navigation system temperature modeling system based on the ultra-high precision fiber optic inertial navigation system temperature modeling method according to any one of claims 1-8, characterized in that, include: Data generation module: Generates training data according to the following process; exist Perform a full parameter self-calibration of the fiber optic inertial navigation system at the temperature point to obtain... The calibration parameters at the temperature point, among which ; The calibration parameters include: , They represent The zero point of the triaxial gyroscope and the zero point of the triaxial accelerometer at the specified temperature; They represent The scaling factor of the triaxial gyroscope and the scaling factor of the triaxial accelerometer at the specified temperature point; They represent Installation errors of the gyroscope and accelerometer at the temperature point; The calibration parameters are iterated and set, including the iteration range, iteration step size and number of iterations for each calibration parameter; Substitute each set of calibration parameters after iteration into the inertial error compensation model to obtain the compensated IMU data; Strapdown navigation simulation was performed on the compensated IMU data to obtain the velocity error under each set of calibration parameters. These are the eastward velocity error, the northward velocity error, and the celestial velocity error. The training data is obtained by taking each set of calibration parameters after traversal as input and the speed error as output. Parameter identification module: Identifies the optimal calibration parameters based on the generated training data; The optimal model determination module iteratively solves for the optimal calibration parameters at each temperature point, establishes the functional relationship between the optimal calibration parameters and the influencing factors, and obtains the optimal temperature model of the fiber optic inertial navigation system by fitting it with a BP neural network.