Inertial microsystem multi-parameter BP neural network temperature compensation method
By using a multi-parameter BP neural network temperature compensation method, a multi-parameter coupled error model is established and trained using an adaptive learning rate momentum method. This achieves high precision and stability of the inertial microsystem under complex temperature environments, solving the problem of insufficient precision and stability in existing technologies.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-18
- Publication Date
- 2026-03-31
AI Technical Summary
Existing temperature compensation technologies for inertial microsystems struggle to achieve a balance between compensation accuracy, physical consistency, and engineering feasibility, and are unable to effectively address the multi-parameter coupling effects under complex temperature scenarios, resulting in insufficient accuracy and stability.
A multi-parameter BP neural network temperature compensation method is adopted. A multi-parameter coupled error model is established through a calibration dataset covering the entire temperature range. A BP neural network compensation model is constructed and trained using the adaptive learning rate momentum method. The learning rate is dynamically adjusted to optimize the network weights and bias parameters, thereby achieving real-time temperature compensation.
It significantly improves the output accuracy and stability of inertial microsystems under complex temperature environments, ensuring high accuracy and long-term stability of the system across the entire temperature range, and solves the problem of insufficient generalization and robustness of compensation models in existing technologies.
Smart Images
Figure CN121761877A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a multi-parameter BP neural network temperature compensation method for inertial microsystems, belonging to the field of inertial navigation technology. Background Technology
[0002] Inertial microsystems (IMS), as core components of navigation, guidance, and attitude control systems, are widely used in microsatellites, missile guidance, and unmanned aerial vehicles (UAVs) due to their small size, low cost, and high reliability. However, compared to high-precision fiber optic or laser inertial systems, the output accuracy of IMS instruments, made entirely of silicon, is significantly affected by changes in ambient temperature. Temperature variations not only cause nonlinear drift in key parameters such as sensor zero bias and scaling factor, but also lead to changes in parameters such as cross-coupling coefficients between axes, installation error angles, and sensitivity, forming a complex multi-parameter coupled temperature effect. This effect severely restricts the accuracy and stability of IMS in a wide temperature range environment.
[0003] The current inertial microsystem temperature compensation technology has the following defects: (1) Based on the physical model method, the compensation is carried out by establishing the fitting relationship between temperature and a single error parameter. However, the coupling temperature effect between multiple parameters is ignored. It is difficult to accurately fit the complex nonlinear and multi-parameter coupled temperature effect. The high-order polynomial fitting is prone to overfitting, resulting in poor generalization of the compensation model and difficulty in adapting to the actual complex dynamic temperature scenario; (2) Based on the data-driven intelligent method, although the nonlinear fitting ability is strong, the network structure and physical error lack physical constraints, which leads to the failure of internal parameters of the system. The generalization ability and robustness under unknown temperature conditions are insufficient, and the engineering practicality is poor.
[0004] In summary, existing technologies struggle to achieve an effective balance between compensation accuracy, physical consistency, and engineering feasibility, thus hindering breakthroughs in the accuracy of inertial microsystems under complex temperature fields. Summary of the Invention
[0005] The technical problem solved by this invention is: addressing the issue that the temperature compensation of inertial systems in the current technology cannot achieve a balance between accuracy and feasibility, a multi-parameter BP neural network temperature compensation method for inertial microsystems is proposed.
[0006] The present invention solves the above-mentioned technical problem through the following technical solution: A multi-parameter BP neural network temperature compensation method for inertial microsystems includes: Inertial microsystem calibration was performed across the entire temperature range, and the raw outputs of the gyroscope and accelerometer were collected at different temperature points. ， Establish a calibration dataset for temperature-output characteristics; A multi-parameter coupling error model, including zero bias, scaling factor, cross-coupling coefficient, and sensitivity coefficient, is established based on the calibration dataset. Using temperature value, zero-bias stability parameter and error coupling coefficient in multi-parameter coupled error model as input, and compensation parameter as output, a BP neural network compensation model for real-time error compensation is constructed. The adaptive learning rate momentum method is used to train the BP neural network compensation model. The learning rate is dynamically adjusted according to the training error to obtain the optimal network weights and bias parameters. The optimal network weights and bias parameters are input into the BP neural network compensation model, and the updated BP neural network compensation model is burned into the inertial microsystem. The inertial microsystem calculates and outputs the temperature-compensated data in real time.
[0007] The multi-parameter coupling error model is as follows:
[0008] In the formula, Y 1 represents the data before compensation. W For scaling factors and cross-coupling matrix, B ( T This is a temperature-dependent zero bias. G for g Sensitivity matrix, A External input of exercise volume ，C This is the temperature hysteresis coefficient matrix. T 0 represents the training temperature.
[0009] The network weights of the BP neural network compensation model The update method is as follows:
[0010] In the formula, E This is a composite loss function that includes temperature drift error and coupling error. or For learning rate, α Momentum factor Network weights The weights of each layer are adjusted through backpropagation of the error in the update after the last training, so as to compensate for the multi-parameter coupling error.
[0011] Based on the change in network weight coefficients A backpropagation (BP) neural network compensation model is established, consisting of an input layer, hidden layers, and an output layer. The compensation parameters output by the BP neural network compensation model are... z j for:
[0012] In the formula, the zero-bias correction of the output layer nodes of the BP neural network compensation model after compensation is ΔB0, the scaling factor correction is ΔK, the cross-coupling correction is ΔC, and the sensitivity correction is ΔS. The activation function of the hidden layer is the modified linear unit function. x i For the first i The input of each input layer node, w ji The connection weights from the input layer to the hidden layer. b j This is the bias of the hidden layer nodes.
[0013] The composite loss function E The weighted sum of temperature drift error and coupling error is calculated as follows:
[0014] In the formula, N The number of training samples, For the first k The system output after neural network compensation for each sample The output is the corresponding compensated output. P m The first parameter in the multi-parameter coupled error model m One error parameter, P m,ref This is the calibration value of the error parameter at the reference temperature. l 1 and l 2 is the weighting coefficient.
[0015] The first parameter in the multi-parameter coupling error model m Error parameters P m The update includes the elastic weights of temperature-zero bias coupling, and the amount of temperature-zero bias coupling elastic weight update. The update method is as follows:
[0016] In the formula, W b For the weights of the neural network with zero bias correlation, Ω b This is a Gaussian temperature-weighted zero-bias matrix. The zero-bias temperature coefficient at the current temperature. It is a periodic temperature characteristic.
[0017] In the adaptive learning rate momentum method, the learning rate is dynamically adjusted. The method is as follows:
[0018] In the formula, γ is the attenuation coefficient. and For the first i、i+1 Learning rate during each training iteration loss function E exist t , t-1 The gradient vector at each iteration, after training, is burned into the storage unit of the inertial microsystem for real-time temperature compensation.
[0019] The inertial microsystem adopts a time-sharing collaborative compensation strategy. By establishing multi-parameter BP neural network compensation models for the gyroscope and accelerometer respectively, CPU memory is dynamically allocated according to the working mode of the inertial microsystem. The workflow of the inertial microsystem includes static and dynamic calibration and navigation calculation. When performing navigation calculations for inertial microsystems, the neural network compensation calculations of the gyroscope are performed first, and the compensation parameters and linear interpolation parameters from the previous moment are used to compensate the accelerometer in real time. When performing static and dynamic calibrations on an inertial microsystem, multi-parameter BP neural network compensation calculations for the gyroscope and accelerometer are performed simultaneously, and the compensation parameters of the accelerometer are smoothed and filtered.
[0020] The inertial microsystem is implemented through an integrated design on an information processing SiP chip, which is designed with a stacked micro interconnect structure.
[0021] The advantages of this invention compared to the prior art are: (1) The present invention provides a multi-parameter BP neural network temperature compensation method for inertial microsystems. By establishing a two-level compensation structure of "multi-parameter physical model + BP neural network", a multi-parameter error model is established based on the system calibration data. The BP neural network takes the real-time error parameters, temperature, and zero-bias stability calculated by the multi-parameter error model as input and outputs the precise compensation increment for the model parameters. This enables the neural network to perform refined nonlinear compensation within the constraint framework of the physical model. (2) The temperature compensation method of multi-parameter BP neural network for inertial microsystems adopted in this invention is based on the dual constraint training mechanism of composite loss function. It combines adaptive learning rate momentum method with simulated annealing weight initialization strategy, dynamically adjusts the learning rate by judging gradient direction consistency, and optimizes the initial point by global random search, which effectively improves training efficiency and convergence quality. Through the triple guarantee of fixed-point weight quantization, quantization-aware retraining and robustness verification before burning, the problem of maintaining the accuracy of floating-point model to embedded system is solved. Attached Figure Description
[0022] Figure 1 A flowchart of the multi-parameter BP neural network temperature compensation method for inertial microsystems provided by the present invention; Figure 2A schematic diagram of the multi-parameter BP neural network structure for an inertial microsystem provided by the present invention; Figure 3 A schematic diagram of the principle of the highly integrated inertial microsystem provided by the present invention; Figure 4 A three-dimensional structural schematic diagram of the highly integrated inertial microsystem provided by the present invention. Detailed Implementation
[0023] A multi-parameter BP neural network temperature compensation method for inertial microsystems includes: full-temperature-domain precise calibration and dataset establishment; establishing a coupled error model that integrates multiple physical effects; constructing a BP neural network with temperature and error parameters as inputs and compensation increments as outputs; and using an adaptive learning rate momentum method to dynamically adjust the learning rate and optimize the convergence process to obtain the optimal network weights and bias parameters, which are then input into the system. This invention combines multi-parameter coupled modeling with online compensation to achieve full-temperature-domain, high-precision, and autonomous temperature compensation for inertial microsystems, ensuring the long-term stability and measurement reliability of the system under complex thermal environments, and significantly improving the output accuracy and stability of inertial microsystems under complex temperature environments.
[0024] The multi-parameter BP neural network temperature compensation method includes the following steps: Inertial microsystem calibration is performed across the entire temperature range. The raw outputs of the gyroscope and accelerometer are collected at different temperature points to establish a calibration dataset of temperature-output characteristics. A multi-parameter coupling error model, including zero bias, scaling factor, cross-coupling coefficient, and sensitivity coefficient, is established based on the calibration dataset. Using temperature value, zero-bias stability parameter and coupling error coefficient of multi-parameter coupled error model as input, and compensation parameter as output, a BP neural network compensation model oriented towards error mechanism is constructed. The adaptive learning rate momentum method is used to train the BP neural network compensation model, and the learning rate is dynamically adjusted according to the training error to obtain the optimal network weights and bias parameters. The optimal network weights and bias parameters are substituted into the BP neural network compensation model, and the BP neural network compensation model is added to the inertial microsystem for online real-time temperature compensation value calculation.
[0025] The multi-parameter coupling error model is as follows:
[0026] In the formula, W For the scaling factor tensor, B ( T This is a temperature-dependent zero bias. G for g Sensitivity matrix, C This is the temperature hysteresis coefficient matrix.T 0 represents the training temperature.
[0027] Changes in network weight coefficients of the BP neural network compensation model The update method is as follows:
[0028] In the formula, E This is a composite loss function that includes temperature drift error and coupling error. or For learning rate, α The momentum factor is used to adjust the weights of each layer through error backpropagation, thereby coordinating the compensation of multi-parameter coupling errors.
[0029] Based on the change in network weight coefficients A backpropagation (BP) neural network compensation model is established, which includes an output layer, hidden layers, and compensation parameters output by the BP neural network compensation model. z j for:
[0030] In the formula, the zero-bias correction of the output layer nodes of the BP neural network compensation model after compensation is ΔB0, the scaling factor correction is ΔK, the cross-coupling correction is ΔC, and the sensitivity correction is ΔS. The activation function of the hidden layer is the modified linear unit function. x i For the first i The input of each input layer node, w ji The connection weights from the input layer to the hidden layer. b j This is the bias of the hidden layer nodes.
[0031] The BP neural network compensation model also includes temperature-zero bias coupling elastic weights, and the update amount of the temperature-zero bias coupling elastic weights. The update method is as follows:
[0032] In the formula, W b For the weights of the neural network with zero bias correlation, Ω b This is a Gaussian temperature-weighted zero-bias matrix. The zero-bias temperature coefficient at the current temperature. It is a periodic temperature characteristic.
[0033] Composite loss function E The weighted sum of temperature drift error and coupling error is calculated as follows:
[0034] In the formula, N The number of training samples, For the first k The system output after neural network compensation for each sample The output is the corresponding compensated output. P m The first parameter in the multi-parameter coupled error model m One error parameter, P m,ref This is the calibration value of the error parameter at the reference temperature. l 1 and l 2 is the weighting coefficient.
[0035] In the adaptive learning rate momentum method, the learning rate is dynamically adjusted. The method is as follows:
[0036] In the formula, γ is the attenuation coefficient. After training, the network weights and bias parameters are burned into the storage unit of the inertial microsystem to achieve real-time temperature compensation.
[0037] The inertial microsystem adopts a time-sharing collaborative compensation strategy. By establishing multi-parameter BP neural network compensation models for the gyroscope and accelerometer respectively, CPU resources are dynamically allocated according to the working mode of the inertial microsystem. The workflow of the inertial microsystem includes navigation calculation and static and low-dynamic calibration. When performing navigation calculations, the inertial microsystem prioritizes the neural network compensation calculation of the gyroscope and uses the compensation parameters and linear interpolation parameters from the previous moment to compensate the accelerometer in real time. When performing static and low-dynamic calibrations, the inertial microsystem simultaneously performs full-parameter neural network compensation calculations for the gyroscope and accelerometer, and performs smoothing filtering on the compensation parameters of the accelerometer.
[0038] The inertial microsystem is implemented through an integrated design on a SiP chip, which is designed with a stacked micro interconnect structure.
[0039] The following description, in conjunction with the accompanying drawings and preferred embodiments, provides further details: In the current embodiment, the inertial microsystem multi-parameter BP neural network temperature compensation method, such as... Figure 1 and Figure 2 As shown, it includes: S1. Perform system calibration of the inertial microsystem across the entire temperature range at multiple set temperature intervals, collect the raw output data of the gyroscope and accelerometer at each temperature point, and establish a calibration dataset including temperature-output characteristics. S2. Based on the calibration dataset, establish a multi-parameter coupled error model including zero bias, scaling factor, cross-coupling coefficient, and sensitivity coefficient, specifically:
[0040] In the formula, W For the scaling factor tensor, B ( T This is a temperature-dependent zero bias. G for g Sensitivity matrix, C This is the temperature hysteresis coefficient matrix. T 0 represents the training temperature.
[0041] S3, Establish based on temperature value T Zero bias stability parameters s B The BP neural network compensation model, with coupling error coefficients as input and compensation parameters as output, updates the weights of the BP neural network as follows:
[0042] In the formula, E This is a composite loss function that includes temperature drift error and coupling error. or For learning rate, α The momentum factor is used to adjust the weights of each layer through error backpropagation, thereby coordinating the compensation of multi-parameter coupling errors.
[0043] The established BP neural network compensation model outputs the compensated zero-bias correction ΔB0, scale factor correction ΔK, cross-coupling correction ΔC, and sensitivity correction ΔS from the output layer nodes. The activation function of the hidden layer is the modified linear unit function, and its output... z j for:
[0044] In the formula, x i For the first i The input of each input layer node, w ji The connection weights from the input layer to the hidden layer. b j This is the bias of the hidden layer nodes.
[0045] Temperature-zero bias coupling elastic weight update in a BP neural network compensation model:
[0046] In the formula, W b For the weights of the neural network with zero bias correlation, Ω b This is a Gaussian temperature-weighted zero-bias matrix. The zero-bias temperature coefficient at the current temperature. It is a periodic temperature characteristic.
[0047] Composite loss function for weight updates E The weighted sum of temperature drift error and coupling error is as follows:
[0048] In the formula, N The number of training samples, For the first k The system output after neural network compensation for each sample The output is the corresponding compensated output. P m The first parameter in the multi-parameter coupled error model m One error parameter, P m,ref This is the calibration value of the error parameter at the reference temperature. l 1 and l 2 is the weighting coefficient.
[0049] S4. The BP neural network compensation model is trained using the adaptive learning rate momentum method. The learning rate is dynamically adjusted according to the changes in training error, and the network weights and bias parameters are input into the inertial microsystem.
[0050] The learning rate in S4 is dynamically adjusted as follows:
[0051] In the formula, γ is the attenuation coefficient. After training, the network weights and bias parameters are burned into the storage unit of the inertial microsystem to achieve real-time temperature compensation.
[0052] The inertial microsystem employs a time-segmented collaborative compensation strategy, establishing multi-parameter BP neural network compensation models for the gyroscope and accelerometer respectively. CPU resources are dynamically allocated according to the working mode of the inertial microsystem: High dynamics and navigation calculation: neural network compensation calculations for the gyroscope are executed first, while the compensation parameters and linear interpolation parameters from the previous moment are used to quickly compensate the accelerometer; Static and low dynamics calibration: full-parameter neural network compensation calculations for the gyroscope and accelerometer are executed simultaneously, and the compensation parameters of the accelerometer are smoothed and filtered.
[0053] like Figure 3 , Figure 4 As shown, the highly integrated inertial microsystem includes a three-axis MEMS gyroscope, a three-axis MEMS accelerometer, a signal conditioning and acquisition module, a distributed storage module, and a multi-core processing module. The signal conditioning and acquisition module, distributed storage module, and multi-core processing module in the inertial microsystem are integrated into a heterogeneous information processing SiP chip. The multi-layered stacked memory dies within this chip are interconnected through a miniaturized interconnect structure.
[0054] This invention presents a multi-parameter BP neural network temperature compensation method for inertial microsystems. It establishes a two-stage compensation structure of a multi-parameter physical model and a BP neural network. A multi-parameter error model is built based on system calibration data. The BP neural network takes the real-time error parameters, temperature, and zero-bias stability calculated by the multi-parameter error model as input and outputs precise compensation increments for the model parameters. This allows the neural network to perform refined nonlinear compensation within the constraints of the physical model.
[0055] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.
[0056] The contents not described in detail in this specification are common knowledge to those skilled in the art.
Claims
1. A multi-parameter BP neural network temperature compensation method for inertial microsystems, characterized in that... include: Inertial microsystem calibration was performed across the entire temperature range, and the raw outputs of the gyroscope and accelerometer were collected at different temperature points. ， Establish a calibration dataset for temperature-output characteristics; A multi-parameter coupling error model, including zero bias, scaling factor, cross-coupling coefficient, and sensitivity coefficient, is established based on the calibration dataset. Using temperature value, zero-bias stability parameter and error coupling coefficient in multi-parameter coupled error model as input, and compensation parameter as output, a BP neural network compensation model for real-time error compensation is constructed. The adaptive learning rate momentum method is used to train the BP neural network compensation model. The learning rate is dynamically adjusted according to the training error to obtain the optimal network weights and bias parameters. The optimal network weights and bias parameters are input into the BP neural network compensation model, and the updated BP neural network compensation model is burned into the inertial microsystem. The inertial microsystem calculates and outputs the temperature-compensated data in real time.
2. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 1, characterized in that: The multi-parameter coupling error model is as follows: In the formula, Y 1 represents the data before compensation. W For scaling factors and cross-coupling matrix, B ( T This is a temperature-dependent zero bias. G for g Sensitivity matrix, A External input of exercise volume ，C This is the temperature hysteresis coefficient matrix. T 0 represents the training temperature.
3. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 1, characterized in that: The network weights of the BP neural network compensation model The update method is as follows: In the formula, E This is a composite loss function that includes temperature drift error and coupling error. η For learning rate, α Momentum factor Network weights The weights of each layer are adjusted through backpropagation of the error in the update after the last training, so as to compensate for the multi-parameter coupling error.
4. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 3, characterized in that: Based on the change in network weight coefficients A backpropagation (BP) neural network compensation model is established, consisting of an input layer, hidden layers, and an output layer. The compensation parameters output by the BP neural network compensation model are... z j for: In the formula, the zero-bias correction of the output layer nodes of the BP neural network compensation model after compensation is ΔB0, the scaling factor correction is ΔK, the cross-coupling correction is ΔC, and the sensitivity correction is ΔS. The activation function of the hidden layer is the modified linear unit function. x i For the first i The input of each input layer node, w ji The connection weights from the input layer to the hidden layer. b j This is the bias of the hidden layer nodes.
5. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 3, characterized in that: The composite loss function E The weighted sum of temperature drift error and coupling error is calculated as follows: In the formula, N The number of training samples, For the first k The system output after neural network compensation for each sample The output is the corresponding compensated output. P m The first parameter in the multi-parameter coupled error model m One error parameter, P m,ref This is the calibration value of the error parameter at the reference temperature. λ 1 and λ 2 is the weighting coefficient.
6. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 5, characterized in that: The first parameter in the multi-parameter coupling error model m Error parameters P m The update includes the elastic weights of temperature-zero bias coupling, and the amount of temperature-zero bias coupling elastic weight update. The update method is as follows: In the formula, W b For the weights of the neural network with zero bias correlation, Ω b This is a Gaussian temperature-weighted zero-bias matrix. The zero-bias temperature coefficient at the current temperature. It is a periodic temperature characteristic.
7. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 3, characterized in that: In the adaptive learning rate momentum method, the learning rate is dynamically adjusted. The method is as follows: In the formula, γ is the attenuation coefficient. and For the first i, i+1 Learning rate during each training iteration loss function E exist t , t-1 The gradient vector at each iteration, after training, is burned into the storage unit of the inertial microsystem for real-time temperature compensation.
8. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 7, characterized in that: The inertial microsystem adopts a time-sharing collaborative compensation strategy. By establishing multi-parameter BP neural network compensation models for the gyroscope and accelerometer respectively, CPU memory is dynamically allocated according to the working mode of the inertial microsystem. The workflow of the inertial microsystem includes static and dynamic calibration and navigation calculation. When performing navigation calculations for inertial microsystems, the neural network compensation calculations of the gyroscope are performed first, and the compensation parameters and linear interpolation parameters from the previous moment are used to compensate the accelerometer in real time. When performing static and dynamic calibrations on an inertial microsystem, multi-parameter BP neural network compensation calculations for the gyroscope and accelerometer are performed simultaneously, and the compensation parameters of the accelerometer are smoothed and filtered.
9. The temperature compensation method for a multi-parameter BP neural network in an inertial microsystem according to claim 8, characterized in that: The inertial microsystem is implemented through an integrated design on an information processing SiP chip, which is designed with a stacked micro interconnect structure.